In this research, new setting is introduced for new SuperHyperNotions, namely, SuperHyperDefensive SuperHyperAlliances and Neutrosophic SuperHyperDefensive SuperHyperAlliances. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The “Cancer’s Recognitions” are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “Cancer’s Recognitions”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “Cancer’s Recognitions”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. An “SuperHyperAlliance” is a minimal SuperHyperSet of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the cardinalities of SuperHyperNeighbors of s∈S:,|S∩N(s)|>|S∩(V \N(s))|,and|S∩N(s)|<|S∩(V \N(s))|.Thefirst Expression, holds if S is SuperHyperOffensive. And the second Expression, holds if S is “SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperDefensive SuperHyperAlliances. Since there’s more ways to get type-results to make SuperHyperDefensive SuperHyperAlliances more understandable. For the sake of having neutrosophic SuperHyperDefensive SuperHyperAlliances, there’s a need to “redefine” the notion of “SuperHyperDefensive SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a SuperHyperAlliance. It’s redefined neutrosophic SuperHyperAlliance if the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” with the key points, “The Values of The Vertices & The Number of Position in Alphabet”, “The Values of The SuperVertices&The Minimum Values of Its Vertices”, “The Values of The Edges&The Minimum Values of Its Vertices”, “The Values of The HyperEdges&The Minimum Values of Its Vertices”, “The Values of The SuperHyperEdges&The Minimum Values of Its Endpoints”. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperDefensive SuperHyperAlliances. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there’s a need to have all SuperHyperConnectivities until the SuperHyperDefensive SuperHyperAlliances, then it’s officially called “SuperHyperDefensive SuperHyperAlliances” but otherwise, it isn’t SuperHyperDefensive SuperHyperAlliances. There are some instances about the clarifications for the main definition titled “SuperHyperDefensive SuperHyperAlliances”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperDefensive SuperHyperAlliances. For the sake of having neutrosophic SuperHyperDefensive SuperHyperAlliances, there’s a need to “redefine” the notion of “neutrosophic SuperHyperDefensive SuperHyperAlliances” and “neutrosophic SuperHyperDefensive SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And SuperHyperDefensive SuperHyperAlliances are redefined “neutrosophic SuperHyperDefensive SuperHyperAlliances” if the intended Table holds. It’s useful to define “neutrosophic” version of SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make neutrosophic SuperHyperDefensive SuperHyperAlliances more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table holds. A SuperHyperGraph has “neutrosophic SuperHyperDefensive SuperHyperAlliances” where it’s the strongest [the maximum neutrosophic value from all SuperHyperDefensive SuperHyperAlliances amid the maximum value amid all SuperHyperVertices from a SuperHyperDefensive SuperHyperAlliances.] SuperHyperDefensive SuperHyperAlliances. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this SuperHyperModel, The “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called “neutrosophic”. In the future research, the foundation will be based on the “Cancer’s Recognitions” and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn’t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it’s said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s happened and what’s done. There are some specific models, which are well-known and they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperDefensive SuperHyperAlliances or the strongest SuperHyperDefensive SuperHyperAlliances in those neutrosophic SuperHyperModels. For the longest SuperHyperDefensive SuperHyperAlliances, called SuperHyperDefensive SuperHyperAlliances, and the strongest SuperHyperCycle, called neutrosophic SuperHyperDefensive SuperHyperAlliances, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, SuperHyperAlliances and Neutrosophic SuperHyperAlliances. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The “Cancer’s Recognitions” are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “Cancer’s Recognitions”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “Cancer’s Recognitions”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. An “SuperHyperAlliance” is a minimal SuperHyperSet of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the cardinalities of SuperHyperNeighbors of s∈S:,|S∩N(s)|>|S∩(V \N(s))|,and|S∩N(s)|<|S∩(V \N(s))|.Thefirst Expression, holds if S is SuperHyperOffensive. And the second Expression, holds if S is “SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperAlliances. Since there’s more ways to get type-results to make SuperHyperAlliances more understandable. For the sake of having neutrosophic SuperHyperAlliances, there’s a need to “redefine” the notion of “SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a SuperHyperAlliance. It’s redefined neutrosophic SuperHyperAlliance if the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” with the key points, “The Values of The Vertices & The Number of Position in Alphabet”, “The Values of The SuperVertices&The Minimum Values of Its Vertices”, “The Values of The Edges&The Minimum Values of Its Vertices”, “The Values of The HyperEdges&The Minimum Values of Its Vertices”, “The Values of The SuperHyperEdges&The Minimum Values of Its Endpoints”. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperAlliances. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there’s a need to have all SuperHyperConnectivities until the SuperHyperAlliances, then it’s officially called “SuperHyperAlliances” but otherwise, it isn’t SuperHyperAlliances. There are some instances about the clarifications for the main definition titled “SuperHyperAlliances”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperAlliances. For the sake of having neutrosophic SuperHyperAlliances, there’s a need to “redefine” the notion of “neutrosophic SuperHyperAlliances” and “neutrosophic SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And SuperHyperAlliances are redefined “neutrosophic SuperHyperAlliances” if the intended Table holds. It’s useful to define “neutrosophic” version of SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make neutrosophic SuperHyperAlliances more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table holds. A SuperHyperGraph has “neutrosophic SuperHyperAlliances” where it’s the strongest [the maximum neutrosophic value from all SuperHyperAlliances amid the maximum value amid all SuperHyperVertices from a SuperHyperAlliances.] SuperHyperAlliances. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this SuperHyperModel, The “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called “neutrosophic”. In the future research, the foundation will be based on the “Cancer’s Recognitions” and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn’t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it’s said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s happened and what’s done. There are some specific models, which are well-known and they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperAlliances or the strongest SuperHyperAlliances in those neutrosophic SuperHyperModels. For the longest SuperHyperAlliances, called SuperHyperAlliances, and the strongest SuperHyperCycle, called neutrosophic SuperHyperAlliances, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, assume a SuperHyperGraph. Then a “SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a “neutrosophic SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then a “SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a “neutrosophic SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then an “δ−SuperHyperForcing” is a minimal SuperHyperForcing of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of s ∈ S : |S∩N(s)|>|S∩(V \N(s))|+δ, |S∩N(s)|<|S∩(V \N(s))|+δ.Thefirst Expression, holds if S is an “δ−SuperHyperOffensive”. And the second Expression, holds if S is an “δ−SuperHyperDefensive”; a“neutrosophic δ−SuperHyperForcing” is a minimal neutrosophic SuperHyperForcing of SuperHyperVertices with minimum neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of s ∈ S : |S ∩ N(s)|neutrosophic > |S ∩ (V \ N (s))|neutrosophic + δ, |S ∩ N (s)|neutrosophic < |S ∩ (V \ N (s))|neutrosophic + δ. The first Expression, holds if S is a “neutrosophic δ−SuperHyperOffensive”. And the second Expression, holds if S is a “neutrosophic δ−SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperForcing. Since there’s more ways to get type-results to make SuperHyperForcing more understandable. For the sake of having neutrosophic SuperHyperForcing, there’s a need to “redefine” the notion of “SuperHyperForcing”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperGirth, is up. $E_1$ and $E_3$ are some empty neutrosophic SuperHyperEdges but $E_2$ is a loop neutrosophic SuperHyperEdge and $E_4$ is an neutrosophic SuperHyperEdge. Thus in the terms of neutrosophic SuperHyperNeighbor, there's only one neutrosophic SuperHyperEdge, namely, $E_4.$ The neutrosophic SuperHyperVertex, $V_3$ is neutrosophic isolated means that there's no neutrosophic SuperHyperEdge has it as an neutrosophic endpoint. Thus the neutrosophic SuperHyperVertex, $V_3,$ is excluded in every given neutrosophic SuperHyperGirth. $ \mathcal{C}(NSHG)=\{E_i\}~\text{is an neutrosophic SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^i~\text{is an neutrosophic SuperHyperGirth SuperHyperPolynomial.} \ \ \mathcal{C}(NSHG)=\{V_i\}~\text{is an neutrosophic R-SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^I~{\small\text{is an neutrosophic R-SuperHyperGirth SuperHyperPolynomial.}} $ The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], is an neutrosophic SuperHyperGirth $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is an neutrosophic type-SuperHyperSet with the maximum neutrosophic cardinality of an neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are not only four neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperGirth isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth is an neutrosophic SuperHyperSet includes only less than four neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], doesn't have less than four SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth isn't up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], isn't the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], is an neutrosophic SuperHyperGirth $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth and it's an neutrosophic SuperHyperGirth . Since it 's the maximum neutrosophic cardinality of an neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are only less than four neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, thus the obvious neutrosophic SuperHyperGirth, is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth, is: ,is the neutrosophic SuperHyperSet, is: does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the neutrosophic SuperHyperGirth , is only and only. A basic familiarity with neutrosophic SuperHyperGirth theory, SuperHyperGraphs, and neutrosophic SuperHyperGraphs theory are proposed.

in this research, new setting is introduced for new SuperHyperNotion, namely, Neutrosophic SuperHyperStable. In this research article, there are some research segments for ``Neutrosophic SuperHyperStable'' about some researches on neutrosophic SuperHyperStable. With researches on the basic properties, the research article starts to make neutrosophic SuperHyperStable theory more understandable. Assume a neutrosophic SuperHyperGraph. Then a ``neutrosophic SuperHyperStable'' $\mathcal{I}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotion, namely, 11 Neutrosophic 1-failed SuperHyperForcing. Two different types of SuperHyperDefinitions 12 are debut for them but the research goes further and the SuperHyperNotion, 13 SuperHyperUniform, and SuperHyperClass based on that are well-defined and 14 well-reviewed. The literature review is implemented in the whole of this research. For 15 shining the elegancy and the significancy of this research, the comparison between this 16 SuperHyperNotion with other SuperHyperNotions and fundamental 17 SuperHyperNumbers are featured. The definitions are followed by the examples and the 18 instances thus the clarifications are driven with different tools. The applications are 19 figured out to make sense about the theoretical aspect of this ongoing research. The 20 “Cancer’s Neutrosophic Recognition” are the under research to figure out the challenges 21 make sense about ongoing and upcoming research. The special case is up. The cells are 22 viewed in the deemed ways. There are different types of them. Some of them are 23 individuals and some of them are well-modeled by the group of cells. These types are all 24 officially called “SuperHyperVertex” but the relations amid them all officially called 25 “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic 26 SuperHyperGraph” are chosen and elected to research about “Cancer’s Neutrosophic 27 Recognition”. Thus these complex and dense SuperHyperModels open up some avenues 28 to research on theoretical segments and “Cancer’s Neutrosophic Recognition”. Some 29 avenues are posed to pursue this research. It’s also officially collected in the form of 30 some questions and some problems. Assume a SuperHyperGraph. Then a “1-failed 31 SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) 32 is the maximum cardinality of a SuperHyperSet S of black SuperHyperVertices 33 (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) isn’t 34 turned black after finitely many applications of “the color-change rule”: a white 35 SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white 36 SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred 37 by “1-” about the usage of any black SuperHyperVertex only once to act on white 38 SuperHyperVertex to be black SuperHyperVertex; a “neutrosophic 1-failed 39 SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) 40 is the maximum neutrosophic cardinality of a SuperHyperSet S of black 41 SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such 42 that V (G) isn’t turned black after finitely many applications of “the color-change rule”: 43 a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only 44 1/128 white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is 45 referred by “1-” about the usage of any black SuperHyperVertex only once to act on 46 white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. 47 Then an “δ−1-failed SuperHyperForcing” is a maximal 1-failed SuperHyperForcing of 48 SuperHyperVertices with maximum cardinality such that either of the following 49 expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of s ∈ S : 50 |S ∩N(s)| > |S ∩(V \N(s))|+δ, |S ∩N(s)| < |S ∩(V \N(s))|+δ. The first Expression, 51 holds if S is an “δ−SuperHyperOffensive”. And the second Expression, holds if S is an 52 “δ−SuperHyperDefensive”; a“neutrosophic δ−1-failed SuperHyperForcing” is a maximal 53 neutrosophic 1-failed SuperHyperForcing of SuperHyperVertices with maximum 54 neutrosophic cardinality such that either of the following expressions hold for the 55 neutrosophic cardinalities of SuperHyperNeighbors of s ∈ S : |S ∩ N(s)|neutrosophic > 56 |S ∩ (V \ N (s))|neutrosophic + δ, |S ∩ N (s)|neutrosophic < |S ∩ (V \ N (s))|neutrosophic + δ. 57 The first Expression, holds if S is a “neutrosophic δ−SuperHyperOffensive”. And the 58 second Expression, holds if S is a “neutrosophic δ−SuperHyperDefensive”. It’s useful to 59 define “neutrosophic” version of 1-failed SuperHyperForcing. Since there’s more ways to 60 get type-results to make 1-failed SuperHyperForcing more understandable. For the sake 61 of having neutrosophic 1-failed SuperHyperForcing, there’s a need to “redefine” the 62 notion of “1-failed SuperHyperForcing”. The SuperHyperVertices and the 63 SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this 64 procedure, there’s the usage of the position of labels to assign to the values. Assume a 65 1-failed SuperHyperForcing. It’s redefined neutrosophic 1-failed SuperHyperForcing if 66 the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, 67 HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” 68 with the key points, “The Values of The Vertices & The Number of Position in 69 Alphabet”, “The Values of The SuperVertices&The maximum Values of Its Vertices”, 70 “The Values of The Edges&The maximum Values of Its Vertices”, “The Values of The 71 HyperEdges&The maximum Values of Its Vertices”, “The Values of The 72 SuperHyperEdges&The maximum Values of Its Endpoints”. To get structural examples 73 and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph 74 based on 1-failed SuperHyperForcing. It’s the main. It’ll be disciplinary to have the 75 foundation of previous definition in the kind of SuperHyperClass. If there’s a need to 76 have all SuperHyperConnectivities until the 1-failed SuperHyperForcing, then it’s 77 officially called “1-failed SuperHyperForcing” but otherwise, it isn’t 1-failed 78 SuperHyperForcing. There are some instances about the clarifications for the main 79 definition titled “1-failed SuperHyperForcing”. These two examples get more scrutiny 80 and discernment since there are characterized in the disciplinary ways of the 81 SuperHyperClass based on 1-failed SuperHyperForcing. For the sake of having 82 neutrosophic 1-failed SuperHyperForcing, there’s a need to “redefine” the notion of 83 “neutrosophic 1-failed SuperHyperForcing” and “neutrosophic 1-failed 84 SuperHyperForcing”. The SuperHyperVertices and the SuperHyperEdges are assigned 85 by the labels from the letters of the alphabets. In this procedure, there’s the usage of 86 the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. 87 It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And 88 1-failed SuperHyperForcing are redefined “neutrosophic 1-failed SuperHyperForcing” if 89 the intended Table holds. It’s useful to define “neutrosophic” version of 90 SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make 91 neutrosophic 1-failed SuperHyperForcing more understandable. Assume a neutrosophic 92 SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended 93 Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, 94 SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are 95 “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic 96 SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic 97 2/128 SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table 98 holds. A SuperHyperGraph has “neutrosophic 1-failed SuperHyperForcing” where it’s 99 the strongest [the maximum neutrosophic value from all 1-failed SuperHyperForcing 100 amid the maximum value amid all SuperHyperVertices from a 1-failed 101 SuperHyperForcing.] 1-failed SuperHyperForcing. A graph is SuperHyperUniform if it’s 102 SuperHyperGraph and the number of elements of SuperHyperEdges are the same. 103 Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as 104 follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given 105 SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one 106 SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s 107 only one SuperVertex as intersection amid all SuperHyperEdges; it’s 108 SuperHyperBipartite it’s only one SuperVertex as intersection amid two given 109 SuperHyperEdges and these SuperVertices, forming two separate sets, has no 110 SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as 111 intersection amid two given SuperHyperEdges and these SuperVertices, forming multi 112 separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one 113 SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has 114 one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes 115 the specific designs and the specific architectures. The SuperHyperModel is officially 116 called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this 117 SuperHyperModel, The “specific” cells and “specific group” of cells are 118 SuperHyperModeled as “SuperHyperVertices” and the common and intended properties 119 between “specific” cells and “specific group” of cells are SuperHyperModeled as 120 “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, 121 indeterminacy, and neutrality to have more precise SuperHyperModel which in this case 122 the SuperHyperModel is called “neutrosophic”. In the future research, the foundation 123 will be based on the “Cancer’s Neutrosophic Recognition” and the results and the 124 definitions will be introduced in redeemed ways. The neutrosophic recognition of the 125 cancer in the long-term function. The specific region has been assigned by the model 126 [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is 127 identified by this research. Sometimes the move of the cancer hasn’t be easily identified 128 since there are some determinacy, indeterminacy and neutrality about the moves and 129 the effects of the cancer on that region; this event leads us to choose another model [it’s 130 said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s 131 happened and what’s done. There are some specific models, which are well-known and 132 they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves 133 and the traces of the cancer on the complex tracks and between complicated groups of 134 cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, 135 SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). 136 The aim is to find either the longest 1-failed SuperHyperForcing or the strongest 137 1-failed SuperHyperForcing in those neutrosophic SuperHyperModels. For the longest 138 1-failed SuperHyperForcing, called 1-failed SuperHyperForcing, and the strongest 139 SuperHyperCycle, called neutrosophic 1-failed SuperHyperForcing, some general results 140 are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have 141 only two SuperHyperEdges but it’s not enough since it’s essential to have at least three 142 SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of 143 any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, 144 literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph 145 theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, an 1-failed SuperHyperForcing and Neutrosophic 1-failed SuperHyperForcing. Assume a SuperHyperGraph. Then an ``1-failed SuperHyperForcing'' $\mathcal{Z}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) \setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex; a ``neutrosophic 1-failed SuperHyperForcing'' $\mathcal{Z}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) \setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. Then an ``$\delta-$1-failed SuperHyperForcing'' is a \underline{maximal} 1-failed SuperHyperForcing of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$1-failed SuperHyperForcing'' is a \underline{maximal} neutrosophic 1-failed SuperHyperForcing of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, an SuperHyperStable and Neutrosophic SuperHyperStable. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer's Recognitions'' are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex'' but the relations amid them all officially called ``SuperHyperEdge''. The frameworks ``SuperHyperGraph'' and ``neutrosophic SuperHyperGraph'' are chosen and elected to research about ``Cancer's Recognitions''. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer's Recognitions''. Some avenues are posed to pursue this research. It's also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Then a``SuperHyperStable'' $\mathcal{I}(NSHG)$ for a SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's no SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$SuperHyperStable'' is a \underline{maximal} SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$SuperHyperStable'' is a \underline{maximal} neutrosophic SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. It's useful to define a ``neutrosophic'' version of an SuperHyperStable. Since there's more ways to get type-results to make an SuperHyperStable more understandable. For the sake of having neutrosophic SuperHyperStable, there's a need to ``redefine'' the notion of an ``SuperHyperStable''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. Assume an SuperHyperStable. It's redefined a neutrosophic SuperHyperStable if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph'' with the key points, ``The Values of The Vertices \& The Number of Position in Alphabet'', ``The Values of The SuperVertices\&The maximum Values of Its Vertices'', ``The Values of The Edges\&The maximum Values of Its Vertices'', ``The Values of The HyperEdges\&The maximum Values of Its Vertices'', ``The Values of The SuperHyperEdges\&The maximum Values of Its Endpoints''. To get structural examples and instances, I'm going to introduce the next SuperHyperClass of SuperHyperGraph based on an SuperHyperStable. It's the main. It'll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there's a need to have all SuperHyperConnectivities until the SuperHyperStable, then it's officially called an ``SuperHyperStable'' but otherwise, it isn't an SuperHyperStable. There are some instances about the clarifications for the main definition titled an ``SuperHyperStable''. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on an SuperHyperStable. For the sake of having a neutrosophic SuperHyperStable, there's a need to ``redefine'' the notion of a ``neutrosophic SuperHyperStable'' and a ``neutrosophic SuperHyperStable''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It's redefined ``neutrosophic SuperHyperGraph'' if the intended Table holds. And an SuperHyperStable are redefined to an ``neutrosophic SuperHyperStable'' if the intended Table holds. It's useful to define ``neutrosophic'' version of SuperHyperClasses. Since there's more ways to get neutrosophic type-results to make a neutrosophic SuperHyperStable more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are ``neutrosophic SuperHyperPath'', ``neutrosophic SuperHyperCycle'', ``neutrosophic SuperHyperStar'', ``neutrosophic SuperHyperBipartite'', ``neutrosophic SuperHyperMultiPartite'', and ``neutrosophic SuperHyperWheel'' if the intended Table holds. A SuperHyperGraph has a ``neutrosophic SuperHyperStable'' where it's the strongest [the maximum neutrosophic value from all the SuperHyperStable amid the maximum value amid all SuperHyperVertices from an SuperHyperStable.] SuperHyperStable. A graph is a SuperHyperUniform if it's a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It's SuperHyperPath if it's only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it's SuperHyperCycle if it's only one SuperVertex as intersection amid two given SuperHyperEdges; it's SuperHyperStar it's only one SuperVertex as intersection amid all SuperHyperEdges; it's SuperHyperBipartite it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it's SuperHyperMultiPartite it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it's a SuperHyperWheel if it's only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph'' and ``Neutrosophic SuperHyperGraph''. In this SuperHyperModel, The ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperVertices'' and the common and intended properties between ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperEdges''. Sometimes, it's useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``neutrosophic''. In the future research, the foundation will be based on the ``Cancer's Recognitions'' and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it's called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn't be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it's said to be neutrosophic SuperHyperGraph] to have convenient perception on what's happened and what's done. There are some specific models, which are well-known and they've got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperStable or the strongest SuperHyperStable in those neutrosophic SuperHyperModels. For the longest SuperHyperStable, called SuperHyperStable, and the strongest SuperHyperCycle, called neutrosophic SuperHyperStable, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it's not enough since it's essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn't any formation of any SuperHyperCycle but literarily, it's the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn't form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

I introduce now for the first time the neutrosophic modal logic. The Neutrosophic Modal Logic includes the neutrosophic operators that express the modalities. It is an extension of neutrosophic predicate logic, and of neutrosophic propositional logic. In order for the paper to be self-contained, I also recall the etymology and definition of neutrosophy and of neutrosophic logic. Several examples are presented as well.

In this research, Assume a neutrosophic SuperHyperGraph. Then a ``Failed SuperHyperStable $\mathcal{I}(NSHG)$ for a SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common; a ``neutrosophic Failed SuperHyperStable'' $\mathcal{I}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's a neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperStable'' is a \underline{maximal} Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperStable'' is a \underline{maximal} neutrosophic Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Neutrosophic Failed SuperHyperClique theory, and (Neutrosophic) SuperHyperGraphs theory are proposed.

In this research, assume a SuperHyperGraph. Then a neutrosophic SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient; a neutrosophic R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient. It's useful to define a ``neutrosophic'' version of a SuperHyperMatching . Since there's more ways to get type-results to make a SuperHyperMatching more understandable. For the sake of having neutrosophic SuperHyperMatching, there's a need to ``redefine'' the notion of a ``SuperHyperMatching ''. A basic familiarity with neutrosophic SuperHyperMatching theory, SuperHyperGraphs theory, and neutrosophic SuperHyperGraphs theory are proposed.

New setting is introduced to study neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic failed-independent number and failed independent neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which have all vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then failed independent number I(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously; failed independent neutrosophic-number In(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum neutrosophic cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously. As concluding results, there are some statements, remarks, examples and clarifications about some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-t-partite-neutrosophic graphs. The clarifications are also presented in both sections “Setting of Neutrosophic Failed-Independent Number,” and “Setting of Failed Independent Neutrosophic-Number,” for introduced results and used classes. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhoods of vertices. In path-neutrosophic graphs, two neighbors, form maximal set but with slightly differences, in cycle-neutrosophic graphs, two neighbors forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of all vertices leads us to neutrosophic failed-independent number and failed independent neutrosophic-number. In star-neutrosophic graphs, a set of vertices containing only center and one other vertex, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices including two vertices from different parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of t vertices from different parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set to extend this set to set of all vertices has key role to have these notions in the form of neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of vertices. The cardinality of a set has eligibility to neutrosophic failed-independent number but the neutrosophic cardinality of a set has eligibility to call failed independent neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connections amid each other, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study quasi-degree and quasi-co-degree arising from co-neighborhood. quasi-degree and quasi-co-degree is about a vertex which are applied into the setting of neutrosophic graphs. . The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs and star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-multipartite-neutrosophic graphs are investigated in the terms of a vertex which is called either quasi-degree or quasi-co-degree. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form quasi-degree and quasi-co-degree. Quasi-degree is a value of a vertex which is maximum amid all values of vertices which are neighbors to a fixed vertex. Quasi-co-degree is a value of an edge which is maximum amid all values of edges which are neighbors to a fixed vertex but corresponded vertex is representative for this notion. Using different values which are related to a vertex inspire us to focus on edge and vertices which are corresponded to a fixed vertex. The notion of neighborhood is used to collect either vertices are titled neighbors or edges are incident to fixed vertex. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definitions are provided. Using fixed vertex has key role to have these notions in the form of vertex or edge. The value of an edge has eligibility to call quasi-co-degree but the value of a vertex has eligibility to call quasi-degree. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connection together, open the way to define neighborhood and co-neighborhood. The maximum values in neighborhood and co-neighborhood introduces quasi-degree and quasi-co-degree, respectively. New name is chosen from degree. Since amid all vertices with different degrees, one vertex is chosen. In other words, one vertex is fixed and its degree turns out quasi-degree where two degrees could be assigned to a vertex. Degree of edges and degree of vertices. The number of edges which are incident to the vertex and the number of vertices which are neighbors to the vertex. Degree and co-degree are the notions which are transformed to use in quasi-style. Two neutrosophic values introduce two neutrosophic vertices separately in each settings. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to purse this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Many various using of this new-born fuzzy model for solving real-world problems and urgent requirements involve introducing new concept for analyzing the situations which leads to solve them by proper, quick and ecient method based on statistical data. This gap between the model and its solution cause that we introduce nikfar domination in neutrosophic graphs as creative and eective tool for studying a few selective vertices of this model instead of all ones by using special edges. Being special selection of these edges aect to achieve quick and proper solution to these problems. Domination hasn't ever been introduced. So we don't have any comparison with another de nitions. The most used graphs which have properties of being complete, empty, bipartite, tree and like stu and they also achieve the names for themselves, are studied as fuzzy models for getting nikfar dominating set or at least becoming so close to it. We also get the relations between this special edge which plays main role in doing dominating with other special types of edges of graph like bridges. Finally, the relation between this number with other special numbers and characteristic of graph like order are discussed.

In this research article, the notions of SuperHyperDominating and SuperHyperResolving are defined in the setting of neutrosophic SuperHyperGraphs. Some ideas are introduced on both notions of SuperHyperDominating and SuperHyperResolving, simultaneously and as the same with each other. Some neutrosophic SuperHyperClasses are defined based on the notion, SuperHyperResolving. The terms of duality, totality, perfectness, connectedness, and stable, are added to basic framework and initial notions, SuperHyperDominating and SuperHyperResolving but the concentration is on the “perfectness” to figure out what’s going on when for all targeted SuperHyperVertices, there’s only one SuperHyperVertex in the intended set. There are some instances and some clarifications to make sense about what’s happened and what’s done in the starting definitions. The key point is about the minimum sets. There are some questions and some problems to be taken as some avenues to pursue this study and this research. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute types of chromatic numbers. This specific relation amid edges is necessary to compute both types of chromatic number concerning the number of representative in the set of representatives and types of neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no intended edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. vital chromatic number and n-vital chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using vital edge from connectedness to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute vital chromatic number. This specific relation amid edges is necessary to compute both vital chromatic number concerning the number of representative in the set of representatives and n-vital chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no vital edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute neutrosophic chromatic number. This specific relation amid edges is necessary to compute both chromatic number concerning the number of representative in the set of representatives and neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no strong edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study co-neighborhood, neutrosophic t-neighborhood, neutrosophic quasi-vertex set, neutrosophic quasi-order, neutrosophic neighborhood, neutrosophic co-t-neighborhood, neutrosophic quasi-edge set, neutrosophic quasi-size, Neutrosophic number, neutrosophic co-neighborhood, co-neutrosophic number, quasi-number and quasi-co-number. Some classes of neutrosophic graphs are investigated.

New setting is introduced to study failed zero-forcing number and failed zero-forcing neutrosophic-number. Leaf-like is a key term to have these notions. Forcing a vertex to change its color is a type of approach to force that vertex to be zero-like. Forcing a vertex which is only neighbor for zero-like vertex to be zero-like vertex but now reverse approach is on demand which is finding biggest set which doesn’t force. LetNTG : (V,E,σ,μ) be a neutrosophic graph. Then failed zero-forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximal cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black after finitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing neutrosophic-number Zn(NTG) for a neutrosophic graphNTG : (V,E,σ,μ) is maximal neutrosophic cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black afterfinitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing number and failed zero-forcing neutrosophic-number are about a set of vertices which are applied into the setting of neutrosophic graphs. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, bipartite-neutrosophic graphs, and t-partite-neutrosophic graphs are investigated in the terms of maximal set which forms both of failed zero-forcing number and failed zero-forcing neutrosophic-number. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form failed zero-forcing number and failed zero-forcing neutrosophic-number. In path-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set but with slightly differences, in cycle-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of vertices excluding two vertices leads us to failed zero-forcing number and failed zero-forcing neutrosophic-number. In star-neutrosophic graphs, a set of vertices excluding only two vertices and containing center, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set not to extend this set to set of all vertices has key role to have these notions in the form of failed zero-forcing number and failed zero-forcing neutrosophic-number. The cardinality of a set has eligibility to form failed zero-forcing number but the neutrosophic cardinality of a set has eligibility to call failed zero-forcing neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices don’t have unique connection together, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study the global powerful alliance. Global powerful alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global powerful alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs excluding empty, path, star, and wheel and containing complete, cycle and r-regular-strong are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is used in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-powerful-alliance number and minimal-global-powerful-alliance-neutrosophic number. Two different types of sets namely global-powerful alliance and minimal-global-powerful alliance are defined. Global-powerful alliance identifies the sets in general vision but minimal-global-powerful alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-powerful-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-powerful alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs has an open avenue, in the way that, the family only contains same classes of neutrosophic graphs. The results are about minimal-global-powerful alliance, minimal-global-powerful-alliance number and its corresponded sets, minimal-global-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-powerful alliances, minimal-t-powerful alliance, minimal-t-powerful-alliance number and its corresponded sets, minimal-t-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-t-powerful alliances. The connections amid t-powerful-alliances are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications and closing remarks. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global powerful alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set and reversely for non-members of set with less members in the way that the set is simultaneously t-offensive and(t-2)-defensive. A set is global if t=0. It leads us to the notion of global powerful alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is defined in new way. It’s first time to define this type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-offensive-alliance number and minimal-global-offensive-alliance-neutrosophic number. Two different types of sets namely global-offensive alliance and minimal-global-offensive alliance are defined. Global-offensive alliance identifies the sets in general vision but minimal-global-offensive alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-offensive-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-offensive alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs is studied in the way that, the family only contains same classes of neutrosophic graphs. Three types of family of neutrosophic graphs including m-family of neutrosophic stars with common neutrosophic vertex set, m-family of odd complete graphs with common neutrosophic vertex set, and m-family of odd complete graphs with common neutrosophic vertex set are studied. The results are about minimal-global-offensive alliance, minimal-global-offensive-alliance number and its corresponded sets, minimal-global-offensive-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-offensive alliances. The connection of global-offensive-alliances with dominating set and chromatic number are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, path, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global offensive alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set. It leads us to the notion of global offensive alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

This article presents a new method of segmenting images with gray levels. The method is based on determining several thresholds for separation of gray levels. The determination of these thresholds is done using the certainty of the neutrosophic information. The concept of this method can be stated simply: to choose the local maximums for the neutrosophic certainty.

In this paper, a geometric model is introduced for Neutrosophic data problem for the first time. This model is based on neutrosophic sets and neutrosophic relations. Neutrosophic control points are defined according to these points, resulting in neutrosophic Bézier curves.

New setting is introduced to study resolving number and chromatic number alongside dominating number. Different types of procedures including set, optimal set, and optimal number alongside study on the family of neutrosophic hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtains these numbers and the representatives of the colors, dominating sets and resolving sets. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing resolving sets and dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about numbers and sets in the way that some numbers get understandable perspective. Family of neutrosophic hypergraphs are studied to investigate about the notions, dimension and coloring alongside domination in neutrosophic hypergraphs. In this way, sets of representatives of colors, resolving sets and dominating sets have key role. Optimal sets and optimal numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, three notions are applied into neutrosophic hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

This article presents a new method of segmenting grayscale images by minimizing Shannon's neutrosophic entropy. For the proposed segmentation method, the neutrosophic information components, i.e., the degree of truth, the degree of neutrality and the degree of falsity are defined taking into account the belonging to the segmented regions and at the same time to the separation threshold area. The principle of the method is simple and easy to understand and can lead to multiple thresholds. The efficacy of the method is illustrated using some test gray level images. The experimental results show that the proposed method has good performance for segmentation with optimal gray level thresholds.

New setting is introduced to study types of coloring numbers, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Different types of procedures including neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtain chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing representatives of the colors are applied in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about number, degree and co-degree in the way that some number, degree and co-degree get understandable perspective. Neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are studied to investigate about the notions, coloring, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. In this way, sets of representatives of colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, notions chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges are applied into neutrosophic hypergraphs, especially, neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

Neutrosophic cubic set is the hybridization of the concept of neutrosophic set and interval neutrosophic set. Neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets appear in the current literature. In the present paper we propose the score, accuracy functions for neutrosophic cubic sets and prove their basic properties. We firstly develop TODIM method to solve multi attribute group decision making in neutrosophic cubic set environment, which we call NC-TODIM. Also, we solve a MAGDM problem using the proposed NC-TODIM method to show the applicability and effectiveness of the developed method. We also conduct sensitivity analysis to show the impact of ranking order of the alternatives for different values of attenuation factor of losses for multi-attribute group decision making problem.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperClique'' is a \underline{maximal} Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperClique'' is a \underline{maximal} neutrosophic Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Neutrosophic Failed SuperHyperClique theory, SuperHyperGraphs theory, and Neutrosophic SuperHyperGraphs theory are proposed.

Neutrosophic cubic set (NCS) is one of the important family members of neutrosophic hybrid sets. Neutrosophic cubic set has more strength than other family members of neutrosophic hybrid sets to express incomplete information due to the presence of interval valued neutrosophic set (IVNS) and single valued neutrosophic set (SVNS) in its structure. Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. In this paper we first define a new cross entropy measure under NCSs environment which we call NC- cross entropy measure. We investigate the basic properties of NC-cross entropy. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision making (MADM) strategy based on weighted NC-cross entropy. To show the feasibility and applicability, we solve a MADM problem using the proposed strategy.

The research is on the SuperHyperGirth and the neutrosophic SuperHyperGirth. A SuperHyperGraph has SuperHyperGirth where it’s the longest SuperHyperCycle. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperGirth. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. This SuperHyperClass is officially called “SuperHyperFlower”. If there’s a need to have all SuperHyperCycles until the SuperHyperGirth, then it’s officially called “SuperHyperOrder” but otherwise, it isn’t SuperHyperOrder. There are two instances about the clarifications for the main definition titled “SuperHyperGirth”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperGirth and they’re called “SuperHyperFlower.” A SuperHyperGraph has “neutrosophic SuperHyperGirth” where it’s the strongest [the maximum value from all SuperHyperCycles amid the minimum value amid all SuperHyperEdges from a SuperHyperCycle.] SuperHyperCycle. In “Cancer’s Recognitions”, the aim is to find either the longest SuperHyperCycle or the strongest SuperHyperCycle in those neutrosophic SuperHyperModels. For the longest SuperHyperCycle, called SuperHyperGirth, and the strongest SuperHyperCycle, called neutrosophic SuperHyperGirth, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

New setting is introduced to study the alliances. Alliances are about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define these notions. Also, neighborhood is defined based on the edges, strong edges and some edges which are coming from connectedness. These three types of edges get a framework as neighborhood and after that, too close vertices have key role to define offensive alliance, defensive alliance, t-offensive alliance, and t-defensive alliance based on three types of edges, common edges, strong edges and some edges which are coming from connectedness. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, bipartite, t-partite, star and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study but it seems that analogous results are determined. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on different edges illustrate open way to get results. A set is alliance when two sets partitioning vertex set have uniform structure. All members of set have different amount of neighbors in the set and out of set. It leads us to the notion of offensive and defensive. New ideas, offensive alliance, defensive alliance, t-offensive alliance, t-defensive alliance, strong offensive alliance, strong defensive alliance, strong t-offensive alliance, strong t-defensive alliance, connected offensive alliance, connected defensive alliance, connected t-offensive alliance, and connected t-defensive alliance are introduced. Two numbers concerning cardinality and neutrosophic cardinality of alliances are introduced. A set is alliance when its complement make a relation in the terms of neighborhood. Different edges make different neighborhoods. Three types of edges are applied to define three styles of neighborhoods. General edges, strong edges and connected edges are used where connected edges are the edges arising from connectedness amid two endpoints of the edges. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for this notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Single valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single valued neutrosophic cross entropy bears an asymmetrical behavior and produce an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under single valued neutrosophic set (SVNS) environment namely SN- cross entropy and prove its basic properties. Also we define weighted SN-cross entropy measure and investigate its basic properties. We develop a new multi attribute group decision making (MAGDM) strategy for ranking of the alternatives based on the proposed weighted SN-cross entropy measure between each alternative and the ideal alternative. Finally, a numerical example of MAGDM problem of investment potential is solved to show the validity and efficiency of proposed decision making strategy. We also present comparative anslysis of the obtained result with the results obtained form the existing solution strategies in the solution.

The concept of neutrosophic number is a significant mathematical tool to deal with real scientific problems because it can tackle indeterminate and incomplete information which exists generally in real problems. In this article, we use neutrosophic numbers (a + bI), where a and bI denote determinate component and indeterminate component respectively. We explore the situations in which the input information is needed to express in terms of neutrosophic numbers. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine unknown criteria weights. We define neutrosophic number harmonic mean operators and proved their basic properties. Then, we develop two novel MCGDM strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility and effectiveness of the proposed two strategies. Sensitivity analysis with variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the obtained results from the proposed strategies with the existing strategies in the literature.

The paper investigates some similarity measures in interval bipolar neutrosophic environment for multi-attribute decision making problems. At first, we define Hamming and Euclidean distances measures between interval bipolar neutrosophic sets and establish their basic properties. We also propose two similarity measures based on the Hamming and Euclidean distance functions. Using maximum and minimum operators, we define new similarity measures and prove their basic properties. Using the proposed similarity measures, we propose a novel multi attribute decision making strategy in interval bipolar neutrosophic set environment. Lastly, we solve an illustrative example of multi attribute decision making and present comparison analysis to show the feasibility, applicability and effectiveness of the proposed strategy.

In this research, the extreme SuperHyperNotion, namely, extreme SuperHyperGirth, is up. $E_1$ and $E_3$ are some empty extreme SuperHyperEdges but $E_2$ is a loop extreme SuperHyperEdge and $E_4$ is an extreme SuperHyperEdge. Thus in the terms of extreme SuperHyperNeighbor, there's only one extreme SuperHyperEdge, namely, $E_4.$ The extreme SuperHyperVertex, $V_3$ is extreme isolated means that there's no extreme SuperHyperEdge has it as an extreme endpoint. Thus the extreme SuperHyperVertex, $V_3,$ is excluded in every given extreme SuperHyperGirth. $ \mathcal{C}(NSHG)=\{E_i\}~\text{is an extreme SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^i~\text{is an extreme SuperHyperGirth SuperHyperPolynomial.} \ \ \mathcal{C}(NSHG)=\{V_i\}~\text{is an extreme R-SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^I~{\small\text{is an extreme R-SuperHyperGirth SuperHyperPolynomial.}} $ The following extreme SuperHyperSet of extreme SuperHyperEdges[SuperHyperVertices] is the extreme type-SuperHyperSet of the extreme SuperHyperGirth. The extreme SuperHyperSet of extreme SuperHyperEdges[SuperHyperVertices], is the extreme type-SuperHyperSet of the extreme SuperHyperGirth. The extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], is an extreme SuperHyperGirth $\mathcal{C}(ESHG)$ for an extreme SuperHyperGraph $ESHG:(V,E)$ is an extreme type-SuperHyperSet with the maximum extreme cardinality of an extreme SuperHyperSet $S$ of extreme SuperHyperEdges[SuperHyperVertices] such that there's only one extreme consecutive sequence of the extreme SuperHyperVertices and the extreme SuperHyperEdges form only one extreme SuperHyperCycle. There are not only four extreme SuperHyperVertices inside the intended extreme SuperHyperSet. Thus the non-obvious extreme SuperHyperGirth isn't up. The obvious simple extreme type-SuperHyperSet called the extreme SuperHyperGirth is an extreme SuperHyperSet includes only less than four extreme SuperHyperVertices. But the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], doesn't have less than four SuperHyperVertices inside the intended extreme SuperHyperSet. Thus the non-obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth isn't up. To sum them up, the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], isn't the non-obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth. Since the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], is an extreme SuperHyperGirth $\mathcal{C}(ESHG)$ for an extreme SuperHyperGraph $ESHG:(V,E)$ is the extreme SuperHyperSet $S$ of extreme SuperHyperVertices[SuperHyperEdges] such that there's only one extreme consecutive extreme sequence of extreme SuperHyperVertices and extreme SuperHyperEdges form only one extreme SuperHyperCycle given by that extreme type-SuperHyperSet called the extreme SuperHyperGirth and it's an extreme SuperHyperGirth . Since it 's the maximum extreme cardinality of an extreme SuperHyperSet $S$ of extreme SuperHyperEdges[SuperHyperVertices] such that there's only one extreme consecutive extreme sequence of extreme SuperHyperVertices and extreme SuperHyperEdges form only one extreme SuperHyperCycle. There are only less than four extreme SuperHyperVertices inside the intended extreme SuperHyperSet, thus the obvious extreme SuperHyperGirth, is up. The obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth, is: ,is the extreme SuperHyperSet, is: does includes only less than four SuperHyperVertices in a connected extreme SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple extreme type-SuperHyperSet called the extreme SuperHyperGirth amid those obvious[non-obvious] simple extreme type-SuperHyperSets called the neutrosophic SuperHyperGirth , is only and only. A basic familiarity with extreme SuperHyperGirth theory, SuperHyperGraphs, and extreme SuperHyperGraphs theory are proposed.

New ideas on the framework of Neutrosophic SuperHyperGraph for different styles of Neutrosophic SuperHyper-Bipartite and Neutrosophic SuperHyper-Path are introduced. More instances and more clarifications alongside sufficient references.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperStable'' $\mathcal{I}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperStable'' is a \underline{maximal} Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperStable'' is a \underline{maximal} neutrosophic Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Neutrosophic Failed SuperHyperClique theory, and (Neutrosophic) SuperHyperGraphs theory are proposed.

In this research, new setting is introduced for new notions, namely, SuperHyperDegree and Co-SuperHyperDegree. Two different types of definitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The cancer’s treatments are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “cancer’s treatments”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “cancer’s treatments”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. If there’s a SuperHyperEdge between two SuperHyperVertices, then these two SuperHyperVertices are called SuperHyperNeighbors. The number of SuperHyperNeighbors for a given SuperHyperVertex is called SuperHyperDegree. The number of common SuperHyperNeighbors for some SuperHyperVertices is called Co-SuperHyperDegree for them and used SuperHyperVertices are called Co-SuperHyperNeighbors. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The number of SuperHyperEdges for a given SuperHyperVertex is called SuperHyperDegree. The number of common SuperHyperEdges for some SuperHyperVertices is called Co-SuperHyperDegree for them. The number of SuperHyperVertices for a given SuperHyperEdge is called SuperHyperDegree. The number of common SuperHyperVertices for some SuperHyperEdges is called Co-SuperHyperDegree for them. The model proposes the specific designs. The model is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this model, The “specific” cells and “specific group” of cells are modeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are modeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise model which in this case the model is called “neutrosophic”. In the future research, the foundation will be based on the caner’s treatment and the results and the definitions will be introduced in redeemed ways. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, assume a SuperHyperGraph. Then an extreme SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; a neutrosophic SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; an extreme SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the extreme SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; a neutrosophic SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient; an extreme R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; a neutrosophic R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; an extreme R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the extreme SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; a neutrosophic R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient. Assume a SuperHyperGraph. Then $\delta-$SuperHyperMatching is a maximal of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a neutrosophic $\delta-$SuperHyperMatching is a maximal neutrosophic of SuperHyperVertices with maximum neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta;$ and $ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a neutrosophic $\delta-$SuperHyperDefensive It's useful to define a ``neutrosophic'' version of a SuperHyperMatching . Since there's more ways to get type-results to make a SuperHyperMatching more understandable. For the sake of having neutrosophic SuperHyperMatching, there's a need to ``redefine'' the notion of a ``SuperHyperMatching ''. A basic familiarity with Extreme SuperHyperMatching theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed.

New ideas on the framework of Neutrosophic SuperHyperGraph for different styles of Neutrosophic SuperHyper-Wheel and Neutrosophic SuperHyper-Star are introduced. More instances and more clarifications alongside sufficient references are featured with a specific type of independency of SuperHyperVertices.

Bipolar neutrosophic set is an important extension of bipolar fuzzy set. This set is a hybridization of bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove its properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove its properties. Thereafter, we develop two novel multi-attribute decision making methods based on the proposed cross entropy measures. In the decision making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision making problems and compare the obtained result with the results of other existing methods to show the applicability and effectiveness of the developed method. In the end, the main conclusion and future scope of research are summarized.

Along with the economic growth, the companies must contribute to social progress and promote environmental sustainability in equal harmony. Sustainable human resource management (SHRM) strategies make it possible to attain the economic, social and environmental goals of a firm. In this regard, a survey method is discussed using the literature review and online questionnaire to identify the main factors/indicators during the SHRM evaluation of manufacturing firms in India. Uncertainty is commonly occurred in the assessment of SHRM factors. As a generalized version of fuzzy sets, single-valued neutrosophic set (SVNS) has been demonstrated as a valuable tool to illustrate the indeterminate, inconsistent and uncertain data of realistic decision-making problems. Considering the idea of SVNSs, this study develops a hybrid multi-criteria group decision-making (MCGDM) approach for assessing the SHRM of manufacturing firms under uncertainty settings. For this purpose, an SVN-alternative ranking order method accounting for two-step normalization (AROMAN) is proposed based on VIFI-score function-based decision experts’ (DEs’) weighting tool and integrated criteria weight-determining model to solve the MCGDM problems with fully unknown DEs and criteria weights. In this regard, we develop new SVN-distance measure to compute the degree of difference between SVNSs. Some examples are presented to demonstrate the efficacy of developed measure over the existing ones. In addition, new criteria weight-determination model is presented with the integration of objective weights through IVIF-distance measure-based model and subjective weights through ranking comparison (RANCOM) tool on SVNSs. The proposed ranking method is applied to an empirical study of SHRM assessment for manufacturing firms in India, which shows its applicability and feasibility. In this study, the evaluation criteria are characterized into social, environmental and economic aspects with DE’s opinions. Comparative and sensitivity analyses are made to show the strength and steadiness of presented approach. This study provides an innovative MCGDM analysis framework, which makes a significant contribution to the SHRM assessment problem under indeterminate, inconsistent and uncertain setting.

New setting is introduced to study “closing numbers” and “super-closing numbers” as optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. In this way, some approaches are applied to get some sets from (Neutrosophic)n-SuperHyperGraph and after that, some ideas are applied to get different types of super-closing numbers which are called by optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. The notion of dual is another new idea which is covered by these notions and results. In the setting of dual, the set of super-vertices is exchanged with the set of super-edges. Thus these results and definitions hold in the setting of dual. Setting of neutrosophic n-SuperHyperGraph is used to get some examples and solutions for two applications which are proposed. Both setting of SuperHyperGraph and neutrosophic n-SuperHyperGraph are simultaneously studied but the results are about the setting of n-SuperHyperGraphs. Setting of neutrosophic n-SuperHyperGraph get some examples where neutrosophic hypergraphs as special case of neutrosophic n-SuperHyperGraph are used. The clarifications use neutrosophic n-SuperHyperGraph and theoretical study is to use n-SuperHyperGraph but these results are also applicable into neutrosophic n-SuperHyperGraph. Special usage from different attributes of neutrosophic n-SuperHyperGraph are appropriate to have open ways to pursue this study. Different types of procedures including optimal-super-set, and optimal-super-number alongside study on the family of (neutrosophic)n-SuperHyperGraph are proposed in this way, some results are obtained. General classes of (neutrosophic)n-SuperHyperGraph are used to obtains these closing numbers and super-closing numbers and the representatives of the optimal-super-coloring sets, optimal-super-dominating sets and optimal-super-resolving sets. Using colors to assign to the super-vertices of n-SuperHyperGraph and characterizing optimal-super-resolving sets and optimal-super-dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on n-SuperHyperGraph to get new results about closing numbers and super-closing numbers alongside sets in the way that some closing numbers super-closing numbers get understandable perspective. Family of n-SuperHyperGraph are studied to investigate about the notions, super-resolving and super-coloring alongside super-dominating in n-SuperHyperGraph. In this way, sets of representatives of optimal-super-colors, optimal-super-resolving sets and optimal-super-dominating sets have key role. Optimal-super sets and optimal-super numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal-super ones. Simultaneously, three notions are applied into (neutrosophic)n-SuperHyperGraph to get sensible results about their structures. Basic familiarities with n-SuperHyperGraph theory and neutrosophic n-SuperHyperGraph theory are proposed for this article.

In this research, new setting is introduced for assuming a SuperHyperGraph. Then a ``SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$SuperHyperClique'' is a \underline{maximal} SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$SuperHyperClique'' is a \underline{maximal} neutrosophic SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme SuperHyperClique theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperClique'' is a \underline{maximal} Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperClique'' is a \underline{maximal} neutrosophic Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Extreme SuperHyperGraphs theory, and Neutrosophic SuperHyperGraphs theory are proposed.

The purpose of this work is to analyze heat-treated ash wood at temperature of 185 ºC, in order to analyze its dimensional stability. For comparison, native ash/ not thermally treated wood, was be used. In order to analyze heat-treated ash wood, some main properties such as water absorption, swelling in thickness, roughness, Brinell hardness, modulus of rupture and elasticity, color change toward black with CIELab space, and many others properties were determined and processed. The results obtained after processing the experimental data have showed that heat-treated ash wood had good physical properties as absorption and swelling in thickness, and the slight increase in elasticity offers new fields of use. As a general conclusion of the work, it was established that the ash wood can be properly thermally treated, the dimensional stability characteristics being very good, and the decrease in bending resistance being almost imperceptible.

Bladder cancer (BC) is one of the most lethal genitourinary malignancies owing to its propensity for recurrence and poor survival. The biochemical pathway, signal transducer and activator of transcription 3 (STAT3), has gained significance as a molecular pathway that promotes proliferation, invasion, and chemoresistance. In this study, we explored the targeting of STAT3 with TTI-101 and SH5-07 in bladder cancer (BCa) and elucidated the mechanisms in three-dimensional (3D) spheroid and tumoroid models. We optimized the growth of spheroids from human, rat, and mouse BCa cell lines (J82, NBT-II, and MB49, respectively), and tumoroids from BBN (N-butyl-N-(4-hydroxybutyl)-nitrosamine) induced rat bladder tumors. Cell viability was assessed using MTT and trypan blue assays. ATP production, ROS production, and calcium AM (CA)/EtBr staining were used to measure the spheroid and organoid inhibition and mitochondrial function. Western blot analysis was performed to evaluate the pharmacodynamic markers involved in cell proliferation, apoptosis, cancer stem cells (CSCs), and STAT3 signaling in BCa. We found that targeting STAT3 (using TTI-101 and SH5-07) significantly reduced the proliferation of BCa spheroids, and tumoroids, which was accompanied by decreased expression of pSTAT3, Cyclin D1, and PCNA. Our data also demonstrated that treatment with STAT3 inhibitors induced ROS production and cell death in BCa spheroids and organoids. STAT3 inhibition induced cell death was associated with the activation of caspase 3/7 and PARP cleavage. Moreover, TTI-101 and SH5-07 targets cancer stem cells by downregulating the expression of CD44 and CD133 in 3D models. This study provides the first evidence for the prevention of bladder cancer with small-molecule inhibitors TTI101 and SH5-07 via suppression of CSCs and STAT3 signaling.

Recently, the concept of participatory democracy developed in the early 1970s has come back into fashion to revitalize the public involvement in political decision-making processes. Public par-ticipation in forest policy has been fully conceptualized by the scientific community in the late 1990s and early 2000s, but in many contexts the practical application remains unfulfilled. The aim of this study is to identify and analyze the participatory techniques used in literature to increase knowledge and facilitate its transferability into forest policies and strategies. A literature review was carried out to offer an overview of the participatory techniques adopted in the deci-sion-making process. At the end of literature review, 25 participatory techniques were identified based on over 2,000 publications. Afterwards, the participatory techniques were assessed using seven indicators (degree of participation, type and number of participants, time scale, cost, po-tential influence on policy). The results showed that the type of actors involved in the participa-tory technique is a key variable for the complexity and usefulness of the process, while the number of participants influences how information is disseminated. The Principal Component Analysis highlighted that the participatory techniques can be divided in three groups: the first group includes those techniques with a high degree of participation and a contextual high po-tential influence on policies, the second one includes techniques with a costs in terms of re-sources, while the third one consists of those with a large number of participants and reduced time requirements.

Amid the array of challenges prompted by the COVID-19 pandemic, the policy response of governments proved vital. The U.S. states pursued varied policy approaches that demonstrated distinct divergences in impact. Particularly, contrasting state contexts produced markedly assorted frameworks for the delivery of public health services, which indicate potential effects for COVID-19 policy implementation. Using the rates of COVID-19 vaccinations as a measure of policy execution, the purpose of this study is to examine the political and administrative influences contributing to differences in COVID-19 public health policy outcomes among the U.S. states. Ordinary least squares (OLS) regression models included data sources of nationally representative information pertaining to state public health attributes of politics and administration during the height of the pandemic and vaccine campaign. The findings suggest that state political and fiscal orientations display significant associations with COVID-19 vaccination disparities, while other administrative indicators did not. The results signal important policy implications for the politics-administration dynamic within the COVID-19 pandemic and offer further understanding toward the roles of federalism and governance in future public health emergencies.

More than 700 anthocyanins are described so far, and many different sources are rich in these natural pigments. During the last few years, researchers have been focusing of strategies to recover and purify anthocyanins, from simple liquid-liquid extractions to more advanced supercritical CO2 extractions, however, with such a huge number of different sources, it’s extremely hard to get a simple and fast methodology that fits several sources, not only by the structural nature of the anthocyanins but also by the presence of specific groups of natural compounds. Using simple methodologies like solid-phase extraction resins represents a powerful economical and efficiency strategy. In this work, we tested several sources of structurally distinct anthocyanins, including purple basil, purple cabbage, purple sweet potato, butterfly pea flower, cornflower and wild pansy, in different resins to assess their efficiency in the obtention of anthocyanin-pure extracts. The results showed us that the combination of oasis HLB® resin followed by a cation-exchange SPE with DSC-MCAX® resulted in high-purity anthocyanin extracts for all the cases.

Ballistic helmets are individual armor equipment designed to protect a soldier's head from projectiles and fragments. Although very common, these helmets are responsible for several causalities due to their low ballistic resistance and large back face deformation to stop the projectile. Therefore, to enhance helmet performance, studies have focused on the development of new materials and new ballistic protection solutions. The purpose of this study was to develop and evaluate a new ballistic solution using thermoplastic-based matrices. The first matrix was based on high-density polyethylene (HDPE). The second matrix was based on HDPE modified with ex-foliated montmorillonite (MMT). The main manufacturing processes of a thermoplastic-based ballistic helmet are presented, along with its ballistic performance, according to the National Institute of Justice (NIJ) standard 0106.01 and an investigation of its failure mechanisms via a non-destructive technique. All the helmets resulted in level III-A ballistic protection. The postimpact helmets were scanned to evaluate the back face deformation dimensions, which revealed that the global cone deformation was deeper in the HDPE than in the HDPE/MMT. The failure analysis revealed an overall larger deformation area in the HDPE and HDPE/MMT helmet delamination zones in regions with a large radius of curvature than in zones with the lowest radius, which is in accordance with previous simulations from the literature.

This article provides a literature review on tubal carcinoma to offer an updated insight into its preventative strategies, diagnosis, treatment, and oncological surveillance. In addition to the search string utilized, the authors' focus extended to key scientific studies, consensus statements, guidelines, and relevant case reports essential for the proper clinical management of the disease, providing a methodologically well-structured literature review combined with the practical expertise in the oncological field. The article also includes two emblematic clinical cases that emphasize the importance of understanding the physiopathology and the current state of the art in the anatomopathological advancements of tubal/ovarian/peritoneal carcinoma, often assimilated into a single clinical entity.

The present work titled QRGB consists of the development of a Python application for generating QR codes using the additive color generation method (RGB). This innovative method increases the information density stored in QR codes by using three color layers (red, green, and blue), each representing a different data set. QRGB offers an efficient and secure solution for storing and transmitting large amounts of information in limited spaces, significantly improving the capabilities of traditional black-and-white QR codes.By using three color layers (red, green, and blue), QRGB codes can store up to three times more information in the same space. This technique not only increases storage capacity but also enhances information security, making it more difficult to counterfeit or manipulate the code. The superposition of multiple data layers allows for redundancy implementation, increasing the code's robustness against damage or reading errors.QRGB codes are especially useful in applications that require the transmission of large amounts of data in limited spaces, such as in the packaging industry, digital business cards, and interactive advertising. Additionally, they have great potential in areas such as document and ticket security, where the authenticity and integrity of information are crucial.These points provide a solid foundation for understanding the innovation and advantages of colored QR codes (QRGB) compared to traditional QR codes, highlighting their applicability and potential in various sectors.The Python application developed for QRGB utilizes advanced color image processing techniques, applying models and methods to generate and decode QR codes using the RGB color system, thus enhancing information density and security through the innovative use of additive color layers.

The Internet of Things (IoT) signifies a revolutionary technological advancement, enhancing various applications through device interconnectivity while introducing significant challenges due to these devices' limited hardware and communication capabilities. To navigate these complexities, the Internet Engineering Task Force (IETF) has tailored the Routing Protocol for Low-Power and Lossy Networks (RPL) to meet the unique demands of IoT environments. However, RPL struggles with traffic congestion and load distribution issues, negatively impacting network performance and reliability. This paper presents a novel enhancement to RPL by integrating learning automata designed to optimize network traffic distribution. This enhanced protocol, the Learning Automata-based Load-Aware RPL (LALARPL), dynamically adjusts routing decisions based on real-time network conditions, achieving more effective load balancing and significantly reducing network congestion. Extensive simulations reveal that this approach outperforms existing methodologies, leading to notable improvements in packet delivery rates, end-to-end delay, and energy efficiency. The findings highlight the potential of our approach to enhance IoT network operations and extend the lifespan of network components. The effectiveness of learning automata in refining routing processes within RPL offers valuable insights that may drive future advancements in IoT networking, aiming for more robust, efficient, and sustainable network architectures.

Antimicrobial resistance (AMR) is a growing concern in healthcare, and the misuse of antibiotics is contributing to the problem. Antimicrobial Stewardship Programs (ASPs) have been proven to help reduce antibiotic consumption, promote appropriate use, and decrease the incidence of AMR and related side effects. In this study, we aimed to evaluate the impact of ASPs on antibiotics consumption and AMR spread in a Southern Italy. Most of the APSs consisted of applying infection control guidelines and WHO recommendations on antibiotic consumption. The results of the study showed that during the study period, the number of hospitalizations increased by 24%, while the total amount of antibiotics administered decreased from 52.1 to 38.6 defined daily doses (DDD) per 100 bed-days. There was also a significant increase in the number of rectal swabs taken to detect carbapenem-resistant Enterobacteriaceae (CRE) and methicillin-resistant Staphylococcus aureus (MRSA), while the positivity rate of these infections decreased significantly. Moreover, the hospital recorded a decrease in the incidence of several infections, including CRPsA, MRSA, PDR, and VanA infections. This study provides further evidence that ASPs can be effective in reducing antibiotic consumption and preventing the spread of AMR. By promoting the appropriate use of antibiotics and implementing infection control measures, we can help preserve the effectiveness of these life-saving drugs and promote better patient outcomes. However, more efforts are needed to improve healthcare practices and reduce related costs. In conclusion, we urge healthcare providers to implement ASPs in their institutions and help combat the growing threat of AMR. By doing so, we can ensure that antibiotics remain effective for future generations.

Background: Chronic Heart failure (CHF)constitutes a major health problem, representing the leading cause of hospitalization in people over 65 years old. Several studies have associated the Mediterranean diet with a cardioprotective function, improving prognosis in patients with high cardiovascular risk. Our main objective is to determine whether greater adherence to the Mediterranean diet is associated with a lower severity of CHF, depending on the number of heart failure decompensations and complications of the disease. Methods: The study was a single-center restrospective cohort study conducted at the Virgen del Rocío Hospital (Seville). Adherence to a Mediterranean diet was determined by the Mediterranean Diet Adherence Screener (MEDAS) in patients with chronic heart failure in a state of clinical stability, and their cardiac and analytical profiles were evaluated. Results: Seventy-two patients were included (35 with high adherence to the Mediterranean diet and 37 with low adherence). The average age was 81.29 ± 0.86 years. A trend towards fewer cardiac decompensations (1,49 ± 0,14 vs 1,92 ± 0,17), p= 0,054) and lower NT-proBNP values 2897,02 ± 617,16 vs 5227,96 ± 1047,12; p = 0,088) was observed in patients with high adherence compared to those with low adherence to the Mediterranean diet. Conclusions: Our results suggest that patients with CHF and high adherence to the Mediterranean diet have a tendency towards improved cardiac profile, indicated by fewer decompensations and lower NT-proBNP levels. Future clinical trials are needed to substantiate these hypotheses.

(1) Background: The aim of this investigation is to determine the effect of archwires’ deflection on the temperature transitions driving the austenite to martensite transformation (and vice versa) and the force released by NiTi and CuNiTi orthodontic wires. (2) Methods: Round cross-section archwires have been investigated. The calorimetric approach has been used for measuring transition temperatures occurring in the unstressed (e.g. undeflected) state of the wires. Static Thermo-mechanical analysis in a temperature controlled wet environment has been performed in the range of temperature between 5°C and 55°C for measuring temperature transitions occurring in highly deflected archwires in conjunction with the force released by these wires. (3) Results: Plateau forces investigated in Part I and those reported in the literature describes the wire’s behaviour only at deflection levels close to the end point of the force plateau extension detected at 37°C. Upon heating or cooling, the austenite finish (Af) transition temperature and the martensite start (Ms) temperature largely depends on the deflection level for both NiTi and CuNiTi. (4) Conclusions: The plateau force levels at 37°C, broadly reported in the literature, only represent the lower boundary force that a superelastic wire releases at 37°C above its elastic limit. For both NiTi and CuNiTi, plateau force levels at 37°C can be predicted by the static TMA profile matching the end point of the force plateau extension. Transition temperatures in largely deflected wires are significantly higher than those determined through the calorimetric approach.

Half-metallic semi-Heusler compounds are currently at the forefront of scientific research due to their potential applications in spintronic devices. Unlike other semi-Heuslers, the p0(d0)-d compounds do not appear to crystallize in the typical variant of the C1b structure. We investigate this phenomenon in the p0-d Heusler compounds LiYGa and LiYGe, where Y varies between Ca and Zn, using first-principles ab-initio electronic band structure calculations. We examine the electronic and magnetic properties of these compounds in relation to the three possible C1b structures. Notably, LiVGa, LiVGe, LiMnGa, and LiCrGe are half-metallic ferromagnets across all three variations of the C1b lattice structure. Our findings will serve as a foundation for future experimental studies on these compounds.

Life is a field of senses and the experience of feeling, thinking, acting, and building relationships with everything around us. These senses and experiences are also consumed in travel destinations to pursue the traveler's escapism and happiness. However, while the field of tourism studies has recognized the importance of experience and focused on the relationship between various travel experiences and happiness, research on the variables that mediate and strengthen these relationships is lacking. Therefore, this study aims to apply the five strategic experiential models proposed by Schmitt [1]— sense, feel, think, act, and relate — to investigate the mediating effect of escapism on travelers' well-being. Data were collected from travelers visiting three major heritage sites in Gyeongju (Bulguksa Temple, Seokguram Grotto, and Bunhwangsa Temple), and 509 responses were used for analysis. The analysis was conducted using statistical package programs SPSS and AMOS employing frequency analysis, reliability analysis, confirmatory factor analysis, and structural equation modeling. The results indicated significant positive effects between variables such as cultural heritage travel experience, escapism, and well-being. In the analysis of the mediating effect of escapism, escapism showed a significant mediating effect on the relationship between travel experience and well-being. This study confirmed that, during cultural heritage travels, individuals’ well-being can be enhanced through a holistic experience encompassing sensory, emotional, cognitive, behavioral, and relational aspects rather than an isolated experience centered on escapism. This finding provides important implications for the design and planning of travel programs and products.

Aiming at solving difficulties related to aero-engine classification and identification, the infrared spectra of aero-engine hot jets are measured by telemetry Fourier transform infrared spectrometer, and a six types aero-engine hot jet spectrum data set is generated. The spectrum data set were randomly sampled at a ratio of 8:1:1 to generate training set, validation set and prediction set. In this paper, a Peak Finding Siamese Convolutional Neural Network (PF-SCNN) is designed to match and classify spectrum data. In the first place, the matching pairs of training set and validation set are made independently with the labels of positive and negative samples creating. The spectrum feature extraction and distance similarity calculation are carried out by the Siamese convolutional neural network (SCNN). When entering the prediction phase, the prediction set and training set are integrated to predict in the trained model. The prediction set labels are ultimately determined by matching them with the training set labels having the highest similarities to ensure accurate predictions. To improve the operation efficiency of the SCNN, a peak finding method is introduced to extract the spectrum peaks. Peak positions of high frequency are counted, while the peak data are extracted. The peak data are used to take the place of the original data for training and prediction. The performance measures are defined as Accuracy, Precision, Recall, Confusion matrix and F1-score, and the prediction accuracy was up to 99%. The experimental results indicate that the proposed PF-SCNN is suitable for our spectral dataset and can complete the task of infrared spectrum classification of aero-engine hot jets.

The characteristics of tight sandstone, such as small pores, complex pore structures, low permeability, and low porosity, make it difficult to accurately characterize its pore structure. This represents a major challenge in the exploration and development of tight sandstone oil and gas reservoirs. This article conducts a simulation study on the impact of characteristic parameters such as pore size, coordination number, pore-throat ratio, and wettability on microscopic remaining oil after polymer flooding, thereby quantifying the types of remaining oil.

This study provides a methodology for optimizing oil production and CO2 sequestration using an integrated asset model of the Farnsworth Unit field, incorporating extensive geological, geophysical, and engineering data. Sensitivity analysis identified critical parameters impacting oil recovery and CO2 storage, leading to the construction of a proxy model using polynomial regression and radial basis function neural networks, with the latter proving more effective for "What-if" analysis. The sensitivity analysis indicated that the Corey parameters impact cumulative oil produced the most. Comprehensive history matching validated the model against historical production data, ensuring reliability for forecasting and optimization. Two scenarios, "Do-Nothing" and development strategy, were forecasted over 15 years (2020-2035). The "Do-Nothing" scenario resulted in 9.57 MMSTB of oil recovery and 2,822.70 MMlbs of CO2 storage. The development strategy case improved outcomes with 13.95 MMSTB of oil recovery and 5,061.68 MMlbs of CO2 stored, and was selected for optimization using particle swarm optimization. The optimized strategy achieved 14,043,372 STB of cumulative oil and 4,832.18 MMlbs of CO2 stored, and increased the field NPV by 25.84% to $114,871,730. This study underscores the significance of integrated asset modeling in enhancing oil recovery and optimizing CO2-EOR processes, providing valuable insights into operational conditions and constraints.

Here, we present a general framework for computing the infrared anharmonic vibrational spectra of polyatomic molecules using the Born-Oppenheimer molecular dynamics (BOMD) with the software PyRAMD. To account for the nuclear quantum effects, we suggest using the simplified Wigner sampling (SWS) approach [\textit{Phys. Chem. Chem. Phys.}, 2023, \textbf{25}, 18406-18423] simultaneously coupled with the Andersen and Berendsen thermostats. We propose a new criterion for selecting the parameter of the SWS based on the molecules' harmonic vibrational frequencies and usage of the large-time-step blue shift correction, allowing for a decrease in computational expenses. For the Fourier transform of the dipole moment autocorrelation function, we propose to use the regularized least-squares analysis, which allows us to obtain higher frequency resolution than the direct application of fast Fourier transform. Finally, we suggest the usage of the pre-parameterized scaling factors for the IR spectra from BOMD, also providing the scaling factors for the spectra at the BLYP-D3(BJ)/6-31G, PBE-D3(BJ)/6-31G, and PBEh-3c levels of theory.

The conservation of the main protease in viral genomes, combined with the absence of a homologous protease in humans, makes this enzyme family an ideal target for developing broad-spectrum antiviral drugs with minimal host toxicity. GC-376, a peptidomimetic 3CL protease inhibitor, has shown significant efficacy against coronaviruses. Recently, a GC-376-based PROTAC was developed to target and induce the proteosome-mediated degradation of the dimeric SARS-CoV-2 3CLPro protein. Extending this approach, the current study investigates the application of the GC-376 PROTAC to the 3CPro protease of Enteroviruses, specifically characterizing its interaction with CVB3 3CPro through X-ray crystallography, NMR and biophysical techniques. The present structural data show that there are some changes between the binding of CVB3 3CPro and SARS-CoV-2 3CLPro, but the overall similarity is strong. The most notable variation is the orientation of the phenylmethyl ester of GC-376 with the S4 subsite of the proteases. This is linked to the flexibility of the protein structure around the region of the catalytic triad shown by our NMR data. Other structural variations include distinct ligand interactions in subsites S1 and S2, influenced by the presence of Glu71 in CVB3 3CPro. Despite these differences, the GC-376 PROTAC fits well within the binding sites of both proteases, demonstrating its potential as a broad-spectrum antiviral agent.

Disaster issue consultation is crucial for effective emergency management, requiring timely and accurate information to support decision-making processes. This paper explores the integration of large language models (LLMs) with advanced prompt engineering to enhance the performance of AI systems in disaster management. We propose a novel multi-round prompt engineering approach that guides LLMs to iteratively refine their responses based on evolving disaster scenarios. Our method leverages diverse disaster-related datasets and employs a combination of accuracy metrics and a customized GPT-4 scoring system for evaluation. We conduct comprehensive experiments across multiple LLM platforms, including Qwen2, ChatGPT, Claude, and GPT-4, comparing our approach with baseline models and the Tree of Thoughts (ToT) method. The results demonstrate significant improvements in both accuracy and response quality, highlighting the effectiveness of our method in providing contextually relevant and actionable insights. Additional analysis confirms the robustness and generalizability of our approach across various disaster scenarios, establishing it as a valuable tool for enhancing disaster management practices.

AI advances integrate generative design tools in architecture, providing architects with sophisticated design options. It enables the creation of intricate, high-performing projects by exploring diverse design possibilities with AI and algorithms. Generative AI and generative design empower architects to create better-performing, sustainable, and efficient design solutions and explore diverse design possibilities. This paper leverages multimodal generative AI to enhance design creativity by combining textual and visual inputs. Blockchain technology converts design metadata into NFTs, ensuring secure, authentic, and traceable data storage. The framework addresses data ownership, legal adherence, and client-architect collaboration and is entirely scalable for digital design authentication. This research exemplifies the pragmatic fusion of Generative AI and blockchain technology applied in architectural design for more transparent, secure, and effective results. This study provides a strategy that uses generative AI technologies to achieve an efficient and creative workflow in the early stages of architectural design.

In the foodservice industry, clients judge not only the product standard but also the service quality they receive during their restaurant experience. Therefore, when the importance of the dining experience is strongly regarded by consumers in terms of intellectual and motivational attributes, they are happier to suggest the establishment to others. The main objective of this research is to study the influence of different service quality factors in restaurants and their impact on customer satisfaction. This research is also undertaken to evaluate the identification of important factors for the restaurant industry and the levels of service quality among customers satisfaction with the services offered by restaurants in India. As factor analysis, correlation, and regression research, this study was conducted using a modified IBM SPSS Statistics 24 and AMOS instrument among the 630 randomly selected customers. A weighted mean was used to describe the levels of service quality and customer satisfaction. Multiple regressions were used to determine the predictors of customer satisfaction. The results reveal the main 12 service quality factors, which are: 1. Process-related factors: system for take-away orders, order tracking system, and time for food preparation 2. People-related factors: focus on customers' special requests, peer group influence, and making you feel special. 3. Physical Environment: Walking Space, Architecture of the Restaurant, and Signals for Direction 4. Performance-related factors: food served at an appropriate temperature; food presentation; portion size of food in the restaurant. The researchers have developed one model on service quality factors that is described in the research paper.

With the digital transformation of the logistics industry, smart logistics algorithms have become a core technology to improve efficiency and reduce costs. This paper reviews the development history of traditional logistics technology and discusses the key role of technologies such as the Internet of Things, big data analysis, artificial intelligence, and automation in logistics technology innovation. It focuses on the application of intelligent logistics algorithms in path optimization, intelligent scheduling, data mining and prediction, and intelligent warehousing. To solve the problem of inconsistency between training and testing objectives, this paper proposes DRL4Route, a deep reinforcement learning-based path optimization framework, and designs the DRL4Route-GAE model. Validated through extensive offline experiments and online deployments, the model significantly outperforms existing optimal benchmark methods on real datasets, improving the location deviation squared metrics and the top-three location prediction accuracy metrics. These research results provide important support to further promote the intelligent development of the logistics industry.

This paper presents a demonstration of a linearly-polarized transmit-arrays antenna with high-efficiency and wideband operating in X-band. The topology of the unit cell consists of two identical patch antennas loaded by C-loop slot and interconnected by a metalized via through a ground plane sandwiched between two identical substrates [18]. A waveguide measurement system WGMS has been used for single cell characterization (reflection/transmission coefficients). Good results have been demonstrated in terms of matching performances; the reflection coefficient S11 is under 10-dB in the 9.4-10.4 GHz band (i.e. 10.1% around 9.9 GHz) and with only 0.35 dB-insertion loss at 10 GHz. The transmit-arrays prototype permitted to achieve 22.4 dBi of directivity and 20.1 dBi of gain. The aperture and radiation efficiencies are about 28.2% and 58.3%, respectively. With a focal ratio (F/D) of 1/2 the spill-over loss is less than 2 dB. Beam-scanning up to ± 35° has been achieved with the same phase quantization (passive) and less than 3 dB of gain losses.

The surface thermodynamic properties of polymers and copolymers modified by supramolecular structures are very used in several industrial processes, such as selective adsorption, paints, coatings, colloids, and adhesion applications. Background: Inverse gas chromatography at infinite dilution was proved to be the best technique to determine the surface properties of solid surfaces by studying the adsorption of some model polar and non-polar organic molecules adsorbed on solid surfaces by varying the temperature. Methods: The retention volume of adsorbed solvents is a precious parameter to obtain the London dispersive and polar free energies and the London dispersive surface energy of styrene–divinylbenzene copolymer modified by supramolecular structure of melamine using the Hamieh thermal model and our new methodology consisting in the separation of the two polar and dispersive free energy of interaction. This led to the determination of the polar acid and base surface energy, and the Lewis’s acid-base constants of the various solid materials. Results: all surface energetic properties of styrene–divinylbenzene copolymer modified by melamine at different percentages were determined as a function of temperature, following our new methodology. Conclusions: It was observed that the styrene–divinylbenzene copolymer exhibited the highest London dispersive surface energy which decreased when the melamine percentage increased. All materials presented higher Lewis’s basicity and this Lewis’s basicity increased with the percentage of melamine.

A high-gain broadband circularly polarized crossed dipole antenna is designed. This antenna utilizes two pairs of cross dipoles and a pair of phase delay lines to form circularly polarized radiation. Open-circuit stubs are loaded on the four arms of these two pairs of cross dipoles to introduce new circularly polarized resonating frequency. A rectangular ring patch is introduced directly below the cross dipoles to form the third circularly polarized resonating frequency, thereby broadening the axial ratio bandwidth of the antenna. In addition, metal posts are loaded at the four right angles of the rectangular ring patch to increase the antenna gain. Measurement results show that the antenna achieves a 3dB axial ratio bandwidth of 29.2% (1.9 GHz-2.55 GHz) and maintains a gain of 7.5 dB within the passband, exhibiting good circularly polarized radiation performance.

Nicotiana benthamiana plants infected with a potato virus Y isolate (PVYO) under ambient conditions of 25 °C and ~405 parts-per-million (ppm) ambient CO2 display symptoms of chlorosis, leaf curling, and stunting. However, under elevated temperature and CO2 levels (30 °C, 970 ppm), systemic viral titers decrease several-fold, and plants appear asymptomatic. Under the latter conditions we have studied how infection, drought, or both combined affect infection, drought-driven loss of leaf turgor, plant water content, stomatal conductance, metabolome, and hormone (ABA, SA, and JA) levels. We found that drought did not affect viral titers. As expected, drought decreased plant water content and stomatal conductance. Under drought conditions, infection did not alter significantly final water content or loss of leaf turgor progression, but it increased the levels of some sugars and other osmo-protectants. Infection and drought altered the levels of many components of the metabolome. Some components altered by infection were not altered by drought, but most of those altered by drought were also altered by infection. Drought increased the levels of ABA, infection increased the levels of ABA, SA, and JA, and altered their relative balance. The effects of drought and of infection on hormone levels were cumulative when combined. Thus, under ambient conditions that turn a severe infection into an asymptomatic one both, plant physiology parameters and the interplay with drought are affected.

We propose a novel approach to quantum theory construction that involves solving a maximization problem on the Shannon entropy of all possible measurements of a system, relative to its initial preparation. This maximization problem is additionally constrained by a phase condition that vanishes under measurements. Specifically, enforcing a vanishing U(1)-valued phase constraint leads to standard quantum mechanics, while a vanishing Spin^c(3,1)-valued phase constraint extends the theory to relativistic quantum mechanics and to quantum gravity. The latter scenario derives the metric tensor as an operator via a double-copy mechanism applied to the Dirac current. Significantly, this solution is consistent exclusively in 3+1-dimensions as all other dimensional configurations lead to fundamental obstructions. Finally, the solution uniquely incorporates the SU(3)xSU(2)xU(1) symmetries of the Standard Model. This framework seamlessly integrates fundamental concepts from quantum mechanics, relativistic quantum mechanics, quantum gravity, the dimensional specificity of spacetime, and particle physics gauge symmetries as the solution to a simple entropy optimization problem.

In vitro cancer cell cytotoxicity (IC50 values) of (E)-3-(4’-methylbenzylidene)-4-chromanone (IIIb) showed &gt;50.0 decreases in comparison to those of the respective tetralone derivative (IIIc). On the other hand, such a decrease was not observed in the analogous 4-OCH3 (IIc and IIIc) derivatives. Since the compounds can be considered cyclic chalcone analogs, kinetics and diastereoselectivity of non-enzyme catalyzed reactions with reduced glutathione (GSH) and N-acetylcysteine (NAC) of IIIb and IIIc were investigated to assess the possible role of thiol-reactivity in the increased cytotoxicity of IIIb. Reactivity of the compounds and stereochemical outcome of the reactions were evaluated using high-pressure liquid chromatography-mass spectrometry (HPLC-MS). Molecular modeling calculations were performed to rationalize the observed differences in the thiol-reactivities of the chromanones (III) and the previously investigated tetralones (II). The results indicated possible role of spontaneous thiol-reactivity of compounds III in their recorded biological effects.

Preeclampsia is a complex pregnancy-related hypertensive disorder which poses significant risks for both maternal and fetal health. Preeclampsia affects 5-8% of the pregnancies in the United States, causing a significant public health and economic burden. Despite extensive research, the etiology and pathogenesis of preeclampsia remain elusive, but have been correlated with maternal conditions such as obesity. In the past decades, the incidence of preeclampsia increased along with the prevalence of obesity among women of reproductive age. Maternal obesity has been shown to negatively affect pregnancy in almost all aspects. However, the precise mechanisms by which obesity influences preeclampsia are unclear. Ankyrin repeat and SOCS Box Containing protein 4 (ASB4) is an E3 ubiquitin ligase that can promote the degradation of a wide range of target proteins. ASB4-null mice display a full spectrum of preeclampsia-like phenotypes during pregnancy including hypertension, proteinuria, and decreased litter size. Furthermore, maternal obesity induced by a high fat diet aggravates preeclampsia-like phenotypes in pregnant mice lacking ASB4. Variants in the ASB4 gene have been associated with obesity in humans, and a functional connection between the ASB4 gene and obesity has been established in mice. This review discusses the connections between preeclampsia, obesity, and ASB4.

Exosomes are small extracellular vesicles produced by almost all cell types in the human body and exosomal microRNAs (miRNAs) are small non-coding RNA molecules that are known to serve as important biomarkers for diseases such as cancer. Given that the upregulation of miR-106b is closely associated with several types of malignancies, the sensitive and accurate detection of miR-106b is important but difficult. In this study, a surface acoustic wave (SAW) biosensor was developed to detect miR-106b isolated from the cancer cells based on immunoaffinity separation technique using our unique paddle screw device. Our novel SAW biosensor could detect a miR-106b concentration as low as 0.024 pM in a linear range from 0.1 pM to 1.0 μM with a correlation coefficient of 0.9939. Additionally, we were able to successfully detect miR-106b in total RNA extracted from the exosomes isolated from the MCF-7 cancer cell line, a model system for human breast cancer, with performance comparable to commercial RT-qPCR methods. Therefore, the exosome isolation by paddle screw method and the miRNA detection using the SAW biosensor has the potential to be used in basic biological research and clinical diagnosis as an alternative to RT-qPCR.

Colloidal quantum dots (CQDs) are valuable for their potential applications in optoelectronic devices. However, they are susceptible to thermal degradation during processing and while in use. Mitigating thermally induced sintering, which leads to absorption spectrum broadening and undesirable changes to thin film electrical properties, is necessary for the reliable design and manufacture of CQD-based optoelectronics. Here, low temperature metal-oxide atomic layer deposition (ALD) was investigated as a method for mitigating sintering while preserving the optoelectronic properties of mercury telluride (HgTe) CQD films. ALD-coated films are subjected to temperatures up to 160oC for up to 5 hours and alumina (Al2O3) is found to be most effective at preserving the optical properties, demonstrating the feasibility of metal-oxide infilling to protect against sintering. HgTe CQD film electrical properties were investigated before and after alumina ALD in-filling, which was found to increase the p-type doping and hole mobility of the films. The magnitude of these effects depended on the conditions used to prepare the HgTe CQDs. With further investigation into the interaction effects of CQD and ALD process factors, these results may be used to guide the design of CQD-ALD materials for their practical integration into useful optoelectronic devices.

In vertical coordinates, (x,y,z), the gradient Richardson number Ri=N^2⁄S^2 is the square of the ratio between buoyancy frequency N and vertical-shear amplitude S, where N^2=-(g⁄ρ) ∂ρ⁄∂z and S^2=(∂u⁄∂z)^2+ (∂v⁄∂z)^2, with ρ potential density, (u,v) the horizontal velocity components and g gravity acceleration, so that a decrease in stratification brings a decrease in dynamic stability and vice versa. In the isopycnic coordinate system, (x,y,ρ), however, Ri=M^2⁄〖S_ρ〗^2 , is the ratio between 〖M^2≡N〗^(-2) and the squared diapycnal shear 〖S_ρ〗^2=(ρ⁄g)^2 [(∂u⁄∂ρ)^2+ (∂v⁄∂ρ)^2 ], so a decrease in stratification leads to an increase in dynamic stability and vice versa. The apparently different role of stratification arises because S and S_ρ are related through the stratification itself, S_ρ=S⁄N^2 or, equivalently, τ=〖t_o〗^2⁄t_d , which is interpreted as a natural oscillation time τ≡S_ρ that equals the buoyancy or oscillation time t_o=N^(-1) normalized by the ratio t_o⁄t_d , where the deformation time is t_d=S^(-1). Here we follow simple arguments and use field data from three different situations (island shelf-break, Gulf Stream and Mediterranean outflow) to endorse the usefulness of the isopycnal approach. In particular, we define the reduced squared vertical σ^2= S^2-N^2 and reduced squared diapycnal shear 〖σ_ρ〗^2= 〖S_ρ〗^2-M^2, which are positive for unstable conditions and negative for stable conditions. It turns out that Ri and σ^2 remain highly variable for all stratification conditions; in contrast, the mean 〖σ_ρ〗^2 values display a univocal tendency, its magnitude decreasing with stratification. We propose 〖σ_ρ〗^2 and 〖S_ρ〗^2 to be good indexes for the occurrence of effective mixing under high stratification conditions.

Glioblastoma is a highly aggressive brain tumor and is considered to be the most common primary one. Recurrence after treatment is a major problem. The recurrence of GBM is related to different cellular mechanisms and molecular signaling. Therapies to prolong survival are not completely effective. Epigenetics and non-coding genetic elements play a crucial role in gliomagenesis. Non-coding RNAs are novel regulatory RNAs that play key roles in different physiological processes such as gene regulation, cell differentiation, and proliferation. Interestingly, some LncRNAs have a tumor suppressor role while others are oncogenic. In this review article, we are going to illustrate the role of a well-known lncRNA HOX transcript antisense intergenic RNA (HOTAIR) in glioma and highlight the possible functions in glioma in both pre-clinical and clinically evident studies.

High consequence pathogens such as Ebola, Marburg and Lassa viruses are handled in maximum containment Biosafety Level 4 (BSL-4) laboratories. Genetic material is often isolated from such viruses and subsequently removed from BSL-4 for a multitude of downstream analyses using readily accessible technologies and equipment available at lower biosafety level laboratories. However, it is essential to ensure that these materials are free of viable viruses before removal from BSL-4 to guarantee sample safety. This study details the in-house procedure used for validating the inactivation of Ebola, Marburg and Lassa virus cultures after incubation with AVL lysis buffer (Qiagen) and ethanol. This study’s findings showed no viable virus was detectable when high-titer cultures of Ebola, Marburg, and Lassa viruses were incubated with AVL lysis buffer for 10 minutes, followed by an equal volume of 95% ethanol for 3 minutes, using a method with a sensitivity of ≤0.8 log10 TCID50 as the limit of detection.

The iron roughneck is an automated equipment utilized for the connection and removal of drilling tools. This paper presents the design of an integrated iron roughneck, providing a detailed introduction to its clamp body structure, along with an analysis of its structural characteristics and performance requirements. The study delves into the integration mode and working characteristics of the clamping mechanism and spin buckle mechanism for the integrated upper clamp body structure of the iron roughneck. Additionally, this paper conducts an in-depth theoretical study on the spin buckle mechanism. Firstly, it analyzes the actual working condition of the spin buckle roller from two perspectives: contact theory and rolling friction theory, determining the structural form of the spin buckle roller. Secondly, it investigates the relative displacement between the spin buckle mechanism and the drilling tool, proposing a design method for the floating device mounted on the spin buckle roller and establishing the kinematic equation of the spin buckle roller under the influence of the floating device. Furthermore, the kinematic equations of the spin buckle roller under the influence of the floating device are established. Finally, a dynamics simulation experiment is performed to simulate the working process of the spin buckle mechanism under actual working conditions, analyzing the dynamics and kinematics of the spin buckle mechanism and obtaining the relevant parameter curves of the spin buckle mechanism and drilling tools. Through data comparison and analysis, the correctness of the theoretical analysis results and the rationality of the performance and structure of the spin buckle mechanism are verified.

The emergence of antibiotic-resistant Campylobacter jejuni, a leading cause of gastroenteritis worldwide, presents a significant public health challenge requiring vigilant surveillance and disease control. This study aimed to characterize C. jejuni strains isolated in Romania from 2017-2020, focusing on genetic diversity, virulence, and antibiotic resistance determinants. The isolates underwent phenotypical testing, PCR, and antibiotic resistance assessment using Disc Diffusion Kirby–Bauer for ciprofloxacin, nalidixic acid, erythromycin, and tetracycline. Genetic analysis identified resistance and virulence genes, point mutations, and performed sequence typing (7-gene MLST) to determine genetic relatedness. Results indicated substitutions at position 86 in the amino acid sequence or position 257 in the nucleotide sequence of the gyrA gene in 47 fluoroquinolone-resistant isolates. Additionally, mutations in the rRNA23S gene at positions 2074 and 2075, associated with macrolide resistance, were found in 12 of the 66 isolates. Allelic profiles generated 38 sequence types (STs), including three new STs not present in the reference database. The sequence data analysis revealed a genetically diverse C. jejuni population with a weak clonal structure. This study provides crucial insights into the genetic diversity and antibiotic resistance of C. jejuni strains in Romania, highlighting the need for ongoing surveillance and control measures.

Idiopathic pulmonary fibrosis [IPF] is a chronic progressive disease characterised by the accumulation of scar tissue in the lung parenchyma. It primarily occurs in middle-aged and elderly adults and results in significant morbidity and mortality worldwide. The disease occurs due to repetitive lung epithelial injury, subsequent fibroblast activation and myofibroblast differentiation, resulting in excessive extracellular matrix deposition. This leads to scar formation and subsequent loss of lung function. Current treatment options for patients with IPF include the two anti-fibrotic drugs, pirfenidone and nintedanib, which can slow disease progression; however, there are currently no known cures for the disease. As such, novel methods and drug targets are warranted. In this review, we provide an up-to-date account of the importance of specific cytokines and the potential role of regulatory immune cells. We discuss their role in the pathogenesis of IPF and address some of the key gaps in knowledge.

Wicked problems, such as climate change, systemic poverty, and healthcare inequalities, rep- resent the most pressing and intractable challenges facing society today. We propose a novel approach that leverages complex systems theory as a comprehensive framework for understanding and tackling these challenges. By applying concepts such as state space analysis, attractors, and nonlinear dynamics, we offer a sophisticated toolkit for mapping the intricate web of interactions defining wicked problems and exploring potential interventions. Our approach moves beyond tradi- tional reductionist methods, embracing the inherent complexity and dynamism of these issues. We demonstrate how this framework can lead to more nuanced, adaptive, and effective strategies for addressing persistent societal problems. Despite the prevalence of wicked problems and the avail- ability of complex systems theory, practical applications of this approach remain uncommon. This paper aims to bridge this gap, illustrating the potential of complex systems theory to transform our engagement with intractable problems and pave the way for more robust, holistic solutions. By synthesizing insights from mathematics, physics, and social sciences, we present a transdisci- plinary approach that promises to revolutionize how we conceptualize and address society’s most challenging issues.

An efficacious treatment of H. pylori infection is cornerstone for the global control of the diseases caused by this bacterium. Continuous epidemiologic surveillance of susceptibility of H. pylori to the antibiotics recommended for its eradication is highly recommended. This study aimed to determine the antimicrobial susceptibility pattern of 651 isolates from five different collections isolated between 1996 to 2008 in México City. The susceptibility profile of H. pylori isolates was determined by the E-test strips for each antibiotic (amoxicillin, clarithromycin, metronidazole, and tetracycline). Antimicrobial susceptibility testing showed a very high proportion of H pylori strains susceptible to amoxicillin, clarithromycin, and tetracycline (94.5%, 95%, and 99.5 %, respectively). In contrast, a high proportion (95%) of isolates was resistant to metronidazole. Notably, the proportion of susceptible/resistant strains to the 4 antibiotics over 5 consecutive time periods remained stable over time. Despite a wide use of amoxicillin and clarithromycin in the general population, the H pylori high susceptibility to these 2 antibiotics has been preserved during more than a decade. The high prevalence of resistance to metronidazole in H. pylori strains in our population compromises its use in the empirical treatment of H. pylori infection.

The diel variations of viruses (< 0.2 μm), picoplankton (0.2—2 μm; heterotrophic bacteria, Syn-echococcus spp., Prochlorococcus spp. and picoeukaryotes) and nanoplankton (2—20 μm; hetero-trophic nanoflagellates and pigmented nanoflagellates) were investigated for 2 days with about 4 hours of temporal sampling in spring 2024 in coastal surface waters of the subtropical western Pacific. A period of wind change associated with rain and increased turbulence, disrupted diel patterns of the overall microbial communities during the second cycle. The abundance of bacteria did not follow a consistent diel pattern, while viral abundance positively correlated with bacterial abundance. Synechococcus spp. and Prochlorococcus spp. grew during the light period and with peak abundance at night, exhibited marked diel variability, however, opposite patterns were observed in picoeukaryotes. According to Synechococcus spp. and Prochlorococcus spp. diel changes, nano-flagellate grazing could control their abundances and may explain temporally varying picocyanobacteria abundances. As we observed in the culture experiments, the results showed a significant increase in picoeukaryotic abundance from noon to nighttime, and a decrease in bacterial abundance during nighttime, to show the prey-predator cycle. Our study suggests picoeukaryotes could serve as bacteria predators by being mixotrophs. Future studies aiming to understand the interactions between prokaryotes and picoeukaryotes within marine microbial communities should take these differences into account.

The Hyper-Torus Universe Model (HTUM) proposes a novel framework to unify quantum mechanics, cosmology, and consciousness. This paper introduces HTUM's core concept: a higher-dimensional hyper-torus encompassing all possible states of existence. HTUM suggests that the universe functions as a quantum system where all outcomes are inherently connected, with consciousness playing a significant role in actualizing reality. The model introduces several key innovations, including the universe's 4-dimensional toroidal structure (4DTS), providing a new geometric interpretation of spacetime. HTUM presents dark matter and dark energy as nonlinear probabilistic phenomena within this toroidal framework, offering a unique perspective on their nature and interactions. The model proposes a mechanism for wave function collapse through universal self-observation, bridging quantum mechanics and gravity. It introduces a Topological Vacuum Energy Modulator (TVEM) function, offering a potential resolution to the cosmological constant problem. Furthermore, HTUM integrates consciousness as a fundamental aspect of the universe, influencing quantum state actualization and potentially resolving the hard problem of consciousness. The model explores the implications of a timeless singularity and the emergence of time as a product of causal relationships within the toroidal structure. This framework addresses critical challenges in modern physics, including the nature of quantum entanglement, the origin and fate of the universe, and the relationship between mind and matter. The paper discusses the mathematical formulation of HTUM, its implications for quantum mechanics and cosmology, and its potential to bridge the gap between science and philosophy. We present detailed predictions for the cosmic microwave background (CMB) power spectrum, gravitational wave signatures, and large-scale structure formation, demonstrating how HTUM differs from the standard ΛCDM model. Our analysis reveals distinctive oscillatory patterns in the relative difference between HTUM and ΛCDM predictions, with deviations reaching up to ±20% at certain scales. The paper also explores the unification of fundamental forces within the HTUM framework, proposing novel approaches to particle physics and quantum field theory. It introduces the concept of unified mathematical operations, suggesting a more holistic approach to mathematical thinking that aligns with the model's interconnected view of the universe. Additional testable predictions and proposed experimental approaches are discussed, including advanced space-based tests and laboratory experiments probing quantum gravity effects. These specific, quantifiable predictions offer multiple avenues for empirical validation, highlighting HTUM's potential to be distinguished from ΛCDM and other alternative cosmological models. HTUM represents a significant new perspective in our understanding of the universe, inviting further research and exploration into the nature of reality, consciousness, and the fundamental structure of the cosmos. By providing a comprehensive framework that unifies various aspects of physics, cosmology, and consciousness studies, HTUM offers a promising path toward a more complete understanding of our universe.

With the continuous advancement of digital transformation, digital payments are playing an increasingly important role in the financial industry. This study aims to utilize machine learning models to predict and analyze digital payment behavior. Initially, the background and significance of digital payments in the financial sector are introduced. Subsequently, the current status and trends of traditional digital payment distribution are reviewed, alongside related work on digital payment behavior prediction. Methodologically, principles and applications of machine learning models such as logistic regression, decision trees, and random forests are elaborated, along with experimental design and data preprocessing methods. The experimental results and discussion section illustrates the performance of each model in digital payment prediction and explores their impact on credit decisions. This exploration equips financial institutions with more effective user behavior analysis and risk management tools, thereby fostering future development and application of digital payment technologies.

The purpose of this narrative review is to provide an overview of the latest literature on bariatric and metabolic surgery for diabetes mellitus type II and obesity (diabesity) and to discuss its implications for future research and clinical practice.

Plant activators have emerged as promising alternatives to conventional pesticides for crop disease manage-ment due to their unique mode of action. By priming the plant's innate immune system, these compounds can induce systemic acquired resistance against a broad spectrum of pathogens without directly inhibiting their proliferation. Key advantages of plant activators include prolonged defense activity, lower effective dosages, and negligible risk of developing pathogen resistance. Among the various defensive pathways tar-geted, the salicylic acid (SA) signaling cascade has been extensively explored, leading to the successful devel-opment of commercial activators like benzothiadiazole for widespread application in crop protection. While the action sites of many SA-targeting activators have been preliminarily mapped to different steps along the pathway, a comprehensive understanding of their precise mechanisms remains elusive. This review provides a historical perspective on plant activator development and outlines diverse screening strategies employed across multiple levels, from whole-plant bioassays to molecular and transgenic approaches. We expound on the intricate components, biological relevance, and regulatory circuits governing the SA pathway, while criti-cally examining the structural features, bioactivities, and proposed modes of action of classical activators such as benzothiadiazole derivatives, salicylic acid analogs, and other small molecules. Insights from field trials as-sessing their practical applicability are also discussed. Furthermore, we highlight the current status, challenges, and future prospects in the realm of SA-targeting activator development globally, with a focus on recent en-deavors in China. Collectively, this comprehensive review aims to synthesize existing knowledge and provide a roadmap for future research toward developing more potent and mechanistically understood plant activa-tors that fortify crop immunity against disease.

In recent years, urbanization and industrialization have significantly increased the levels of outdoor noise pollution, affecting the quality of life in residential areas. In Uzbekistan, rapid development in urban centers has led to heightened concerns about the impact of noise on residents' health and well-being. Noise pollution can result from various sources, including traffic, construction, and industrial activities, causing disturbances and potential health issues such as stress, sleep disorders, and cardiovascular problems. Addressing this issue is crucial for creating a healthier living environment. This article explores effective strategies for mitigating the impact of outdoor noise on residential buildings in Uzbekistan.

At the end of the dry season in early March to early April each year, extensive agricultural biomass waste burnings occur throughout insular mainland Southeast Asia. During this biomass burnings period, smoke aerosols blanket the whole regions and were transported and dispersed by predominant westerly and south westerly winds to southern China, Taiwan and as far southern Japan and the Philippines. The extensive and intense burnings coincided with some wildfires in the forests due to high temperature making the region one of the global hot spots of biomass fires. In this study, we focus on the effect of pollutants emitted from biomass burnings in March 2019 at the height of the burnings period to the exposed population and their health impact. The Weather Research Forecast- Chemistry (WRF-Chem) model was used to predict the PM2.5 concentration over the simulating domain and health impacts are then assessed on the exposed population in the four countries of Southeast Asia, namely Thailand, Laos, Cambodia and Vietnam. Using the health impact based on log-linear concentration response function and Integrated Exposure Response (IER), the results show that at the peak period of the burnings from 13 to 20 March 2019, Thailand experienced the highest impact, with an estimated 2170 premature deaths. Laos, Vietnam, and Cambodia followed, with estimated mortalities of 277, 565, and 314 deaths respectively. However, when considering the impact per head of population, Laos exhibited the highest impact, followed by Thailand, Cambodia, and Vietnam. The results highlight the significant health impact and associated economic cost of agricultural waste burnings in Southeast Asia at the end of the dry season. And hence policy makers should take these into account to design measures to reduce the negative impact of widespread burnings on exposed population in the region.

The enzyme acetylcholinesterase (AChE) plays a crucial role in the termination of nerve impulses by hydrolyzing the neurotransmitter acetylcholine (ACh). The inhibition of AChE has emerged as a promising therapeutic approach for the management of neurological disorders such as Lewy body dementia and Alzheimer's disease. The potential of various compounds as AChE inhibitors has been investigated. In this study, we evaluated the impact of natural compounds of interest on the intrinsic deformability of human AChE using computational biophysical analysis. Our approach incorporates classical dynamics, elastic networks, statistical potentials, energy frustration, and volumetric cavity analyses. The results revealed that cyanidin induced significant changes in the flexibility and rigidity of AChE, especially in the distribution and volume of internal cavities, compared to model inhibitors such as TZ2PA6, and through a distinct biophysical-molecular mechanism from the other inhibitors considered. These findings suggest that cyanidin could offer potential mechanistic pathways for future research and applications in the development of new treatments for neurodegenerative diseases.

Obstructive sleep apnea (OSA) often goes unrecognized despite common symptoms such as excessive daytime sleepiness, fatigue, and impaired quality of life (QoL). CPAP is the gold standard treatment for OSA, but optimal daily usage and time needed for observable effects remain unclear. This study aimed to investigate the short-term effects of CPAP on daytime sleepiness and QoL in patients with severe OSA. Medical records were collected from 87 patients with severe OSA who initiated CPAP therapy. Also, validated questionnaires were used before and after one month of CPAP to analyze QoL - the Calgary Sleep Apnea Quality of Life Index (SAQLI), the Cues to CPAP Use Questionnaire (CCUQ), and daytime sleepiness - the Epworth Sleepiness Scale (ESS). Multiple regression analysis was conducted to identify predictors of CPAP usage. Of the total participants aged 55.6±12.5, 77% were males, and 62% were CPAP adherent. Reductions in daytime sleepiness (ESS) were noted, as well as improvements in both overall QoL (SAQLI) and specifically in the domains of daily functioning, social interactions, emotional well-being, and symptom perception. Important cues for CPAP usage recognized by patients were physicians’ instructions and physicians’ worry regarding patients' condition. Furthermore, multiple regression revealed higher SAQLI scores and lower ESS scores as positive predictors of CPAP usage, along with lower AHI after one month of CPAP being associated with sufficient adherence.

The signs and symptoms of Long COVID can be explained by a shortage of blood in the body and a resulting deficient blood flow through nearly all organs. This shortage arose during the acute phase of COVID19 by an increased breakdown of haematocytes, to which the liver responds by reducing the production of plasma. In order to prevent a too large decrease in haematocrit. In order to ensure the perfusion of organs that are directly necessary for survival, the body takes the emergency measure of diverting blood from other organs and tissues. The perfusion of the blood-producing organs is also affected by this distribution measure, which hinders the smooth recovery of the total blood volume. The body is stuck in this vicious circle: a shortage of circulating blood hinders the recovery of blood production. This explains the long duration of Long COVID. My proposed treatment of Long COVID focuses on the recovery of the correct volume of blood in the body of the right composition by the intravenous administration of donor blood products, starting with albumin concentrate. A trial treatment can be performed in any hospital without much additional preparations, and has a lower associated risk for the patient than analysing the total blood. A diagnosis ex juvantibus, by therapeutic response, is therefore preferable. I suspect that we will find a haematocrit value at the high extreme of the reference range, and an albumin value at the low extreme of the reference range in most Long COVID patients before the start of the treatment, because the liver can not keep up with the recovery of the red bone marrow.

Substance abuse is a significant public health issue both globally and nationally. Substance abuse involves the detrimental or risky consumption of psychoactive substances, posing a significant global issue, particularly among the youth. In India, cannabis abuse is a major concern. Cannabis is consumed legally in many states as Bhang, also known as marijuana or weed, while Charas and Ganja are illegal under both international drug conventions and the Indian NDPS Act of 1985. The Cannabis users are at great risk of developing Cannabis use disorder which is a pattern of problematic cannabis use leading to clinically significant impairment or distress. It is the most widely used illegal substance worldwide, showing a high prevalence in India.

Conclusions: CGP do not substantially differ between initial tumor vs tumor recurrence and recurrent thymomas vs non-recurrent thymomas. Cell-cycle control genes alterations are associated with an early recurrence after thymectomy. Multiple target therapies are potentially available by performing a comprehensive CGP, suggesting that a precision medicine approach on these patients could be further explored.

Background: Low back pain (LBP) is a major cause of disability globally, and the diagnosis of LBP is challenging for clinicians. Objective: This study aimed to assess the accuracy level of arti-ficial intelligence as a Clinical Decision Support System (CDSS) called Therapa compared to MRI in predicting lumbar disc herniated patients. Methods: One hundred low back pain patients aged ≥18 years old were included in the study. The study was conducted in 3 stages, at first, a case se-ries was conducted by matching MRI and Therapha diagnosis for 10 patients. Subsequently, Delphi methodology was employed to establish a clinical consensus. Lastly, to determine the ac-curacy of the newly developed software, a cross-sectional study was undertaken, involving 100 patients. Results: The software showed a significant diagnostic accuracy with the area under the curve in the ROC analysis determined as 0.84 with a sensitivity of 88% and a specificity of 80%. Conclusion: The study’s findings revealed that CDSS using Therapha has a reasonable level of ef-ficacy, and this can be utilized clinically to acquire faster and more accurate screening of patients with lumbar disc herniation.