The design of binders plays a pivotal role in achieving enduring high power in lithium-ion batteries (LIBs) and extending their overall lifespan. This review underscores the indispensable characteristics that a binder must possess when utilized in LIBs, considering factors such as electrochemical, thermal, and dispersion stability, compatibility with electrolytes, solubility in solvents, mechanical properties, and conductivity. In the case of anode materials, binders with robust mechanical properties and elasticity are imperative to uphold electrode integrity, par-ticularly in materials experiencing substantial volume changes. For cathode materials, the se-lection of a binder hinges on the crystal structure of the cathode material. Other vital consid-erations in binder design encompass cost-effectiveness, adhesion, processability, and envi-ronmental friendliness. Incorporating low-cost, eco-friendly, and biodegradable polymers can contribute significantly to sustainable battery development. This review serves as an invaluable resource for comprehending the prerequisites of binder design in high-performance LIBs and offers insights into binder selection for diverse electrode materials. The findings and principles articulated in this review can be extrapolated to other advanced battery systems, charting a course for the development of next-generation batteries characterized by enhanced perfor-mance and sustainability.

We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in $\mathbb{F}_p^{n \times n}$. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We show that the public, secret and channel keys become indistinguishable to the eavesdropper under matrix multiplication. Remarkably, for achieving a 512-bit security level, the public key is 1024 bits and the private key is 768 bits, making them the smallest keys among post-quantum key exchange algorithms. Also, we discuss how to achieve key authentication, interdomain certification and Perfect Forward Secrecy (PFS). Therefore, Lizama's algorithm becomes a promising candidate to establish shared keys and secret communication between (IoT) devices in the quantum era.

We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in $\mathbb{Z}_p^{n \times n}$. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We claim that the unique eavesdropper's opportunity to get the secret/private key is by means of an exhaustive search which is equivalent to the unsorted database search problem. Furthermore, we show that the secret/private keys become indistinguishable to the eavesdropper. Remarkably, to achieve a 512-bit security level, the keys (public/private) are of the same size when matrix multiplication is done over a reduced 8-bit size modulo. Also, we discuss how to achieve key certification and Perfect Forward Secrecy (PFS). Therefore, Lizama's algorithm becomes a promising candidate to establish shared keys and secret communication between (IoT) devices in the quantum era.

Heparanase (HPSE) has been defined as a multitasking protein that exhibits a peculiar enzymatic activity towards HS chains but which simultaneously performs other non-enzymatic functions. Through its enzymatic activity, HPSE catalyzes the cutting of the side chains of heparan sulfate (HS) proteoglycans, thus contributing to the remodeling of the extracellular matrix and of the basal membranes. Furthermore, thanks to this activity, HPSE also promotes the release and diffusion of various HS-linked molecules as growth factors, cytokines and enzymes. In addition to being an enzyme HPSE has been shown to possess the ability to trigger different signaling pathways by interacting with transmembrane proteins. In normal tissue and in physiological conditions, HPSE exhibits only low levels of expression restricted only to keratinocytes, trophoblast, platelets and mast cells and leukocytes. On the contrary, in pathological conditions, such as in tumor progression and metastasis, inflammation and fibrosis, it is overexpressed. With this brief review, we intend to provide an update on current knowledge about the different role of HPSE protein exerted by its enzymatic and not-enzymatic activity.

Heparanase (HPSE) has been defined as a multitasking protein that exhibits a peculiar enzymatic activity towards HS chains but which simultaneously performs other non-enzymatic functions. Through its enzymatic activity, HPSE catalyzes the cutting of the side chains of heparan sulfate (HS) proteoglycans, thus contributing to the remodeling of the extracellular matrix and of the basal membranes. Furthermore, thanks to this activity, HPSE also promotes the release and diffusion of various HS-linked molecules as growth factors, cytokines and enzymes. In addition to being an enzyme HPSE has been shown to possess the ability to trigger different signaling pathways by interacting with transmembrane proteins. In normal tissue and in physiological conditions, HPSE exhibits only low levels of expression restricted only to keratinocytes, trophoblast, platelets and mast cells and leukocytes. On the contrary, in pathological conditions, such as in tumor progression and metastasis, inflammation and fibrosis, it is overexpressed. With this brief review, we intend to provide an update on current knowledge about the different role of HPSE protein exerted by its enzymatic and not-enzymatic activity.

Among the five human senses, light, sound, and force perceived by eye, ear, and skin, respectively are physical actions, and therefore can be easily measured and expressed as objective, univocal, and simple digital data with physical quantity. However, taste and odor molecules perceived by tongue and nose are chemical actions, it has been difficult to express them as objective and univocal digital data, since no reference chemicals can be defined. Therefore, while the recording, saving, transmitting to remote locations, and replaying human visual, auditory, and tactile information as digital data in digital devices has been realized (this series of data flow is defined as DX (digital transformation) in this review), the DX of human taste and odor information is not yet in the realization stage. Particularly, since there are at least 400,000 types of odor molecules and an infinite number of complex odors that are mixtures of these molecules, it has been considered extremely difficult to realize "human olfactory DX" by converting all odors perceived by the human olfaction into digital data. In this review, we discuss the current status and future prospects of the development of "human olfactory DX," which we believe can be realized by utilizing odor sensors that employ the olfactory receptors (ORs) that support human olfaction as sensing molecules (i.e., human OR sensor).

Matrix multiplication is probably one of the most basic and important operations having a wide range of applications in studying Linear algebra. We will be primarily focused on reviewing different algorithms for the multiplication of two n×n matrices. The most Naive method has a complexity of O(n3) but interestingly, algorithms with better complexity have been achieved. We will get to see how the complexity can be improved further, occasionally giving a survey.

Cancer invasion through basement membranes represents the initial step of tumor dissemination and metastasis. However, little is known about how human cancer cells breach basement membranes. Here, we used a 3-dimensional in vitro invasion model consisting of cancer spheroids encapsulated by a basement membrane and embedded in 3D collagen gels to visualize the early events of cancer invasion by confocal microscopy and live-cell imaging. Human breast cancer cells generated large numbers of basement membrane perforations, or holes, of varying sizes that expanded over time during cell invasion. We used a wide variety of small molecule inhibitors to probe the mechanisms of basement membrane perforation and hole expansion. Protease inhibitor treatment (BB94), led to a 63% decrease in perforation size. After myosin II inhibition (blebbistatin), basement membrane perforation area decreased by only 15%. These treatments produced correspondingly decreased cellular breaching events. Interestingly, inhibition of actin polymerization dramatically decreased basement membrane perforation by 80% and blocked invasion. Our findings suggest that human cancer cells can primarily use proteolysis and actin polymerization to perforate the BM and to expand perforations for basement membrane breaching, with a relatively small contribution from myosin II contractility.

Sustainability in Additive Manufacturing (AM) is an emerging area of research that examines the environmental impacts and potential benefits of AM processes compared to traditional manufacturing methods. This paper analyzes the environmental footprint of additive manufacturing technologies, including material usage, energy consumption, and waste production. AM techniques, such as fused deposition modeling (FDM), stereolithography (SLA), and selective laser sintering (SLS), are evaluated for their efficiency and sustainability. Key factors such as resource utilization, lifecycle emissions, and recyclability are assessed to determine how AM can contribute to a more sustainable manufacturing paradigm. The study highlights that while AM offers advantages such as reduced material waste and the potential for localized production, it also poses challenges, including high energy consumption and limited material options. The paper concludes with recommendations for improving the environmental performance of AM, including advancements in material science, energy-efficient technologies, and the integration of circular economy principles. By addressing these aspects, AM can play a significant role in achieving sustainability goals in manufacturing.

A computational model for analysing the tooth deflection of polymer gears is presented in this paper. Because polymer gears have less stiffness compared to metal gears, the proposed approach considers a comprehensive analysis to determine the most suitable numerical model, i.e., the number of teeth that should be modelled. The developed computational model has been evaluated on the spur gear pair, where the pinion made of POM has meshed with a support gear made of steel. Material properties were assigned with linear elastic characteristics for the gear, while the pinion was characterised by hyperelastic properties using POM material. Furthermore, a nonlubricated frictional contact between the gear and pinion was considered in the numerical computations. The computational results that were obtained were compared to the empirical results according to VDI 2736 guidelines. Here, the computational approach showed more accurate results due to the hyperelastic material characteristics of POM. However, VDI 2736 calculation showed the comparability with computational results with a slightly larger deviation at lower loads.

Deformation behavior of the composite "hen's eggshell - polymer plomb" under bending is examined. Polymer coating does not change the type of behavior of the composite based on eggshell that continues to be brittle despite the mechanical characteristics of the composite could vary in wide limits for brittle structure. Joining "hen's eggshell – polymer plomb" never crack under loading and, hence, it exhibits the high cohesion strength under stresses applied in these experiments. It seems that the composite "hen's eggshell - polymer plomb" could apply as the substitution of the composite "tooth enamel - polymer plomb" under elaboration of novel restorative materials for dentistry, namely, for estimation of their mechanical properties including cohesive strength.

Bipolar plates significantly contribute in the development of the polymer electrolyte membrane (PEM) fuel cells technology due to their ability to produce high electrical conductivity based on type of materials used. Mismatching of inappropriate materials and manufacture may lead to the inferior performance of PEM fuel cells. Hence, material development was determined crucial to balance the overall performance of PEM fuels including the mechanical properties and electrical conductivity of the materials. Studies on conductive polymer composites (CPCs) offered filler orientation as an alternative method to enhance the overall performance of bipolar plate. Filler orientations permit an excellent conductivity network formation while controlling the filler alignment based on required applications. This paper reviewed various studies of filler orientations including materials used and methods of manufacture of CPC materials for the effective development of bipolar plate.

Controlling the concentration of free radicals in polymerization systems is advantageous for preparing cationic polyacrylamide (CPAM) with high molecular weight and acceptable dissolvability. In this study, a novel ultraviolet (UV)-initiated system characterized with adjustable light intensity and redox-azo complex initiator was used to synthesize a CPAM flocculant named NP. Comparatively, another CPAM flocculant named SP with stable UV light intensity and single initiator was prepared. The chemical structure, morphology, and thermal stability were analyzed through instrumental analysis. Proton nuclear magnetic resonance indicated that NP was successfully prepared, and a small fraction of cationic homopolymer was mixed in the product. Polymerization conditions were optimized, and polymerization mechanism was determined by investigating the effects of various parameters on intrinsic viscosity, conversion, and dissolvability. Results showed that the best performance was obtained at indexes of 0.45 wt‰ redox initiator concentration, 0.2 wt‰ azo initiator concentration, 40.0 wt% of cationic monomer, first- and second-stage light intensities of 8.5 and 13 mW/cm², respectively, and 3 wt% urea. Sludge conditioning performances of NP and SP were comparatively evaluated, and the mechanism was determined by investigating the sedimentation behavior and floc size distribution. High intrinsic viscosity, porous morphology structure, and the mixed cationic homopolymer of NP resulted in better sludge conditioning performance.

Search for appropriate materials with favorable staggered energy band arrangements is important and of great challenge to fabricate Z-scheme photocatalysts with high activity in visible light. In this study, we demonstrated a facile and feasible strategy to construct highly active organic-inorganic Z-scheme hybrids (P-BMO) with linear pyrene-based conjugated polymer (P17-E) and Bi₂MoO₆ via in-situ palladium-catalyzed cross-coupling reaction. Characterization results revealed C-O chemical bond formed at the heterointerface between P17-E and Bi₂MoO₆ after in-situ polycondensation and endowed the hybrids with observably improved photogenerated carries transfer capability. Visible light driven photocatalytic removal of ciprofloxacin and Cr(VI) were significantly enhanced after the incorporation of P17-E into Bi₂MoO₆ whether with the morphology of nanosheets, nanobelts or microspheres. Moreover, this P-BMO hybrids were also found to exhibit sustainable excellent photocatalytic performance after four runs of photocatalytic evaluation test, suggesting its high activity and stability. To better eliminate the redox ability enhancement of P-BMO, a reasonable Z-scheme electrons transferring mechanism between P17-E and Bi₂MoO₆ was proposed and proved by the determination of •O₂^– and •OH and Pt nanoparticles photodeposition experiments. This work might provide a viable source and insight into the design of Z-scheme photocatalysts with excellent redox ability for environmental remediation.

Several series of new polymers were synthesized: binary copolyesters of vanillic (VA) and hydroxybiphenylcarboxylic (HBCA) acids, as well as ternary copolyesters additionally containing hydroxybenzoic acid (HBA) and obtained via three different ways (in solution, in melt and in solid state). The high values of logarithmic intrinsic viscosities and insolubility of several samples proved its high molecular weights. It has been shown that the use of vanillic acid leads to the production of copolyesters with a relatively high glass transition temperature (about 130°C). Thermogravimetric analysis revealed onset of weight loss temperatures of ternary copolyesters occurred at 330-350 °C, the temperature of 5% mass loss is in the range of 390-410 °C. Two-stage thermal destruction is observed for all aromatic copolyester of vanillic acid: decomposition begins with VA units at 420-480 °C, and then decomposition of more heat-resistant units demonstrated above 520 °C. The copolyesters are thermotropic and exhibit a typical nematic type of liquid crystalline order. Mechanical characteristics of copolyesters are close to those for semi-aromatic copolyesters, but are much lower than typical values for fully aromatic thermotropic polymers. Thus, vanillic acid is a mesogenic monomer suitable for the synthesis of thermotropic fully aromatic and semi-aromatic copolyester, but resulting processing temperature must not exceed 280°C.

Recent developments in mid-infrared (MIR) spectroscopic ellipsometry enabled by quantum cascade lasers (QCLs) resulted in a drastic improvement in signal-to-noise ratio compared to conventional thermal emitter based instrumentation. Thus, it was possible to reduce the acquisition time for high-resolution broadband ellipsometric spectra from multiple hours to less than 1 second. This opens up new possibilities for real-time in-situ ellipsometry in polymer processing. To highlight these evolving capabilities we demonstrate the benefits of a QCL based MIR ellipsometer by investigating single and multilayered polymer films. The molecular structure and reorientation of a 2.5m thin biaxially oriented polyethylene terephtalate film is monitored during a stretching process lasting 24.5 s to illustrate the perspective of ellipsometric measurements in dynamic processes. In addition, a polyethylene/ethylene vinyl alcohol/polyethylene multilayer film is investigated at continuously varying angle of incidence ( 0∘ – 50∘) in 17.2 s, highlighting an unprecedented sample throughput for the technique of varying angle spectroscopic ellipsometry in the MIR spectral range. The obtained results underline the superior spectral and temporal resolution of QCL ellipsometry and qualify this technique as suitable method for advanced in-situ monitoring in polymer processing.

In extant biology, biopolymers perform multiple crucial functions. The biopolymers are synthesized by enzyme-controlled biosystems that would not have been available at the earliest stages of chemical evolution and consist of correctly sequenced and/or linked monomers. Some of the abiotic “messy” polymers approximate some functions of biopolymers. Condensation polymers are an attractive search target for abiotic functional polymers since principal polymers of life are produced by condensation and since condensation allows for the accurate construction of high polymers. Herein the formation of hyperbranched polyesters that have been previously used in the construction of enzyme-like catalytic complexes is explored. The experimental setup compares between the branched polyesters prepared under mild continuous heating and the wet-dry cycle conditions. The results reveal that period wetting during which partial hydrolysis of the polyester occurs, helps control the chain growth and retards the gel transition. It is significant to the origin of life studies that environmental, prebiotically plausible conditions could achieve such control without enzymes or a skilled chemist. As expected in marginally controlled systems, the identification of each component of the heterogeneous system has proved challenging, but it is not crucial for drawing the conclusions.

Li⁺-conducting polyethylene oxide-based membranes, incorporating the N-butyl-N-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide, are as electrolyte separators for all-solid-state lithium polymer batteries operating at medium-high temperatures. The incorporation of the ionic liquid remarkably improves the thermal, ion-transport and interfacial properties of the polymer electrolyte, which, in combination with the wide electrochemical stability even at medium-high temperatures, allow high current rates without any appreciable lithium anode degradation. Battery tests carried out at 80 °C have shown excellent cycling performance and capacity retention even at high rates, never tackled by ionic liquid-free polymer electrolytes. No dendrite growth onto the lithium metal anode was observed.

This document focuses attention on the fundamental solution of an autonomous linear retarded functional differential equation (RFDE) along with its supporting cast of actors: kernel matrix, characteristic matrix, resolvent matrix, and the Laplace transform. The fundamental solution is presented in a form of the convolutional powers of the kernel matrix in the manner of a convolutional exponential matrix function. The fundamental solution combined with a solution representation gives an exact expression in explicit form for the solution of a RFDE. Algebraic graph theory is applied to the RFDE in the form of a weighted loop-digraph to illuminate the system structure and system dynamics and to identify the strong and weak components. Examples are provided in the document to elucidate the behavior of the fundamental solution. The paper introduces fundamental solutions of other functional differential equations.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

RNA interference (RNAi) molecules have tremendous potential for cancer therapy but are limited by insufficient potency after i.v. administration. We previously found that polymer complexes (polyplexes) formed between 3’-cholesterol-modified siRNA (Chol-siRNA) or DsiRNA (Chol-DsiRNA) and the cationic diblock copolymer PLL[30]-PEG[5K] greatly increase RNAi potency against stably expressed LUC mRNA in primary syngeneic murine breast tumors after daily i.v. dosing. Chol-DsiRNA Polyplexes, however, maintain LUC mRNA suppression ~48 h longer after the final dose than Chol-siRNA Polyplexes, suggesting they are a better candidate formulation. Here, we directly compared the activities of Chol-siRNA and Chol-DsiRNA Polyplexes in primary murine 4T1 breast tumors against STAT3, a therapeutically relevant target gene overexpressed in many solid tumors including breast cancer. We found that Chol-siSTAT3 Polyplexes suppressed STAT3 mRNA in 4T1 tumors with similar potency (half-maximal ED₅₀ 0.3 mg/kg) and kinetics over 96 hours as Chol-DsiSTAT3 Polyplexes but with slightly lower activity against total Stat3 protein (29% vs. 42% suppression) and tumor growth (11.5% vs. 8.6% rate-based T/C ratio) after repeated i.v. administration of tumor-saturating doses every other day. Thus, both Chol-siRNA Polyplexes and Chol-DsiRNA Polyplexes may be suitable clinical candidates for RNAi therapy of breast cancer and other solid tumors.

Polymer flooding is one of the most successful chemical EOR methods, and is primarily implemented to accelerate oil production by sweep improvement. However, other benefits have extended the utility of polymers. During the last decade, it has been evaluated for an increasing number of fields, both offshore and onshore. This is a consequence of improved polymer properties, which extends the use to HTHS (high temperature high salinity) conditions and of improved understanding of flow mechanisms such as for heavy oil mobilization. A key issue in understanding polymer performance is to control and predict in-situ porous medium rheology. The first part of this paper reviews recent developments in understanding polymer flow in porous medium. Especially, polymer in-situ rheology and injectivity is discussed. The second part of this paper reports polymer flow experiments using the most applied polymer for EOR processes, HPAM (partially hydrolyzed polyacrylamide). The experiments address high rate near-wellbore behavior (radial flow) as well as reservoir rate steady state flow (linear flow) and discuss differences observed in terms of flow conditions. In addition, impact of oil on polymer rheology was investigated, and compared to single-phase polymer flow in Bentheimer sandstone rock material. Presence of oil leads to a reduction in apparent viscosity.

In this study, in order to determine the effect of matrices shape on percolation threshold values, computer simulations were performed using the Monte Carlo method for a 200x200 square-shaped matrix and rectangular matrices containing the same number of nodes as the square matrix. Based on the simulations, the average values of percolation thresholds and standard deviations for current flow along and across the matrices were determined. It was determined that for a square-shaped matrix, the average values of percolation thresholds in both directions of current flow were the same. Extending the rectangular matrix while reducing its height causes the average value of the percolation threshold in the direction of current flow along the matrix to increase from 0.592740 to 0.759847, while in the transverse direction it decreases from 0.592664 to 0.403614. The values of the classical asymmetry coefficients of the probability distributions of percolation thresholds for both directions of current flow were determined. Histograms of the probability distributions of percolation threshold values for square-shaped matrix and rectangular matrices were made and compared with normal distributions. It was found that the occurrence of two percolation thresholds in rectangular layers should be considered when analyzing electrical conductivity measurements of nanocomposite thin films.

Childhood glaucoma encompasses congenital and juvenile primary glaucoma, which are heterogeneous, uncommon, and irreversible optic neuropathies leading to visual impairment with poorly understood genetic basis. Our goal was to identify gene variants associated with these glaucoma types by assessing the mutational burden in 76 matrix metalloproteinase-related genes. We studied 101 childhood glaucoma patients with no identified monogenic alterations using next-generation sequencing. Gene expression was assessed through immunohistochemistry. Functional analysis of selected gene variants was conducted in cultured cells and in zebrafish. Patients presented a higher proportion of rare variants in four metalloproteinase-related genes, including CPAMD8 and ADAMTSL4, compared to controls. ADAMTSL4 protein expression was observed in the anterior segment of both the adult human and zebrafish larvae's eye, including tissues associated with glaucoma. In HEK-293T cells, expression of four ADAMTSL4 variants identified in this study showed that two variants (p.Arg774Trp and p.Arg98Trp) accumulated intracellularly, inducing endoplasmic reticulum stress. Additionally, overexpressing these ADAMTSL4 variants in zebrafish embryos confirmed partial loss-of-function effects for p.Ser719Leu and p.Arg1083His. Double heterozygous functional suppression of adamtsl4 and cpamd8 zebrafish orthologs resulted in reduced volume of both the anterior eye chamber and lens within the chamber, supporting a genetic interaction between these genes. Our findings suggest that accumulation of partial functional defects in matrix metalloproteinases-related genes may contribute to increased susceptibility to early-onset glaucoma and provide further evidence supporting the notion of a complex genetic inheritance pattern underlying the disease.

The extracellular matrix (ECM) provides structural support for tissues and regulatory signals for resident cells. ECM requires a careful balance between protein accumulation and degradation for homeostasis. Disruption of this balance can lead to pathological processes such as fibrosis in organs across the body. Post-translational crosslinking modifications to ECM proteins such as collagens alter ECM structure and function. Dysregulation of crosslinking enzymes as well as changes in crosslinking composition are prevalent in fibrosis. Because of the crucial roles that ECM crosslinking pathways play in disease, the enzymes that govern crosslinking events are being explored as therapeutic targets for fibrosis. Here we review in-depth the molecular mechanisms underlying ECM crosslinking, how ECM crosslinking contributes to fibrosis, and therapeutic strategies being explored to target ECM crosslinking in fibrosis to restore normal tissue structure and function.

This paper attempts to propose a Riemann spring model via an analogy between the Riemann Zeta function of a complex number and the elastic spring in series.

This paper attempts to extend the Riemann Zeta function of a complex number to a function of a matrix and/or a tensor $A$, namely $$\zeta (A)=\sum _{n=1}^{\infty} \frac{1}{n^{A}}= \sum _{n=1}^{\infty} \sum_{k=1}^n\lambda_k A^k$$ and inverse $$A=\sum _{n=1}^{\infty} \sum_{k=1}^n \mu(n)\lambda_k \zeta(A^k)$$ where $\mu(n)$ is the M\"obius function, $A$ is a complex matrix or tensor with any order, and $\lambda_k$ is eigenvalue of the matri/tensor $A$. This kind of calculations on the Riemann Zeta function has never been seen in the literature. Some examples are provided.

The aim of this paper is to show how the mathematical basis is used for a precise treatment of double-entry bookkeeping, which was firstly developed in the nineteenth century by Sir William Rowan Hamilton. This is done by using basic notions of matrix algebra with the roots to the idea of using ordered pairs. We also reveal how the complex numbers and the rationals (fractions) developed in a mainstream of accounting science and became a leading platform for the ongoing processes within the Industry 4.0. The paper concludes with the examples on how accounting operations can be represented by matrix equations with a result of the essential report generating. The author represents a mathematical model of accounting which is independent of the specific existential forms but is capable to undertake the form of any of them and thus has the prospect of being understood and accepted by specialists globally.

Matrix metalloproteases (MMPS) are a family of well-known enzymes which operate prevalently in the extracellular domain, where they fulfil the function of remodeling the extracellular matrix. Within the about 26 family members, encoded by 24 genes in humans, MMP-2 and MMP-9, have been regarded as the primary responsibility for the basement membrane and pericellular ECM rearrangement. In cases of infiltrating carcinomas, which arise from the epithelial tissues of a gland or of an internal organ, a marked alteration of the expression and the activity levels of both MMPs is known to occur. Present investigation represents the continuation and upgrading of our previous studies, now focusing on the occurrence and intensity levels of MMP-2 and -9, and their proteomic correlations, in a cohort of 80 breast cancer surgical tissues

Many authors proposed analytical methods for solving fully fuzzy Sylvester matrix equation (FFSME) based on Vec-operator and Kronecker product. However, these methods are restricted to nonnegative fuzzy numbers and cannot be extended to FFSME with near-zero fuzzy numbers. The main intention of this paper is to develop a new numerical method for solving FFSME with near-zero trapezoidal fuzzy numbers that provides a wider scope of trapezoidal fully fuzzy Sylvester matrix equation (TrFFSME) in scientific applications. This numerical method can solve the trapezoidal fully fuzzy Sylvester matrix equation with arbitrary coefficients and find all possible finite arbitrary solutions for the system. In order to obtain all possible fuzzy solutions, the TrFFSME is transferred to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication between trapezoidal fuzzy numbers. The fuzzy solutions to the TrFFSME are obtained by developing a new two-stage algorithm. To illustrate the proposed method numerical example is solved.

In this paper we perform numerous numerical studies for the problem of low-rank matrix completion. We compare the Bayesian approaches and a recently introduced de-biased estimator which provides a useful way to build confidence intervals of interest. From a theoretical viewpoint, the de-biased estimator comes with a sharp minimax-optimal rate of estimation error whereas the Bayesian approach reaches this rate with an additional logarithmic factor. Our simulation studies show originally interesting results that the de-biased estimator is just as good as the Bayesian estimators. Moreover, Bayesian approaches are much more stable and can outperform the de-biased estimator in the case of small samples. However, we also find that the length of the confidence intervals revealed by the de-biased estimator for an entry is absolutely shorter than the length of the considered credible interval. These suggest further theoretical studies on the estimation error and the concentration for Bayesian methods as they are being quite limited up to present.

Various slow-release fertilizers (SRFs) have been developed and commercialized, particularly over the past two decades, with the primary aim of mitigating environmental issues associated with excessive fertilizer use. A range of methodologies, including chemical and physical reactions, incorporation into carriers with porous and layered structures, and coating techniques, have been explored and refined. On the other hand, dry and desertification are big challenges for agriculture in many countries in the world. Application of hydrogels or superabsorbent polymers as carrier materials to develop SRFs could add the function of moisture retention. This paper reviewed the development of application eco-friendly starch hydrogels as fertilizer carrier and water retention to develop SRFs, in particular starch-based superabsorbent polymers through grafting copolymerization with acrylamide. The reviewer includes both scientific issues like general microstructures of various starch hydrogels and releasing mechanisms, and technical development involving copolymerization technologies, multi-initialization and loading fertilizer into hydrogel etc. Starch, recognized as one of the most abundant carbohydrate polymers, is both biodegradable and renewable. It exhibits excellent chemical stability and high reactivity. The fabrication technique of starch hydrogels though grafting polymerization have been developed from batch chemical reaction in aqueous solution to high efficient and no-solvent reactive extrusion. The benefits of SRFs based on starch hydrogel encompass enhanced soil aeration, prevention of soil deterioration, minimization of water evaporation, environmental pollution control, reduction in plant mortality, and prolonged nutrient retention within the soil. Based on the literatures and our experience, we have not only discussed and summarized the achievements, but also pointed out the weakness of current technologies and proposed research directions in this review.

This study addresses the global issue of recycling used vehicle rubbish tires, typically burned out or trimmed to be reused in playground floors or road banks. In this study we explore a novel environmentally responsive approach or decomposing and recovering the carbon black particles contained in tires (25-30 wt.%) by vacuum pyrolysis. Given that carbon black is well known for its UV protection in plastics, the objective of this research is to provide an ecological alternative to commercial carbon black of fossil origin by recycling the carbon black (rCB) from used tires. In our research, we create a composite material using rCB and high density polyethylene (HDPE). In this article we present the environmental aging studies carried out to this composite material. The topographic evolution of the samples with aging and the oxidation kinetic of the surface and through the thickness were studied. A Beer-Lambert law is used to relate the oxidative index to the characteristic depth of the samples. This work helps to demonstrate the feasibility of using recycled carbon black particles from waste tires as a filler for UV protection.

Shale formations present significant challenges to traditional drilling fluids due to fluid infiltration, cuttings dispersion, and shale swelling, which can destabilize the wellbore. While oil-based drilling fluids (OBM) effectively address these problems concerns about their environmental impact and cost limit their widespread use. Recently, nanomaterials (NPs) have emerged as a promising approach in drilling fluid technology, offering an innovative solution to improve the efficiency of water-based drilling fluids (WBDF) in shale operations. This study evaluates the potential of utilizing modified silica nanocomposite and graphene nanopowder to formulate a nanoparticle-enhanced water-based drilling fluid (NP-WBDF). The main objective is to investigate the impact of these nanoparticle additives on the flow characteristics, filtration efficiency, and inhibition properties of the NP-WBDF. In this research, a silica nanocomposite was successfully synthesized using emulsion polymerization and analyzed using FTIR, PSD, and TEM techniques. Results showed that the silica nanocomposite exhibited a unimodal particle size distribution ranging from 38 nm to 164 nm, with an average particle size of approximately 72 nm. Shale samples before and after interaction with Graphene nanopowder-WBDF and NFC-WBDF were analyzed using scanning electron microscopy (SEM). The NP-WBM underwent evaluation through API filtration tests (LTLP), high-temperature/high-pressure (HTHP) filtration tests, and rheological measurements conducted with a conventional viscometer. Experimental results showed that silica nanocomposite and graphene nanopowder effectively bridged and sealed shale pore throats, demonstrating superior inhibition performance compared to conventional WBDF. Post adsorption, the shale surface exhibited increased hydrophobicity, contributing to enhanced stability. Overall, silica nanocomposite and graphene nanopowder positively impacted rheological performance and provided favorable filtration control in water-based drilling fluids.

In the last decade, a higher level of reliability became a compulsory demand when it comes to modern DC-DC converters. This work addresses the main reliability metrics: the failure rate λλ and MTBF of an output capacitor bank used within a high current low voltage buck converter due to many studies have shown that the output capacitor bank was demonstrated being the most critical component within the converter. Many authors treated this issue, usually by doing reliability predictions. The majority of the papers use only one specific Standard Prediction to solve the problem. Herein calculation was done using both the older standard MIL-HDBK-217 and the latest one Telcordia SR-332, providing a benchmark comparison between the two which is a helpful tool for the output capacitor selection in the early stage design. Military standard was well accepted for decades in order to reliability prediction even on industrial electronics and is still used today under a critical manner because no more update after the latest version MIL-HDBK-217F - Notice 2 released in 1995. Since then, newer prediction standards had appeared in the electronics reliability market. Over time, this standard was mostly used but it does not accurately model the reliability because lack of taking account of mission profile. The above-mentioned newer standard – i.e., Telcordia SR-332 is trying to compensate also the lack of the newest component technology in the older standard (which is the first standard released on the market) supplying useful design data for design engineers who use the so-called “design with the reliability in mind” concept. Within the paper were established the environmental condition for the passive components by means of a PoL (Point of load) buck converter that is used for both calculation methods. The influence of temperature and several specific concepts like reference conditions, operating conditions, ripple, and internal self-heating were taking account in order to display the results. The temperature for the capacitor’s capsule needed in π_T stress factor calculation was derived by PSPICE simulation. High fidelity and dedicated SPICE models provided by the manufacturer were used for MOSFETs, polymer electrolytic, and MLCC capacitors that compose the converter.

Reactions of Co(OAc)24H2O, N‚N'-bis(3-pyridylmethyl)oxalamide (L) and 4,4’-sulfonyldibenzoic acid (H2SDA) afforded four coordination polymers with the same mixed ligands, {[Co(L)(SDA)(H2O)2]·H2O·CH3OH}n, 1, {[Co(L)0.5(SDA)]·2H2O·0.5L}n, 2, {[Co(L)1.5(SDA)(H2O)]·H2O}n, 3, and {[Co2(L)1.5(SDA)2(H2O)2]·4H2O}n, 4, which have been structurally characterized by using single crystal X-ray crystallography. Complexes 1 – 4 are 2D layers, revealing the topologies of sql, 2,6L1, (4,4)Ia and 6L12, respectively, and demonstrating that the metal to ligand ratio, solvent system and reaction temperature are important in determining the structural diversity. Immersion of these complexes into various solvents show that the structural types govern the chemical stabilities of 1 – 4. Reversible structural transformation can be shown for complexes 1 and 2 upon solvent removal and adsorption, while those of 3 and 4 are irreversible.

Bottlebrush (BB) elastomers with water-soluble side chains and tissue-mimetic mechanical properties are promising for biomedical applications like tissue implants and drug depots. This work investigates the microstructure and phase transitions of BB elastomers with crystallizable polyethylene oxide (PEO) side chains by real-time synchrotron X-ray scattering. In the melt, the elastomers exhibit the characteristic BB peak corresponding to the backbone-to-backbone correlation. Upon crystallization of the side chains, the intensity of the peak decays linearly with crystallinity, and eventually vanishes due to BB packing disordering within intercrystalline amorphous gaps. This behavior of the bottlebrush peak differs from an earlier study of BBs with poly(ε-caprolactone) side chains, explained by stronger backbone confinement in the case of PEO, a high-crystallinity polymer. Microstructural models based on 1D SAXS correlation function analysis suggest crystalline lamellae of PEO side chains separated by amorphous gaps of monolayer-like BB backbones.

Modeling the flow of polymer solutions requires knowledge at various length and time scales. The macroscopic behavior is described by the overall velocity, pressure and stress. The polymeric contribution to the stress requires knowledge of the evolution of polymer chains. In this work, we use a microscopic model, the finitely extensible nonlinear elastic (FENE) model, to capture the polymer behavior. The benefit of microscopic models is they remain faithful to the polymer dynamics without information loss via averaging. The downside is the computational cost needed to solve the thousands to millions of differential equations describing the microstructure. We thus describe a multiscale flow solver that utilizes GPUs for massively parallel, efficient simulations. We compare and contrast the microscopic model with its macroscopic counterpart under various flow conditions. In particular, significant differences are observed under nonlinear flow conditions, where the polymers become highly stretched and oriented.

In a blood purification technique continuous renal replacement therapy called CRRT , a porous hollow-fiber polymeric membrane is exposed to prolonged contact with blood. In that condition, like with any other submerged filtration membrane, hemofilter loses its properties over time and use which results in a rapid decline in flux. The most significant reason for this loss is the formation of a biofilm. Protein, blood cells and bacterial cells attach to the membrane surface in complex and fluctuating processes. Anticoagulation allows for longer patency of vascular access and a longer lifespan of the membrane. Other preventive measures include modification of the membrane itself. In this article, we focused on the role of nanoadditives in the mitigation of bio-fouling. Nanoparticles such as graphene, carbon nanotubes, silica effectively change surface properties towards more hydrophilic, affect pore size and distribution, decrease protein adsorption and damage bacteria cells. As a result, membranes modified with nanoparticles show better flow parameters, longer lifespan and increased hemocompatibility.

Despite the immense application of combustion in reactive materials, one of the challenges people are facing globally is the auto-ignition of such materials, resulting in fire and explosion hazards if proper measures are not considered. To avoid this unfortunate occurrence, a mathematical model describing the thermal decomposition of combustible polymer material in a rectangular stockpile is formulated. A nonlinear momentum equation is provided with the assumption that the combustible polymer follows Carreau constitutive relation. The chemical reaction of the polymer material is assumed exothermic; therefore, Arrhenius’s kinetic theory is considered in the energy balance equation. The bivariate spectral local linearization Scheme (BSLLS) is utilized to provide a numerical solution for the dimensionless equations governing the problem. The obtained results are validated by the collocation weighted residual method (CWRM) and a good agreement is achieved. Dimensionless velocity, temperature, and thermal stability results are presented and explained comprehensively with suitable applications.

The aim of this study was to analyse the biocompatibility of a material based on lactic acid (PLA)/polyhydroxybutyrate(PHB)/thermoplastic starch (TPS) in combination with additives (plasticizers: acetyltributyl citrate (ATBC) and oligomeric lactic acid ( OLA)). Three types of materials were tested: I: PLA/PHB/TPS + 25% OLA, II: PLA/PHB/TPS + 30% ATBC, III: PLA/PHB/TPS + 30% OLA. The 3D printing itself was preceded by the creation of filaments from granulate and the design of samples. A filament production machine – Composer 450 (3devo; The Netherlands) was used to produce the filaments. Experimental samples were produced by FDM technology on a 3D printer DeltiQ2 (Trilab, Czech Republic). The evaluation of the biocompatibility of the materials included cytotoxicity tests such as the monitoring of viability, proliferation, morphology of cells, and their settlement on the surface of the materials. The cell line 7F2 osteoblasts (Mus musculus) was used in the experiments. Based on the tests, results confirmed the significant influence of plasticizers and their proportions in the mixtures. PLA/PHB/ATBC + 25% OLA was evaluated as the optimal material for biocompatibility with 7F2 osteoblasts. The tested biomaterials have the potential for further investigation, with a possible change in the proportion of the plasticizer, which has a fundamental impact on their biological properties.

Biocidal compositions based on interpolyelectrolyte complexes and a low molecular weight antibiotic can become a promising material for creating biocidal coatings, as they combine wash-off resistance and dual biocidal action due to the biocide and the polycation. Molecular mass characteristics of polymers play essential role in physics and mechanical properties of the coatings. In this work, the properties of polydiallyldimethylammonium chloride (PDADMAC) coatings of various molecular weights are investigated and assumptions are made about the optimal molecular weight needed to create antibacterial compositions. To study the resistance to washing off and moisture saturation of the coatings, the gravimetric method was used, the adhesive properties of the coatings were studied by dynamometry. It has been established that an increase in molecular weight affects the wash-off resistance of coatings, but does not affect moisture absorption and adhesion mechanics of coatings. All samples of PDADMAC were demonstrated to exhibit the same antibacterial activity. Thus, when developing systems for creating antibacterial coatings, it must be taken into account that in order to create stable coatings. The requirement to use PDADMAC with a high degree of polymerization is necessary for control the desorption of coating during wash off-but not mandatory for the control of mechanical and antibacterial properties of the coating.

The power conversion efficiency (PCE) of polymer solar cells (PSCs) are strongly depended on the bulk-heterojunction active layer. Here, the 1,8-diiodooctane (DIO) additives have been added into the PCDTBT: PC70BM blend PSCs. Based on the higher boiling point than host solvent ODB and better solubility of PC71BM, the device photovoltaic properties with DIO additive were changed obviously. The investigations of EQE indicate that the DIO can influence the charge recombination and transportation process, and absorption studies demonstrate that the charge carriers generation process can also be affected by DIO. The overall impact reflected on the decreased equivalent resistant. With 3% v/v DIO, the Jsc, Voc and FF are both increased. Correspondingly, a highest PCE is achieved of 6.15%, while the reference device without DIO only has a PCE of 5.23%. Hence, adding DIO solvent additive is a effective method for the photovoltaic properties improving of PCDTBT: PC70BM blend PSCs.

The interaction of solution of poly (diallyldimethylammonium) chloride, PDADMAc and sodium dodecylsulfate, SDS has been studied using conductometric, densimeter and zeta potential methods. the critical micellization concentration (cmc) was determinated with conductance results and increased with the addition of PDADMAc comparing with solutions containing pure SDS. Further the degree of dissociation,  and thermodynamic parameters viz. free energy of micellization, and entropy of micellization, has been evaluated. there results demonstrated that surfactant/polymer complex is governed by both electrostatic and hydrophobic interactions. The apparent molar volume, Vϕ and adiabatic compressibility, Kϕ;s have been determined for the SDS solution from density and speed sound data. the negative charge of the SDS solutions with polymer shows that these complexes probably do not contain surfactant in the form of micelles.

In this paper, first the Self-Written Waveguide (SWW) process in wet photopolymer media (liquid solutions), are examined for three examples: single-, counter-, and co-fibers exposure. Then the SWWs formed inside solid material are examined including the effects of manipulating the alignment of the fibers. In all cases high precision measurements are used to position the fiber optic cables (FOCs) before exposure using a microscope. The self-writing process is indirectly monitored by observing (imaging) the light emerging from the side of the material sample during SWW formation. In this way the optical waveguide trajectories formed in an Acrylamide/Polyvinyl Alcohol (AA/PVA) a photopolymer material (sensitized at 532 nm) are examined. First the transmission of light by this material is characterized. Then the bending and merging of the waveguides which occur are investigated. The predictions of our model are shown to qualitatively agree with the observed trajectories. The largest index changes taking place at any time during the exposure, i.e. during SWW formation, are shown to take place at the positions where the largest exposure light intensity is present. Typically, such maxima exist close to the input face and the first maximum is referred to as the location of the Primary Eye. Other local maxima also appear further along the SWW and are referred to as Secondary Eyes, i.e. deeper within the material.

This study aimed to evaluate the physico-chemical properties, biocompatibility and bioabsorption of 3 different new membranes for bone guided regeneration (PLGA associated with hydroxyapatite and beta-TCP) with three thicknesses (200, 500 and 700 µm) implanted in mice subcutaneously. Scanning electron microscopy (SEM), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and the quantification of Carbon, Hidrogen and Nitrogen were used to characterize the physico-chemical properties. One hundred Balb-C mice were divided into 5 experimental groups: Group 1 - Sham (without implantation); Group 2 - 200 μm; Group 3 - 500 μm; Group 4 - 700 μm; and Group 5 - Pratix®. Each group was subdivided into four experimental periods (7, 30, 60 and 90 days). Samples were collected and processed for histological and histomorphometrical evaluation. The membranes showed no moderate or severe tissue reactions in the experimental periods studied. The 500 μm membrane did not show tissue reaction for any experimental periods studied. The 200 μm membrane membranes began to exhibit fragmentation after 30- day, while the 500 and 700 µm membranes started the fragmentation at 90-day. All membranes studied were biocompatible, and the 500µm membrane showed the best results being a promissory membrane for bone guided regeneration.

In the European Union, the demand for polyurethane is continually growing. In 2017, the estimated production value of polyurethane was 700,400T, of which 27.3% is taken to landfill, which causes an environmental problem. In this paper the behaviour of various polyurethane foams from the waste of different types of industries will be analysed with the aim of assessing their potential use in construction materials. In order to this, the wastes were chemically tested by means of CHNS, TGA, and leaching tests. They were tested microstructurally by means of SEM. The processing parameters of the waste was calculated after finding out its granulometry and its physical properties i.e. density and water absorption capacity. In addition, the possibility of incorporating these wastes in plaster matrices was studied by determining its rendering in an operational context, finding out its mechanical resistance to flexion and compression at 7 days, its reaction to fire as well as its weight per unit of area and its thermal behaviour. The results show that in all cases, the waste is inert and does not undergo leaching. The generation process of the waste determines the foam’s microstructure in addition to its physical-chemical properties that directly affect building materials in which they are included, thus offering different ways in which they can be applied.

With the rapid development of MEMS (Micro-electro-mechanical Systems) fabrication technologies, manifolds microelectrodes with various structures and functions have been designed and fabricated for applications in biomedical research, diagnosis and treatment through electrical stimulation and electrophysiological signal recording. The flexible MEMS microelectrodes exhibit multi-aspect excellent characteristics beyond stiff microelectrodes based on silicon or SU-8, which comprising: lighter weight, smaller volume, better conforming to neural tissue and lower fabrication cost. In this paper, we mainly reviewed key technologies on flexible MEMS microelectrodes for neural interface in recent years, including: design and fabrication technology, flexible MEMS microelectrodes with fluidic channels and electrode-tissue interface modification technology for performance improvement. Furthermore, the future directions of flexible MEMS microelectrodes for neural interface were described including transparent and stretchable microelectrodes integrated with multi-aspect functions and next-generation electrode-tissue interface modifications facilitated electrode efficacy and safety during implantation. Finally, the combinations among micro fabrication techniques with biomedical engineering and nanotechnology represented by flexible MEMS microelectrodes for neural interface will open a new gate to human lives and understanding of the world.

In this paper, some mixed type bounds on the spectral radius $\rho(A\circ B)$ for the Hadamard product of two nonnegative matrices ($A$ and $B$) and the minimum eigenvalue $\tau(C\star D)$ of the Fan product of two $M$-matrices ($C$ and $D$) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several $M$-matrices is also presented: $$ \tau(A_{1}\star A_{2}\cdots\star A_{m})\geq \min_{1\leq i\leq n}\{\prod^{m}_{k=1}A_{k}(i,i)-\prod^{m}_{k=1}[A_{k}(i,i)^{P_{k}}-\tau(A_{k}^{(P_{k})})]^\frac{1}{P_{k}}\}, $$ where $A_{1},\ldots, A_{k}$ are $n\times n$ $M$-matrices and $P_{1},\ldots, P_{k}>0$ satisfy $\sum^{m}_{k=1}\frac{1}{P_{k}}\geq 1$. Some special cases of the above result and numerical examples show that this new bound improves some existing results.

The rapid, sensitive, and selective detection of pathogenic bacteria is of utmost importance in ensuring food safety and preventing the spread of infectious diseases. Here, we present a novel, reusable, and cost-effective impedimetric sensor based on a dual bacteria-imprinted polymer (DBIP) for the specific detection of Escherichia coli O157:H7 and Staphylococcus aureus. The DBIP sensor stands out with its remarkably short fabrication time of just 20 minutes, achieved through the efficient electro-polymerization of o-phenylenediamine monomer in the presence of dual bacterial templates, followed by in-situ template removal. The key structural feature of the DBIP sensor lies in the cavity-free imprinting sites, indicative of a thin layer of bacterial surface imprinting. This facilitates rapid rebinding of the target bacteria within a mere 15 minutes, while the sensing interface regenerates in just 10 minutes, enhancing the sensor's overall efficiency. A notable advantage of the DBIP sensor is its exceptional selectivity, capable of distinguishing the target bacteria from closely related bacterial strains, including different serotypes. Moreover, the sensor exhibits high sensitivity, showcasing a low detection limit of approximately 9 CFU mL-1. The sensor's reusability further enhances its cost-effectiveness, reducing the need for frequent sensor replacements. The practicality of the DBIP sensor was demonstrated in the analysis of real apple juice samples, yielding good recoveries. The integration of quick fabrication, high selectivity, rapid response, sensitivity, and reusability makes the DBIP sensor a promising solution for monitoring pathogenic bacteria, playing a crucial role in ensuring food safety and safeguarding public health.

In order to assess the human exposure risks from the release of contaminants from water pipes made of polyvinyl chloride (PVC), experiments were carried out by subjecting the PVC pipe material to burning and leaching conditions followed by analysis of the emission and leachate samples. The emissions of burning pipes were analyzed by both infrared spectrometry and gas chromatography-mass spectrometry (GC-MS). The emission results indicate the presence of chlorinated components including chlorine dioxide, methyl chloride, methylene chloride, allyl chloride, vinyl chloride, ethyl chloride, 1-chlorobutane, tetrachloroethylene, chlorobenzene, and hydrogen chloride were detected in the emissions of burning PVC pipes. Furthermore, the concentrations of benzene, 1,3-butadiene, methyl methacrylate, carbon monoxide, acrolein, and formaldehyde were found at levels capable of affecting human health adversely. The analysis of PVC pipe leachates using GC-MS shows that there are 40-60 tentatively identified compounds, mostly long-chain hydrocarbons such as tetradecane, hexadecane, octadecane, and docosane, were released when the burned PVC materials were soaked in deionized water for one week. Quantitative analysis shows that 2-butoxyethanol, 2-ethyl-1-hexanol, and diethyl phthalate were found in the burned PVC polymer at the average levels of 2.7, 14.0, and 3.1 micrograms per gram (g/g) of pipe material. This study has significant implications for understanding the benzene contamination of drinking water in the aftermath of wildfires that burned polymer pipes in California.

Purpose: To compare the efficacy and safety of trabeculectomy with a collagen matrix implant (Ologen®) versus trabeculectomy with mitomycin C (MMC) versus trabeculectomy with both Ologen® and MMC (OLO+MMC). Methods: This non-randomized study included 119 eyes of 101 patients with uncontrolled open-angle glaucoma who underwent trabeculectomy, either alone or combined with phacoemulsification. Data were initially registered following a standard surgical protocol and using an electronic database with structured fields. Patients were divided into three groups: 44 received trabeculectomy with adjunctive MMC (MMC group), 34 with Ologen® (OLO group), and 41 with both Ologen® and MMC (OLO+MMC group). The main outcome measures were the change in intraocular pressure (IOP), change in number of medications needed, complete success rate (defined as IOP≤20 mmHg and at least 20% IOP reduction without hypotensive medications), rate of complications, and rate of postoperative interventions. The follow-up period was 36 months.
 Results: IOP significantly decreased (p=0,01) in all groups across all study visits, decreasing from 19.8 ± 4.6 mmHg to 12.7 ± 4.2 mmHg in the MMC group, from 20.5 ± 4.7 mmHg to 13.9 ± 3.5 mmHg in the OLO group, and from 23.5 ± 6.1 mmHg to 13.1 ± 3.5 mmHg in the OLO+MMC group. After correcting for baseline IOP, only the first two postoperative visits (first week and first month) showed significantly greater IOP reduction in the OLO+MMC group. The number of hypotensive medications was significantly reduced from 3.1±0.6 to 0.56±1.1 in the MMC group, from 2.9±0.4 to 0.83±1.1 in the OLO group, and from 3.0±0.6 to 0.45±0.95 in OLO + MMC group, with no statistically significant differences among the groups (p=0,57). Complete success rates were 63,6% in the MMC group, 67,6% in the OLO group, and 80,5% in the OLO +MMC group, with no statistically significant differences among the groups (p=0,21). Suture release was significantly more frequent in the MMC group (86,1%) than in the OLO group (62,1%) and in the OLO + MMC group (45,9%; p=0,02). Bleb needling, with (33.3%; p=0.005) or without (66.7%; p=0.0001) 5-Fluorouracil injection (5-FU), was significantly more common in the MMC group. The highest complete-success rate (61%) was offered by the OLO+MMC group. Conclusion: The use of Ologen® and Mitomycin C provided similar surgical IOP reduction in glaucoma surgery compared with MMC or Ologen® either alone but significantly reduced the need for postoperative interventions.

The SK model proposed by Sherrington and Kirkpatrick is an important mean field model for spin glasses. The dependence structure of Hamiltonians of the SK model is considered in this paper. We have investigated the covariance matrix of Hamiltonians of the SK model, and establish a relationship between the rank of the corresponding covariance matrix and the dimension of the space spanned by the Hamiltonians. Finally, we also give an upper bound for the rank of the covariance matrix, which might be the best.

Pulmonary infections with Mycobacterium avium occur in susceptible individuals following exposure to the bacterium in the environment, where it often persists in biofilms. Many methods have been used to generate biofilms of M. avium, and it is unknown whether different approaches generate similar structures and cell phenotypes. To make a parallel comparison of in vitro biofilm ultrastructure, extracellular matrix (ECM) composition, and drug susceptibility of biofilm resident bacteria, we used two published methods to generate M. avium biofilms: four week incubation in M63 medium or 24 hour exposure to dithiothreitol (DTT). Scanning electron microscopy revealed differences in biofilm ultrastructure between the two methods, including variation in appearance of ECM materials and morphology of resident cells, while light microscopy and staining with calcofluor white indicated that both biofilms contained polysaccharides characteristic of cellulose. Measuring susceptibility of biofilms to degradation by enzymes suggested differences in structurally important ECM molecules, with DTT biofilms having important protein and, to a lesser extent, cellulose components, and M63 biofilms having moderate protein, cellulose, and DNA components. Both biofilms conferred resistance to the bactericidal effects of amikacin and clarithromycin, with resident cells being killed at >10-fold lower rates than planktonic cells at almost all concentrations. Though these comparisons indicate differences in biofilm responses by M. avium under differing conditions, they also suggest common features of biofilm formation including cellulose production and antimicrobial resistance.

We formulate a more straightforward, symmetry-based techniques in manually computing the determinant of any n×n matrix by revisiting Dodgson’s condensation method and strategically applying elementary row operations and the definition and properties of determinants. The result yields a more simplified mnemonical algorithm than the usual reduction by elementary row operations and co-factor expansion and with minimal terminal divisions performed compared to Dodgson’s internal divisions.

The orthogonal matrix with cube be symmetric is a common class of matrices with important properties. We pay attention to this kind of matrices. By using the close relationship between the eigenvalues of a matrix and the trace of its power, we obtain the algorithm for its all possible different eigenvalues and multiplicities. The calculation formula is expressed only by the trace of a matrix and its power, avoiding solving the characteristic polynomial. The method is simple and practical. Furthermore, a new essential characterization for the sum of orthogonal matrix pairs being orthogonal is given as well.

In this paper, we propose a quantitative definition of emergence from the density matrix framework as a state of knowledge of the system and its generalized probability formulation, in order to detect emergent properties. We propose the use of a descriptor based on the difference of von Neumann entropy, to calculate if subsystems of systems have inner correlations by defining emergent systems in terms of emergent information.

The extracellular matrix (ECM) plays a key role as both structural scaffold and regulator of cell signal transduction in tissues. In times of ECM assembly and turnover, cells upregulate assembly of the ECM protein, fibronectin (FN). FN is assembled by cells into viscoelastic fibrils that can bind upward of 40 distinct growth factors and cytokines. These fibrils play a key role in assembling a provisional ECM during embryonic development and wound healing. Fibril assembly is also often upregulated during disease states, including cancer and fibrotic diseases. FN fibrils have unique mechanical properties, which allow them to alter mechanotransduction signals sensed and relayed by cells. Binding of soluble growth factors to FN fibrils alters signal transduction from these proteins, while binding of other ECM proteins, including collagens, elastins, and proteoglycans, to FN fibrils facilitates the maturation and tissue specificity of the ECM. In this review, we will discuss the assembly of FN fibrils from individual FN molecules; the composition, structure, and mechanics of FN fibrils; the interaction of FN fibrils with other ECM proteins and growth factors; the role of FN in transmitting mechanobiology signaling events; and approaches for studying the mechanics of FN fibrils.

Numerical weather prediction is an initial-value problem, for determination of the initial conditions, there are many methods and one of the most classical methods is variational methods in three dimensions, or 3D-Var. In this approach, with a defined cost function proportional to the square of the distance between the analysis and both the background and the observations, one can obtain the analysis. In the cost function, the background and the observations are reshaped to vectors; within this step, the order of the background error covariance matrix and the observational error covariance matrix becomes huge, which is not convenient to one to obtain the analysis. In this paper, according to the matrix analysis approach, we put forward some possible improvements to the dimension-reduction algorithm of 3D-Var, so that provide some references for data assimilation.

Low-frequency peaks in the Raman spectra of amorphous poly (ether ketone) (PEEK) are investigated. An amorphous sample with zero crystallinity, as confirmed by WAXRD, was used in this study. In a previous study, two peaks were observed in the low-frequency Raman spectra of crystallized samples. One of the peaks at 135 cm-1, disappeared for the amorphous sample. Furthermore, the peak at 50 cm-1 was observed for the first time in the crystallized sample. The peak at 50 cm-1, similar to the peak at 135 cm-1, disappeared in the amorphous state, and its intensity increased with increasing crystallinity. The origins of the two peaks were both associated with the Ph-CO-Ph-type intermolecular vibrational modes in the simulation. It was suggested that the Ph-CO-Ph vibrational mode observed in the low-frequency region of PEEK was strongly in-fluenced by the intermolecular order.

Reactions of N‚N'-bis(3-methylpyridyl)oxalamide (L1), N,N’-bis(3-methylpyridyl)adipoamide (L2) and N,N’-bis(3-methylpyridyl)sebacoamide (L3) with tricarboxylic acids and Cu(II) salts afforded {[Cu(L1)(1,3,5-HBTC)]·H2O}n (1,3,5-H3BTC = 1,3,5-benzenetricarboxylic acid), 1, {[Cu1.5(L2)1.5(1,3,5-BTC)(H2O)2]·6.5H2O}n, 2, [Cu(L2)0.5(1,3,5-HBTB)]n (1,3,5-H3BTB = 1,3,5-tri(4-carboxyphenyl)benzene), 3, [Cu4(L3)(OH)2(1,3,5-BTC)2]n, 4, {[Cu3(L3)2(1,3,5-BTB)2]·2.5MeOH·2H2O}n, 5, and {[Cu3(L3)2(1,3,5-BTB)2 ]·DMF·2H2O}n, 6, which have been structurally characterized by using single crystal X-ray crystallography. Complexes 1 – 4 form a 2D layer with the {44.62}-sql topology, a 2D layer with the (4.62)2(42.62.82)-bex topology, a 3-fold interpenetrated 3D net with the (412.63)-pcu topology and a 3D framework with the (410.632.83)(42.6)2(43.63) topology, respectively, whereas 5 and 6 are 3D frameworks with the (63)2(64.82)(68.85.102) topology. Complex 5 shows a better iodine-adsorption factor of 290.0 mg g-1 at 60 oC for 360 minutes than the other ones, revealing that the flexibility of the spacer ligand governs the structural diversity and the adsorption capacity.

The conducted investigation encompassed the comprehensive integration of mechanical, envi-ronmental, chemical, and microstructural evaluations of a composite amalgamating sandy soil and a synthetic polymer at two distinct concentrations (2.5% and %) across multiple curing in-tervals (0, 1, 2, 4, 7, 15, 30, and 45 days). The studied soil originates from an environmentally sig-nificant protected area in Brazil. The implementation of mechanisms for soil improvement in the region must adhere to technical criteria without causing environmental harm. Direct shear testing was conducted, permeability was assessed, and microstructure analysis and XRD and XRF/EDX studies of both the soil and composites were conducted. It was observed that longer curing times yielded improved results in shear stress, friction angle, and cohesive intercept, with SP_5% exhibiting the highest values compared to the soil and SP_2.5%. Adding the polymeric so-lution to the soil contributed to cementation and cohesion gains in the substrate. Through mi-crostructural characterization, the polymer's role as a cementing agent for the grains is evident, forming a film on the grains and binding them together. Based on the analyses and studies con-ducted in the research, it can be concluded that there is technical feasibility for applying the pol-ymeric solution at both dosages in geotechnical projects.

Dental polymers are often advertised and selected for use in restorations based upon the flexural strength of prefabricated discs, which may not accurately reflect their performance in dental applications. The objectives of this study were, therefore, to determine whether the three-point bending (3PB) test for flexural strength would be predictive of the “crunch-the-crown” CTC test for the failure load. Three brands of polymers (Trilor, Juvora, and Pekkton) were fabricated into rectangular bars and fully contoured crowns (10 specimens of each polymer brand, 30 specimens of each shape). Bars were tested in 3PB to determine flexural strength, and crowns were CTC tested to determine failure load after luting to resin abutments. Statistical significance was evaluated by one-way ANOVA ( = 0.05) and Pearson’s correlation coefficient. The fracture mechanisms were characterized by scanning electron microscopy (SEM). There were significant differences (p < 0.05) in the mean crown failure loads (Trilor [7,033 N] > Juvora [5,217 N] > Pekkton [3,023 N]) and mean flexural strengths of the bars (Trilor [468 MPa] > Juvora [197 MPa] = Pekkton [192 MPa]). There were no correlations between flexural strength and failure load. The mode of crown fracture was different between the polymers, and included deformation (Juvora), ductile-to-brittle fracture (Pekkton), and a combination of cracks and deformation (Trilor). The flexural strength was not correlated with the corresponding crown failure load. Dental practitioners should not rely on the value of flexural strength obtained from the three-point bending test, as advertised from the manufacturer, to predict the performance of polymeric crowns.

The main purpose of this work is to contribute to understanding the mechanism of oxidation of the polymeric components of common disposable masks used during the COVID-19 pandemic to offer the chemical basis to predict their long-term behaviour under typical environmental conditions. Artificial ageing of representative mask layers under isothermal conditions (110℃) or accelerated photoageing showed that all the PP-made components underwent a fast oxidation process, following the typical hydrocarbon oxidation mechanism. In particular, yellowing and the melting temperature drop are early indicators of their diffusion-limited oxidation. Morphology changes also induced a loss of mechanical properties, observable as embrittlement of the fabric fibres. Results were validated through preliminary outdoor ageing of masks, which allows us to predict they will suffer fast and extensive oxidation only in the case of contemporary exposure to sunlight and relatively high environmental temperature, leading to their extensive breakdown in the form of microfiber fragments, i.e., microplastics.

: We report on a direct correlation between macroscale structural variations and the gas sorption capacities of an ion gel. Here, we chose 1-ethyl-3-methylimidazolium bis(trifluoromethyl sulfonyl)imide ([Emim][TF2N]) and poly(vinylidene fluoride)-co-hexafluoropropylene (PVDF-HFP) as the ionic liquid and host polymer, respectively. The CO2 sorption in the thin films of IL-polymer was measured by the gravimetric method. The results of our experiment show that the trend of CO2 uptake of these mixtures is non-linearly correlated with the content of IL. Here we highlight the variation in the molecular structure of the polymers is the main reason behind the observed trend. The presented data suggest the possibility of using the composition of mixtures containing IL and polymers to realize a synergistic gain for gas sorption in these mixtures.

This paper is focused on understanding multiscale modelling to obtain a bridge among different time and length scales of simulation techniques. These techniques are vital as it holds the potential to understand and predict the capabilities of polymer nanocomposites (PNCs). However, an appropriate approach in controlling the interfacial interaction between nanoparticle and polymer in nanocomposites structure is still needed to develop. In this review, an initial brief introduction to various trending simulation techniques has been discussed at all three levels of scale (nm, μm, mm). Later, descriptive study on fundamental issues such as thermodynamics, kinetics, mechanical properties, and morphology has been studied deeply. The multiscale modeling bridges the gaps of simulation between the different scales of models from molecular to mesoscale levels working over the broad range of length and timescale. Through the sequential, adaptive, and concurrent approaches, we can develop a system that may comprehend multiscale mode modeling adaptive resolution approach has recently added approach the molecule of the subject can shift their position freely in the domain and through this approach and studied the Brownian motion. Co-The co-current coach is also termed as handshaking path and it is linked aiming at different scale models. Covering the rigid techniques smoothly and linking them at different scales helps in normalizing the statistical behaviour.

The coexistence of ferroelectric and magnetic order parameters in multiferroic materials opens up a host of new collective properties. In particular, the magnetoelectric (ME) effect namely the induction of electric polarization by a magnetic field or magnetization by an electric field has been widely studied in multiferroics. PVDF is a ferroelectric polymer that has attracted considerable research interest for sensing applications. Compared to traditional ceramic composites, the polymer-ceramic nanocomposites offer inherent advantages, including easy processing, mechanical flexibility and the ability to be moulded into complicated configurations for advanced devices with reduced volume and weight. Additionally, polymer composites generally exhibit superior ME coefficients, attributable to the improved displacement transfer capability of the flexible polymer matrix. In this report, free-standing, flexible and lightweight polymer–ceramic nanocomposite thin films with a fixed weight percentage of ferromagnetic CoFe2O4 nanoparticles have been fabricated using a solution casting technique. The structural, microstructural, and electrical properties of the composite have been characterized by standard experimental techniques. The structural and chemical analyses prove a homogeneous dispersion of the fillers in the microstructure of the composite. The electrical response investigated by impedance spectroscopy reveals the contributions of grains and grain boundaries to the whole impedance of the composites. The ac conductivity as a function of frequency obeys Jonscher’s power law. The improved magnetoelectric properties suggest promising applications in multifunctional devices, including field sensor applications.

A major obstacle faced by nanopore-based polymer sequencing and analysis is the high speed of translocation of an analyte (nucleotide, DNA, amino acid (AA), peptide) through the pore; the rate currently exceeds available detector bandwidth. Except for one method that uses an enzyme ratchet to sequence DNA, attempts to resolve the problem satisfactorily have been largely unsuccessful. Here a counterintuitive method based on reversing the pore voltage, and, with some analytes, increasing their mobility, is described. A simplified Fokker-Planck model shows a significant increase in translocation times for single nucleotides and AAs (up from ~10 ns to ~1 ms). More realistic simulations show that with a bi-level positive-negative pore voltage profile all four nucleotides in DNA (dAMP, dTMP, dCMP, and dGMP) and the 20 proteinogenic amino acids can be trapped inside the pore long enough for detection with bandwidths of ~1-10 Khz.

Two region asymmetric polymers PR2F and PR1F with three repeat units of A-D-A, π-D-A, and π-D-π along the polymer backbone were attained by polymerizing different fluorinated benzothiadiazole-thiophene units, FBT-T and 2FBT-T units (A–π), with benzodithiophene unit (D), respectively. Here, the new region asymmetric polymers were in contrast to the traditional polymers featuring a D–A or D–π–A–π backbone. Both the region asymmetric polymers showed a low lying of HOMO energy level in relation to that of the PC61BM acceptor and then obtained the high open-circuit voltage of ~1 V in both PR2F and PR1F devices. Bulk-heterojunction devices based on PR2F with difluorinated BT exhibited an appreciable power conversion efficiency (PCE) of 4.73% due to the relatively high and balanced charge carrier mobilities, while the mono-fluorinated BT polymer PR1F-based devices gave a lower PCE of 2.92%. These results indicate that the region asymmetric conjugated polymer is a promising class of materials for polymer solar cell applications, and it is significant to further understand the influence of polymer structure on optoelectronic properties.

Polymeric drag reducers have been developed over many years due to the great number of practical applications. In all of them, the molecular stability is an essential requirement. Usually, polymers break down under turbulent flows, which causes a decrease in their efficiency as drag reducers. Besides that, some specific applications, in agro and biomedical fields, impose a specific requirement that must be fulfilled, which is the use of non-toxic materials. A suitable stable material that is elected to accomplish this necessity is the mucilage of aloe vera, which is a bio-polymer that can be used as an alternative to the synthetic ones. Here, we investigate the role played by the aging of aloe vera on its capacity to reduce drag. The results obtained by ¹H nuclear magnetic resonance indicate that the compositions of young and mature leaves of aloe vera are different and such a difference plays an important role on their efficiency as drag reducers. Tests were performed to analyse the drag reduction in a rotating apparatus and in a pipeline system and the efficiencies of leaves of different ages were compared to their composition. The main conclusion of these experiments is that the young mucilage samples, which are richer in complex polysaccharides and exhibit lower acid contents, are more efficient drag reducers.

The synthesis these past few years of novel organic molecules that spontaneously self-assemble into a large variety of molecular architecture, particularly generating organogels, has opened up new horizons for preparing functional materials. Here, we present an original preparation path of such materials through the making of hybrid gels of these molecules together with covalent polymers. Three types of systems are described: i) intermingled gels where a polymer gel and an organogel pervade one another; ii) encapsulation of self-assembled filaments in polymer fibrils, which provides a system with unusual magnetic properties; iii) the reverse situation where self-assembled nanotubes sheathe polymer fibrils. Here two covalent polymers are considered: a neutral polymer, namely stereoregular polystyrene (isotactic or syndiotactic), and a semi-conducting polymer, P3BT. In the latter case, semi-conducting nanowires are obtained.

The global polyvinyldene flouride market is estimated to reach $937,278.5 thousand by 2019, therefore to develop new membranes and gain pioneering ideas, which could create innovative business opportunities, a fundamental knowledge about membrane properties fabricated from recent commercially available PVDF polymers is highly mandatory. In this study, we successfully prepared nine non-woven supported PVDF membranes using a phase inversion precipitation method starting from a 15 wt% PVDF solution in N-methyl-2-pyrrolidone. Various membrane morphologies were obtained by using (1) PVDF polymers with diverse molecular weight in a range from 300.000 Da to 700.000 Da and (2) different temperatures of the coagulation bath (20, 40, and 60 ±2°C) used for the films precipitation. Environmental Scanning Electron Microscope (ESEM) was used for surface and cross-section morphologies characterization. Atomic Force Microscope (AFM) was employed to investigate surface roughness, while Contact Angle (CA) instrument was used for membranes wettability studies. Fourier Transform Infrared Spectroscopy (FTIR) results show that the fabricated membranes are formed by a mixture of TGTG’ chains in α phase crystalline domains and all-TTTT trans planar zigzag chains characteristic to β phase. Moreover, generated results indicate that the phases content and membrane morphologies depend on the polymer molecular weight and conditions used for the membranes preparation. The diversity of fabricated membranes could be applied by the End User Industries for different applications.

The review is devoted to the physical, chemical and technological aspects of the breath-figures self-assembly process. Main stages of the process and the impact of the polymer architecture and physical parameters of the breath-figures self-assembly on the eventual pattern are covered. The review is focused on the hierarchy of spatial and temporal scales inherent for the breath-figures self-assembly. Multi-scale patterns arising from the process are addressed. The characteristic spatial lateral scales of patterns vary from nanometers to dozens of micrometers. The temporal scales of the process span from micro-seconds to seconds. The qualitative analysis performed in the paper demonstrates that the process is mainly governed by the interfacial phenomena, whereas the impact of inertia and gravity is negligible. Characterization and applications of polymer films manufactured with breath-figures self-assembly are discussed.

Carbon nanotube (CNT) yarns are fiber-like materials that exhibit excellent mechanical, electrical and thermal properties. More importantly, they exhibit a piezoresistive response that can be tapped for sensing purposes. The objective of this study is to determine experimentally the piezoresistive response of CNT yarns that are embedded in a polymeric medium while subjected to either compression or tension, and compare it with that of the free or unconstrained CNT yarns. The rationale for this study is the need to know the response of the CNT yarn while in a medium, which provides a lateral constraint to the CNT yarn thus mimicking the response of integrated CNT yarn sensors. The experimental program will include the fabrication of samples and their electromechanical characterization. The CNT yarns are integrated in polymeric beams and subjected to four-point bending, allowing the determination of their response under tension and compression. The electrical resistance data from an Inductance-Capacitance-Resistance (LCR) device is used with the data acquired from the mechanical testing system to determine the piezoresistive response of the CNT yarns. This data and information will be used for future modeling efforts and to study the phenomena that occur when CNT yarns are integrated in polymeric and composite materials and structures.

We investigate the existence and representation of the generalized core-EP inverse of some triangular matrices over a Banach algebra. Further, the general representations of the generalized core-EP inverse of a triangular matrix over a $C^*$-algebra are presented. As applications, the generalized core-EP inverses of some block operator matrices over Hilbert spaces are given.

Matrices and their inverses allow accurate calculations to be produced quickly and compactly and can be used to control any process represented by a system of equations. Singular matrices require extensive workarounds (costing time and money) to solve these systems of equations because they have no inverse. Finding their inverse involves division by zero. Nevertheless, recently a new number set called semi-structured complex numbers was developed to enable division by zero in algebraic equations. The aim of this research was to demonstrate that the inverse of a singular matrix can be found using semi-structured complex numbers. This research reveals (1) Singular matrices and their inverses can be used to find a unique solution to a pair of simultaneous equations that appear to have infinitely many solutions or appear to have no solution; (2) Singular matrices map coordinates in projective space to coordinates in Euclidean space and their inverse maps coordinates in Euclidean space to coordinates in projective space; (3) the inverse of a singular matrix proves that parallel lines in Euclidean space do not intersect but in projective space intersect at a “point at infinity” and (4) collinear lines that intersect at infinitely many points in Euclidean space only intersect at one point in projective space.

Empirical equations representing, interpolating and smoothing groups of measurement results by regression methods are in widespread use in metrology and other fields of science and engineering. Standard equations for the propagation of measurement uncertainties to values computed from such equations are available but suffer from a lack of general acceptance and are only infrequently applied in practice. One reason for the slow uptake is the lack of clear methods to account for systematic error. In this paper, uncertainty propagation equations in terms of covariance matrices are generalized to allow for systematic errors in least-squares regression, and effects of the resulting uncertainties are investigated analytically. A stochastic ensemble model of systematic error is proposed for the computation of the non-diagonal elements of the weight matrix of the Generalized Least-Squares method (GLS) from the measurement uncertainty. A GLS projector formalism is described which separates the effects of measurement scatter on values calculated by the equation from those on the related “residuals”, i.e., the residual errors in the fitted data. The same projectors act similarly on the associated uncertainties and covariance matrices and permit the effects of systematic errors on the simulation covariance to be quantified. It is demonstrated that, in order to include systematic errors in the uncertainty estimates of GLS, covariance matrices may be substituted by novel, specifically defined dispersion matrices that are not specified yet by the GUM[1]. Systematic measurement errors may be estimated from various sources; a particularly easy way suggested here involves analyzing the structure in the regression residuals. It is demonstrated that GLS projectors exhibit inherent features of “error blindness” also with respect to systematic errors. [1] GUM: Guide to the Expression of Uncertainty in Measurement, http://www.bipm.org/en/publications/guides

In this work, we offer a novel and accurate method in order to find the solution of the linear differential equations over the intervals [0, 1) based on the generalization of Legendre wavelets. The mechanism is still upon workable implementation of the operational matrix of integration and its derivatives. This method reduces the problems into algebraic equations via the properties of generalized Legendre wavelet (GLW) together with the operational matrix of integration. The function approximation has been picked out in such a way so as to enumerate the connection coefficients in an facile manner. The proposed numerical technique, based on the GLW, has been examined on three linear problems as a consequence of this investigation. The outcomes have shown that this method, as opposed to some other existing numerical and analytical methods, is a very useful and advantageous for tackling such problems.

The extracellular matrix (ECM) is a ubiquitous member of the body and is key to the maintenance of tissues and organs integrity. Initially thought to be a by-stander in many cellular processes, the extracellular matrix has been shown to have diverse components that regulate and activate many cellular processes and ultimately influence cell phenotype. Importantly, the ECM composition, architecture, and stiffness/elasticity influence cellular phenotypes. Under normal conditions and during development, the synthesized ECM is constantly undergoing degradation and remodeling processes via the action of matrix proteases that maintain tissue homeostasis. In many pathological conditions including fibrosis and cancer, the ECM synthesis, remodeling, and degradation is dysregulated causing its integrity to be altered. Both physical and chemical cues from the ECM are sensed via receptors including integrins and play key roles in driving cellular proliferation and differentiation and in various disease progression such as cancers. Advances in ‘omics’ technologies have seen an increase in studies focussing on bi-directional cell-matrix interactions and here we highlight emerging knowledge on the role played by the ECM during normal development and in pathological conditions. This review summarizes current ECM-targeted-therapies that can modify tumor ECM to overcome drug resistance and better cancer treatment.

Background: This study attempted to construct musculoskeletal JEM using KWCS data and use it to evaluate the burden of these disorders in Korean workers. Methods: This study was conducted using data from the second to the sixth KWCS, and a total of 210,500 people were included. The jobs of the subjects were reclassified based on the unit groups of the 7th Korean Standard Classification of Occupation (KSCO). The intensity of exposure to work-related risk factors for musculoskeletal disorders was classified into ‘high’, ‘moderate’, and ‘low’ for the body segments involving the ‘upper extremities and neck’, ‘lower back’, and ‘lower extremities’. Results: The time of exposure was longest in the standing posture and repetitive hand and arm movements. An analysis of the intensity of exposure by body segments revealed that the highest intensity of exposure was to the upper extremities. For the upper extremities and neck, and the lower back, there was a exposure-response relationship in the association between intensity of exposure and musculoskeletal symptoms. However, for the lower extremities, there was a exposure-response relationship only at high exposure. Conclusion: In this study, a JEM for work-related risk factors for musculoskeletal disorders was constructed for the first time in Korea. The intensity of exposure to musculoskeletal risk factors was estimated for each occupation. The JEM constructed in this study is expected to have high applicability for assessing the risk of musculoskeletal disorders for each job with respect to the upper extremities and neck, and lower back.

In this study, Al-Al4C3 compounds were manufactured by mechanical milling followed by heat treatment. To analyze the microstructural evolution, the composites were sintered at 550°C during different sintering times of 2, 4 and 6 hours. The mechanical results suggest that dislocation density and crystallite size primary contribute to hardening before the sintering process, with a minimal contribution from particle dispersion in this condition. The compound exhibited a significant 75% increase in hardness after 2 hours of sintering, primarily attributed to the nucleation and growth of Al4C3 nanorods. The HRTEM analysis, combined with ge-ometric phase analysis (GPA) at and near the Al-Al4C3 interface of the nanorods, revealed strain field distributions primarily associated with partial screw dislocations and the presence of closely spaced dislocation dipoles. These findings are consistent with the microstructural parameters determined from X-ray diffraction pattern analysis using the convolutional multi-ple whole profile (CMWP) method. This analysis showed that the predominant dislocation character is primarily of the screw type, with the dislocation dipoles being closely correlated. Based on these results, it is suggested that samples with a lower weight percentage of rein-forcement and longer sintering times may experience reduced brittleness in Al/Al4C3 compo-sites. Strengthening contributions were calculated using the Langford–Cohen and Taylor equations.

Ewing sarcoma (ES) is an aggressive bone and soft-tissue pediatric cancer. High vitronectin (VN) expression has been associated with poor prognosis in other cancers, and we aimed to determine the utility of this extracellular matrix glycoprotein as a biomarker of aggressiveness in ES. Silk-fibroin plus gelatin-tyramine hydrogels (HGs) were fabricated with and without cross-linked VN and cultivated with A673 and PDX73 ES cell lines for two and three weeks. VN secretion to culture media was assessed using ELISA. Morphometric analysis was applied for phenotypic characterization. VN release to culture media was higher in 3D-models than in monolayer cultures, and intracellular, intercellular and pericluster presence was also observed. A673-HGs showed lower density of clusters but a proportion of larger clusters than PDX73-HGs, which presented low cluster circularity. The cluster density of A673-HGs without added VN was higher than with added VN, and slightly lower in the case of PDX73-HGs. Furthermore, a culture time of three weeks provided no benefits in cluster growth compared to two weeks, especially in A673 -HGs. These advances in 3D modeling and digital quantification pave the way for future studies in ES and other cancers to deepen understanding about intra- and intercellular heterogeneity and anti-adhesion VN therapies.

Uterine tube extracellular matrix is a key component that regulates tubal tissue physiology, and it has a region-specific structural distribution, which are directly associated to their functions. Considering this, application of biological matrices in culture systems is an interesting strategy to develop biomimetic tubal microenvironments and enhance their complexity. However, there are no established protocols to produce tubal biological matrices that consider the organ morphophysiology for such applications. Therefore, this study aimed to establish region-specific protocols to obtain decellularized scaffolds derived from porcine infundibulum, ampulla, and isthmus to provide suitable sources of biomaterials for tissue-engineering approaches. Porcine uterine tubes were decellularized in solutions of 0.1% SDS and 0.5% Triton X-100. Decellularization efficiency was evaluated by DAPI staining and DNA quantification. We analyzed ECM composition and structure by optical and scanning electronic microscopy, FTIR and Raman spectroscopy. DNA and DAPI assays validated the decellularization, presenting significative reduction of cellular content. Structural and spectroscopy analyses revealed that produced scaffolds remained well structured and with ECM composition preserved. YS and HEK293 cells were used to attest cytocompatibility, allowing cell survival and successful interaction with the scaffolds. These results suggest that such matrices are applicable for future biotechnological approaches in the reproductive field.

Several Lung diseases can result in lung damage structural changes, with lung transplantation as a only therapeutic option when the disease reaches an advanced progression, unfortunately, the success of lung transplantation is limited. In this context, lung bioengineering is considered a potential therapeutic alternative and the current approach is based on the use of the natural extracellular matrix (ECM) of the decellularized lung. The use of undifferentiated cells to seed an ECM can be a more practical strategy for lung bioengineering but the sterilization of the organ for this recellularization process is still a challenge. In this sense, Low-Level Laser Therapy (LLLT) can emerge as a potential treatment alternative. Therefore, the objective of this study was to verify if LLLT, can optimize lung recelularization with mesenchymal stem cells by cytokine modulation. For this, we decellularized lungs from C57BL/6 mice perfusing SDS 1% via pulmonary artery, sterilized with LLL (660nm, 100mW, 30s). Whole lung scaffolds were recellularized: (1) Recellularized Lung (2) Recellularized Lung + LLLT. Mesenchymal stem cells derived from human tooth pulp (DPSc) were seeded into lungs and incubated for 24 hours at 37ºC, 5% CO₂, in a bioreactor-like conditions, maintaining CPAP at 20cmH2O, 90% O2, and LLL at wavelength of 808nm, 100mW, 30s. Culture medium were analyzed at 24 hours. H&amp;E, immunostaining, SEM and ELISA assay were performed. We produced viable biological scaffolds absent of DNA content, preserving glycosaminoglycans and collagen I, III and IV, fibronectin, laminin and elastin and lung structure (SEM). The levels of IL-6 and IL-8 were stable during the 24 hours of culture. IFN-γ levels showed significant difference in the DPSc and DPSc+LLLT group in the 24-hour evaluation. The levels of IL-10 decreased after LLLT. These findings highlight LLLT's role in cytokine regulation and contamination prevention during lung recellularization with mesenchymal stem cells. Overall, these results demonstrated that LLLT's modulated cytokine levels and could prevent contamination during the lung recellularization process with mesenchymal stem cells, offering promise for enhanced therapeutic strategies in lung bioengineering.

The release of the active substance from the matrix modified-release tablets based on Kollidon®SR and chitosan depends on its solubility in the dissolution medium and on the composition of the matrix-forming polymers. The study is based on new oral matrix tablets based on Kollidon®SR and chitosan, formulated to optimize the low oral bioavailability of chlorzoxazone, a non-steroidal anti-inflammatory drug, a class II Biopharmaceutical Classification System. Nine types of chlorzoxazone matrix tablets were obtained using the direct compression method, and their combination at 1:1, 1:2, 1:3 chlorzoxazone/ excipients, 20%-40% (w/w) Kollidon®SR, 3-7% (w/w) chitosan and the auxiliary substances were formulated in constant concentrations. Pharmaco-technical characterization included the analysis of flowability and compressibility properties (flow time, friction coefficient, angle of repose, Hausner ratio, Carr Index), and of pharmaco-chemical characteristics (mass and dose uniformity, thickness, diameter, mechanical strength, Friability, degree of softening, in vitro release profile) of the tablets. Based on the initial evaluation of the pharmaco-technical analysis, pharmaco-chemical characteristics, and in vitro release profile, only three matrix tablet formulations (F1b, F2b, and F3b) were further tested. They were evaluated through Fourier-transform infrared spectrometry, X-ray Diffraction, thermogravimetry, differential scanning calorimetry, and in vitro dissolution tests. The three formulations were comparatively studied regarding the release kinetics of active substances using in vitro release testing. The results were analyzed by fitting into four representative mathematical models for the modified release oral formulations. In vitro kinetic study reveals a complex mechanism of release occurring in the first (0 - 2 hours) and second (2.0 hours – 36 hours) steps of drug release. Two factors have been calculated to assess the release profile of chlorzoxazone: f1 - the similarity factor and f2 - the factor difference. The results have shown that both Kollidon®SR and chitosan may be used as matrix-forming agents when combined with chlorzoxazone. In vitro dissolution tests revealed the F2b sample, data suggesting a faster drug release. The three formulations showed optimum pharmaco-technical properties and in vitro kinetic study, and they had tremendous potential to be used in oral pharmaceutical products for the controlled delivery of chlorzoxazone.

Abstract: Chemical burns are one of the most dangerous and aggressive types of burns as they can cause significant tissue damage, leading to pain, inflammation, necrosis, and scarring. We present a burn case report associated with the use of Acellular Dermal Matrix (MatriDerm® MedSkin Solution Dr. Suwelack AG, Billerbeck, Germany) for the reconstruction of a Hallux after the patient was mistakenly administered intramuscular Nitric Acid at another institution. The patient presented with a third degree burn that compromised the medial aspect of the hallux’s skin, the distal phalanx and nail bed. Early debridement was performed, and Negative Pressure Wound Therapy (NPWT VAC, 3M, US) was used to preserve and promote tissue viability. Eight days later, the patient was taken to the OR, and Acellular Dermal Matrix and split-thickness skin graft were used to reconstruct her right hallux’s defect. The patient achieved adequate clinical evolution and was discharged with complete reconstruction of the burned area. Acellular Dermal Matrix proved to be an important and viable option for reconstructive surgery after a chemical burn, and further studies are warranted to ensure its routine usage in this kind of lesions. Keywords: chemical burn, acellular matrix, hallux reconstruction, NPWT

Fibrosis is a prevalent and detrimental condition associated with various diseases with a high impact on global morbidity and mortality rates. Despite its diverse causes and affected organs, common underlying mechanisms drive the development and progression of the disease. These mechanisms include an exaggerated inflammatory response, excessive activation of fibroblasts, and abnormal tissue remodeling following severe or repetitive tissue injury. Although significant advancements have been achieved to enhance our understanding of fibrosis, there is still a gap between identifying potential antifibrotic targets and successfully translating them into effective clinical interventions. Novel approaches that target specific cellular and molecular processes involved in fibrosis hold promise for reducing the pathological consequences of the disease. Understanding the pathogenesis and clinical implications of fibrotic diseases is crucial for developing effective therapeutic strategies and improving patient outcomes. In this review, we introduce the concept of fibrosis, discuss the mechanisms by which it arises, and explore existing and emerging therapeutic approaches in development.

Background: During placental formation, cytotrophoblasts (CTBs) fuse into multinucleate, microvilli-coated syncytiotrophoblasts (STBs), which contact maternal blood, mediating nutrient, metabolite, and gas exchange between mother and fetus, and providing a barrier against fetal infection. Trophoblasts remodel the surrounding extracellular matrix through the secretion of matrix metalloproteinases (MMPs). Maternal obesity and diabetes mellitus can negatively impact fetal development and may impair trophoblast function. We sought to model the impact of metabolic stress on STB function by examining MMP and hormone secretion. Methods: The BeWo CTB cell line was syncytialized to STB-like cells with forskolin. Cell morphology was examined by electron microscopy and immunofluorescence; phenotype was further assessed by ELISA and RT-qPCR. STBs were exposed to a metabolic stress cocktail (MetaC: 30 mM glucose, 10 nM insulin, and 0.1 mM palmitic acid). Results: BeWo syncytialization was demonstrated by increased secretion of HCGβ and progesterone, elevated syncytin gene expression (ERVW-1 and ERVFRD-1), loss of tight junctions, and increased surface microvilli. MetaC suppressed HCGβ and progesterone and altered both MMP-9 and MMP-2. Conclusions: Metabolic stress modeling diabetes and obesity altered BeWo STB hormone and MMP production in vitro. These results compel further study into the potential impact of metabolic stress on trophoblast formation and function.

Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous PT-symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum-mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric and seismoelectric waves. Based on the symmetry properties of the operator matrix in this equation, we derive unified reciprocity theorems for wave fields in 3D arbitrary inhomogeneous media and 3D inhomogeneous media with PT-symmetry. These theorems form the basis for deriving unified wave field representations and relations between reflection and transmission responses in such media. Among the potential applications are interferometric Green’s matrix retrieval and Marchenko-type Green’s matrix retrieval in PT-symmetric materials.

Impaired wound healing is a significant financial and medical burden. The synthesis and deposition of extracellular matrix (ECM) in a new wound is a dynamic process that is constantly changing and adapting to the biochemical and biomechanical signaling from the extracellular microenvironments of the wound. This drives either a regenerative or fibrotic and scar-forming healing outcome. Disruptions in ECM deposition, structure, and composition lead to impaired healing in diseased states, such as in diabetes. Valid measures of the principal determinants of successful ECM deposition include bacterial contamination, tissue perfusion, and mechanical injury and strain. These measures are used by wound-care providers to intervene upon the healing wound to steer healing toward a more functional phenotype with improved structural integrity and healing outcomes and to prevent adverse wound developments.In this review, we discuss bioengineering advances in non-invasive detection of biologic and physiologic factors of the healing wound, visualizing and modeling the ECM, and computational tools to efficiently evaluate the complex data acquired from the wounds to prognosticate healing outcomes and intervene effectively. We focus on bioelectronics and biologic interfaces of the sensors and actuators for real time biosensing and actuation. We also discuss high-resolution, advanced imaging techniques, which go beyond traditional confocal and fluorescence microscopy to visualize microscopic details of the composition of the matrix, linearity of collagen, and live tracking of components within the ECM. Computational modeling of the matrix, including partial differential equation datasets as well as machine learning models that can serve as powerful tools for physicians to guide their decision-making process are discussed.

Bonchev and Trinajstic defined two distance based entropy measures to measure the molecular branching of molecular graphs in 1977 [Information theory, distance matrix, and molecular branching, J. Chem. Phys., 38 (1977), 4517–4533]. In this paper we use these entropy measures which are based on distance matrices of graphs. The first one is based on distribution of distances in distance matrix and the second one is based on distribution of distances in upper triangular submatrix. We obtain the two entropy measures of paths, stars, complete graphs, cycles and complete bipartite graphs. Finally we obtain the minimal trees with respect to these entropy measures with fixed diameter.

The unexploited unification of general relativity and quantum mechanics (QM) prevents the proper understanding of the micro- and macroscopic world. Here we put forward a mathematical approach that introduces the problem in terms of negative curvature manifolds. We suggest that the oscillatory dynamics described by wave functions might take place on hyperbolic continuous manifolds, standing for the counterpart of QM’s Hilbert spaces. We describe how the tenets of QM, such as the observable A, the autostates ψa and the Schrodinger equation for the temporal evolution of states, might work very well on a Poincaré disk equipped with rotational groups. This curvature-based approach to QM, combined with the noncommutativity formulated in the language of gyrovectors, leads to a mathematical framework that might be useful in the investigation of relativity/QM relationships. Furthermore, we introduce a topological theorem, termed the punctured balloon theorem (PBT), which states that an orientable genus-1 surface cannot encompass disjoint points. PBT suggests that hyperbolic QM manifolds must be of genus ≥ 1 before measuring and genus zero after measuring. We discuss the implications of PBT in gauge theories and in the physics of the black holes.

The aim of this paper is to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. As a crucial part, alternative approach for generalized quaternion matrix with elliptic number entries are developed.

Full Matrix Capture is a multi-channel data acquisition method which enables flexible, high resolution imaging using ultrasound arrays. However, the measurement time and data volume are increased considerably. Both of these costs can be circumvented via compressed sensing, which exploits prior knowledge of the underlying model and its sparsity to reduce the amount of data needed to produce a high resolution image. In order to design compression matrices that are physically realizable without sophisticated hardware constraints, structured subsampling patterns are designed and evaluated in this work. The design is based on the analysis of the Cramér-Rao Bound of a single scatterer in a homogeneous, isotropic medium. A numerical comparison of the point spread functions obtained with different compression matrices and the Fast Iterative Shrinkage/Thresholding Algorithm shows that the best performance is achieved when each transmit event can use a different subset of receiving elements and each receiving element uses a different section of the echo signal spectrum. Such a design has the advantage of outperforming other structured patterns to the extent that suboptimal selection matrices provide a good performance and can be efficiently computed with greedy approaches.

As the coproduct of steelmaking, steelmaking slag, volumetrically expansive-prone without treatment, has been satisfactorily used as an aggregate base course material in highway construction. Although numerous technical reports and papers have revealed that steel slag aggreged using in rigid matrixes, the end product, paving block, non-structural concrete, for example, possesses superb strength and durability properties, the application of steel slag aggregate as a concrete aggregate is currently prohibited in highway construction. Naturally, researchers explore the practicality of use of steel slag, how to connect the laboratory experiment results to the end-product behavior, and further convert the research results into real construction? For all nontraditional or secondary materials utilization, the procedure of laboratory material examination, lab and field trial test are critical. To generalize the utilization, usability criteria establishment is necessary. This paper tries to use step-by-step method and plain language to explain how the volumetrically expansion can be simulated in lab testing apparatus, and based on the model, the mathematical deduction can result in a numerical usability criterion for steel slag use as a coarse aggregate in concrete (a rigid material). Therefore the paper is composed four main parts, laboratory test methods to examine the expansion force resulted from steel slag; converting the measured expansion force in a given volume of mass aggregate to the expansion (body) force of a single particle; modeling of slag and end material disruption; and a usability criterion from numerical deduction for the use of expansive-prone coarse slag in concrete or other rigid matrices. The paper provides the solutions to answer the above questions. Through the mathematical and mechanical modeling, provides the potential criteria that could result in specifications and guidance establishment for broad volumetric expansive-prone slags.

This study was to investigate and assess salivary biomarkers as a means of diagnosing periodontitis. A total of 121 subjects were included: 28 periodontally healthy subjects, 24 with stage I, 24 with stage II, 23 with stage III, and 22 with stage IV periodontitis. Salivary proteins including active matrix metalloproteinase-8 (MMP-8), pro-MMP-8, total MMP-8, C-reactive protein, secretory immunoglobulin A and planktonic bacteria including Aggregatibacter actinomycetemcomitans, Porphyromonas gingivalis, Tannerella forsythia, Treponema denticola, Fusobacterium nucleatum, Prevotella intermedia, Porphyromonas nigrescens, Parvimonas micra, Campylobacter rectus, Eubacterium nodatum, Eikenella corrodens, Streptococcus mitis, Streptococcus mutans, Staphylococcus aureus, Enterococcus faecalis, and Actinomyces viscosus were measured from salivary samples. The performance of the diagnostic models was assessed by receiver operating characteristics (ROC) and area under the ROC curve (AUC) analysis. The diagnostic models were constructed based on the subjects’ proteins and/or microbial profiles, resulting in two potential diagnosis models, which achieved better diagnostic powers with an AUC value &gt; 0.750 for the diagnosis of stage II, III, and IV periodontitis (Model PC-I; AUC: 0.796, sensitivity: 0.754, specificity: 0.712) and for the diagnosis of stage III and IV periodontitis (Model PC-II; AUC: 0.796, sensitivity: 0.756, specificity: 0.868). This study can contribute to screening for periodontitis based on salivary biomarkers.

BACKGROUND Relaxin (RLX), a hormone-like molecule with pleiotropic effects, has been found to reduce matrix deposition and mediate collagen degradation in animal models of chronic liver injuries and might be considered as an adjuvant therapeutic agent for progressive liver diseases. AIMS In the present study, we evaluated whether RLX affects the development of liver fibrosis in an experimental mouse model of NASH in C57BL6 male mice fed with a methionine-choline deficient diet (MCD). Methods Mice were treated per os as we intended to assess the enteric absorption and bioavailability of orally administered RLX (RLX purified from pig ovaries, IBSA SA, Lugano, Switzerland). Mice were fed the MCD diet for 6 weeks. After the initial 3 weeks, one group received drinking water supplemented with RLX (25 mcg/ml) whereas the other continued to receive regular water. A third group of mice fed a regular diet served as control. After 3 additional weeks mice were anesthetized and sacrificed. Results A significant, reduced expression of the pro-inflammatory cytokines TNF-α and of relevant markers of active fibrogenesis and extracellular matrix deposition, Col1A1 and α-SMA, was observed in mice treated with RLX vs controls. RLX also induced a significant decrease of TIMP1 and an increase of both MMP 2 and 9 when evaluated by zymographic analysis in liver extracts. Conclusions Although preliminary pharmacokinetics experiments showed barely detectable amounts of RLX in the blood of mice treated per os, these data support the absorption of orally administered RLX and confirm its potential therapeutic use in the management of liver fibrosis.

Autogenous demineralized dentin matrix (ADDM), derived from human extracted tooth, is commonly used as a bone-graft substitute to reconstruct alveolar defects when placing dental implants. The purpose of this retrospective study is to examine efficacy of ADDM in terms of surgical complications and marginal bone resorption by analyzing the medical records and radiographs of patients who received ADDM graft from 2008 to 2011 in our institute. Occurrence of complications, marginal bone loss around implants were investigated with regard to the type of defect, location of bone grafting, and types of bone graft techniques. ADDM-based bone grafting was performed on 221 sites in 82 patients and 208 implants were placed afterwards: The percentage of complications after bone grafting was 15.84%, and the implant survival rate was 95.19%. All complications were resolved with conventional treatment except for the 10 cases of osseointegration failure. The average marginal bone loss was 0.31 mm at the last examination after the average follow-up period of 7.2 years. Within the limitation of this study, the results of long-term follow-up are consistent with the short-term results of relevant studies. ADDM can produce promising clinical outcomes when used for alveolar ridge augmentation around implants.

This study aimed to investigate Coll-I, III, IV and elastin in canine normal prostate and PC, using Picrosirius red (PSR) and Immunohistochemical (IHC) analysis. Eight normal prostates and 10 PC from formalin-fixed, paraffin-embedded samples were used. Collagen fibers area was analyzed with ImageJ software. The distribution of Coll-I and Coll-III was approximately 80% around prostatic ducts and acini, 15% among smooth muscle and 5% surrounding blood vessels, in both normal prostate and PC. There was a higher median area of Coll-III in PC, when compared to normal prostatic tissue (p=0.001 for PSR and p= 0.05 for IHC). Immunostaining for Coll-IV was observed in the basal membrane of prostate acini, smooth muscle, blood vessels, and nerve fibers of normal and PC samples. Although there was no difference in Coll-IV area between normal tissue and PC, tumors with Gleason score 10 showed absence of Coll-IV, when compared to scores 6 and 8 (p=0.0095). Elastic fibers were found in the septa dividing the lobules and around the prostatic acini of normal samples, and was statistically higher in PC, compared to normal tissue (p=0.00229). Investigation of ECM components brings new information and should be correlated with prognosis in future studies.

The practice of spatial econometrics revolves around a weighting matrix, which is often supplied by the user on previous knowledge. This is the so called $\mathbf{W}$ issue. Probably, the aprioristic approach is not the best solution although, nowadays, there few alternatives for the user. Our contribution focuses on the problem of selecting a $\mathbf{W}$ matrix from among a finite set of matrices, all of them considerer appropriate for the case. We develop a new and simple method based on the Entropy corresponding to the distribution of probability estimated for the data. Other alternatives, which are common in current applied work, are also reviewed. The paper includes a large Monte Carlo to calibrate the effectiveness of our approach compared to the others. A well-known case study is also included.