In the era of big data with increasingly complex data structures and ever-larger data scales, matrix-type data are becoming highly valued and their applications in the fields of medicine, industry, education, geography, and astronomy are growing in extent. In recent years, significant progress has been made in the practical use of matrix variable t-distribution finite mixture models for handling data in order to address the issues of multi-subgroup structures and long data tails. In this paper, the expectation-maximization (EM) algorithm with penalized maximum likelihood is proposed to resolve the problem of the unbounded nature of the likelihood function applied to the model by considering the degeneracy of the variance-covariance matrix of this model. Our data were analyzed through simulations and real data, and the results demonstrate that our model is effective in both preventing the likelihood function from being unbounded and in ensuring the accuracy of the estimated parameters of the EM algorithm.

Matrix-variate Gaussian type or Wishart type distributions in the real domain are widely used in the literature. When the exponential trace has an arbitrary power and when a factor involving a determinant enters into the model or a matrix-variate gamma type or Wishart type model with exponential trace having an arbitrary power, is extremely difficult to handle. Evaluation of the normalizing constant in such a model is the most important part because when studying the properties of such a model, the method used in the evaluation of the normalizing constant will be the relevant steps in all the computations involved. One such model with a factor involving a trace and the exponential trace having an arbitrary power, in the real domain, is known in the literature as Kotz' model. No explicit evaluation of the normalizing constant in the model involving trace with an exponent and determinant with an exponent entering into the model and at the same time the exponential trace having an arbitrary exponent seems to be available in the literature. The normalizing constant widely used in the literature and interpreted as the normalizing constant in the general model and refers to as a Kotz' model does not seem to be correct. Corresponding model in the complex domain, with the correct normalizing constant, does not seem to be available in the literature. One of the main contributions in this paper is the matrix-variate distributions in the complex domain belonging to Gaussian type, gamma type, type-1 and type-2 beta type when the exponential trace has an arbitrary power. All these models are believed to be new. A second main contribution is the explicit evaluation of the the normalizing constants, in the real and complex domains especially in the complex domain, in a matrix-variate model involving a determinant and a trace as multiplicative factors and at the same time the exponential trace having an arbitrary power. Another main contribution is the introduction of matrix-variate models with exponential trace having an arbitrary exponent, in the categories of type-1 beta, type-2 beta and gamma distributions or in the family of Mathai's pathway models [1], both in the real and complex domains. Another new contribution is the logistic-based extensions of models in the real and complex domains with exponential trace having an arbitrary exponent and connecting to extended zeta functions introduced by this author recently. Some properties of such models are indicated but not derived in detail in order to limit the size of the paper. The techniques and steps used at various stages in this paper will be highly useful for people working in multivariate statistical analysis as well as people applying such models in engineering problems, communication theory, quantum physics and related areas, apart from statistical applications.

This article presents a review of the distribution system state estimation (DSSE) algorithms from the model-based approach to the recent data-driven methodologies. The insufficient measurements which result in low observability have motivated the need to shift from the conventional algorithm to data-driven approaches that can successfully estimate states despite the DSSE challenges. This article discusses the nonlinearity in the DSSE problem formulation and how different model-based methods have been proposed to mitigate the problems of robustness, ill-conditioning, and complexity. Moreover, approximate DSSE to obviate nonlinearity were discussed: complex linearization, small angle approximation, convexification and compressed sensing. Furthermore, probabilistic DSSE methods were also discussed in the need to quantify the uncertainty associated with the state estimation results. Also, data-driven methods applicable to DSSE, pseudo measurement generations, and topology identification were also discussed using machine and deep learning methods. Lastly, a recent approach that employs a hybrid of model-based and data-driven methods using matrix and tensor completion is surfacing because they work in a low observable condition of the network and can estimate the states satisfactorily. With this review, researchers can look further into developing and improving on the model-based data-driven methods less susceptible to the barriers in conventional DSSE algorithms.

In this paper, we deduce explicit formulas to evaluate the determinants of nonsymmetrical structure Toeplitz Bohemians by two determinants of specific Hessenberg Toeplitz matrices, which are linear combinations in terms of determinants of specific Hessenberg Toeplitz matrices. We get some new results very di¤erent from [Massimiliano Fasi, Gian Maria Negri Porzio, Determinants of normalized upper Hessenberg matrices, Electronic Journal of Linear Algebra, Volume 36, pp. 352-366, June 2020].

In this note we construct explicit complex and real matrix representations for the generators of real Clifford algebra $C\ell_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. We find two classes of representation, the normal representation and exceptional one. The normal representation is a large class of representation which can only be expanded into $4m+1$ dimension, but the exceptional representation can be expanded as generators of the next period. In the cases $p+q=4m$, the representation is unique in equivalent sense. These results are helpful for both theoretical analysis and practical calculation. The generators of Clifford algebra are the faithful basis of $p+q$ dimensional Minkowski space-time or Riemann space, and Clifford algebra converts the complicated relations in geometry into simple and concise algebraic operations, so the Riemann geometry expressed in Clifford algebra will be much simple and clear.

In this study, we prove the norm separating property for the composition of Cesàro 1 and Gamma matrices with their transpose. As a result, we compute the ℓp-norms of six classes of operators that commute with the infinite Hilbert operators. Additionally, we find the norm of 3 Hilbert’s commutants on some well-known sequence spaces.

A complex square matrix $A$ is said to be Hermitian if $A= A^{\ast}$, the conjugate transpose of $A$. The topic of the present note is concerned with the characterization of Hermitian matrix. In this note, the we show that each of the two triple matrix product equalities $AA^{\ast}A = A^{\ast}AA^{\ast}$ and $A^3 = AA^{\ast}A$ implies that $A$ is Hermitian by means of decompositions and determinants of matrices, which are named the two-sided removal and cancellation laws associated with Hermitian matrix, respectively. We also present several general removal and cancellation laws as the extensions of the preceding two facts about Hermitian matrix.

One of matrix equalities composed of multiple products of matrices and their generalized inverses is given by $A_1B_1^{-}A_2B_2^{-} \cdots A_kB_k^{-}A_{k+1}= A$ where $A_1$, $B_1$, $A_2$, $B_2$, $\ldots$, $A_k$, $B_k$, $A_{k+1}$, and $A$ are given matrices of appropriate sizes, and $B_1^{-}$, $B_2^{-}$, $\cdots$, $B_k^{-}$ are generalized inverses of matrices. The cases for $k = 1, 2$ and their special forms were properly approached in the theory of generalized inverses of matrices. In this note, the author presents an algebraic procedure to derive explicit necessary and sufficient conditions for the equality with $k = 3$ to always hold using certain rank equalities for the block matrices constructed by the given matrices, and then mention a key step of extending the previous work to a general situation.

The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.

Though the cancer research community has used mouse xenografts for decades more than zebrafish xenografts, zebrafish have much to offer: they are cheap, easy to work with, and the embryonic model is relatively easy to use in high-throughput assays. Zebrafish can be imaged live, allowing us to observe cellular and molecular processes in vivo in real time. Opponents dismiss the zebrafish model due to the evolutionary distance between zebrafish and humans, as compared to mice, but proponents argue for the zebrafish xenograft’s superiority to cell culture systems and its advantages in imaging. This review places the zebrafish xenograft in the context of current views on cancer and gives an overview of how several aspects of this evolutionary disease can be addressed in the zebrafish model. Zebrafish are missing homologs of some human proteins and (of particular interest) several members of the matrix metalloproteinase (MMP) family of proteases, which are known for their importance in tumour biology. This review draws attention to the implicit evolutionary experiment taking place when the molecular ecology of the xenograft host is significantly different than that of the donor.

In this paper we have studied some properties for determinant-calculating for cubic-matrix of order 2 and order 3. These properties are analogous to some properties for determinants of square matrix we have proved and noted that these properties also are applicable (or not in some details) on this concept for cubic-matrix of orders 2 and 3. All results in this paper, are presented in detail during the theorem proofs.

Iyer Markoulakis Helmholtz Hamiltonian mechanics formalisms mathematically modeled physics with vortex rotational fields acting with gradient fields, typically in zero-point microblackhole general fields. Here, Helmholtz metrics have been gaged to Coulombic Hilbert metrics, representing Gilbertian and Amperian natures of electromagnetic fields out of the mechanical fields from Helmholtz Hamiltonian mechanics. This ansatz general gaging helps to properly isolate field effects – mechanical, electric, magnetic components within the analytical processes. Vacuum gravitational fields and the flavor Higgs-Boson matter inertial gravitational fields have been thus quantified extending to stringmetrics constructs matrix showing charge asymmetry gage metrics, having the power to analyze dark energy superluminal phase, dark matter luminal phase, and light matter subluminal phase. Interpreting particle physics gage matrix pointing to Dirac seas electrons, monopoles with positrons, electron-positron annihilation leading to energy production, relativistic energy generating matter, and both monopoles – vacuum and compressed out of vortex Helmholtz decomposition fields have been interpolated. Quantum ASTROPHYSICS gage metrix posits superluminal profile of signals velocity generating electron-positron chain like “curdling” action that is consistent with physics literature reporting nature electron photon observed oscillatory fields configurations. This helps proposing creation of neutrino antineutrino pair orthogonal to electron positron “curdling” planes, that may lead to formation of protonic hydrogen of stars or orthogonally muon. These aspects will explain receding or fast expanding universe with dark matter in terms of flavor metrics versus gage associating metrics flavor. Additional interpretations of virtual gravitational dipoles that have gravitational charge of opposite signs, reported per physics literature at Planck dimensions, that may originate at the center of supermassive blackhole. On the other hands, vacuum monopoles occur probably at infinity with cosmos extent.

In this paper, we define Tetranacci and Tetranacci-Lucas matrix sequences and investigate their properties.

Acoustic emission (AE) has proven to be a very useful technique for determining damage in ceramic matrix composites (CMCs). CMCs rely on various cracking mechanisms which enable non-linear stress-strain behavior with ultimate failure of the composite due to fiber failure. Since these damage mechanisms are all micro-fracture mechanisms, they emit stress waves ideal for AE monitoring. These are typically plate waves since for most specimens or applications one dimension is significantly smaller than the wavelength of the sound waves emitted. By utilizing the information of the sound waveforms captured on multiple channels from individual events, the location and identity of the sources can often be elucidated. The keys to the technique are the use of wide-band frequency sensors, digitization of the waveforms (modal AE), strategic placement of sensors to sort the data and acquire important contents of the waveforms pertinent for identification, and familiarity with the material as to the damage mechanisms occurring at prescribed points of the stress history. The AE information informs the damage progression in a unique way which adds to the understanding of the process of failure for these composites. The AE methodology was applied to composites tested in fatigue at different frequencies where identification of when and where AE occurred coupled with waveform analysis leads to source identification and failure progression.

Parallel decompositions have proved to be powerful tools for the analysis and interpretation of the physical information provided by Mueller matrices experimentally obtained. In this work, the procedure for the so-called arbitrary decomposition of Mueller matrices is validated through its application to a set of representative experimentally determined Mueller matrices. The covariance and passivity criteria required for the physical realizability of the Mueller matrices involved in the parallel decompositions are integrated in the procedure, which ensures the physical consistency of the results presented.

One of the typical forms of linear matrix expressions (linear matrix-valued functions) is given by $A + B_1X_1C_1 + \cdots + B_kX_kC_k$, where $X_1, \ldots, X_k$ are independent variable matrices of appropriate sizes, which include almost all matrices with unknown entries as its special cases. The domain of the matrix expression is defined to be all possible values of the matrix expressions with respect to $X_1, \ldots, X_k$. I this article, we approach some problems on the relationships between the domains of two linear matrix expressions by means of the block matrix method (BMM), the matrix rank method (MRM), and the matrix equation method (MEM). As application, we discuss some topics on the relationships among general solutions of some linear matrix equations and their reduced equations.

It is shown that a Mueller quaternion can be formulated as a quaternion with matrix coefficients, and this Mueller quaternion transforms the Stokes quaternion for depolarizing process as well as for nondepolarizing process. Mueller quaternion keeps track of the phase acquired by the Stokes quaternion and, in general, quaternion states of optical media comprises all properties of Jones, Mueller-Jones and Mueller matrices.

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

The new barrier mode in Apache Spark allows embedding distributed deep learning training as a Spark stage to simplify the distributed training workflow. In Spark, a task in a stage doesn’t depend on any other tasks in the same stage, and hence it can be scheduled independently. However, several algorithms require more sophisticated inter-task communications, similar to the MPI paradigm. By combining distributed message passing (using asynchronous network IO), OpenJDK’s new auto-vectorization and Spark’s barrier execution mode, we can add non-map/reduce based algorithms, such as Cannon’s distributed matrix multiplication to Spark. We document an efficient distributed matrix multiplication using Cannon’s algorithm, which improves significantly on the performance of the existing MLlib implementation. Used within a barrier task, the algorithm described herein results in an up to 24% performance increase on a 10,000x10,000 square matrix with a significantly lower memory footprint. Applications of efficient matrix multiplication include, among others, accelerating the training and implementation of deep convolutional neural network based workloads, and thus such efficient algorithms can play a ground-breaking role in faster, more efficient execution of even the most complicated machine learning tasks

Given several nonnegative matrices with a single pattern of allocation among their zero/nonzero elements, the average matrix should have the same pattern, too. This is the first tenet of the pattern-multiplicative average (PMA) concept, while the second one suggests the multiplicative (or geometric) nature of averaging. The original concept of PMA was motivated by the practice of matrix population models as a tool to assess the population viability from long-term monitoring data. The task has reduced to searching for an approximate solution to an overdetermined system of polynomial equations for unknown elements of the average matrix (G), hence to a nonlinear constrained minimization problem for the matrix norm. Former practical solutions faced certain technical problems, which required sophisticated algorithms but returned acceptable estimates. Fresh idea to use the eigenvalue approximation ensues also from the basic equation of averaging, which determines the exact value of λ1(G), the dominant eigenvalue of matrix G, too, and the corre-sponding eigenvector. These are bound by the well-known linear equations, which reduce the task to a standard problem of linear programing (LP). The LP approach is realized for 13 fixed-pattern matrices gained in a case study of Androsace albana, an alpine short-lived perennial, monitored on permanent plots during 14 years. A standard software routine reveals the unique exact solution, rather than an approximate one, to the PMA problem, which turns the LP approach into ‘’the best of versatile optimization tools”. The exact solution turns out to be peculiar in reaching zero bounds for certain nonnegative entries of G, which deserves a modified problem formulation separating the lower bounds from zero.

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.

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.

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.

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.

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.

Objective: Regeneration of bone defects remains a challenge for maxillofacial and reparative surgeons. The purpose of this histological study was to assess the osteogenic potential of octacalcium phosphate (OCP) and bone matrix gelatin (BMG) alone and in combination in artificially created mandibular bone defects in rats. The quality of the newly formed bone was also evaluated. Methods: Thirty-six male Sprague Dawley rats (6-8 weeks old with 120-150 g weight) were randomly divided into four groups. Defects (3 mm in diameter and 2 mm in depth) were created in the mandible of rats and filled with 6 mg of OCP, BMG or a combination of both (1/4 ratio), respectively. Defects were left unfilled in the control group. To assess osteoinduction and bone regeneration and determine the quality of the newly formed bone, tissue specimens were harvested at seven, 14, and 21 days post-implantation. The specimens were processed, stained with hematoxylin and eosin (H&E) and histologically analyzed under light microscopy. Results: In the experimental groups, new bone formation was initiated at the margins of defects from seventh day after implantation. At the end of the study period, the amount of the newly formed bone increased and the bone was relatively mature. Osteoinduction and new bone formation were greater in OCP/BMG group. In the control group, slight amount of new bone had been formed at the defect margins (next to host bone) on day 21. Conclusion: Combination of OCP/BMG may serve as an optimal biomaterial for treatment of mandibular bone defects.

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.

The need to recycle carbon fibre reinforced composite polymers (CFRP) has grown significantly to reduce the environmental impact generated by their production. To meet this need, thermoreversible epoxy matrices have been developed in recent years. This study investigates the performance of an epoxy vitrimer made by introducing a metal catalyst (Zn2+) and its carbon fibre composites focusing on the healing capability of the system. The dynamic crosslinking networks endow vitrimers with interesting rheological behaviour, the capability of the formulated resin (AV-5) has been assessed by creep tests. The analysis showed increased molecular mobility above a topology freezing temperature (Tv). However, the reinforcement phase inhibits the flow capability reducing the flow. The fracture behaviour of CFRP made with the vitrimeric resin has been investigated by Mode I and Mode II tests and compared with the conventional system. The repairability of the vitrimeric CFRP has been investigated by attempting to recover the delaminated samples, which yielded unsatisfactory results. Moreover, the healing efficiency of the modified epoxy composites has been assessed by using the vitrimer as an adhesive layer. The joints were able to recover about 84% of the lap shear strength of the pristine system.

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.

In contrast to the traditional fillers, clay, in particular, natural smectite clay represents an environmentally significant alternative to improve the properties of polymers. Compared to con-ventional nanofillers, smectite clay can effectively enhance the physical and mechanical properties of polymer nanocomposites with a relatively small amount of addition (< 5 wt%). The present study focuses on investigating the reinforcing efficiency of different amounts (up to 5 wt%) of a natural Brazilian smectite clay on the mechanical and thermal properties of poly(butylene terephthalate) (PBT) nanocomposites. Natural Brazilian clay modified by addition of quaternary salt and sodium carbonate (MBClay) was infused into the PBT polymer by melt extrusion, using a twin-screw extruder. It was found that the best properties for PBT were obtained at 3.7 wt% of modified BClay. Tensile strength at break exhibited an increase of about 60 %, flexural strength increased by 24 % and flexural modulus increased by 17 %. In addition, an increase in the crystallinity percentage of PBT/BClay nanocomposite was confirmed by DSC and XRD analysis, and a gain of about 45 % in HDT was successfully achieved due to incorporation of 3.7 wt% of MBClay.

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.

Paclitaxel is a natural, highly lipophilic anti proliferative drug widely used in medicine. We have studied the release of tritium-labeled paclitaxel (³H-PTX) from matrices destined for the coating of vascular stents and produced by the electrospinning method from the solutions of polycaprolactone (PCL) with paclitaxel (PTX) in hexafluoisoropropanol (HFIP) and/or solutions of PCL with PTX and human serum albumin (HSA) in HFIP or HIFP-dimethyl sulphoxide (DMSO) blend. The release of PTX has been shown to depend on the solvent and the composition of electrospinning solution, as well as the composition of the surrounding medium, particularly the concentration of free PTX and PTX-binding biomolecules present in human serum. It was shown that 3D matrices can completely release PTX without weight loss. Two-phase PTX release from optimized 3D matrices was obtained: ~27% of PTX was released in the first day, another 8% were released over the next 26 days. Wherein ~2.8%, ~2.3%, and ~0.25% of PTX was released on day 3, 9, and 27, respectively. Considering PTX toxicity, the rate of its diffusion through the arterial wall, and the data obtained the minimum cytostatic dose of the drug in the arterial wall will be maintained for at least three months.

In this study, a 5vol. % (TiBw+TiCp)/Ti composite pancake with a diameter of 260mm was prepared by casting followed by open die forging in (α+β) phase region. The microstructures of the composite pancake are inhomogeneous, in terms of both matrix microstructure and distribution of reinforcements. The matrix microstructures were gradually refined from the periphery to centre of the pancake. The TiBw and TiCp reinforcements tend to be uniformly distributed in the centre region and. It is suggested that the microstructure difference can be mainly ascribed to the temperature variation from the periphery to the centre. Additionally, tensile testing results showed that the centre region of the composite pancake exhibits higher strength than the peripheral region. The strengthening mechanism and the softening behavior of the composite pancake with temperature is discussed.

Composite fiber materials are superior materials due to their high strength and light weight. Composites reflect the properties of their constituents, which is proportional to the volume fraction of each phase. There are different fiber reinforcement types and each affects it’s flexural, tensile and compression strength. When selecting a composite for a specific application, the forces excreted on the composite must be known in order to determine the reinforcement type. Unidirectional fiber reinforcement will allow very strong load resistance but only in one direction where as a random orientated fiber reinforcement can resist less load but can maintain this quota in all directions. These materials are said to be anisotropic. Certain composite fibers, taking into consideration there weights, are physically stronger than conventional metals. This research deals with the analysis of three composite materials with different reinforcement types, volume fraction and phase content. It was found that material A (glass epoxy) was the strongest in the longitudinal direction with a flexural strength of 534 MPa in the longitudinal and 420 MPa in the transverse direction. The flexural stresses of material B (glass silicone) and material C (glass polyester) where both found in the 120 to 135 MPa range. Differences were due to their differences in matrix composition and reinforcement type.

Phylogenomic analyses have revolutionized the study of biodiversity, but they have revealed that estimated tree topologies can depend, at least in part, on the subset of the genome that is analyzed. For example, estimates of trees for avian orders differ if protein coding or non-coding data are analyzed. The bird tree is a good study system because the historical signal for relationships among orders is very weak, which should permit subtle non-historical signals to be identified, while monophyly of orders is strongly corroborated, allowing identification of strong non-historical signals. Hydrophobic amino acids in mitochondrially-encoded proteins, which are expected to be found in transmembrane helices, have been hypothesized to be associated with non-historical signals. We tested this hypothesis by comparing the evolution of transmembrane helices and extramembrane segments of mitochondrial proteins from 420 bird species, sampled from most avian orders. We estimated amino acids exchangeabilities for both structural environments and assessed the performance of phylogenetic analysis using each data type. We compared those relative exchangeabilities with values calculated using a substitution dataset for transmembrane helices from a variety of sampled set of nuclear- and mitochondrially-encoded proteins, allowing us to compare the bird-specific mitochondrial models with a general model of transmembrane protein evolution. To complement our amino acid analyses, we examined the impact of protein structure on patterns of nucleotide evolution. Models of transmembrane and extramembrane sequence evolution for amino acids and nucleotides exhibited striking differences, but there was no evidence for strong topological data type effects. However, incorporating protein structure into analyses of mitochondrially-encoded proteins improved model fit. Thus, we believe that considering protein structure will improve analyses of mitogenomic data, both in birds and in other taxa.

(1) Background: Vitamin K deficiency is a common feature of chronic kidney disease (CKD), leading to impaired bone quality and increased risk of vascular calcifications. A method to indirectly measure Vitamin K status is measuring the blood level of Vitamin K dependent proteins (VKDP)- osteocalcin (OC) and matrix GLA protein (MGP). The aim of this study is to correlate the level of OC and MGP with markers of CKD mineral bone disorder (CKD-MBD). (2) Methods: We conducted a single-center cross-sectional study that included 45 CKD G5D patients and measured blood biochemistry, complete blood count and intact osteocalcin and matrix GLA protein. (3) Results: We found a strong statistically significant correlation of OC with the markers of CKD-MBD such as: iPTH , serum calcium and serum phosphorus and a strong indirect statistically significant correlation with abdominal circumference. There was also a statistically significant correlation of MGP with markers of inflammation (CRP). Higher levels of MGP were found in patients treated with vitamin K antagonists, non-calcium based phosphate binders and vitamin D receptor activator- paricalcitol. (4) Conclusions: In our study, we found that vitamin K deficiency, measured indirectly using the level of VKDP is associated to CKD-MBD. The use of medication such as phosphate binders, that reduce vitamin K absorbtion, Vitamin D that increases Vitamin K requirements and also vitamin K antagonists, seem to have an influence on the blood level of VKDPs.

Diminished ovarian reserve can be regarded as a sentinel indicator to foreshadow severe follicular loss and, ultimately, systemic aging. The negative slope of human ovulatory fidelity begins with a robust follicular endowment which gradually declines over time. In contrast, the youthful ovarian phenotype requires the coordinated work of endothelial, granulosa, immune, perivascular, stromal and possibly germline stem cells. Such a diverse tissue matrix can, in general, be influenced by platelet (PLT)-derived factors but this has not yet been specifically confirmed in the ovary after platelet-rich plasma (PRP). How could a comparable response be validated? Here a prospective, experimental study is proposed whereby eligible patients already undergoing scheduled laparoscopy provide ovarian tissue via biopsy submitted for co-culture with autologous Ca⁺² activated PRP. Recognizing the interlocking, central roles of nuclear factor κB (NF-κB) and tumor necrosis factor-α (TNF-α), incubated samples would be assessed for these in vitro before vs. after PRP exposure, in addition to stereomicroscopy. A mathematical model is available to track NF-κB oscillations and estimate gene expression, cell development, growth, apoptosis, and key immune and inflammatory actions. Since NF-κB and TNF-α are discharged in activated PLT releasate (or react to its cargo proteins) this audit permits extraction of response markers observed post-stimulus, thus linking discrete signals to transcriptional output, cellular fitness, and ovarian cytoarchitecture. From this, a hypothesis could emerge where intraovarian PRP is found to make no direct impact on follicles, although modified ovarian field function and curtailed local entropy incidentally favor optimized oocyte competence as a secondary effect.

Matrix Factorization is a long established method employed for analyzing and extracting valuable insight recommendations from complex networks containing user ratings. The execution time and computational resources demanded by these algorithms pose limitations when confronted with large datasets. Community detection algorithms play a crucial role in identifying groups and communities within intricate networks. To overcome the challenge of extensive computing resources, we present a novel parallel computation framework utilizing community information available in the rating network. Our proposed approach named as Community-based Matrix Factorization(CBMF), parallelizes matrix factorization technique by dividing the network into communities using existing community detection algorithms. We prove that this parallel approach not only increases the quality of recommendations in connection with Root Mean Square Error (RMSE), but also yields substantial performance improvement. We empirically evaluate our idea on diverse datasets and present comprehensive experimental results. These results serve as empirical evidence of the effectiveness and performance gains offered by our parallel computation framework.

In this study, the concentrations of metals (As, Cd, Co, Cr, Cu, Hg, Ni, Pb, and Zn) were deter-mined in two freshwater fish species. The same fish were also used to determine the content of fatty acids (FA), including saturated fatty acids (SFA), monounsaturated fatty acids (MUFA), and polyunsaturated fatty acids (PUFA). We investigated the species-specific relationship between bioaccumulation of metals and the content of FA. Roach and white bream were caught at two different sites in the Serbian part of the Danube. The measured metal concentrations were below the standard concentrations recommended in the guidelines of the EU and the Republic of Ser-bia. Among the non-essential metals, Ni had the highest concentration, ranging from 0.158 to 0.591 µg g-1. The muscle of the two fish species contained high concentrations of SFA, ranging from 36.31 to 51.79%, and MUFA, ranging from 33.56 to 43.70%. Polyunsaturated fatty acids were represented with the lowest percentage (5.32 - 27.18). Four of the nine metals studied (As, Hg, Ni and Pb) in one fish species and five of the nine metals studied (A, Cu, Ni, Pb and Zn) in the other fish species showed correlations with fatty acid content. These results help to reveal potential biomarkers of metal stress in lipid composition.

Novel tetragonal matrix Ba0.5Gd0.5-xNaxF2.5-x, where x = 0.05, doped by Yb3+, Ho3+, Er3+, was synthesized by molten salt synthesis (MSS) from nitrate flux. XRD data show that tetragonal phase with a = 4.122(1) Å, c = 17.672(1) Å is stable in argon atmosphere up to 960 °C. Luminescence spectra recorded in 500-900 nm and 1050-1700 nm upon 974 nm pumping demonstrated the characteristic luminescence at 1550 nm (4I13/2 → 4I15/2) for Er3+ and 1150 nm (5I6 → 5I8) for Ho3+. The relative thermal sensitivity (Sr) at 296-316 K were 0.3 %*K-1 and 5.5%*К-1 in shortwave infrared (SWIR) and visible range, respectively. Synthesized luminophores can be used as dual-range optical temperature sensors, which simultaneously operating in visible and SWIR ranges.

In estimating logistic regression models, convergence of the maximization algorithm is critical, however, this may fail. Numerous bias correction methods for maximum likelihood estimates of the parameters have been conducted for cases of complete data sets and also longitudinal models. For binary response fixed effects panel data model, the conditional logit estimator is consistent for balanced data. When faced with missing covariates problem, researchers opt for various imputation techniques to make the data complete and without loss of generality consistent estimates still suffice asymptotically. For maximum likelihood estimates of the parameters for logistic regression in cases of imputed covariates, the optimal choice of an imputation technique which yields the best estimates with minimum variance is still elusive. The main aim of this paper is to examine the behaviour of the Hessian matrix with optimal values of the imputed covariates vector which will make the Newton-Raphson algorithm to converge faster through a reduced absolute value of the product of the score function and the inverse fisher information component. We focus on a method used to modify the conditional likelihood function through partitioning of the covariate matrix. We also confirm from the moduli of the Hessian matrices that the log likelihood of a panel data logistic model has a global maximum as the parameter estimates. Simulation results reveal that model based simulation perform better than classical imputation techniques yielding estimates with smaller bias and higher precision for the conditional maximum likelihood estimation of nonlinear panel models with single fixed effects.

Matrix metalloproteinases (MMPs) are often considered biomarkers of skin fibrosis. At the early stages of the pathological process, an elevation of their enzymatic activity causes significant changes in the composition of the extracellular matrix. MMPs secreted by immune cells facilitate their migration to the site of damage. Then, the immune cells eliminate the affected cells and biomolecules. Moreover, bidirectional changes in the activity of proteolytic enzymes, including MMPs, accompany wound healing. This study aimed to assess changes in the expression of Mmp2, Mmp3, and Mmp9 after treating the mice with laser therapy using the experimental model of bleomycin-induced skin fibrosis. Using immunohistochemistry, we characterized the histological features of scarred skin. We also analyzed changes in the expression of MMPs using real-time polymerase chain reaction before and after the irradiation with laser. We showed that treatment of the mice with CO2 laser partially normalized the histological features of scarred skin. We also noticed a decrease in the expression of Mmp2, Mmp3 (both p &lt; 0.05), and Mmp9 (p = 0.065) during scar healing. The obtained results suggest that normalization of skin homeostasis requires a control of MMPs activities via induction of their genes.

Cells actively sense differences in topology, matrix elasticity and protein composition of the extracellular microenvironment and adapt their function and morphology. In this study, we focus on the cross-talk between matrix stiffness and protein coating density that regulate morphology and proliferation dynamics of single myocytes. For this, C2C12 myocytes were monitored on L-DOPA functionalized hydrogels of 22 different elasticity and fibronectin density compositions. Static images were recorded and statistically analyzed to determine morphological differences and to identify the optimized extracellular matrix (ECM). Using that information, selected ECMs were used to study the dynamics before and after cell proliferation by statistical comparison of distinct cell states. We observed a fibronectin density independent increase of the projected cell area until 12 kPa. Additionally, changes in the fibronectin density led to an area optimum at about 2.6 μg/cm, which was confirmed by an independent F-actin analysis, revealing a maximum actin filament to cell area ratio of 7.5 %. The proliferation evaluation showed an opposite correlation between cell spreading duration and speed to the matrix elasticity and protein density, which did not affect the cell cycle duration. In summary, we identified an optimized ECM composition, while independent matrix properties regulate distinct cell characteristics.

There is need to address the challenges of organ shortage, through development of tissues and organs with alternatives to those of the allograft-kind. This illustrates the quest behind novel biofabrication strategies such as 3D bio-printing, which is necessary to create artificial multi-cellular tissues/organs. Several findings have been reported in this review. First, the role of ECM components in tissue regenerative medicine is presented. Different ECM components such as collagen, gelatin, elastin, fibronectin, laminins and glycosaminoglycans are concisely examined for their tissue regenerative medicine applications. Next, current state of research on extrusion-based 3D bio-printing techniques and their limitations are reviewed. For example, we show that cell viability is still a challenge with extrusion, while the use of natural polymers such as collagen in improving composites’ mechanical properties is limited. Lastly, we examine unresolved research questions necessary to advance the present state of research in the field.

Matrix metalloproteinases have been implicated in muscular dystrophy progression and recent studies described the role of MMP-10 in skeletal muscle pathology of young dystrophic mice. Nevertheless, its implication in dystrophin deficient hearts is still missing. Here, we aimed at investigating MMP-10 implication in severe muscular dystrophic progression and characterize MMP-10 loss in skeletal and cardiac muscles of aged dystrophic mice. We examined the histopathological effect of MMP-10 ablation in aged mdx mice, both in the hind limb muscles and heart tissues. We have found that MMP-10 loss compromises survival rates of aged mdx mice, with skeletal and cardiac muscles developing a chronic inflammatory response. Our findings indicate that MMP-10 is implicated in severe muscular dystrophy progression, identifying a new area of investigation that could lead to future therapies for dystrophic muscles.

A distributed bragg reflector is designed to get an optical reflectance on visible electromagnetic spectrum i.e. ~800 nm in this work. Device is realized based on Abele’s matrix for TE mode.

Studying various marine biomineralized ultrastructures reveals the appearance of common architectural designs and building blocks in materials with fascinating mechanical properties that match perfectly to their biological tasks. Advanced mechanical properties of biological materials are attributed to evolutionary optimized molecular architectures and structural hierarchy. One example which has not yet been structurally investigated in great detail is the shell of Mytilus edulis L. (Finnish blue mussel) found in the archipelago of SW-Finland. Through a combination of various state-of-the-art techniques such as high-resolution electron microscopy imaging, Fourier-transformed infrared spectroscopy, powder X-ray diffraction, synchrotron wide-angle X-ray diffraction, nanoindentation and protein analysis, both the inorganic mineralized components as well as the organic-rich matrix were extensively characterized. We found very similar ultra-architecture across the shell of M. edulis L. as compared to the widely studied and closely related M. edulis. However, we also found interesting differences, for instance in the thickness and degree of orientation of the mineralized layers indicating dissimilar properties and related alterations in the biomineralization processes. Our results show that the shell of M. edulis L. has a gradient of mechanical properties, with the increase in the stiffness and the hardness from anterior to the posterior region of the shell. The shell is made from distinct and recognizable mineralized layers each varying in thickness and microstructural features. At posterior regions of the shell, moving from dorsal to ventral side, these layers are an oblique prismatic layer, a prismatic layer and a nacreous layer, in which the oblique prismatic layer is found to be the main and thickest mineralized layer of the shell. Probing the calcified rods in the oblique prismatic layer using high resolution SEM imaging revealed opening of channels with a diameters of 40-50 nm and lengths up to a micrometer extending through the rods. The chitin and protein have been found to be the main component of the organic-rich interfacial matrix as expected. Protein analysis showed two abundant proteins with sizes around 100 kD and 45 kD which likely not only regulates biomineralization and adhesion of the crystals but also governing the intrinsic-extrinsic toughening in the shell. Overall, this detailed analysis provides new structural insights into biomineralization of marine shells in general.

The purpose of this study is to estimate the mean transitioning probabilities from a Healthy state to malaria positive uncomplicated state or to malaria positive severe state. It also classifies the various transitioning probabilities of moving through the various states based on some baseline characteristics. Malaria test results for 2019 over a 12-month period were collected from the University of Ghana school clinic. An H-U model for the study was developed and the transition rates from the cross-sectional data are indicated. With two states Healthy (H) and Uncomplicated (U) forming a state space, there were four possible transitions. The results show that the probability of transitioning from a Healthy state to a malaria positive state is 0.03% while the probability that an individual will remain at Healthy state (H) after the test is 99.73%. It was found that if an individual is already positive and has taken medication the probability that its second test came out negative is 6.45% while the chances that it will remain positive but uncomplicated is 93.55%. The study also showed that in the long run, about 95.98% of persons who visited the student clinic with malaria symptoms recorded negative tests for malaria parasite while about 4% recorded positive for malaria. In terms of disaggregation by gender, it was realized that the number of reported negative test results were higher for females (97.08%) than for males (96.13%). However, the infection rate is higher for males (3.87%) than females (2.92%). It is recommended that in as much as the University of Ghana has two health centers (a clinic and hospital), there should be a centralized system to track students’ health so research done would not be biased.

Milk and dairy foods are naturally rich sources of a wide range of nutrients, and when consumed according to recommended intakes contribute essential nutrients across all stages of the life cycle. Since then, seminal studies recommendations with respect to intake of saturated fat have been consistent and clear; limit total fat intake to 30% or less total dietary energy, with a specific recommendation for intake of saturated fat to less than 10% of total dietary energy. However, recent work has re-opened the debate on intake of saturated fat in particular, with suggestions that recommended intakes be considered not at a total fat intake within the diet, but at a food specific level. A large body of evidence exists examining the impact of dairy consumption on markers of metabolic health, both at a total dairy intake and also at a food level, with mixed findings to date, but suggests that the impact of saturated fat intake on health differs both across food groups and even between foods within the same good group such as dairy. Milk and dairy foods contain a range of nutrients and bioactive components in different levels, housed within very different food structures. The interaction of the overall food structure and the nutrients describes the concept of the ‘food matrix effect’ which has been well documented for dairy foods. Studies show that nutrients from different dairy food sources can have different effects on health and for this reason, they should be considered individually rather than grouped as a single food category in epidemiological research. This review examines the current evidence from randomised controlled trials and meta-analyses, with respect to dairy, milk, yoghurt and cheese on aspects of metabolic health, and summarises some of the potential mechanisms for these findings.

Viral protein 24 (VP24) from Ebola virus (EBOV) was first recognized as a minor matrix protein that associates with cellular membranes. However, more recent studies shed light on its roles in inhibiting viral genome transcription and replication, facilitating nucleocapsid assembly and transport, and interfering with immune responses in host cells through downregulation of interferon (IFN)-activated genes. Thus, whether VP24 is a peripheral protein with lipid binding ability for matrix layer recruitment has not been explored. Here we examined the lipid binding ability of VP24 with a number of lipid binding assays. The results indicated that VP24 lacked the ability to associate with lipids tested regardless of VP24 posttranslational modifications. We further demonstrate that the presence of the EBOV major matrix protein VP40 did not promote VP24 membrane association in vitro or in cells. Further, no protein-protein interactions between VP24 and VP40 were detected by co-immunoprecipitation. Confocal imaging and cellular membrane fractionation analyses in human cells suggested VP24 did not specifically localize at the plasma membrane inner leaflet. Overall, we provide evidence that EBOV VP24 is not a lipid binding protein and its presence in the viral matrix layer is likely not dependent on direct lipid interactions.

Metal matrix composite are used in such fields of technology, such as: aerospace, electronics, energy, industry, defense, automotive, aviation, shipbuilding, and more. Composite coatings of ceramic - metals is used primarily to enhance the durability of machine parts. Therefore, new materials are permanently looked for, what has resulted in the past in development of composite materials. The coatings dispersed are consisting of metallic matrix (metals and their alloys) and small non-metallic particles. The deposition of ceramic particles simultaneously with metallic matrix leads often to composite coatings possessing properties much better than those of metallic coating. The nickel and less often, other iron group elements are usually used as a matrix and Al2O3 as tough particles. The welding technology of applying alloy and composite coatings is widely used. The technology of infrasound thermal spraying of metal matrix composite coatings was presented. It is a simple technology and a very useful one in ship machinery regeneration during the cruise craft (e.g. internal combustion engines, torque pumps, separators). The metal matrix composite coatings must undergo finishing due to high surface roughness after application. In the article to used finishing by plastic working and machining of coatings nickel matrix composite was proposed.

Collisions of low energy electrons with molecules are important for understanding many aspects of the environment and technologies. Understanding the processes that occur in these types of collisions can give insights into plasma etching processes, edge effects in fusion plasmas, radiation damage to biological tissues and more. A radical update of the previous expert system for computing observables relevant to these processes, Quantemol-N, is presented. The new Quantemol Electron Collision (QEC) expert system simplifyies the user experience, improving reliability and implements new features. The QEC GUI interfaces the Molpro quantum chemistry package for molecular target setups and to the sophisticated UKRmol+ codes to generate accurate and reliable cross-sections. These include elastic cross-sections, super elastic cross-sections between excited states, electron impact dissociation, scattering reaction rates, dissociative electron attachment, differential cross-sections, momentum transfer cross-sections, ionization cross sections and high energy electron scattering cross-sections. With this new interface we will be implementing dissociative recombination estimations, vibrational excitations for neutrals and ions, and effective core potentials in the near future.

Portfolio weights solely based on risk avoid estimation error from the sample mean, but they are still affected from the misspecification in the sample covariance matrix. To solve this problem, we shrink the covariance matrix towards the Identity, the Variance Identity, the Single-index model, the Common Covariance, the Constant Correlation and the Exponential Weighted Moving Average target matrices. By an extensive Monte Carlo simulation, we offer a comparative study of these target estimators, testing their ability in reproducing the true portfolio weights. We control for the dataset dimensionality and the shrinkage intensity in the Minimum Variance, Inverse Volatility, Equal-risk-contribution and Maximum Diversification portfolios. We find out that the Identity and Variance Identity have very good statistical properties, being well-conditioned also in high-dimensional dataset. In addition, the these two models are the best target towards to shrink: they minimise the misspecification in risk-based portfolio weights, generating estimates very close to the population values. Overall, shrinking the sample covariance matrix helps reducing weights misspecification, especially in the Minimum Variance and the Maximum Diversification portfolios. The Inverse Volatility and the Equal-Risk-Contribution portfolios are less sensitive to covariance misspecification, hence they benefit less from shrinkage.

The implementation of graphene-based electronics requires fabrication processes able to cover large device areas since exfoliation method is not compatible with industrial applications. Chemical vapor deposition of large-area graphene represents a suitable solution having the important drawback of producing polycrystalline graphene with formation of grain boundaries, which are responsible for limitation of the device performance. With these motivations, we formulate a theoretical model of graphene grain boundary by generalizing the graphene Dirac Hamiltonian model. The model only includes the long-wavelength regime of the particle transport, which provides the main contribution to the device conductance. Using symmetry-based arguments deduced from the current conservation law, we derive unconventional boundary conditions characterizing the grain boundary physics and analyze their implications on the transport properties of the system. Angle resolved quantities, such as the transmission probability, are studied within the scattering matrix approach. The conditions for the existence of preferential transmission directions are studied in relation with the grain boundary properties. The proposed theory provides a phenomenological model to study grain boundary physics within the scattering approach and represents per se an important enrichment of the scattering theory of graphene. Moreover, the outcomes of the theory can contribute in understanding and limiting detrimental effects of graphene grain boundaries also providing a benchmark for more elaborated techniques.

In this article, bio-composites derived from starch-glycerol biodegradable matrix reinforced with jute fibers have been fabricated using the wet hand lay-up and compression moulding techniques. Samples having different weight percentages of jute fiber in the starch matrix have been analysed. The fibers surface was chemically treated by alkaline sodium hydroxide for improving the interphase bonding between fiber and matrix. Tensile test for the composites were done and the sample with highest tensile strength was selected for further tests that included water absorption, scanning electron microscopy and thermal analysis. It has been concluded that the ultimate tensile strength was found to be maximum for the composition of 15% fiber by weight composite as 7.547 MPa without epoxy coating and 10.43 MPa with epoxy coating. The major disadvantage of bio-composite is its high water absorption property, which in this study has been inhibited by the epoxy resin layer. Herein, the results of various tests done disclose a noteworthy improvement in the overall properties of bio-composite, in comparison to the neat biodegradable starch matrix.

The primary purpose of this article is to deduce specific order estimates for the \textit{Mertens Function} $M(n)$, which facilitates us to analyze the location of zeros of the \textit{Riemann Zeta function} $\zeta(s)$. The paper also provides a brief overview about the notion of the \textit{Mertens Function} $M(n)$ and \textit{Redheffer Matrices} $\mathbb{A}_{n}$. In addition to learning about various \textit{spectral properties} of $ \mathbb{A}_{n}$, we shall also deduce the relation between these two, which, eventually would lead us to establish a necessary and sufficient condition for the \textit{Riemann Hypothesis} to hold true, as justified by \textit{Redheffer} himself. We shall also observe several numerical evidence as well as theoretical justification behind the falsity of the famous \textit{Mertens Hypothesis}, along with how researchers over the years have approached towards deriving an estimate of the smallest possible natural number $n$ for which the first such violation of the theorem occurs, utilizing numerous conjectures annotating about the order of $M(n)$. Readers who are highly motivated in pursuing research in any of the topics relevent to the contents of this paper will surely find the \texttt{References} section to be extremely resourceful.

Cerebral palsy (CP) is the most common movement disorder in children with a prevalence rang-ing from 1.5 to 4 per 1000 live births. CP is caused by a non-progressive lesion of the developing brain, leading to progressive alterations of the musculoskeletal system, including spasticity, often leading to the development of fixed contractures, necessitating tendon lengthening surgery. Total RNA-sequencing analysis was performed on semitendinosus tendons from diplegic and tetraple-gic CP patients subjected to tendon lengthening surgery compared to control patients undergoing anterior cruciate ligament reconstructive surgery. Tetraplegic CP patients showed increased ex-pression of genes implicated in collagen synthesis and extracellular matrix (ECM) turnover, while only minor changes were observed in diplegic CP patients. In addition, tendons from tetra-plegic CP patients showed an enrichment for upregulated genes involved in vesicle-mediated transport and downregulated genes involved in cytokine and apoptotic signaling. Overall, our results indicate increased ECM turnover with increased net synthesis of collagen in tetraplegic CP patients without activation of inflammatory and apoptotic pathways similar to observations in athletes where ECM remodeling results in increased tendon stiffness and tensile strength. Never-theless, the resulting increased tendon stiffness is an important issue in clinical practice, where surgery is often required to restore joint mobility.

In this study we assessed the electrical and optical behavior of semiconductor hybrid films fabricate from octaethyl-21H,23H-porphine copper (CuP), embedded in polymethylmethacrylate (PMMA), and polystyrene (PS). The hybrid films were characterized structurally and morphologically by means of Infrared spectroscopy (IR), atomic force microscopy (AFM), scanning electron microscopy (SEM) and X-ray diffraction (XRD). Subsequently, the PMMA:CuP and PS:CuP hybrid films were evaluated optically by UV-vis spectroscopy, as well as electrically, with the four-point collinear method. Hybrid films present a homogeneous and low roughness morphology, besides; the PS matrix allows the crystallization of the porphin, while the PMMA promotes the amorphous structure in CuP. The polymeric matrix also has an effect on the optical behavior of the films, since the smallest optical gap (2.16 eV) and onset gap (1.89 eV) and the highest transparency are obtained in the film with a PMMA matrix. Finally, the electrical behavior in hybrid films is also affected by the matrix: the largest amount of current carried is around 0.01 A for PS:CuP film, while for PMMA:CuP film it is 0.0015 A. Thanks to the above properties, hybrid films are promising candidates for use in optoelectronic devices.

Nonnegative matrix factorization (NMF) has been shown to be a strong data representation technique, with applications in text mining, pattern recognition, image processing, clustering and other fields. In this paper, we propose a hypergraph regularized Lp smooth nonnegative matrix factorization (HGSNMF), by incorporating hypergraph regularization and Lp smoothing constraint terms into the standard NMF. The hypergraph regularization term can capture the intrinsic geometry structure of the high dimension space data more comprehensively than simple graph, the Lp smoothing constraint may yield a smooth and more accurate solution to the optimization problem. The updating rules are given using multiplicative update techniques, and the convergence of HGSNMF is theoretically investigated. The experimental results on four different data sets show that the proposed method has better clustering effect than the related state-of-the-art methods in the vast majority of cases.

Through the arrow decomposition of the Mueller matrix, respective sets of sixteen independent polarimetric images of biological tissues are obtained for enpolarizing, retarding and depolariz-ing descriptors. In addition to the mean intensity coefficient and the three indices of polarimetric purity, the absolute values and Poincaré orientations of diattenuation, polarizance, entrance re-tardance and exit retardance vectors are considered. In this work we use for the first time this set of polarimetric observables for the visualization of biological structures, both of animal and vege-tal origin. Results show images with enhanced visualization derived from the spatial variation of such significant polarimetric properties. The experimental results are discussed, showing the suit-ability of such set of observables for applications in biophotonics imaging, providing not only ex-cellent visualization of biological tissues, but also showing structures not visible in non-polarimetric images.

The use of tungsten fiber-reinforced tungsten composites (Wf/W) has been demonstrated to significantly enhance the mechanical properties of tungsten (W) by incorporating W-fibers into the W-matrix. However, prior research has been restricted by the usage of single fiber-based textile fabrics, consisting of 150 µm warp and 50 µm weft filaments, with limited homogeneity, reproducibility, and mechanical properties in bulk structures due to the rigidity of the 150 µm fibers. To overcome this limitation, two novel textile preforms were developed utilizing radial braided yarns with 7 core- and 16 sleeve filaments (R.B. 16+7) as the warp material. In this study, bulk composites of two different fabric types were produced via a layer-by-layer CVD-process, utilizing single 50 µm filaments (type 1) and R.B. 16+7 yarns (type 2) as weft materials. The produced composites were sectioned into KLST-type specimen based on DIN EN ISO 179-1:2000 using electrical discharge machining (EDM), and subjected to three-point bending tests. Both composites demonstrated enhanced mechanical properties with pseudo-ductile behavior at room temperature and endured over 10,000 load cycles between 50-90 % of their respective maximum load without sample fracture. Composites based on fabric type 1 demonstrated superior manufacturing performance and mechanical properties, a high relative average density (>97 %), and high fiber volume fraction (14-17 %). Furthermore, a novel approach to predict the fatigue behavior of the material under cyclic loading was developed based on the high reproducibility of the mechanical properties of type 1, providing a new benchmark for upscaling endeavors.

Fibreglass composite plates are used for applications ranging from aerospace and automotive industries to construction industry. Vibroacoustic properties of the fibreglass plate has been investigated for different boundary conditions. The theory of the plate vibration and sound radiation has been used to determine the deflection of the composite plate at different locations on its surface. 3-Dimentional (3D) deformations and their corresponding contour velocities of plate have been computed for a range of frequencies. It has been shown that clamping the plate at four edges delayed first resonance of the plate by 15 Hz and second resonance of the plate by 30 Hz. Vibroacoustic indicators and the radiation impedance matrix of the plate have also been calculated. The results of this study show that fibreglass plate could be used in building industry to dampen the vibration of machine and structural vibration of buildings, and to sandwich building structures to form panels in order to attenuate airborne sound and to lower noise transmission of structural borne sound

This study investigated and classified typical structures in rural village and analyzed the vulnerability of various typical types of structures. Based on the statistics of earthquake damages with magnitudes above 5 from 1996 to 2013 in China, the damage matrixes of different types of structures in rural village are obtained. And The vulnerability index and the vulnerability equation of structure are crucial to assess the earthquake losses of typical structures under different magnitudes earthquakes. According to the seismic loss of different types of structures under different earthquake magnitudes, there are possible to improve the seismic resilience of the buildings in rural village. Moreover, the regional vulnerability is analyzed by β probability distribution function, and the comprehensive seismic performance index of different types of agricultural buildings in the region is obtained. The main research is to predict the loss of different types of structures under different earthquake magnitudes in the future, and to provide technical support for different types of building in rural village reinforcement.

Various studies have addressed the role of neutrophils in cancer wherein the focus has been drawn on the elevated neutrophil count in blood or at tumor loci. However, cancer has a systemic impact which targets various organs thus challenging the overall physiology of the host. So, it is worthwhile to explore whether and how neutrophils contribute to systemic deterioration in cancer. To discern the systemic role of neutrophils, we monitored their number and function at different stages of tumor growth in Dalton’s lymphoma mice model. Notably, we observed a gradual increase in neutrophil count in blood and their infiltration in vital organs of tumor bearing mice. In parallel, we observed damaged histoarchitecture with significant alterations in biochemical parameters that aggravated with tumor progression. We next examined systemic impact of neutrophil by assessing neutrophil elastase, myeloperoxidase, and matrix metalloproteinases (MMP-8 and MMP-9) wherein we found their upregulated expression and activity in tumor condition. Taken together, our results demonstrate high infiltration and hyperactivation of neutrophils which possibly account for gradual systemic deterioration during cancer progression. Our findings thus implicate neutrophils as a potential therapeutic target that may help to reduce the overall fatality rate of cancer.

Recently, we have witnessed a booming development of composites and multi-dopant metal oxides to be employed as novel photocatalysts. Yet the practical application of photocatalysis for environmental purposes is still elusive. Concerns about the unknown fate and toxicity of nanoparticles, unsatisfactory performance in real conditions, mass transfer limitations and durability issues have so far discouraged investments in full-scale applications of photocatalysis. Herein, we provide a critical overview of the main challenges that are limiting large-scale application of photocatalysis in air and water/wastewater purification. We then discuss the main approaches reported in the literature to tackle these shortcomings, such as the design of photocatalytic reactors that retain the photocatalyst, the study of degradation of micropollutants in different water matrices, and the development of gas-phase reactors with optimized contact time and irradiation. Furthermore, we provide a critical analysis of research-practice gaps such as treatment of real water and air samples, degradation of pollutants with actual environmental concentrations, photocatalyst deactivation, and cost and environmental life-cycle assessment.

The diffusion process of water molecules within a polyetherimide (PEI) glassy matrix has been analyzed by combining the experimental analysis of water sorption kinetics performed by FTIR spectroscopy with theoretical information gathered from Molecular Dynamics simulations and with the expression of water chemical potential provided by a non-equilibrium lattice fluid model able to describe the thermodynamics of glassy polymers. This approach allowed to construct a convincing description of the diffusion mechanism of water in PEI providing molecular details of the process related to the effects of the cross- and self-hydrogen bondings established in the system on the dynamics of water mass transport.

This study presents an in–depth analysis and strategic planning techniques for approaching a situation or achieving progress related to information technology services of Nueva Ecija University of Science and Technology, particularly the San Isidro Campus. As an educational organization and one in the region excellence providers in education, the University has so much vital information to manage and services to offer to provide the student's needs through the Management Information System department, application of IT services as a competing instrument to combat tedious tasks such as online admission, grade release, enrollment information, and online learning, university announcement, and possible students’ internship. The objective of this study is to determine the influence of information technology in day–to–day activities of the organization and strategy applied to streamline processes more conveniently. The researchers develop a conceptual model that would analyze the IT services' impact by identifying its strengths, weaknesses, opportunities, and threats and cleverly act on it using the TOWS Matrix in generating strategic decisions. The overall results were beneficial to the University and MIS as a basis for formulating competitive strategies and integrating it in an extended development plan.

One of the main challenges for autonomous learning in virtual environments is finding the right material that fits students’ needs and supports their learning process. Personalized recommender systems partially solve this problem by suggesting online educational resources to students based on their preferences. However, in educational environments (which need a proper characterization of both users and educational resources), most existing recommendation algorithms either fail to include all the available information or use hybrid processes that do not exploit possible relationships between users and item features. This article presents a personalized recommender system for educational resources aimed at combining user and item information into a single mathematical model based on matrix factorization. As a result, estimated latent factors can provide insight into possible interactions between users and item features, improving the quality of the information retrieval process. We validated the proposed model on a real dataset that contains the ratings assigned by students from Universidad Nacional de Colombia and Universidade Feevale to educational resources in the Colombian Federation of Learning Object Repositories (FROAC in Spanish). User characterization included learning style and educational level, whereas item characterization (obtained from the objects’ metadata), included interactivity level, aggregation level and type, and resource format. These results, compared to those obtained when not all the available information is included, show that our method can improve the recommendation process.

Magnesium is one of the lightest structural metal used in different industrial sector and many works are present in literature about the study of its reinforcement by fillers addition. Basalt fibres are natural fillers with good mechanical properties, excellent resistance to high temperature and lower cost than carbon fibres. For these aspects, in the last years they are increasingly used in the production of composite materials with polymeric matrices. However, very few information are presents in literature about the use of basalt fibres as reinforcement in metal matrix composite materials. It is well known that the impregnation of fibres reinforcement affects the mechanical behavior of composites materials. The aim of this study is to investigate the impregnation and the behavior of basalt fibres in a magnesium alloy composite material manufactured by a centrifugal casting technique.