The water cushion depth of stilling basin with shallow-water cushion is a key factor that affects the flow regime of hydraulic jump in the basin. However, the specific depth at which the water cushion is considered as “shallow” has not be stated clearly for now, and only conceptual description is provided. This paper attempts to specify the best water cushion depth based on the flow regime of hydraulic jump and underflow speed; namely, in case of critical hydraulic jump in the basin, the best water cushion depth is located where the minimum distance to the bottom plate of the stilling basin is 1/5~1/4 of the water cushion depth. The theoretical analysis indicates, at different inclinations of discharge chute (θ) and depth ratios of inlet (m), instead of monotonic change, the Froude number (Fr) at inlet of the stilling basin with shallow-water cushion firstly reduces and then increases as the flow velocity at discharge chute inlet (V) increases; the parameters of inflection point (critical flow velocity and critical Fr) increase as the inclinations of discharge chute (θ) and depth ratios of inlet (m) increase. Such regularity is the theoretical basis for selecting representative study cases. The reliability of the large eddy simulation calculation results are verified by a model test; in the paper, 30 cases including five different Froude numbers and six shallow-water cushion depths are selected, for calculating the hydraulic factors such as flow profile, flow regime and flow velocity in the stilling basin with shallow-water cushion; and the varying pattern between the best depth of stilling basin with shallow-water cushion (depth-to-length ratio) and the inflow Froude number is obtained which indicates that the best depth of stilling basin with shallow-water cushion varies little as the change of the Froude number before reaching the critical Froude number; however, the best depth-to-length ratio of stilling basin with shallow-water cushion increases as the Froude number increases after the critical Froude number is reached. The study results in this paper are of reference significance to design and calculation of the stilling basin with shallow-water cushion.

Euler’s product formula over the primes and Euler’s zeta function equate to enshrine the Fundamental Theorem of Arithmetic that every integer > 1 is the product of a unique set of primes. The product formula has no zero, and with a domain ≤1 Euler’s zeta diverges. Dirichlet’s eta function η(s), negates alternate terms of zeta, permitting convergence when s∈C and Re(s) < 1, and its non-trivial zeros {ρ}, have a deep relationship with the distribution of the primes. The Riemann Hypothesis is that all the non-trivial zeros have Re(ρ) = 1/2. This work examines the symmetries in a partial Euler’s zeta series with a complex domain equating it to the difference between two finite vector series whose matched terms have mirror-image arguments, but whose magnitudes differ when Re(s) ≠ 1/2. Analytical continuation generates a modified eta series η_l(s), in which every l^th term is multiplied by (1-l). If the integer l is appropriately determined by the Im(s), similar paired finite vector series have a difference that closely follows η_l (s) and their terminal vectors intersect in a unique way permitting zeros only when Re(s) = 1/2. Furthermore, those vectors tracking the derivatives of the series, have a special relationship permitting zeros of the differential only when Re(s) > 1/2.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

We presented a fractional order model to capture the transmission dynamics of Anthrax infection with a nonlinear force of infection and its long-term impacts. Analysis by the standard Fabrizio Caputo approach established the model is well-posed and investigation on the stability of the model, Anthrax-free equilibrium as connected to the basic reproduction number R0

Abstract: In this study, a computational fluid dynamics (CFD) simulation was conducted to validate the CFD model with experimental data from Zimparov et.al (2012), which investigates the heat transfer performance in a spirally corrugated tube that has a twisted tape inserted. The heat transfer was then compared to a simple corrugated tube without the twisted tape and to a smooth tube with no corrugations and no twisted tape. This simulation is compared with a previous experimental study conducted by (Zimparov et al. 2012), which focuses on tubes with a height-to-diameter ratio e/Di > 0.04 and small relative pitches of the twisted tape, H/Di. The largest improvement was noticed in the tube with e/Di= 0.057 and ridge pitch-to-height ratio p/e=6.77 with a twisted tape of H/Di= 4.7. This tube is labeled 5035. Tube 5035 was found to have the most significant enhancement, hence the focus of the CFD simulation will be on this tube, and the simulation will range for Reynolds numbers, 3.5 x 103 < Re < 5.0 x 104. The focus of this simulation is the evaluation of heat transfer and friction factors; a metric was used to obtain an empirical representation of the tube’s performance. Keywords: Spirally corrugated tube; Twisted tape; Heat transfer enhancement; Friction factor; Nusselt number; Computational fluid dynamics (CFD); Star CCM+

The divination function of China's Yijing has led to its circulation for thousands of years. In our exploration of Yijing's characteristics using big data, we have discovered variations in results between the coin toss method and the ancient yarrow-stalk method of divination, known as "the number for the great expansion method of divination(大衍之数)". The yarrow-stalk method serves as the fundamental method of divination in Yijing and continues to hold significance in studying the essential characteristics of Yijing. Despite the complexity of yarrow calculations, advancements in computer technology and big data have simplified its application. By employing the yarrow-stalk method, we simulated changes in the 64 hexagrams, calculated probabilities and proportions of hexagram alterations, and derived fundamental characteristics and patterns of hexagrams. Additionally, we constructed the spatial representation of lines and hexagrams. Through a binary system rearrangement, we created a 64x64 matrix illustrating hexagram transformations. Subsequently, we generated 100 million random hexagrams and analyzed line and hexagram changes accordingly. Our findings indicate the following:(1) Big data analysis reveals evident asymmetry in the hexagrams obtained through the yarrow-stalk method, with a triangular fractal characteristic forming the background.(2) Each of the 64 hexagrams exhibits a distinct probability distribution when transforming into other hexagrams, which can be categorized into five types.(3)The occurrence probabilities of Laoyang, Laoyin, Shaoyang, and Shaoyin are 18.61%, 6.387%, 31.38%, and 43.62% respectively. The probabilities of Yin and Yang occurrences are nearly equal, each close to 50%. However, the probability of Laoyang is approximately three times higher than that of Laoyin.(4) Visualized and analyzed the characteristics of hexagram changes greater than 100000 times using 3D statistical maps and Sankey diagram.These results demonstrate that the yarrow-stalk method effectively unveils the characteristics and underlying patterns of the 64 hexagrams. This study provides a novel approach for scientifically exploring the internal laws governing the 64 hexagrams in Yijing.

This study presents the numerical investigation of bioconvective nanofluid (NF) flow compris-ing gyrotactic microorganisms through convective boundary conditions (CBC) enclosing heat and mass transmission analysis above an inclined extending cylinder. Via appropriate transfor-mation, the set of Partial Differential Equations is transformed into a scheme of nonlinear ODEs. A new set of variables are presented in the directive to get the first-order convectional equations and, then solved numerically by using bvp4c. The influence of several factors on velocity, ener-gy, concentration, and the density of motile microorganisms (DMM) is investigated and exam-ined. The analysis describes and addresses all physical measures of concentration such as Skin Friction (SF), Sherwood number (SN), DMM, and Nusselt number (NN). The present conse-quences display a validation with published. For confirmation of bvp4c, the ND-solve approach is also applied. Error analysis is also examined for the confirmation of the mathematical model.

Prostate cancer (PC) is the most frequently diagnosed non-skin cancer in the world. Previous studies showed that genomic alterations represent the most common mechanism for molecular alterations that cause the development and progression of PC. Great efforts have been done to identify common protein-coding genetic variations; however, the impact of non-coding variations including regulatory genetic variants is not still well understood. To gain an understanding of the functional impact of genetic variants, particularly, regulatory variants in PC, we developed an integrative pipeline (AGV) that used whole genome/exome sequences, GWAS SNPs, chromosome conformation capture data, and ChIP-Seq signals to investigate the potential impact of genomic variants on the underlying target genes in PC. We identified 646 putative regulatory variants, of which 30 of them significantly altered the expression of at least one protein-coding gene. Our analysis of chromatin interactions data (Hi-C) revealed that the 30 putative regulatory variants may affect 131 coding and non-coding genes. Interestingly, our study showed the 131 protein-coding genes are involved in disease-related pathways including Reactome and MSigDB in which for most of them targeted treatment options are currently available. Together, our results provide a comprehensive map of genomic variants in PC and revealed their potential contribution to prostate cancer progression and development.

IL1RA intron 2 86-bp repeat and IL4 intron 3 70-bp repeat are VNTRs that have been associated with various diseases, but their role in obesity is elusive. The objective of this study was to investigate the association of IL1RA and IL4 VNTRs with obesity and adiposity in 315 Malaysian subjects (128 M/187 F; 23 Malays/251 ethnic Chinese/41 ethnic Indians). The allelic distributions of IL1RA and IL4 were significantly different among ethnicities, and the alleles were associated with total body fat (TBF) classes. Individuals with IL1RA I/II genotype or allele II had greater risk of having higher adiposity - even after controlling for ethnicity [Odds Ratio (OR) of I/II genotype = 12.21 (CI = 2.54, 58.79; p = 0.002); II allele = 5.78 (CI = 1.73, 19.29; p = 0.004)]. However, IL4 VNTR B2 allele was only significantly associated with overall adiposity status before adjusting for ethnicity [OR = 1.53 (CI = 1.04, 2.23; p = 0.03)]. TBF was also significantly higher in those with IL1RA II allele compared with I allele (31.79 ± 2.52 vs. 23.51 ± 0.40; p = 0.005). Taken together, IL1RA intron 3 VNTR seems to be a genetic marker for overall adiposity status in Malaysian subjects.

In this article, we present solutions for one of the oldest mathematical problems, the Collatz Conjecture, and provide a proof for the Riemann Hypothesis, utilizing a new number theory based on newly discovered number properties, which will also be presented in this paper. This is made possible through the Sophy-Peter mathematical framework, built upon this new number theory. The Collatz Conjecture will be disproven, but as an alternative, the Oscillating Theorem will be introduced, with its correctness proven within this article. Furthermore, we present the general version of the Riemann zeta function, developed based on the new number theory. The correctness of this function is verified by comparing it with existing results of the zeta function. Using this approach and the Sophy-Peter framework, we have successfully proven the Riemann Hypothesis, long considered a millennium problem. Moreover, since the general zeta function is proven, this implies the correctness of the new number theory and the Sophy-Peter framework.

In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and an edge clique cover of a graph we introduce the notion of a vertex-clique incidence matrix for a graph and produce new lower bounds for the negative eigenvalues and negative inertia of a graph. Moreover, utilizing these vertex-clique incidence matrices, we generalize several notions such as the signless Laplacian matrix, and develop bounds on the incidence energy and the signless Laplacian energy of the graph. %The tight upper bounds for the energies of a graph and its line graph are given. More generally, we also consider the set $S(G)$ of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent. An important parameter in this setting is $q(G)$, and is defined to be the minimum number of distinct eigenvalues over all matrices in $S(G)$. For a given graph $G$ the concept of a vertex-clique incidence matrix associated with an edge clique cover is applied to establish several classes of graphs with $q(G)=2$.

In this part of the series of two papers, we extend the theorems discussed in part I for infinite series. We then use these theorems to develop distinct novel results involving the Hurwitz zeta function, Riemann zeta function, Polylogarithm and Fibonacci numbers. In continuation, we obtain some zeros of the newly developed zeta functions and explain their behaviour using plots in complex plane. Furthermore, we provide particular cases for the theorems and corollaries which show that our results generalise the currently available functions and series such as the Riemann zeta function and the geometric series. Finally, we provide four miscellaneous examples to showcase the vast scope of the developed theorems.

This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.

Mitochondrial malfunction is supposed to be involved in the etiology and pathology of major depressive disorder (MDD). Here, we aimed to identify and characterize the molecular pathomechanisms related to mitochondrial disfunction in adult human skin fibroblasts which were derived from MDD patients or non-depressive control subjects. We found that MDD fibroblasts showed significantly impaired mitochondrial functioning: basal and maximal respiration, spare respiratory capacity, non-mitochondrial respiration and ATP-related oxygen consumption was lower. Moreover, MDD fibroblasts harbor lower ATP levels and showed hyperpolarized mitochondrial membrane potential. To investigate cellular resilience, we challenged both groups of fibroblasts with hormonal (dexamethasone) or metabolic (galactose) stress for one week, and found that both stressors increased oxygen consumption but lowered ATP content in MDD as well as in non-depressive control fibroblasts. Interestingly, the bioenergetic differences between fibroblasts from MDD or non-depressed subjects, which were observed under non-treated conditions, could not be detected after stress. Our findings support the hypothesis that altered mitochondrial function causes a bioenergetic imbalance which is associated with the molecular pathophysiology of MDD. The observed alterations in OXPHOS and other mitochondria-related properties represent a basis for further investigations of pathophysiological mechanisms and might open new ways to gain insight into antidepressant signaling pathways.

This article presents a rigorous approach to the Collatz Conjecture, focusing on fundamental properties of Collatz sequences. We establish key properties of the Collatz function and its inverse, including surjectivity and injectivity. The structure of Collatz sequences is analyzed in depth, proving important results such as the Bounded Subsequence Property and the uniqueness of cycles. Central theorems on the properties of Collatz sequences, including the boundedness of all sequences and the nature of the unique cycle, are presented and proved. These results culminate in a complete resolution of the Collatz Conjecture, demonstrating that all Collatz sequences eventually reach the cycle {1, 4, 2}. We provide a rigorous proof of the conjecture, while emphasizing the need for thorough peer review and verification by the mathematical community given the significance of this long-standing problem.

Physics-informed neural networks can be trained to serve as surrogate models by learning how spatial physical fields develop with change of parameters. This is an advantage over traditional numerical methods that can only be used to calculate a single solution field for a single discrete setting of a parameter. While many studies report accurate results of physics-informed deep learning of laminar flows, evaluations of surrogate modeling of high Reynolds number flows remain sparse. To contribute to this question, we here explore the capabilities and limits of physics-informed deep learning to solve the Reynolds-averaged Navier-Stokes equations for the flow around two airfoils under variable angles of attack. No labeled training data were provided and a single network was trained to simultaneously learn several solution fields in a single training run. The network captured essential flow features such as boundary layers and high and low pressure regions. Moreover, the qualitative correlations of lift and drag with the angle of attack and the higher drag of the thicker airfoil were captured. However, comparisons with reference simulations revealed an underestimation of the shear layer gradients as well as deviations of the fields' extrema. Thus, we also debate potential future improvements to increase the accuracy of the predicted flow. This work offers a prospect on the capabilities and current limitations of physics-informed neural networks for surrogate modeling of high Reynolds number flows. We argue that the method is promising and this work is aimed to encourage further research and development of the method when applied to Reynolds-averaged flows at high Reynolds numbers.

With the rapid development of intelligent logistics and network environment, it has become an urgent problem to efficiently and accurately handle and analyse the huge amount of uncertain decision information. Traditional decision making methods often fail to make the best use of complex and incomplete information, especially in the field of cyber defence. To address these problems, this paper introduces a new mathematical tool, discrete multidimensional Z-numbers (MZs), for expressing and dealing with uncertainty and reliability in network defence decisions. In this paper, we first introduce the synthesis method of discrete multidimensional Z-numbers, which allows us to consider the uncertainty and reliability of multi-source information in network defence strategy. Then, the hidden probability of MZs is calculated by using the hidden probability model, and the multidimensional Z+−number is proposed, which improves the expressiveness of the model in dealing with information uncertainty. Based on MZs, we define a variety of utility functions and build a multi-attribute group decision framework for network defence around these functions. The MZs provides a novel perspective for analysing and designing response strategies, especially against highly adaptive and covert attacks. The method in this paper is verified by a case of network security assessment of an intelligent logistics company. The results show that this method can significantly improve the accuracy and efficiency of decision making, demonstrating its unique advantages and wide application potential in network defence. This integrated discrete multidimensional Z-number group decision method is not only suitable for intelligent logistics decision making, but also provides an efficient decision support tool for network defence, which helps to improve the intelligence and adaptability of network security defence.

Chromosome analysis (CA) and chromosomal microarray analysis (CMA) have been successfully used to diagnose genetic disorders. However, many conditions remain undiagnosed due to limitations in resolution (CA) and detection of only unbalanced events (CMA). Optical genome mapping (OGM) has the potential to address these limitations by capturing both structural variants (SVs) resulting in copy number changes and balanced rearrangements with high resolution. In this study, we investigated OGM’s concordance using 87 SVs previously identified by CA, CMA, or Southern blot. Overall, OGM was 98% concordant with only three discordant cases: (1) uncalled translocation with one breakpoint in a centromere; (2) uncalled duplication with breakpoints in the pseudoautosomal region 1; and (3) uncalled mosaic triplication originating from a marker chromosome. OGM provided diagnosis for three previously unsolved cases: (1) disruption of the SON gene due to a balanced reciprocal translocation; (2) disruption of NBEA gene due to an inverted insertion; (3) disruption of the TSC2 gene due to a mosaic deletion. We show that OGM is a valid method for detection of many types of SVs in a single assay and is highly concordant with legacy cytogenomic methods; however, it has limited SV detection capabilities in centromeric and pseudoautosomal regions.

Climate change-induced temperature fluctuations pose a significant threat to crop production, particularly in the Southern Hemisphere. This study investigates the transcriptome and physiological responses of rapeseed to post-flowering temperature increases, providing valuable insights into the molecular mechanisms underlying rapeseed tolerance to heat stress. Two rapeseed genotypes, Lumen and Solar, were assessed under control and heat stress conditions in field experiments conducted in Valdivia, Chile. Results showed that seed yield and seed number were negatively affected by heat stress, with genotype-specific responses. Lumen exhibited a 9.3% average seed yield reduction, while Solar showed a 28.7% reduction. RNA-seq analysis of siliques and seeds revealed tissue-specific responses to heat stress, with siliques being more sensitive to temperature stress. Hierarchical clustering analysis identified distinct gene clusters reflecting different aspects of heat stress adaptation in siliques, with a role for protein folding in maintaining silique development and seed quality under high temperature conditions. In seeds, three distinct patterns of heat-responsive gene expression were observed, with genes involved in protein folding and response to heat showing genotype-specific expression. Gene coexpression network analysis revealed major modules for rapeseed yield and quality, as well as the trade-off between seed number and seed weight. Overall, this study contributes to understanding the molecular mechanisms underlying rapeseed tolerance to heat stress and can inform crop improvement strategies targeting yield optimization under changing environmental conditions.

The DNS of film boiling requires strong computational resources that are difficult to obtain for a daily CFD use by the practitioners of the industrial R&amp;D experts. On the other hand, the film boiling experiments are associated with the usage of the expensive and highly sophisticated apparatus, and the research to this end is found to be relatively difficult due to high heat flow rates that are present in the process itself. When combined with a transient heat conduction in a solid, the problem becomes significantly difficult. Therefore, a novel method in computation of conjugate heat transfer during film boiling in a quiescent liquid has been proposed in this paper. The method relies on the solution of mass, momentum and energy conservation equations in a two-fluid framework, supplemented with the appropriate closures. Furthermore, the turbulent flow has been found as an important parameter in obtaining the accurate solution of the temperature field evolution in a solid specimen, via the proper modeling of turbulent kinetic energy (TKE) value, that has been imposed as a constant value, i.e., the frozen turbulence approach. It was found, in addition, that the appropriate TKE value can be obtained by use of Kelvin-Helmholtz instability theory in conjunction with the boundary layer theory. The obtained results show excellent agreement with the experimental data within the first 15 s of the experiment, i.e., the first ca. 10 % of the total duration of the film boiling mode of heat transfer. Furthermore, the heat transfer coefficient has matched the error bands prescribed by the authors of the paper that has presented the correlations, whilst the averaged values are far beyond this band, i.e., are slightly more than 30 % higher. The further inspection has revealed a measure of similarity between the computational result of the volume fraction field distribution and the experiment, thus confirming the capability of the method to obtain realistic interface evolution in time. The method has shown full capability for further pursuing the industrial-scale film boiling problems that involve turbulent flow and the conjugate heat transfer approach.

We prove the continuous non-Archimedean (resp. p-adic) Banach space and Hilbert space versions of non-Archimedean (resp. p-adic) Welch bounds proved by M. Krishna. We formulate continuous non-Archimedean and p-adic functional Zauner conjectures.

We prove the non-Archimedean (resp. p-adic) Banach space version of non-Archimedean (resp. p-adic) Welch bounds recently obtained by M. Krishna. More precisely, we prove following results. \begin{enumerate}[\upshape(i)] \item Let $\mathbb{K}$ be a non-Archimedean (complete) valued field satisfying $\left|\sum_{j=1}^{n}\lambda_j^2\right|=\max_{1\leq j \leq n}|\lambda_j|^2$ for all $ \lambda_j \in \mathbb{K}, 1\leq j \leq n$, for all $n \in \mathbb{N}.$ Let $\mathcal{X}$ be a $d$-dimensional non-Archimedean Banach space over $\mathbb{K}$. If $\{\tau_j\}_{j=1}^n$ is any collection in $\mathcal{X}$ and $\{f_j\}_{j=1}^n$ is any collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) satisfying $f_j(\tau_j) =1$ for all $1\leq j \leq n$ and the operator $S_{f, \tau} : \text{Sym}^m(\mathcal{X})\ni x \mapsto \sum_{j=1}^nf_j^{\otimes m}(x)\tau_j^{\otimes m} \in \text{Sym}^m(\mathcal{X})$, is diagonalizable, then \begin{align}\label{NONFUNCTIONALWELCH} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{NONFUNCTIONALWELCH}) as non-Archimedean functional Welch bounds. \item For a prime $p$, let $\mathbb{Q}_p$ be the p-adic number field. Let $\mathcal{X}$ be a $d$-dimensional p-adic Banach space over $\mathbb{Q}_p$. If $\{\tau_j\}_{j=1}^n$ is any collection in $\mathcal{X}$ and $\{f_j\}_{j=1}^n$ is any collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) satisfying $f_j(\tau_j) =1$ for all $1\leq j \leq n$ and there exists $b \in \mathbb{Q}_p$ such that $ \sum_{j=1}^{n}f_j^{\otimes m}(x) \tau_j^{\otimes m} =bx$ for all $ x \in \text{Sym}^m(\mathcal{X}),$ then \begin{align}\label{PADICFUNCTIONALWELCH} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{PADICFUNCTIONALWELCH}) as p-adic functional Welch bounds. \end{enumerate} We formulate non-Archimedean functional and p-adic functional Zauner conjectures.

In this paper, we present the extension of the pressure-based solver designed for the simulation of compressible and/or incompressible two-phase flows of viscous fluids. The core of the numerical scheme is based on the hybrid Kurganov— Noele — Petrova/PIMPLE algorithm. The governing equations are discretized in the conservative form and solved for velocity and pressure, with the density evaluated by an equation of state. The acoustic-conservative interface discretization technique helps to prevent the unphysical instabilities on the interface. The solver was validated on various cases in wide range of Mach number, both for single-phase and two-phase flows. The numerical algorithm was implemented on the basis of the well-known open-source Computational Fluid Dynamics library OpenFOAM in the solver called interTwoPhaseCentralFoam. The source code and the pack of test cases are available on GitHub: https://github.com/unicfdlab/hybridCentralSolvers

The lightcone gauge is a set of what are called the observational coordinates adapted to our past lightcone. We develop this gauge by producing a perturbed spacetime metric that describes the geometry of our past lightcone where observations are usually obtained. We connect the produced observational metric to the perturbed Friedmann-Lema\^itre-Robertson-Walker metric in the standard general gauge or what is the so-called 1+3 gauge. We derive the relations between these perturbations of spacetime in the observational coordinates and those perturbations in the standard metric approach, as well as the dynamical equations for the perturbations in observational coordinates. We also calculate the observables in the lightcone gauge and re-derive them in terms of Bardeen potentials to first order. A verification is made of the observables in the perturbed lightcone gauge with those in the standard gauge. The advantage of the method developed is that the observable relations are simpler than in the standard formalism, and they are expressed in terms of the metric components which in principle are measurable. We use the perturbed lightcone gauge in galaxy surveys and the calculations of galaxy number density contrast. The significance of the new gauge is that by considering the null-like light propagations the calculations are much simpler due to the non-consideration of the angular deviations.

Multidrug resistant organisms (MDROs) outbreaks have been steadilyincreasing in Intensive care units (ICUs). Still, healthcare institutions and workers (HCW) reached no unanimity on how and when implementing infection prevention and control (IPC) strategies. We aimed to provide a pragmatic, physician practice-oriented, resume of strategies towards different MRDOs outbreaks in ICU. We performed a narrative review on IPC in ICUs, investigating patient-to-staff ratios, education, isolation, decolonization, screening and hygiene practices, outbreak reporting, cost-effectiveness, reproduction-number(R0), and future perspectives. The most effective IPC strategy remains unknown. Most studies focus on a specific pathogen or disease, making the clinician losing the big picture. IPC strategies proved their cost-effectiveness regardless typology, country, or pathogen. A standardized, universal, pragmatic protocol for HCW education should be elaborated. Likewise, a rapid outbreak recognition tool elaboration (i.e., an easy-to-use mathematical model) would improve early diagnosis and spreading prevention. Further studies are needed to express in favor or against MDROs decolonization. New promising strategies are emerging and need to be tested in the field. The lack of IPC strategies application has made, and still makes ICUs a major MDROs reservoir into the community. In a not-too-distant future genetic engineering and phage therapies could represent a plot-twist in MDROs IPC strategies.

This article introduces a new way of using a Fibre Bragg Grating (FBG) sensor for detecting the presence and number of occupants in the monitored space in a Smart Home (SH). CO₂ sensors are used to determine the CO₂ concentration of the monitored rooms in an SH. CO₂ sensors can also be used for occupancy recognition of the monitored spaces in SH. To determine the presence of occupants in the monitored rooms of the SH, the newly devised method of CO₂ prediction, by means of an Artificial Neural Network (ANN) with a Scaled Conjugate Gradient (SCG) algorithm using measurements of typical operational technical quantities (indoor temperature, relative humidity indoor and CO₂ concentration in the SH) is used. The goal of the experiments is to verify the possibility of using the FBG sensor in order to unambiguously detect the number of occupants in the selected room (R104) and, at the same time, to harness the newly proposed method of CO₂ prediction with ANN SCG for recognition of the SH occupancy status and the SH spatial location (rooms R104, R203, and R204) of an occupant. The designed experiments will verify the possibility of using a minimum number of sensors for measuring the non-electric quantities of indoor temperature and indoor relative humidity and the possibility of monitoring the presence of occupants in the SH using CO₂ prediction by means of the ANN SCG method with ANN learning for the data obtained from only one room (R203). The prediction accuracy exceeded 90% in certain experiments. The uniqueness and innovativeness of the described solution lie in the integrated multidisciplinary application of technological procedures (the BACnet technology control SH, FBG sensors) and mathematical methods (ANN prediction with SCG algorithm, the Adaptive Filtration with of LMS algorithm) employed for the recognition of number persons and occupancy recognition of selected monitored rooms of SH.

This paper briefly reviews the state of the art in artificial intelligence including inductive and deductive methods. Deep learning and ensemble machine learning lie in inductive methods while automated reasoning implemented in deductive computer languages (Prolog, Otter, and Z3) is based on deductive methods. In the inductive methods, intelligence is inferred by pseudorandom number for creating the sophisticated decision trees in Go (game), Shogi (game), and quiz bowl questions. This paper demonstrates how to wisely use the pseudorandom number for solving coin-weighing puzzles with the deductive method. Monte Carlo approach is a general purpose problem-solving method using random number. The proposed method using pseudorandom number lies in one of Monte Carlo methods. In the proposed method, pseudorandom number plays a key role in generating constrained solution candidates for coin-weighing puzzles. This may be the first attempt that every solution candidate is solely generated by pseudorandom number while deductive rules are used for verifying solution candidates. In this paper, the performance of the proposed method was measured by comparing with the existing open source codes by solving 12-coin and 24-coin puzzles respectively.

Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving some multi-criteria decision-making problems by developing a new triangular intuitionistic fuzzy geometric aggregation operator, that is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator, and defining some triangular intuitionistic fuzzy geometric aggregation operators including the triangular intuitionistic fuzzy weighted geometric averaging (TIFWGA) operator, the ordered weighted geometric averaging (TIFOWGA) operator and the hybrid geometric averaging (TIFHWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed has been proposed. Finally, the proposed method has been compared with some similar existing computational approaches by virtue of a numerical example to verify its feasibility and rationality.

Seed longevity is a crucial trait for the seed industry and genetic resource preservation. To develop excellent cultivars with extended seed lifespans, it is important to understand the mechanism of keeping seed germinability long-term and to find useful genetic resources as prospective breeding materials. This study was conducted to identify the best cultivars with a high and stable seed longevity trait in the germplasm of rice (Oryza sativa L.) and to analyse the correlation between seed longevity and embryonic RNA integrity. Seeds from 69 cultivars of the world rice core collection selected by the NIAS in Japan were harvested in different years and subjected to long-term storage or controlled deterioration treatment (CDT). The long-term storage (4 °C, RH under 35%, 10 years) was performed on seeds harvested in 2010 and 2013. The seeds harvested in 2016 and 2019 were used for CDT (36 °C, RH of 80%, 40 days). Seed longevity and embryonic RNA integrity were estimated by a decrease in germination rate and RNA integrity number (RIN) after long-term storage, or CDT. The RIN value was obtained by electrophoresis of total RNA extracted from seed embryos. Seeds of ‘Vandaran (Indica)’, ‘Tupa 729 (Japonica)’, and ‘Badari Dhan (Indica)’ consistently showed higher seed longevity and embryonic RNA integrity both under long-term storage and CDT conditions, regardless of the harvest year. A strong correlation (R2 = 0.93) was observed between germination rates and RIN values of the seeds after long-term storage or CDT among nine cultivars selected based on differences in their seed longevity. The study findings revealed the relationship between rice seed longevity and embryo RNA stability and suggested potential breeding materials, including both Japonica and Indica cultivars, for improving rice seed longevity.

This paper presents a novel approach to demonstrate the Collatz Conjecture, an unsolved problem in mathematics stating that all positive integers will eventually converge to 1 when subjected to a recursive sequence of operations. We introduce Algebraic Inverse Trees (AITs), innovative data structures that characterize relationships within the Collatz sequence by tracing inverse transformations back to the origin. Leveraging properties unveiled through this inverted representation, including absence of non-trivial cycles and guaranteed convergence of paths, we construct a topological framework to formally prove that all trajectories invariably lead to 1 under the Collatz iterative process. This modern technique provides not only the machinery to manifest a rigorous proof, but also grants intuitive insights into the deep complexity of this notorious yet elementary conjecture.

The traditional sequent peak algorithm (SPA) was used to assess the reservoir volume (VR) for comparison with deficit volume, DT, (subscript T representing the return period) obtained from the drought magnitude (DM) based method with draft level set at the mean annual flow on 15 rivers across Canada. At an annual scale, the SPA based estimates were found to be larger with an average of nearly 70% compared to DM based estimates. To ramp up DM based estimates to be in parity with SPA based values, the analysis was carried out through the counting and the analytical procedures involving only the annual SHI (standardized hydrological index, i.e. standardized values of annual flows) sequences. It was found that MA2 or MA3 (moving average of 2 or 3 consecutive values) of SHI sequences were required to match the counted values of DT to VR. Further, the inclusion of mean, as well as the variance of the drought intensity in the analytical procedure, with aforesaid smoothing led DT comparable to VR. The distinctive point in the DM based method is that no assumption is necessary such as the reservoir being full at the beginning of the analysis - as is the case with SPA.

Multi-stakeholder based construction projects are subject to various risk factors due to dynamic business environments. These risks affect project activities which indirectly impact construction costs, resulting in delays and poor building quality. So, managing these project risks requires suitable risk mitigation strategies to evaluate and analyse their severity. Hence, risk evaluation and assessment of construction projects is a multi-criteria decision making (MCDM) problem. In present real-life problems, evaluation of project risks is often uncertain and even incomplete, and the prevailing methodologies fail to handle such situations. To address the problem, this paper extends the analytical network process (ANP) methodology in the D number domain to handle three types of ambiguous evaluations, viz. complete, uncertain, and incomplete, and assesses the weight of risk criteria. The D number based approach overcomes the deficiencies of the exclusiveness hypothesis and completeness constraint of Dempster-Shafer (D-S) theory. Here, preference ratings of the decision matrix for each decision-maker are determined using a D number extended consistent fuzzy preference relation (D-CFPR). An extended multi-attributive border approximation area comparison (MABAC) method in D number is then developed to rank and select the best alternative risk response strategy. Finally, an illustrative example from construction sector is presented to check the feasibility of the proposed approach. For checking the reliability of alternative ranking, a comparative analysis is performed with different MCDM approaches (D-COPRAS, D-ARAS, D-MABAC, and D-TOPSIS). Based on different criteria weights, a sensitivity analysis of obtained ranking of the hybrid D-ANP-MABAC model is performed for verify the robustness of the proposed method.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

Based on three assumptions of our 4G model of final unification, we have developed simple logics for estimating the unified atomic mass unit, atomic electrochemical equivalents, Faraday constant and Avogadro number. We appeal the science community to review the following points. 1) Unified atomic mass or energy unit can be considered as ‘average rest energy of nucleons minus average binding energy per nucleon of all atomic nuclides plus electron rest energy’. 2) Electrochemical equivalent of any atomic ion is nothing but the ratio of its mass to its charge. 3) Faraday charge is nothing but the ratio of elementary charge to unified atomic mass unit. 4) Faraday mass can be considered as the inverse of Faraday charge. 5) Avogadro number is nothing but the inverse of unified atomic mass unit. 6) Number of atoms per kg can be called as Kg-mole and number of atoms per gram can be called as gram-mole. Following our 4G model, starting form A=5 to 340, for isobars, ‘average binding energy per nucleon’ having maximum binding energy can be estimated with a simple relation of the form, BE/A=A^-1[1-(0.5+0.000935A²)-A^1/3]10.1MeV. It needs a review and fine tuning.

This review is a first attempt at bringing together various concepts from research on wall- and magnetically-bounded turbulent flows. Brief reviews of both fields are provided: The main similarities identified are coherent (turbulent) structures, flow generation and transport barriers. Examples are provided and discussed.

We have considered a SEIR-SEI Vector-host mathematical model which captures malaria transmission dynamics, described and built on 7-dimensional nonlinear ordinary differential equations. We compute the basic reproduction number of the model; examine the positivity and boundedness of the model compartments in a region using well established methods viz: Cauchy’s differential theorem, Birkhoff & Rota’s theorem which verifies and reveals the well-posedness, and carrying capacity of the model respectively, the existence of the Disease-Free (DFE) and Endemic (EDE) equilibrium points were determined and examined. Using the Gaussian elimination method and the Routh-hurwitz criterion, we convey stability analyses at DFE and EDE points which indicates that the DFE (malaria-free) and the EDE (epidemic outbreak) point occurs when the basic reproduction number is less than unity (one) and greater than unity (one) respectively. We obtain a solution to the model using the Variational iteration method (VIM) (an unprecedented method) to each population compartments and verify the efficacy, reliability and validity of the proposed method by comparing the respective solutions via tables and combined plots with the computer in-built Runge-kutta-Felhberg of fourth-fifths order (RKF-45). We illustrate the combined plot profiles of each compartment in the model, showing the dynamic behavior of these compartments; then we speculate that VIM is efficient and capable to conduct analysis on Malaria models and other epidemiological models.

In the paper, by virtue of the Fa`a di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers.

This paper identifies a criterion for choosing the largest set of rejected hypotheses in high-dimensional data analysis where Multiple Hypothesis testing is used in exploratory research to identify significant associations among many variables. The method neither requires predetermined thresholds for level of significance, nor uses presumed thresholds for false discovery rate. The upper limit for number of rejected hypotheses is determined by finding maximum difference between expected true hypotheses and false hypotheses among all possible sets of rejected hypotheses. Methods of choosing a reasonable number of rejected hypotheses and application to non-parametric analysis of ordinal survey data are presented.

This paper investigates the search for an exact analytic solution to a temporal first-order differential equation that represents the number of customers in a non-stationary or time-varying

Variational Auto-Encoders (VAEs) are deep generative models used for unsupervised learning, however their standard version is not topology-aware in practice since the data topology may not be taken into consideration. In this paper, we propose two different approaches with the aim to preserve the topological structure between the input space and the latent representation of a VAE. Firstly, we introduce InvMap-VAE as a way to turn any dimensionality reduction technique, given an embedding it produces, into a generative model within a VAE framework providing an inverse mapping into original space. Secondly, we propose the Witness Simplicial VAE as an extension of the Simplicial Auto-Encoder to the variational setup using a witness complex for computing the simplicial regularization, and we motivate this method theoretically using tools from algebraic topology. The Witness Simplicial VAE is independent of any dimensionality reduction technique and together with its extension, Isolandmarks Witness Simplicial VAE, preserves the persistent Betti numbers of a data set better than a standard VAE.

Liquid biopsies are an integral part of the diagnosis of cancer. Here, we have extended previous validation studies of a new targeted NGS panel to include the detection of copy number amplifications (CNAs), fusions, and exon skipping variants. Detection of these gene classes included specimens from clinical and healthy donors and cell lines (fusions: ROS1, EML4-ALK, NTRK1), (exon skipping: MET exon 14), and (CNAs: HER2, CDK6, EGFR, MYC and MET). The limit of detection (LOD) for fusion/skipping was 42 copies (QC threshold = 3 copies) and was verified using 3 additional fusion/skipping variants. LOD for CNAs was 1.40-fold-change (QC threshold = 1.15-fold change) and was verified with 3 additional CNAs. In precision studies, all fusion/skipping variants were detected in all runs and all days of testing (n=18/18; 100%); average CV for repeatability was 20.5% (range 8.7% - 34.8%), and for reproducibility was 20.8% (range 15.7% - 30.5%). For CNAs, 28/29 (96.6%) copy gains were detected. For CNAs, average CV of 1.85% (range 0% to 5.49%) for repeatability and 6.59% (range 1.65% to 9.22%) for reproducibility. The test panel meets the criteria for being highly sensitive and specific and extends its utility for the detection of clinically relevant variants in cancer.

It has been more than a century since Erlang published his paper in 1909. The classical queueing system for the M/D/c queue has been investigated by many authors. The key is to find the roots of an equation using explicit or numerical methods. We present an alternate form of explicit solution(s) of this/these root(s) using the Lambert-W function in this paper. In addition, the unsaturated probabilities of the number of customers in the system is derived explicitly in terms of this/these root(s). Finally, the mean number of customers in the system and the mean queueing delay are obtained from these probabilities. The exact queueing delay formula for the M/D/c queue is expressed in closed-form in terms of the root(s). Numerical results show that they are in excellent agreement with the numerical results published by Seelen, Tijms and Van Hoorn.

The influence of linear and nonlinear modes of ADC driver on the operational amplifier (Op-Amp), which has different values of maximum output voltage slew rate, on the effective number of bits of ADC is considered. It is shown that the effective number of bits of ADC when op-amps on bipolar transistors with input signal amplitudes exceeding 50-100 mV is determined by the nonlinear modes of its input differential stage.

The object of this work is to determine the correlation on the Nusselt number on the individual rows of a four-row tubular finned heat exchanger with continuous fins with a staggered tube arrangement using CFD modelling. Correlations for calculating Darcy-Weisbach friction factors on individual tube rows were also determined. Relationships for the Nusselt number and friction factor derived for the entire exchanger based on CFD modelling were compared with those available in the literature determined using experimental data. The maximum relative differences between the Nusselt number for a four-row exchanger determined experimentally and by CFD modelling are in the range from 22% for a Reynolds number based on a tube's outside diameter of 1,000 to 30% for a Reynolds number of 13,000. The maximum relative differences between the friction factor for a four-row exchanger determined experimentally and by CFD modelling are in the range of 50% for a Reynolds number based on a tube outer diameter of 1,000 to 10% for a Reynolds number of 13,000. The CFD modeling performed shows that in the range of Reynolds numbers based on hydraulic diameters from 150 to 1,400, the Nusselt number for the first row in a four-row finned heat exchanger is about 22% to 15% higher than the average Nusselt number for the entire exchanger. In the range of Reynolds number changes based on hydraulic diameter from 2,800 to 6,000, the Nusselt numbers on the first and second rows of tubes are close to each other. Correlations on Nusselt numbers and friction factors derived for individual tube rows can be used in the design of plate-fin and tube heat exchangers used in equipment such as air-source heat pumps, automotive radiators, air-conditioning systems and in air hot-liquid coolers. In particular, the correlations can be used to select the optimum number of tube rows in the exchanger.

Finding out how cells with the same genome change fates in differentiation commitment is a challenge of biology. We used MCF-7 breast cancer cells treated with the ErbB2 ligand heregulin (HRG), which induces differentiation, to address if and how the constitutive pericentromere-associated domains (PADs) may be involved in this process. PAD-specific repressive heterochromatin (H3K9me3) and active euchromatin (H3K4me3) marking, centromere (CENPA) labelling, qPCR, acridine-orange-DNA structural test, and microscopic image analysis were applied. We found a two-step DNA unfolding, at 15-20 min and 60 min after HRG treatment, coinciding with bi-phasic activation of the early response genes (c-FOS family) and two steps of critical phase transition which were revealed in transcriptome studies. In control, the distribution of PAD number and size displays a power-law scaling with a boundary at the nucleolus. PADs’ clustering correlates with centromere numbers. 15 min after HRG treatment, the unravelling of PADs occurs, coinciding with the first step of euchromatin unfolding. The second step is associated with transcription of long-non-coding-RNA from satellite III DNA. We hypothesize that splitting of the PAD clusters under the critical size threshold of the silencing domain abrupts position effect variegation. It allows the first genome transcription avalanche to occur, starting differentiation commitment.

New insights into the causes and mechanisms of congenital heart disease (CHD) have been gained through the use of next-generation sequencing. Examination of the whole exome sequence detects detrimental gene variations modifying single or contiguous nucleotides, that are characterised as pathogenicity based on statistical assessments of families. and correlates with congenital heart disease, elevated expression during heart development, and reduction of harmful protein-coding mutations in the general population. Patients with CHD and extracardiac abnormalities enriched for gene classes meeting these criteria. CHDs and extracardiac defects, supporting a common set of pathways in the organogenesis of CHDs. Single-cell transcriptomics data reveal the expression of genes associated with CHD in specific cell lineages, and emerging evidence suggests that genetic variants disrupt multicellular genes essential for cardiogenesis. Metrics and units are being tracked in whole genome sequence studies.

In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

Background: Cervical cancer prevention in regions with limited access to screening and HPV vaccination necessitates innovative approaches. This study explored the potential of a test-and-treat strategy using mRNA HPV tests to impact cervical cancer prevention in a high-prevalence HIV population. Methods: A cervical screening study was conducted at three South African hospitals involving 710 under-screened, non-pregnant women (25 to 65 years) without known cervical diseases. Cytology, HPV testing, colposcopy, and biopsies were performed concurrently. Histopathologists determined final histological diagnoses based on biopsy and LLETZ histology. mRNA-HPV-genotyping for 3 (16, 18, 45) to 8 (16, 18, 31, 33, 35, 45, 52, 58) high-risk types was performed on leftover liquid-based cytology material. The preventive potential of the test-and-treat approach was estimated based on published data, reporting the causative HPV types in cervical cancer tissue from South African women. Treatment was provided as needed. Results: HPV positivity rate more than doubled from 3-type (15.2%; 95% CI: 12.6-17.8) to 8-type mRNA (31.5%; 95% CI: 28.8-34.9) combinations, significantly higher among HIV-positive women. CIN3+ prevalence among HIV-positive women (26.4%) was double that of HIV-negative women (12.9%) (p&lt;0.01). The 6-type combination showed the best balance of sensitivity, specificity and treatment group size, and effectiveness to prevent cervical cancer. A 4-type combination (16, 18, 35, 45) could potentially prevent 77.6% (95% CI: 71.2-84.0) of cervical cancer burden by treating 20% and detecting 41.1% of CIN3 cases in the study group. Similarly, a 6-type combination (16, 18, 31, 33, 35, 45), treating 25% and including 62% of CIN3 cases, might prevent 85% of cervical cancer cases (95% CI: 79.6-90.6) among HIV-positive and negative women. Conclusion: Employing mRNA HPV tests within a test-and-treat approach holds huge promise for targeted cervical cancer prevention in under-screened populations. Testing for mRNA of the 6 highest-risk HPV types in this population and treating them all is projected to effectively prevent progression from CIN3 to invasive cervical cancer while reducing overtreatment in resource-constrained settings.

This paper attempts to develop a Dynamic Mode Decomposition (DMD) based Reduced Order Model (ROMs) which can quickly but accurately predict the forces and moments experienced by a road vehicle such that they be used by an on-board controller to determine the vehicle's trajectory. DMD can linearize a large dataset of high-dimensional measurements by decomposing them into low-dimensional coherent structures and associated time-dynamics. This ROM then also can be applied to predict the future state of the fluid flow. Existing literature on DMD is limited to low Reynolds number applications. This paper presents DMD analyses of the flow around an idealized road vehicle, called the Ahmed body, at a Reynolds number of 2.7E6. The high dimensional dataset used in this paper was collected from a computational fluid dynamics (CFD) simulation performed using Menter's shear stress transport (SST) turbulence model within the context of Improved Delayed Detached Eddy Simulations (IDDES). The DMD algorithm, as available in literature, was found to suffer nonphysical dampening of the medium-to-high frequency modes. Enhancements to the existing algorithm were explored, and a modified DMD approach is presented in this paper which includes: (a) a requirement of higher sampling rate to obtain higher resolution of data, and (b) a custom filtration process to remove spurious modes. The modified DMD algorithm thus developed was applied to the high Reynolds number, separation dominated flow past the idealized ground vehicle. The effectiveness of the modified algorithm was tested by comparing future predictions of force and moment coefficients as predicted by the DMD-based ROM to the reference CFD simulation data, and found to offer significant improvement.

Recent wastewater testing suggests the poliovirus is reemerging, raising questions about the efficacy of the current inactivated polio vaccine and mass vaccination to eradicate poliomyelitis. The present study reassessed reported outcomes from the placebo-control study of the 1954 Salk inactivated poliomyelitis vaccine field trial, which studied a population of 1,829,916 U.S. school children from the first three grades. The placebo-control study of the trial reported that the polio vaccine was 80% to 90% effective in reducing cases of laboratory confirmed paralytic poliomyelitis, 60% to 70% effective against type 1 of the virus, and greater than 90% effective against types 2 and 3 of the poliovirus. However, these outcomes are reported as relative risk reductions, and the absolute risk reductions of the 1954 polio vaccine field trial were never reported to the public. The present paper’s analysis reveals to the public for the first time that the inactivated poliomyelitis vaccine's absolute risk reduction of laboratory confirmed paralytic poliomyelitis in the placebo-control study is 0.01% to 0.02%, an extraordinarily low clinical effect that impugns the Salk polio vaccine’s reported effectiveness. Furthermore, absolute risk reductions for the three poliovirus types are 0.01%, 0.00%, and 0.01%, respectively. Outcome reporting bias in the 1954 inactivated poliomyelitis vaccine field trial casts doubt on eradication of the poliovirus through mass vaccination.

Deterministic-stochastic empirical mode decomposition (EMD) is used to obtain low-frequency (non-diffusive, i.e., background velocity) and high-frequency (diffusive, i.e., eddies) components from a Lagrangian drifter‘s trajectory. Eddy characteristics are determined from the time series of eddy trajectories from individual Lagrangian drifter such as the eddy radial scale, eddy velocity scale, eddy Rossby number, and eddy-background kinetic energy ratio. A long-term dataset of the SOund Fixing And Ranging float time series obtained near the California coast by the Naval Postgraduate School from 1992 to 2004 at depth between 150 and 600 m (http://www.oc.nps.edu/npsRAFOS/) is used as an example to demonstrate the capability of the deterministic-stochastic EMD.

On February 24, 2022 Russia started the full-scale invasion of Ukraine, which created an unprecedented number of refugees. To estimate the influence of this humanitarian disaster on the COVID-19 pandemic dynamics, the averaged daily numbers of cases and reproduction numbers in Ukraine, the UK, Poland, Germany, the Republic of Moldova, and in the whole world were calculated for the period February-April 2022. The registered numbers of cases were compared with ones calculated with the use of the generalized SIR-model and corresponding parameter identification procedure for the previous epidemic waves in Ukraine, Poland, Germany, and the world. Since before February 24, 2022 the estimation of the number of infectious persons per capita in Ukraine 3.6 times exceeded the global figure, the increase of the number the new cases and the pandemic duration was expected. In March 2022 the increase of the averaged number of new cases in the UK, Germany, and worldwide was visible. A simple formula to estimate the effective reproduction number based on the smoothed accumulated numbers of cases is proposed. The results of calculations agree with the figures presented by John Hopkins University and demonstrate a short-term growth of the reproduction number in the UK, Poland, Germany, Moldova, and worldwide in March 2022.

Extensive genome structure variation, such as copy number variations (CNVs) and presence/absence variations, is the basis for the remarkable maize genetic diversity; however, the effect of CNVs on maize herbivory defense remains largely underexplored. Here, we report that the naturally occurring duplication of the maize 9-lipoxygenase gene, ZmLOX5, leads to increased resistance of maize to herbivory by fall armyworms (FAW). Previously, we showed that ZmLOX5-derived oxylipins are required for defense against chewing insect herbivores and identified several inbred lines, including Yu796, that contained duplicated CNVs of ZmLOX5, referred to as Yu796-2×LOX5. To test whether introgression of the Yu796-2×LOX5 locus into the herbivore-susceptible B73 background that contains a single ZmLOX5 gene is a feasible approach to increase resistance, we generated a series of near-isogenic lines that contained either 2, 1 or 0 copies of the Yu796-2×LOX5 locus in the B73 background by six back crosses (BC6). Droplet digital PCR (ddPCR) confirmed the successful introgression of the Yu796-2×LOX5 locus in B73. The resulting B73-2×LOX5 inbred line displayed increased resistance against FAW associated with increased expression of ZmLOX5, increased wound-induced production of its primary oxylipin product, the α-ketol, 9-hydroxy-10-oxo-12(Z),15(Z)-octadecadienoic acid (9,10-KODA), and the downstream defense hormones regulated by this molecule, 12-oxo-phytodienoic acid (12-OPDA) and abscisic acid (ABA). Surprisingly, wound-induced JA-Ile production was not increased in B73-2×LOX5, resulting from the increased JA catabolism. Furthermore, B73-2×LOX5 displayed enhanced drought tolerance likely due to increased ABA and 12-OPDA content. Taken together, this study revealed that the duplicated CNV of ZmLOX5 quantitively contributes to maize antiherbivore defense and presents proof-of-concept evidence that the introgression of naturally occurring duplicated CNVs of a defensive gene into the productive, but susceptible, crop varieties is a feasible breeding approach for enhancing plant resistance to herbivory and tolerance to abiotic stress.

Dirac's Large Number Hypothesis (LNH), proposed in 1937, has captivated the scientific community with its exploration of profound correlations between cosmic and atomic scales. This hypothesis delves into the intricate interplay between the infinitesimally small and the vastly large, offering potential insights into the fundamental nature of the universe. As we continue to uncover the mysteries of the cosmos, the LNH oscillates on the precipice of scientific acceptance—neither fully validated nor entirely dismissed. In this review paper, we embark on a comprehensive journey through Dirac's LNH, shedding light on its theoretical underpinnings, its implications for universe models, and its resonance with the Anthropic Principle. We delve into the possibilities of variable gravitational constants and continuous mass creation, inviting further exploration into the intricacies of our cosmic symphony. By embracing the ongoing quest for understanding, we endeavor to unravel the profound harmonies that connect the infinitesimal with the infinite, contributing to the symphony of knowledge in theoretical physics and cosmology.

Current prenatal genetic evaluation showed a significantly increase in non-invasive screening and the reduction of invasive diagnostic procedures. To evaluate the diagnostic efficacy on detecting common aneuploidies, structural chromosomal rearrangements and pathogenic copy number variants (pCNV), we performed a retrospective analysis on a case series initially analyzed by aneuvysion fluorescence in situ hybridization (FISH) and karyotyping then followed by array comparative genomic hybridization (aCGH). Of the 386 cases retrieved from the past decade, common aneuploidies were detected in 137 cases (35.5%), other chromosomal structural rearrangements were detected in four cases (1%), and pCNV were detected in five cases (1.3%). The relative frequencies for common aneuploidies suggested a under detection of sex chromosome aneuploidies. Approximately 9.5% of cases with common aneuploidies showed a mosaic pattern. Inconsistent results between FISH and karyotyping were noted in cases with pseudo-mosaicism introduced by culture artifact or variable cellular proliferation from cells with mosaic karyotypic complements under in vitro cell culture. Based on findings from this case series, cell-based FISH and karyotyping should be performed to detect common aneuploidies, structural chromosomal abnormalities, and mosaic pattern. DNA-based aCGH and reflex FISH should be performed to detect and confirm genomic imbalances and pCNV. Practice points to ensure the diagnostic accuracy and efficacy were summarized.

During the conceptual and preliminary design stage of a ship, designers need to ensure that the selected principal dimensions and parameters are good enough to deliver a stable ship (statically and dynamically) besides deadweight and speed. To support this, the initial intact stability of the proposed ship is required to be calculated, and in doing so, the lightship weight and its detailed breakdown are necessary to be known. After hull steel weight, machinery weight, mainly, marine propulsion and power generation machinery, play a vital role in the lightship weight estimate of a ship due to its robustness. The correct estimation of respective weights improves the accuracy of calculating a ship's initial stability typically to be designed and built. Hence, it would be advantageous for the designer to convince the ship owner. A total of 3006 marine propulsion (main marine diesel) engines and 348 power generation (auxiliary marine diesel) engines/generators of various power output (generators output for auxiliary engines), engine RPM and cylinder number of different engine makers are collected. These are analyzed and presented in both tabular and graphical forms to demonstrate the possible relationship between marine propulsion engine weight and power generation engine weight, and their respective power output, RPM, cylinder number, power-RPM ratio and power-RPM ratio per cylinder.In this article, the authors have attempted to investigate the behavior of marine propulsion engine weight and power generation engine/generator weight regarding engine power output, generator power output, engine RPM and cylinder number (independent variables). Further attempts have been made to identify those independent variables that influence the weight of the marine propulsion engine and power generation engine/generator (dependent variables), and their interrelationships. A mathematical model has thus been developed and proposed, as a guiding tool, for the designer to estimate the weight of main and auxiliary engines more accurately during the conceptual and preliminary design stage.

The aim of the studies was to test the hydraulic pressure losses along the length, local pressure losses, absolute and relative roughness values of the pipeline walls made of modern polymer material. The article presents the results of the experimental studies of hydraulic resistance of pipelines from modern polymer materials, the method of theoretical determination of resistance coefficients in the VALTEC ISO 21003 metal polymer pipeline, the classification and method of determining the values of local hydraulic resistance coefficients of T-Junctions are given, the dependence for determining the Darcy λ hydraulic friction coefficient associated with the value of the equivalent hydraulic roughness coefficient of the inner surface of pipes and the Reynolds number. The experimental data of the hydraulic coefficient of friction Darcy λ was compared with the known theoretical relationships of A.D. Altschul, Colbrooke for smooth pipes, Colbrooke and White, an alternative to the Colbrooke-White, Offengenden equation for low-shear pipes and pipes from polymer materials with Reynolds numbers Re>10^4. Dependence of hydraulic coefficient of friction on relative equivalent roughness of pipeline walls and Reynolds number, specific energy loss per one linear meter on total flow rate in system of hydraulically short pipeline is obtained. The empirical dependence of values of coefficients of local resistance ζ=f(Q2/Q3) from a ratio of the divided expenses of Q2/Q3 of the equal-pass T-Junction α=90 the pipeline to a branch up, on pass in the direct T-Junction and division of streams at various internal pipeline diameters of VALTEC.

In our recent publications pertaining to 4G model of final unification and based on strong and electroweak interactions, we have developed a completely new formula for estimating nuclear binding energy. With reference to currently believed Semi Empirical Mass Formula (SEMF), we call our formula as ‘Strong and Electroweak Mass Formula’ (SEWMF). Our formula constitutes 4 simple terms and only one energy coefficient of magnitude 10.1 MeV. First term is a volume term, second term seems to be a representation of free nucleons associated with electroweak interaction, third term is a radial term and fourth one is an asymmetry term about the mean stable mass number. Considering this kind of approach, nuclear structure can be understood in terms of strong and weak interactions and cold nuclear fusion like complicated concepts can be understood in a theoretical approach positively. In this paper, by considering the accountability of we are making an attempt to improve the applicability and effectiveness of SEWMF. Number 0.00125 being a workable electroweak coefficient for Z=6 to 132 and A=2Z to 3.5Z, number of free nucleons assumed to be associated with electroweak interaction can be expressed as Improved asymmetry term can be expressed as, where represents the light house like stable mass number. With reference to old version, our improved binding energy formula can be expressed as, We are working on its possible modification for mass numbers less than the stable mass numbers. Following this approach, it is possible to show that nuclear binding energy scheme is associated with strong and weak interactions and is practically independent of Coulombic repulsions. Proceeding further, currently believed cold nuclear fusion assumed be associated with hydrated metals can be understood and can be confirmed with strong and weak interactions independent of coulombic repulsions. We are very confident to say that our approach will certainly motivate modern science community in this new direction.

Quantum mechanics could be studied through polynomial algebra, as has been demonstrated by a work (“An approach to first-principles electronic structure calculation by symbolic-numeric computation” by A. Kikuchi). We carry forward the algebraic method of quantum mechanics through algebraic number theory; the basic equations are represented by the multivariate polynomial ideals; the symbolic computations process the ideal and disentangle the eigenstates as the algebraic variety; upon which one canbuild the Galois extension of the number field, in analogy with the univariate polynomial case, to investigate the hierarchy of solutions; the Galois extension is accompanied with the group operations, which permute the eigenstates from one to another, and furnish the quantum system with a non-apparent symmetry. Besides, this sort of algebraic quantum mechanics is an embodiment of the class field theory; some of the important consequences of the latter emerge in quantum mechanics. We shall demonstrate these points through simple models; we will see the use of computational algebra facilitates such sort of analysis, which might often be complicated if we try to solve them manually.

This paper offers a novel geometric and visual approach to the renowned Four Color Map Theorem and K5 non-planarity problem while unveiling their profound connection to the "kissing number" problem in 2D. We represent planar graphs through circles and tangents, simplifying complex structures and shedding light on these classic problems. Our proofs by contradiction, rooted in the kissing number concept, reveal that both the Four Color Map Theorem and K5 non-planarity are fundamentally linked, as they pivot around the concept of coloring. This study bridges the realms of geometry and graph theory, providing fresh insights and emphasizing the significance of the kissing number problem in various fields.

Spinors are used for the computation of probability in quantum mechanics. They are treated as elements of a complex vector space in contrast to a real vector space. Spinor theory is abstract mathematics with an ambiguous interpretation. The overall phase of spinors does not affect the computation of probability in quantum mechanics. If two spinors have an overall phase of imaginary number i, then they can be treated like vectors in a real vector space. The square of the magnitude of the number, which is the sum of dot product and the term having basis vector i of cross product of two such vectors, is equal to the probability computed using the corresponding spinors. Therefore, the geometry of such spinors can be easily depicted in a three-dimensional space like vectors in a real vector space. Spinors are not isotropic vectors in Hilbert space. The sum of dot product and cross product of two complex numbers is equivalent to the quotient of the division of one complex number by another. Similarly, the sum of dot product and cross product of two vectors is the quotient of the division of one vector by another. Using the rules of division of vectors, we can find the rules of multiplication of vectors. The rules of multiplication and division of basis vector i match the rules of multiplication and division of imaginary number i. Therefore, basis vector i is nothing but imaginary number i. Multiplication of dot and cross product of two vectors to the second vector will give us the components of the first vector that are parallel and orthogonal to the second vector. Vectors are also made up of complex numbers like spinors. The reason for finding dot product of complex numbers in the process of computing the probability is to ignore the overall phase in contrast to the phase difference. This is misconstrued as complex vector space in quantum mechanics. 3-D number which is nothing but a spinor with new notation is an extension of vector algebra. It can have a real number as a term in addition to the terms i, j and k. In all other respects, it is a vector. 3-D numbers are part of the number system like real numbers and complex numbers. The real numbers are one dimensional numbers, the complex numbers are two-dimensional numbers and the 3-D numbers as well as vectors and spinors are three-dimensional numbers. As polarisation and spin are one and the same, we can straight away apply 3-D numbers to polarisation of light. 3-D numbers will greatly simplify the study of areas of science where three-dimensional space is involved.

Let $f\left(1\right)=1$ , and let $f(n+1)=2^{2^{f\left(n\right)}}$ for every positive integer n. We consider the following hypothesis: if a system S ⊆ {x_i · x_j = x_k : i, j, k ∈ {1, . . . , n}} ∪ {x_i + 1 = x_k : i, k ∈{1, . . . , n}} has only finitely many solutions in non-negative integers x₁, . . . , x_n, then each such solution (x₁, . . . , x_n) satisfies x₁, . . . , x_n ≤ f (2n). We prove: (1) the hypothesisimplies that there exists an algorithm which takes as input a Diophantine equation, returns an integer, and this integer is greater than the heights of integer (non-negative integer, positive integer, rational) solutions, if the solution set is finite; (2) the hypothesis implies that there exists an algorithm for listing the Diophantine equations with infinitely many solutions in non-negative integers; (3) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many rational solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has a rational solution; (4) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many integer solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has an integer solution; (5) the hypothesis implies that if a set $\mathfrak{M}$ ⊆ has a finite-fold Diophantine representation, then $\mathfrak{M}$ is computable.

SARS-CoV-2 Omicron variant spike RBD epitopes in complex with spike (S) -protein D614G mutations now predominate globally and increase infectivity by assembling more functional S proteins into the virion. On average, homeopathic medicine contains less than one molecule per dose on average. Single variable SphericalHarmonicY, LaguerreL, WhittakerM, SphericalBesselJ, LegendreP, LegendreQ, LaguerreL, ChebyshevT, and Hypergeometric1F1 Functions pFqarise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantum mechanics. A quantum interpretation of the homeopathic method is presented here through a novel algebraic topology approach to supersymmetry and symmetry breaking in quantum fields and quantum gravity theory with the aim of developing a wide range of physical-based drug design applications in a Small Molecule Quantized Water Memory Network suggesting that the Hidden Black Hole Paradox of Information Loss might be solved under suitable conditions.