This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. To illustrate our main findings, we present two numerical algorithms and examples in this paper.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

Lignin fibers typically influence the mixture performance of stone matrix asphalt (SMA), such as strength, stability, durability, noise level, rutting resistance, fatigue life, and water sensitivity. However, limited studies were conducted to analyze the influence of fibers on the percent voids in mineral aggregate in bituminous mixture (VMA) during the mixture design. This study analyzed the effect of different fibers and fiber contents on the VMA in SMA mixture design. A surface-dry condition method test and Marshall Stability test were applied on the SMA mixture with four different fibers (i.e., flocculent lignin fiber, mineral fiber, polyester fiber, blended fiber). The test results indicated that the bulk specific gravity of SMA mixtures and asphalt saturation decreased with the increasing fiber content, whilst the percent air voids in bituminous mixtures (VV), Marshall Stability and VMA increased. Mineral fiber had the most obvious impact on the bulk specific gravity of bituminous mixtures, while flocculent lignin fiber had a minimal impact. The mixture with mineral fiber and polyester fiber had significant effects on the volumetric properties, and, consequently, exhibited better VMA over the conventional SMA mixture with lignin fiber. Modified fiber content range was also provided, which will widen the utilization of mineral fiber and polyester fiber in the applications of SMA mixtures. The mixture evaluation suggested no statistically significant difference between lignin fiber and polyester fiber on the stability. The mineral fiber required a much larger fiber content to improve the mixture performance than other fibers. Overall, the results can be a reference to guide SMA mixture design.

In this work, a generalized analogue to the Pauli spin matrices is presented and investigated. The proposed Hermitian spin matrices exhibit a general symmetry. The generalized spin projection operators are derived and the electrodynamics for hypothetical fermions are explored using the proposed spin matrices. The fermionic quantum Heisenberg model is constructed using the proposed spin matrices and comparative studies against simulation results using the Pauli spin matrices are conducted. Further analysis on key findings as well as discussions on extending the proposed spin matrix framework to describe hypothetical bosonic systems (spin-1) are provided.

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

There is great current interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a "phase" parameter that characterises the way "exceptional points" (singularities of various sorts) determine the system. These systems are briefly reviewed with an emphasis on their geometrical thermodynamics properties.

There is great current interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a "phase" parameter that characterises the way "exceptional points" (singularities of various sorts) determine the system. These systems are briefly reviewed with an emphasis on their geometrical thermodynamics properties.

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 investigation mainly focused on the microstructural analysis of Al based hybrid metal matrix composites. Aluminium as base metal and reinforced with 2% B4 C, ZrO2 (2%,4%,6%), SiC (4%,8%,12%). Specimens were manufactured by using conventional stir casting technique. Hybrid metal matrix composites were examined by using Scanning electron microscope. This research explained XRD, EDS and Fractography analysis. This investigation shows the reinforced material has given better results in all aspects than pure Al6061 alloy and homogeneous dispersion of particles inside the matrix. Porosity, delamination, cracks, particle distributions were observed through microstructural analysis. Additionally determined the crystal size of pure Aluminium 6061 alloy and hybrid composites.

Thin people who undergo implant insertion into the chest wall face a high risk of implant exposure to the external environment. Five months after an 8-year-old boy underwent implantable cardioverter-defibrillator (ICD) implantation in a subcutaneous pocket in the left anterolateral chest wall to manage long QT syndrome, ICD replacement became necessary owing to exposure risk from distal and lateral thinning of the ICD pocket. Pocket rupture and exposure would increase the risk of infection; therefore, we performed ICD removal and primary pocket closure. Two weeks later, a new suprafascial pocket was created, acellular dermal matrix (ADM) was attached to the inner wall to prevent ICD protrusion, and a new ICD was inserted. One year postoperatively, the ADM was engrafted, and no complications were observed. A thin subcutaneous layer increases the risk of ICD implantation complications. Inner wall strengthening with ADM can help prevent pocket rupture.

We study almost hypercomplex structure with Hermitian-Norden metrics on 4-dimensional Lie groups considered as smooth manifolds. All the basic classes of a classification of 4-dimensional indecomposable real Lie algebras depending on one parameter are investigated. There are studied some geometrical characteristics of the respective almost hypercomplex manifolds with Hermitian-Norden metrics.

In Indonesia, types of meat are still identified manually due to increasing prices for beef and buf-falo ahead of Idul Fitri. Traders mix beef with pork to thwart the beef scam. Haar wavelet and GLCM, GLCM with angles of 0°, 45°, 90°, and 135°, as well as matrices using contrast, correlation, energy, homogeneity, and entropy, are used in feature extraction. The following are the results of meat image classification testing using k-NN, Haar wavelet, and GLCM: The k-NN algorithm shows superiority in identifying fresh (99%), frozen (99%), and rotten (96%) meat texture images with the most fantastic accuracy results in every situation. Meanwhile, GLCM routinely provides good results, especially regarding the texture image of fresh meat (183.21) and rotten meat (115.79). However, despite delivering less throughput than k-NN and GLCM, Haar wavelets are still helpful, especially when dealing with fresh meat texture images (89,96).

The transformation of the states of polarization of electromagnetic waves that interact with polarimetrically linear media can be represented by means of the associated Mueller matrix. A global measure of the ability of a linear medium to modify the states of polarization of incident waves, due to any combination of enpolarizing, depolarizing and retarding properties, is introduced as a distance of the Mueller matrix to the identity matrix. This new descriptor, called the polarizing power, is applicable to any Mueller matrix and can be expressed as a function of the degree of polarimetric purity and the trace of the Mueller matrix. The graphical representation of the feasible values of the polarizing power provides a general view of its main peculiarities and features. The values of the polarizing power for several typical devices are analyzed.

In this paper after introducing a model of binary data matrix (BDM) for physical parameters of an evolving system (of particles), we develop a Hilbert space as an ambient space to derive induced metric tensor on embedded parametric manifold identified by associated joint probabilities of particles observables (parameters). Parameter manifold assumed as space-like hypersurface evolving along time axis, an approach that resembles 3+1 formalism of ADM and numerical relativity. We show the relation of endowed metric with related density matrix. Identification of system density matrix by this metric tensor, leads to the equivalence of quantum Liouville equation and metric compatibility condition while covariant derivative of metric tensor has been calculated respect to Wick rotated time or spatial coordinates. After deriving a formula for expected energy per particles, we prove the equality of this expected energy with local scalar curvature of related manifold. We show the compatibility of BDM model with Hamilton-Jacobi formalism and canonical forms. On the basis of the model, I derive the Ricci flow like dynamics as the governing dynamics and subsequently derive the action of BDM model and Einstein field equations. Given examples clarify the compatibility of the results with well-known principles such as equipartition energy principle and Landauer’s principle. This model provides a background for geometrization of quantum mechanics compatible with curved manifolds and information geometry. Finally, we conclude a “bit density principle” which predicts the Planck equation, De Broglie wave particle relation, , Beckenstein bound and Bremermann limit.

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.

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

Hydrogels can be considered as mimics of extracellular matrix (ECM).Cytoskeleton through integrins is connected with ECM and cytoskeleton tension depends on ECM stiffness.A number of age-related diseases depend on cellular processes related with cytoskeleton function.Some examples of cancer initiation and progression and heart disease in relationship with ECM stiffness has been analysed.Incorporation of rigid particles in ECM can increase ECM stifness and to promote formation of internal residual stresses. Water migration, changes of water binding energy to biomactomolecules, changes of the state of water from tightly bound water to free and loosely bound water changes stiffness of ECM. Risks related with rigid particles incorporation into ECM have been also iscussed.

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.

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.

Matrix metalloproteinases (MMPs) have been demonstrated to have both detrimental and protective functions in inflammatory diseases. Several MMP inhibitors, with the exception of Periostat®, have failed in Phase III clinical trials. As an alternative strategy, recent efforts have been focussed on the development of more selective inhibitors or targeting other domains than their active sites (e.g., exosites, ectosites) through specific small molecule inhibitors or monoclonal antibodies. Here, we present some examples that aim to better understand the mechanisms of conformational changes/allosteric control of MMPs functions. In addition to MMP inhibitors, we discuss unbiased global approaches such as proteomics and N-terminomics to identify new MMP substrates and achieve a better understanding of the roles of these proteases in diseases.

Introduced in 1967 by Lov\'{a}sz, graph exponentiation has received little attention over the past several decades. Since graph exponentiation produces large graphs and any graph can be constructed utilizing its adjacency matrix, we provide a four step linear construction algorithm that generates the adjacency matrix for the graph exponential.

Biofilm matrix is akin to bacterial abodes, primarily composed of proteins, polysaccharides, extracellular DNA, and lipids, providing essential structural support to bacteria. While some biofilm matrix offers significant benefits, such as engineered biofilm reactors that assist in water pollutant removal, others pose risks to human health, potentially leading to conditions like lung infections. Realizing the potential of advantageous biofilm matrix and mitigating the harmful effects of detrimental ones necessitates a comprehensive and systematic exploration of this intricate domain. To facilitate this examination, our study leveraged a dataset of the 1000 most pivotal papers in the field and conducted an exhaustive bibliographic review. This paper serves as a valuable resource for understanding the current progress in biofilm matrix research and delving into vital avenues for future exploration in this dynamic field.

We report a theoretical derivation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing flavor eigenstates (i.e. left-chiral states) as superposition of mass eigenstates (i.e. the right-chiral states) weighted by square-root of mass. Flavor mixing for quarks is mediated by the square-root mass eigenstates, and the mass ratios used have been derived in earlier work from a left-right symmetric extension of the standard model. This permits a construction of the CKM matrix from first principles. There exist only four normed division algebras, they can be listed as follows - the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, the quaternions $\mathbb{H}$ and the octonions $\mathbb{O}$. The first three algebras are fairly well known; however, octonions as algebra are less studied. Recent research has pointed towards the importance of octonions in the study of high energy physics. Clifford algebras and the standard model are being studied closely. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. Also the action of various Spin Groups on these representations too can be studied easily. In this work, we build on some recent advances in the field and try to determine the CKM angles from an algebraic framework. We obtain the mixing angle values as $\theta_{12}=11.093^o, \theta_{13}=0.172^o, \theta_{23}=4.054^o$. In comparison, the corresponding experimentally measured values for these angles are $13.04^o \pm 0.05^o, 0.201^o \pm 0.011^o, 2.38^o \pm 0.06^o $. The agreement of theory with experiment is likely to improve when running of quark masses is taken into account.

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.

Gastric inflammation-related disorders are commonly observed digestive system illnesses char-acterized by the activation of proinflammatory cytokines, particularly tumor necrosis factor-α (TNF-α). This results in the induction of cyclooxygenase-2 (COX-2)/prostaglandin E2 (PEG2) and matrix metallopeptidase-9 (MMP-9). These factors contribute to the pathogenesis of gastric in-flammation disorders. We examined the preventive effects of Lonicera japonica Thunb. ethanol ex-tract (Lj-EtOH) on gastric inflammation induced by TNF-α in normal GES-1 cells. The GES-1 cell line was used to establish a model that simulated the overexpression of COX-2/PGE2 and MMP-9 proteins induced by TNF-α, to examine the anti-inflammatory properties of Lj extracts. The re-sults indicated that Lj-EtOH exhibits significant inhibitory effects on COX-2/PEG2 and MMP-9 ac-tivity, attenuates cell migration, and provides protection against TNF-α-induced gastric inflam-mation. The protective effects of Lj-EtOH are associated with the modulation of COX-2/PEG2 and MMP-9 through activation of TNFR–ERK 1/2 signaling pathways as well as the involvement of c-Fos and nuclear factor kappa B (NF-κB) signaling pathways. Based on our findings, Lj-EtOH ex-hibits a preventive effect on human gastric epithelial cells. Consequently, it may represent a novel treatment for the management of gastric inflammation.

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.

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.

Abstract: Congenital cytomegalovirus (cCMV) infection poses significant risks to fetal development, particularly affecting the nervous system. This study reports a fetal autopsy case, examining cCMV infection and focusing on CMV DNA measurements in various fetal organs before formalin fixation, a novel approach for comprehensive CMV DNA evaluations in fetal organs affected by cCMV. A 20-week-old male fetus was diagnosed with cCMV following the detection of CMV DNA in ascites obtained via abdominocentesis in utero. After termination of pregnancy, multiple organs of the fetus, including the cerebrum, thyroid gland, heart, lungs, liver, spleen, kidneys, and adrenal glands, were extracted and examined for CMV DNA loads using real-time polymerase chain reaction. Histopathological examination involved hematoxylin-eosin and CMV-specific immunostaining. A correlation was found between CMV DNA loads and pathology, with higher CMV-infected cell numbers observed in organs positively identified with both staining methods, exhibiting CMV DNA levels of ≥1.0 × 104 copies/mL, compared to those detected solely by CMV-specific immunostaining, where CMV DNA levels ranged from 1.0 x 103 to 1.0 x 104 copies/mL. These results highlight a quantifiable relationship between organ infection extent and CMV DNA concentration, providing insights into cCMV pathogenesis and potentially informing future diagnostic and therapeutic strategies for cCMV infection.

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.

We work with reference to a well-known semiclassical model, in which quantum degrees of freedom interact with classical ones. We show that, in the classical limit, it is possible to represent classical results (e.g., classical chaos) by means a pure-state density matrix.

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.

This article is devoted to the results of in-depth analysis of the system of binary-oppositional structures in DNA n-plet alphabets and their algebraic-matrix representations. These results show that the molecular complementary replication of DNA strands is accompanied by the presence of an algebraic version of the principle "like begets like" in matrix representations of DNA alphabets having internal structures. This algebraic version is based on binary-oppositional structures in the genetic molecular system, which can be represented by binary numbers and corresponding matrices of DNA alphabets. The received results allow thinking that the phenomenon "like begets like" (or a complementary replication in a wide sense) is systemic in the genetic organization and is connected with algebraic features of biological organization. Correspondingly, the biological principle "like begets like" can be additionally modeled by algebraic-matrix methods and approaches. Such algebra-matrix modeling of the genetic coding system gives new ways for studying and understanding the key role of the named principle in genetic and other inherited physiological complexes. On this way, the author discovered general rules of stochastic organization of information binary sequences of genomic DNAs of eukaryotes and prokaryotes. The presented rules are connected with information dichotomies of probabilities and corresponding fractal-like trees of probabilities, which fundamentally differ from constructional dichotomies in biological bodies. The received phenomenological data and rules lead to new biological ideas.

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.

By constructing a static map, the library robot can navigate and access documents autonomously, which greatly improves efficiency; however, for libraries where shelves can be moved, map changes do not allow for direct navigation, and also sensors such as radar and camera are relatively expensive, so we propose a low-cost navigation algorithm based on real-time ranging data and map matrices, and designed a mobile archive access robot. In order to obtain real-time distance data, nine near/long range sensors were mounted on the chassis and a composite digital filtering algorithm was designed based on different moving area characteristics; then the access task matrix and map matrix were designed based on the archive access task and the location characteristics of the archive shelf placement, the robot can rely on the range data to update the map matrix during the moving process, complete its own positioning, and use the task matrix The robot can use the task matrix to complete autonomous navigation and access to multiple files. Experiments show that the filtered positioning accuracy can reach 1cm, while the robot can move to the target shelf autonomously, which is more practical and less costly.

The paper summarizes in a step by step ‘recipe’ format a model of developing new ideas (Ideation) that can be used to form a new venture or develop a new product. The proposed ‘recipes’ are widely used and can be applied in tandem with other prevalently available models or tools. The intention of the paper is also to serve as a resource for entrepreneurs and innovators, and the links and references munificently used in the paper are serving this purpose. The author has used the outline and the tools described here in numerous Ideation classes taught for over a decade in several countries around the world. The paper’s intention is not to conduct a systematic review on the subject of new venture creation or propose new research agenda (for that, see for example Shepherd et al., 2021). The purpose is to provide an effective and efficient set of tools, models and techniques that can assist the entrepreneur in her journey to create and achieve her dreams. One such tool is the matrix of Reasonings-Outcomes introduced here for the first time.

The bottleneck in creating dynamic models of biological networks and processes often lies in estimating unknown kinetic model parameters from experimental data. In this regard, experimental conditions have a strong influence on parameter identifiability and should therefore be optimized to give the maximum information for parameter estimation. Existing model-based design of experiment (MBDOE) methods commonly rely on the Fisher Information Matrix (FIM) for defining a metric of data informativeness. When the model behavior is highly nonlinear, FIM-based criteria may lead to suboptimal designs since the FIM only accounts for the linear variation of the model outputs with respect to the parameters. In this work, we developed a multi-objective optimization (MOO) MBDOE, where model nonlinearity was taken into consideration through the use of curvature. The proposed MOO MBDOE involved maximizing data informativeness using a FIM-based metric and at the same time minimizing the model curvature. We demonstrated the advantages of the MOO MBDOE over existing FIM-based and other curvature-based MBDOEs in an application to the kinetic modeling of fed-batch fermentation of Baker's yeast.

This paper explores the application of Random Matrix Theory (RMT) as a methodological enhancement for portfolio selection within financial markets. Traditional approaches to portfolio optimization often rely on historical estimates of correlation matrices, particularly susceptible to instability. To address this challenge, we combine a data preprocessing technique based on the Hilbert transformation of returns with RMT to refine the accuracy and robustness of correlation matrix estimation. By contrasting empirical correlations with those derived from random matrices, we uncover non-random properties and underlying relationships within financial data. We then utilize this methodology to construct the correlation network dependence structure used in portfolio optimization. The empirical analysis presented in this paper validates the effectiveness of RMT in enhancing portfolio diversification and risk management strategies. This research contributes by offering investors and portfolio managers with methodological insights to construct portfolios that are more stable, robust, and diversified. At the same time, it advances our comprehension of the intricate statistical principles underlying multivariate financial data.

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.

Matrix metalloproteinases are involved in extracellular matrix remodeling through the degradation of extracellular matrix components and are involved in the inflammatory response by regulating the activities of TNF-alpha and IL-1beta, which are pro-inflammatory cytokines, in addition to extracellular matrix components. Since the regulation of inflammatory response and changes in the extracellular matrix by MMPs are related to the development of various diseases including lung and cardiovascular diseases, many studies have been conducted on the role of MMPs in pathogenesis. In addition, various studies have demonstrated that MMPs are involved in the pathogenesis of infectious diseases by regulating the expression and activity of MMPs by infection with pathogens. In this review, we discuss the role of MMPs in infectious diseases and the role of MMPs in inflammatory responses and present their potential as therapeutic targets in infectious diseases.

The theory of one-photon ionization and two-photon above-threshold ionization is formulated for applications to heavy atoms in attosecond science using the Dirac-Fock formalism. A direct comparison of the Wigner-Smith-Eisenbud delays for photoionization is made with delays from the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBIT) method. Photoionization by an attosecond pulse train, consisting of monochromatic fields in the extreme ultraviolet range, is computed with many-body effects at the level of the Relativistic Random Phase Approximation (RRPA). Subsequent absorption and emission processes of infrared laser photons in RABBIT are evaluated using static ionic potentials as well as asymptotic properties of relativistic Coulomb functions. As expected, light elements, such as Argon, show negligible relativistic effects, while heavier elements, such a Krypton and Xenon, exhibit delays that depend on the fine-structure of the ionic target. The relativistic effects are notable close to ionization thresholds and Cooper minima with differences in fine-structure delays predicted to be as large as tens of attoseconds. The separability of relativistic RABBIT delays into a Wigner-Smith-Eisenbud delay and a universal continuum--continuum delay is studied with reasonable separability found for photoelectrons emitted along the laser polarization axis in agreement with prior non-relativistic results.

Formalism proofing general derivation, applying matrix properties operations, showing fundamental relationships with inner product to outer product has been advanced here. This general proof formalism has direct application with physics to quantify quantum density at micro scale level to time commutator at macro scale level. System of operator algebraic equations have been rigorously derived to obtain analytic solutions which are physically acceptable. Extended physics application will include metricizing towards unitarization to achieve gaging Hamiltonian mechanics to electromagnetic gravitational strong theory, towards grand unifying physics atomistic to astrophysics or vice versa via quantum relativistic general physics thereby patching to classical physics fields energy.

The matrix converter converts the input line voltage into a variable voltage with an unrestricted output frequency without using an intermediate circuit, dc link circuit. A pure sine in and pure sine out is the unique feature of the matrix converter. This research paper also analyzes the basic operating principle and the simulation modeling of the direct matrix converter, which is controlled by the Space Vector Pulse Width Modulation technique by using the software which is known as MATLAB/Simulink. The most desirable features in the power frequency changes can be fulfilled by using the matrix converters, and this is the reason for the tremendous interest in the topology. Since the power electronic circuits which is known as the motor drives are used to operate the AC motors at the frequencies other than that of the supply.

An oil and vinegar scheme is a signature scheme based on multivariate quadratic polynomials over finite fields. The system of polynomials contains $n$ variables, divided into two groups: $v$ vinegar variables and $o$ oil variables. The scheme is called balanced (OV) or unbalanced (UOV), depending on whether $v = 0$ or not, respectively. These schemes are very fast and require modest computational resources, which make them ideal for low-cost devices such as smart cards. However, the OV scheme has been already proven to be insecure and the UOV scheme has been proven to be very vulnerable for many parameter choices. In this paper, we propose a new multivariate public key signature whose central map consists of a set of polynomials obtained from the multiplication of block matrices. Our construction is motivated by the design of the Simple Matrix Scheme for Encryption and the UOV scheme. We show that it is secure against the Separation Method, which can be used to attack the UOV scheme, and against the Rank Attack, which is one of the deadliest attacks against multivariate public-key cryptosystems. Some theoretical results on matrices with polynomial entries are also given, to support the construction of the scheme.

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.

Epoxy matrix composites reinforced with high-performance fibers such as carbon, Kevlar, and glass, exhibit excellent specific stiffness and strength in many mechanical applications. However, these composites are disappointingly non-recyclable and are usually disposed of in landfill sites, with no realistic prospect for biodegradation in reasonable time. In contrast, moldable composites with carbonized elastomeric matrices developed in the last decades possess attractive mechanical properties in final net-shape products and can also be incinerated or recycled. Many carbon and inorganic fillers have recently been evaluated to adjust the properties of carbonized elastomeric composites. Renewable organic fillers such as human or animal hair offer an attractive fibrous material with substantial potential for reinforcing composites with elastomeric matrices. Samples of unidirectional fiber composites (with hair volume fraction up to 7 %) and quasi-isotropic short fiber composites (with hair volume fraction up to 20 %) of human hair-reinforced nitrile butadiene rubbers (HH-NBR) were produced in the peroxide-cured and carbonized states. The samples were characterized using SEM, Raman spectroscopy and photoacoustic microscopy. Mechanical tests were performed in tension using a miniature universal testing machine. The expected effect of fiber reinforcement on the overall mechanical performance has been demonstrated for both cured and carbonized composites. Considerable enhancement of the elastic modulus (up to 10 times), ultimate tensile strength (up to 3 times) and damage tolerance was achieved. The evidence of satisfactory interfacial bonding between hair and rubber was confirmed by SEM imaging of fracture surfaces. The suitability of photoacoustic microscopy was assessed for 3D reconstruction of the fiber sub-system spatial distribution and non-destructive testing.

(1) Background: Breast cancer is a frequent heterogeneous disorder diagnosed in woman and is a high cause of mortality of them in reason to rapid metastasis and disease recurrence. Ferroptosis can inhibit breast cancer cell growth, improve the sensitivity of chemotherapy and radiotherapy and inhibit distant metastases so potentially acts on tumor micro-environment; (2) Methods: Ferroptosis/Extracellular matrix remodeling literature text-mining results were integrated in breast cancer transcriptome cohort according their distant relapse free survival (DRFS) under adjuvant therapy (anthracyclin+taxanes) and also in MDA-MB-231 transcriptome functional experiments with ferroptosis activations (GSE173905); (3) Results: Ferroptosis/Extracellular matrix remodeling text-mining identified 910 associated genes in at list 10 articles. Univariate Cox analyses censored on breast cancer (GSE25066) selected 252 individual significant genes and 171 of them found with an adverse expression. Functional enrichment of these 171 adverse genes predicted basal breast cancer signatures. By text-mining some ferroptosis significant adverse selected genes shared citations in domain of ECM remodeling such as: TNF, IL6, SET, CDKN2A, EGFR, HMGB1, KRAS, MET, LCN2, HIF1A, TLR4. A molecular score based on expression the eleven genes was found predictive of worst prognosis breast cancer at univariate level: basal subtype, short DRFS, high grade values 3 and 4, estrogen and progesterone receptors negative and nodal stages 2 and 3. This eleven gene signature was validated as regulated by ferroptosis inductors (erastin and RSL3) in triple negative breast cancer cellular model MDA-MB-231.; (4) Conclusions: Crosstalk between ECM remodeling-Ferroptosis functionalities allowed to define a molecular score which have been characterized as an independent adverse parameter in prognosis of breast cancer patients. Gene signature of this molecular score have been validated to be regulated by erastin/RSL3 ferroptosis activators. This molecular score could be promising to evaluate ECM impact of ferroptosis target therapies in breast cancer.

This paper seeks to optimize the mechanical and durability properties of ultra-high performance concrete (UHPC). To meet this objective, concrete specimens were manufactured by using 1,100 kg/m3 of binder, water/binder ratio 0.20, silica sand and last generation of superplasticizer. Silica fume, metakaolin and two types of nano silica were used for improving the performances of the concrete. Additional mixtures included 13mm long OL steel fibers. Compressive strength, electrical resistivity, mercury intrusion porosimetry tests and differential and thermogravimetric thermal analysis were carried out. The binary combination of nano silica and metakaolin, and the ternary combination of nano silica with metakaolin and silica fume, led to the best performances of the UHPC, both mechanical and durable performances.

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.

Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics and others. Due to its application in control theory, the matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C over the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of the dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for the dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.

In this paper, we introduce ResNetMF, a groundbreaking approach that harnesses the power of residual network matrix factorization to revolutionize recommendation systems. ResNetMF integrates residual networks, renowned for their ability to capture intricate patterns and features, with matrix factorization techniques that excel in modelling user-item interactions. This fusion presents a novel solution that surpasses the limitations of traditional recommendation systems. Through comprehensive experimentation and evaluation of diverse datasets, ResNetMF demonstrates remarkable enhancements in recommendation accuracy and efficiency. By effectively capturing both linear and nonlinear relationships in user-item interactions, ResNetMF provides superior recommendation quality. The outcomes from experiments unequivocally highlight the superiority of ResNetMF over existing state-of-the-art recommendation approaches, thereby validating its innovative nature and underscoring its potential to shape the future of recommendation systems. Through the integration of the deep residual network, ResNetMF approach facilitates the training of neural networks, enabling them to explore the underlying data layers more comprehensively. Extensive experimentation and evaluation across various datasets provide compelling evidence for the superiority of ResNetMF. Moreover, the proposed method utilized natural language processing (NLP) techniques for targeted information dissemination in recommendation systems, emphasizing the importance of personalized and relevant recommendations for user satisfaction and engagement.

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.

This article shows how to establish expansion formulas for calculating the mixed operations $(A^{\dag})^{\#}$, $(A^{\#})^{\dag}$, $((A^{\dag})^{\#})^{\dag}$, $((A^{\#})^{\dag})^{\#}$, $\ldots$ of generalized inverses, where $(\cdot)^{\dag}$ denotes the Moore--Penrose inverse of a matrix and $(\cdot)^{\#}$ denotes the group inverse of a square matrix. As applications of the formulas obtained, the author constructs and classifies some groups of matrix equalities involving the above mixed operations, and derives necessary and sufficient conditions for them to hold.

In order to meet the diversified rehabilitation needs of people, it is necessary to design a product for active rehabilitation of patients. Existing rehabilitation chairs use intelligent massage, which can cause problems such as large massage area, inability to local massage, large chair size, and inability to meet the continuous use of the damaged parts. In this paper, modular design method and multi-layer evaluation method are used to solve the problems related to rehabilitation chairs. The authors use the questionnaire survey method and the functional technology matrix method to determine the functional requirements of the rehabilitation chair, and then use the multilevel evaluation methods, including the AHP method, entropy weight method main and grey correlation analysis, to optimize the functional solutions of the rehabilitation chair, and finally obtain a chair for the rehabilitation of patients with upper and lower limb disorders. Problems such as generalisation of rehabilitation scope and non-durable use of components were solved, and the purpose of active exercise was achieved. This study verifies that the use of multilevel decision evaluation method can effectively improve the efficiency of programme decision-making, and provides theoretical and practical basis for the design of similar products.

Uterine fibroid (UF) is a tumour in some parts of the uterus, which introduces health challenges or death due to failed surgery among women globally. This study was designed to ascertain the involvement of micro-nutrients, inflammation, and antioxidant enzymes in the UF development to gain further insights and provide a strategy for managing the disease. One hundred ninety reproductive-aged women were recruited and classified equally into case and control subjects. The supernatant obtained from excised tissues from the fibroid and the normal samples from the adjacent myometrium were assessed for the selected biochemical parameters with standard methods. The levels of vitamin A and sodium between 26-35 years; vitamins D, E, zinc, and selenium between 46-55 years; and vitamin E at 56 years and above significantly decreased (p<0.05). Interleukin-2 (IL-2) level significantly increased (P < 0.05) among the case between 36-45 years. An increase in the activity of glutathione-s-transferase and the reduction in glutathione peroxidase activity and vitamin A level in the uterus between 26-45 years were the most pronounced significant findings (p<0.05) recorded. Prolonged vitamin A deficiency coupled with excess sodium salts facilitating inflammation induced by IL-2 are critical factors for UF development.

Computation of Discrete Fourier Transform (DFT) is a challenging task. Especially, on computational machines/embedded systems where resources are limited. The importance of Fourier Transform (FT) cannot be denied in the field of signal processing. This paper proposes a technique that can compute Discrete Fourier Transforms for a matrice or vector with the help of matrix multiplication. Moreover, this paper discusses the trivial methods used for computation of DFT along with methods based on matrix multiplication used to compute discrete Fourier Transform in addition to the shortcomings. The proposed method can help in the calculation of a Discrete Fourier Transformation matrix by truncation of values from the proposed generic method which can help in computing DFT of varying lengths of vectors. On legacy computing machines and programming environments, having support for matrix multiplication, the proposed methodology can be implemented.

Tenascin C (TNC) is an element of the extracellular matrix (ECM) of various tissues, including the skin, and is involved in modulating ECM integrity and cell physiology. Although skin aging is apparently associated with changes in the ECM, little is known about the role of TNC in skin aging. Here we found that Tnc mRNA level was significantly reduced in the skin tissues of aged mice compared with young mice, consistent with reduced TNC protein expression in aged human skin. TNC-large (TNC-L; 330-kDa) and -small (TNC-S; 240-kDa) polypeptides were observed in conditional media from primary dermal fibroblasts. Both recombinant TNC polypeptides, corresponding to TNC-L and TNC-S, increased the expression of type I collagen and reduced the expression of matrix metalloproteinase-1 in fibroblasts. Treatment of fibroblasts with a recombinant TNC polypeptide, corresponding to TNC-L, induced phosphorylation of SMAD2 and SMAD3. TNC increased the level of TGF-β1 mRNA and upregulated the expression of type I collagen by activating the TGF-β signaling pathway. In addition, TNC also promoted the expression of type I collagen in fibroblasts embedded in a three-dimensional collagen matrix. Our findings suggest that TNC contributes to the integrity of ECM in young skin and to prevention of skin aging.

The use of biodegradable materials has a growing field of application due to environmental concerns, however, scientific research on incremental forming using biomaterials is scarce. Thus, this study focuses on the single point incremental forming (SPIF) process applied to a composite sheet that combines a biodegradable thermoplastic matrix (Solanyl) reinforced with natural fibres (flax). The influence of the process parameters on the final geometry is determined, evaluating the effect of the following factors: step depth, wall angle and temperature reached during the process. Additionally, a heated aqueous medium is incorporated which facilitates the formability of the composite sheets. This method is especially useful for materials that have poor formability at room temperature. The benefits of using controlled heat include the reduction of formation forces applied to the plate, improved accuracy due to the reduction of elastic recovery, and the manipulation of the samples remarkably close to the glass transition temperatures. Through this experimental study with the variables analysed, a maximum shaping depth of 310 mm is obtained. These results confirm that the single point shaping used with bioplastic materials is possible and has positive outcomes for incremental forming.

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.

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.

Magnetic resonance elastography (MRE) has revealed sexual dimorphism in brain stiffness in healthy individuals and multiple sclerosis (MS) patients. In the animal model of MS, experimental autoimmune encephalomyelitis (EAE), we showed previously that inflammation-induced brain softening was associated with alterations of the extracellular matrix (ECM). However, it remained unclear whether the brain ECM presents sex-specific properties that can be visualized by MRE. Therefore, we aimed here at quantifying sexual dimorphism in brain viscoelasticity in association with ECM changes in healthy and inflamed brains. Multifrequency MRE was applied to the midbrain of healthy and EAE mice of both sexes to quantitatively map regional stiffness. To define differences in brain ECM composition, gene expression of the key basement membrane components laminin (Lama4, Lama5), collagen (Col4a1, Col1a1) and fibronectin (Fn1) was investigated by RT-qPCR. We showed that the healthy male cortex expressed less Lama4, Lama5, Col4a1 but more Fn1 (all p < 0.05) than the healthy female cortex, which was associated with 9% softer properties (p = 0.044) in that region. At peak EAE, cortical softening was similar in both sexes compared to healthy tissue, with an 8% difference remaining between males and females during EAE (p < 0.001). Cortical Lama4, Lama5 and Col4a1 expression increased 2 to 3-fold in EAE in both sexes while Fn1 decreased only in males (all p < 0.05). No significant sex differences in stiffness were detected in other brain regions. In conclusion, sexual dimorphism in the ECM composition of cortical tissue in the mouse brain is reflected by in vivo stiffness measured with MRE and should be considered in future studies by sex-specific reference values.

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.

This study provides an in-depth review of the available literature on metal composite material machining, focusing on traditional machining operations such as turning, milling, shaping, drilling, and grinding. The motivation for the study is that this composite type has emerged as a vital material in applications requiring functionality, resilience, cost-effective operation, low consumption of energy and lightweight. Despite its superior characteristics, the manufacturing complexity and poor machinability of metal matrix composites have been the primary barriers to its adoption. Nevertheless, there is a reduction of exceptional efficiency, increase in surface roughness, tool wear and so on in metal matrix composites throughout machining. As a result, this review gives a comprehensive investigation of metal matrix composite machining and effect on process parameters and procedures. Furthermore, this study distinguishes metal matrix composites towards sustainable manufacturing and the metals employed by the researchers, as well as the gaps discovered for future recommendations in metal-based composites.

The main purpose of the work was to determine the powder composition and properties of iron-based sinters used as a matrix in metallic diamond tools. The FeCuSnNi sinters obtained from a mixture of commercial powders were used for research. The material was subjected to milling in a ball mill and sinter have been performed with the hot-pressing technique in a graphite mold. The physical and mechanical properties of the sinters were tested. The investigations of obtained sinters concerned density, porosity, hardness, oxygen content, static tensile test and analysis of microstructure. The static tensile test was carried out with the use of a universal testing machine UTS-100. The study of the microstructure of sinters was performed using the JSM-7100F scanning electron microscope. The sinters are characterized by a high coefficient of thermal expansion and good mechanical properties. The FeCuSnNi sinter revealed a complex phase structure. Spot chemical analysis revealed the presence of Fe solution, Cu solution and the presence of iron oxides oxides. Nickel atoms were present throughout the sinter volume. The obtained results indicate that the presented material can be used as a matrix of a diamond-metal composite in diamond tools for the processing of natural stones and building materials.

Collagen, the most abundant structural protein found in mammals, plays a vital role as a constituent of the extracellular matrix (ECM) that surrounds cells. Collagen fibrils are strengthened through the formation of covalent cross-links, which involve complex enzymatic and non-enzymatic reactions. Lysyl oxidase (LOX) is responsible for catalyzing the oxidative deamination of lysine and hydroxylysine residues, resulting in the production of aldehydes, allysine, and hydroxyallysine. These intermediates undergo spontaneous condensation reactions, leading to the formation of immature cross-links, which are the initial step in the development of mature covalent cross-links. Additionally, non-enzymatic glycation contributes to the formation of abnormal cross-linking in collagen fibrils. During glycation, specific lysine and arginine residues in collagen are modified by reducing sugars, leading to the creation of Advanced Glycation End-products (AGEs). These AGEs have been associated with changes in the mechanical properties of collagen fibers. Interestingly, various studies have reported that plant polyphenols possess amine oxidase-like activity and can act as potent inhibitors of protein glycation. This review article focuses on compiling literature describing polyphenols with amine oxidase-like activity and antiglycation properties. Specifically, we explore the molecular mechanisms by which specific flavonoids impact or protect the normal collagen cross-linking process. Furthermore, we discuss how these dual activities can be harnessed to generate properly cross-linked collagen molecules, thereby promoting the stabilization of highly organized collagen fibrils.

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.

Atomic structure of N-electron atoms is often determined using the Hartree-Fock method, which is an integro-differential equation. The exchange term of the Hartree-Fock equations is usually treated as an inhomogeneous term of a differential equation, or with a local density approximation. This work uses matrix methods to solve for the Hartree-Fock equations, rather than the more commonly-used shooting method to integrate an inhomogeneous differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using computer linear-algebra packages. We extend the same technique to integro-differential equations, where a discretized integral can be written as a sum in matrix form. This method is compared against experiment and standard atomic structure calculations. We also can use this method for free-electron wavefunctions. This technique is important for spectral line broadening in two ways: improving the atomic structure calculations, and improving the motion of the plasma electrons that collide with the atom.

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

Adult mesenchymal stem cells (MSCs) are a promising cell source for tissue regeneration. However, ex vivo expansion results in cell senescence; cells lose their proliferation and differentiation capacity. Fetal MSCs can be an alternative due to their robust proliferation and differentiation capacities as well as immune privilege properties. Given the rejuvenation effect of decellularized extracellular matrix (dECM) on adult MSCs, it remains unknown whether dECM influences the regenerative potential of fetal stem cells. In this study, passage five fetal nucleus pulposus cells (fNPCs) and fetal synovium-derived stem cells (fSDSCs) were expanded on dECMs deposited by fNPCs (NECM) and fSDSCs (SECM) for one passage with expansion on tissue culture plastic (Plastic) as a control. We found that dECM expanded fNPCs and fSDSCs exhibited both similarities and differences in expression of stemness genes and surface markers. Expanded fNPCs yielded more differentiated pellets after chondrogenic induction but no adipogenic differentiation following adipogenic induction in both Plastic and dECM groups than the corresponding fSDSC group. Despite a significant increase in fNPCs, dECM expanded fSDSCs exhibited no increase in chondrogenic potential; however, compared to the Plastic group, dECM expanded fSDSCs exhibited a small increase in osteogenic potential and a great increase in adipogenic potential. These results suggest that fNPCs are more sensitive to NECM rejuvenation for cartilage tissue engineering and regeneration; in contrast, dECMs exhibited limited effects on fSDSC rejuvenation in chondrogenic capacity except for enhanced adipogenic capacity following expansion on SECM.

Due to the great threat of torpedo against surface warships, an efficient hydroacoustic countermeasure system must output realtime strategies that can accommodate varied antagonizing scenarios. Aiming at the decision-making problem in the anti-torpedo hydroacoustic countermeasure cases, this paper proposes an intelligent adversarial strategy based on the game theory. By discretizing the strategy space of both sides, a matrix game model is established with the payoff characterized by the capture probability of attacking torpedo. An improved simplex algorithm is then developed to get the mixed-strategy Nash equilibrium of the game model, with which preferred avoiding strategies can be obtained to minimize the risk of being captured by the attacking torpedo. Based on the probabilistic view of preferred adversarial strategy, the launching strategy of floating acoustic decoy can be achieved, and the evasion trajectory of warship can be confirmed simultaneously. Numerical simulation demonstrates that the proposed method can generate realtime intelligent antagonizing strategy, and consequently, can improve the survival rate of surface warships in the of anti-torpedo countermeasure scenarios.

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.

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.

Work from the last years indicate that the extracellular matrix (ECM) plays a direct role in vari-ous cellular processes including proliferation, migration and differentiation. Besides homeostat-ic processes, its regulatory function in inflammation becomes more and more evident. In in-flammation like inflammatory bowel disease, the ECM composition is constantly remodeled which can result in a structuring of fistulizing disease course. Thus, tracking early ECM changes might bear the potential to predict the disease course. In this review, we will provide an over-view of relevant diagnostic methods focusing on ECM changes.

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

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.

In this paper, the notion of θ∗-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan [Amer. Math. Monthly 76:1969] and Rhoades [Contemp. Math. 72:1988] on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

This study introduces an innovative approach to designing membranes capable of separating CO2 from industrial gas streams at higher temperatures. The novel membrane design seeks to leverage the well-researched high-temperature CO2 adsorbent, hydrotalcite, by transforming it into a membrane. This is achieved by combining it with an amorphous organo-silica-based matrix, extending the polymer-based Mixed Matrix Membrane concept to inorganic compounds. Following the membrane material preparation and investigation of the individual membrane in Part 1 of this study, we examine its permeation and selectivity here. The pure 200 nm thick hydrotalcite membrane exhibits Knudsen behavior due to large intercrystalline pores. In contrast, the organo-silica membrane demonstrates a permselectivity of 13.5 and permeance for CO2 of 1.3 107 mol m2 s1 Pa1 at 25°C, at 150°C the good separation behavior is reduced. Combining both components results in a hybrid microstructure, featuring selective surface diffusion in the microporous regions and unselective Knudsen diffusion in the mesoporous regions. Further attempts to bridge both components to form a purely microporous microstructure are outlined.

This study describes the synthesis and characterization of mixed hydrotalcite–organosilica membrane for gas separation. Hydrotalcite exhibits the capability to adsorb carbon dioxide at elevated temperatures. High surface area and favorable coating properties are essential to harness its potential for practical applications. Stable alcohol-based dispersions are needed for thin film applications of mixed membranes containing hydrotalcite. Currently, producing such dispersions without the need for delamination and dispersion agents is a challenging task. This work introduces for the first time a manufacturing approach to overcoming the drawbacks mentioned above. It includes a synthesis of hydrotalcite nanoparticles, followed by agent-free delamination of their layers and final dispersion into alcohol without dispersion agents. Further, the hydrotalcite-derived sorption agent is dispersed in a matrix based on organo-silica gels derived from 1,2-bis(triethoxysilyl)ethane (BTESE). The analytical results indicate that the interconnection between hydrotalcite and BTESE-derived gel occurs via forming a strong hydrogen bonding system between the interlayer species (OH groups, CO32-) of hydrotalcite and oxygen and silanol active gel centers. These findings lay the foundation for applications involving incorporating hydrotalcite-like compounds into silica matrices, ultimately enabling the development of materials with exceptional mass transfer properties. In part 2 of this study, gas separation performance of the organo-silica and the hydrotalcite-like materials and their combined form will be investigated

When it comes to financial transactions and counterfeit detection systems, banknote classification is crucial. In this paper, we propose an approach for the classification of Kazakhstan banknote images integrating Learning Vector Quantization (LVQ) with Statistical Texture Feature Extraction using the Gray Level Co-occurrence matrix (GLCM). Our methodology demonstrates effectiveness in accurately classifying banknote images, as evidenced by experimental results. The comprehensive testing scenarios show promising outcomes, with the combination of GLCM and Color Histogram under the LVQ algorithm achieving a high accuracy of 94.87 percent at distance 1 and 90°. These findings indicate the robustness and practical viability of the proposed method for authenticating banknotes.

Structural evolution, mechanical and tribological properties of Al-Mg alloy admixed with 5, 10 and 15 vol.% of iron powder using multi-pass friction stir processing (FSP) have been studied. Homogeneous distribution of intermetallic compound (IMC) particles were achieved after 4 FSP passes what resulted in increasing the stir zone hardness and ultimate tensile stress with simultaneous loss in the ductility. The reinforcement of the aluminum alloy matrix with IMCs allowed reducing wear at the same magnitude of friction. Subsurface composite tribological layer was formed on the FSPed samples as a result of rubbing against a steel counterbody.

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.

High density polyethylene (HDPE) and poly(lactic) acid (PLA) blends with different ratios of both polymers, namely 30:70, 50:50 and 70:30, were produced. Polyethylene grafted maleic anhydride and a random copolymer of ethylene and glycidyl methacrylate, were also proposed as compatibilizers to modify HDPE-PLA optimal blends and were added in the amounts of 1, 3 and 5 wt.%. Blends properties have been evaluated through different aspects by performing tensile tests, scanning electron microscopy to analyze blend morphology and interfaces, and thermomechanical analysis through differential scanning calorimetry, thermo-gravimetric analyses and infrared spectroscopy. The second blend, the one with equal amounts of HDPE and PLA seems to represent a good balance between high amount of bio-derived charge and acceptable mechanical properties. This suggests a good potential of these blends, which would be a good starting point for the production of composites with lingo-cellulosic fillers.

A rigorous perturbation analysis of the singular value decomposition of a real matrix of full column rank is presented. It is shown that the SVD perturbation problem is well posed only in case of distinct singular values. The analysis involves the solution of coupled systems of linear equations and produces asymptotic (local) componentwise perturbation bounds of the entries of the orthogonal matrices participating in the decomposition of the given matrix and of its singular values. Local bounds are derived for the sensitivity of the singular subspaces measured by the angles between the unperturbed and perturbed subspaces. An iterative scheme is described to find global bounds on the respective perturbations. The analysis implements the same methodology used previously to determine componentwise perturbation bounds of the Schur form and the QR decomposition of a matrix.

Camera malfunctions or loss of storage elements in imaging devices may lead to loss of important image information or random impulse noise interference. Low rank is one of the important prior information in image optimization processing. This paper uses different low-rank constraint models of the image matrices to recover the impulse interference satellite images. Firstly, an overview of image inpainting models based on nuclear norm, truncated nuclear norm, weighted nuclear norm, and matrix-factorization-based F-norm is presented, and corresponding optimiza-tion iterative algorithms are provided. Then, we conducted experiments under three types of pulse interference and provided visual and numerical results. Finally, it is concluded that the WSVT_ADMM method based on the weighted nuclear norm can obtain the best image inpainting results; The UV_ADMM method based on F norm of matrix factorization has the least computa-tion time and can be used for large-scale low-rank matrix computation; The WSVT_ADMM method based on weighted nuclear norm and the TSVT_ ADMM method based on truncated nuclear norms can significantly improve the repair effect compared to the nuclear norm-based methods such as SVT, SVP, and n_ADMM.

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.

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 cystic fibrosis (CF), pulmonary infection with Pseudomonas aeruginosa is a cause of increased morbidity and mortality, especially in patients for whom infection becomes chronic and there is reliance on long-term suppressive therapies. Current antimicrobials, though varied mechanistically and by mode of delivery, are inadequate not only due to eradication failure in many cases, but also because they do not halt the progression of lung function decline over time. One of the reasons for this failure is thought to be the biofilm mode of growth of P. aeruginosa, wherein self-secreted exopolysaccharides (EPSs) provide physical protection against antibiotics and an array of niches with resulting metabolic and phenotypic heterogeneity. Targeting the three EPSs secreted by P. aeruginosa (alginate, Psl and Pel) is currently under investigation as a way of disrupting the biofilm extracellular matrix to potentiate the action of antibiotics. In this review, we look at each EPS as a potential therapeutic target for combatting pulmonary infection with P. aeruginosa in CF, with a particular focus on the current evidence for these emerging therapies and barriers to bringing these therapies into clinic.

Mechanically strong and thermally stable films obtained from a water-based polyurethane (PU) dispersion with small (0.1–1.5 wt.%) additions of graphene oxide nanosheet (GO) were studied through elemental analysis, X-ray photoelectron spectroscopy, differential thermogravimetry, and Raman spectroscopy. Moreover, the depletion of near-surface layers in nitrogen was presented for all the samples under study. It was found that the introduction of GO into a PU matrix was ac-companied by a partial reduction of graphene oxide nanosheet and an increase in the concentra-tion of defects in its structure.

In this study, we designed a new biosensing membrane for the development of an electrochemical glucose biosensor. To proceed, we used a chitosan-based hydrogel that entraps glucose oxidase enzyme (GOx) and we crosslinked the whole matrix using glutaraldehyde, which is known for its quick and reactive crosslinking behavior. Then, the stability of the designed biosensors was investigated over time according to different storage conditions (in PBS solution at temperatures of 4 °C and 37 °C and in the presence or absence of glucose). In some specific conditions, we found that our biosensor is capable to keep its stability for more than six months of storage. We also included catalase to protect the biosensing membranes from the enzymatic reaction by-products (e.g., hydrogen peroxide). This design protects the biocatalytic activity of GOx and enhances the biosensor lifetime.

An evolutionary game is introduced which considers game-theoretic strategies in the context of non-linear population matrix models. This game considers the states and actions of the organisms of the evolving population, and a notion of dynamic equilibrium between strategies is described. The game’s formalism is expounded and a proof about equilibrium is given; specifically that any stable equilibrium can be described by proportions of pure strategies; particularly when population matrices are not defective.

We have studied on the stress measurement by making use of salivary nitrate, which can be a candidate of stress markers, with ion-selective field-effect transistors (ISFETs). ISFETs are suitable for on-site single-drop analysis of salivary nitrate within 10 seconds. However, when ISFETs are used for salivary nitrate, ISFETs have a problem which is called the initial drift. The initial drift makes it difficult for determination of an accurate nitrate monitoring. Thus, the purpose of this study is to suppress an initial drift and to search for new easy polymer to possess more performance of sensor responses than conventional matrix membrane such as PVC. In this research, we investigated ISFETs using specific matrix membrane for example, KP-13, Pellethane^® and P7281-PU. The initial drift was evaluated from the fluctuation of the response values generated by ISFETs which are immersed in saliva or aqueous solution. As a result, P7281-PU showed its suppression effect for the initial drift in the whole saliva and various solutions. Furthermore, the cause of drift may be H⁺ diffusion, and drift suppression effect of P7281-PU may be affected by urethane bond capturing H⁺ in ion-selective membrane. This result suggests a continuous nitrate monitoring and development of wearable sensors.

This article puts forward the bi-matrix games with crisp parametric payoffs based on interval value function approach. We conclude that the equilibrium solution of the game model can converted into optimal solutions of the pair of the non-linear optimization problem. Finally, experiment results show the efficiency of the model.

The occurrence of bone-related disorders and diseases has increased dramatically in recent years around the world. Demineralized bone matrix (DBM) has been widely used as a bone implant due to its osteoinduction and bioactivity. However, the use of DBM is limited because it is a particulate material, which makes it difficult to manipulate and implant with precision, in addition, these particles are susceptible to migrate to other sites. To address this situation, DBM is commonly incorporated into a variety of carriers. An injectable scaffold has advantages over bone grafts or preformed scaffolds, such as the ability to flow and fill the bone defect. The aim of this research is to develop a DBM carrier with such viscoelastic properties to obtain an injectable bone substitute (IBS). The DBM carrier developed consisted of a PVA/glycerol network cross-linked with borax and reinforced with CaCO3 as a pH neutralizer, porosity generator, and source of Ca. The physicochemical properties were determined by the injectability test, FTIR, SEM, and TGA. Porosity, degradation, bioactivity, possible cytotoxic effect, and proliferation in osteoblasts were also determined. The results show that the developed material has great potential to be used in bone tissue regeneration

Matrix Metaloproteinase-2 (MMP-2) is an extracellular Zn²⁺ protease specific to type I and IV collagens. Its expression is associated with several inflammatory, degenerative, and malignant diseases. Conformational properties, domain movements, and interactions between MMP-2 and its associated metal ions were characterized using a 1.0 µs molecular dynamics simulation. Dihedral principle component analysis revealed 10 families of conformations with the greatest degree of variability occurring in the link region connecting the catalytic and hemopexin domains. Dynamics cross correlation analysis indicated domain movements corresponding to opening and closing of the hemopexin domain in relation to the fibronectin and catalytic domains facilitated by the link region. Interaction energies were calculated using the MMPBSA-interaction entropy analysis method and revealed strong binding energies for the catalytic Zn²⁺ ion 1, Ca²⁺ ion 1, and Ca²⁺ ion 3 with significant conformational stability at the binding sites of Zn²⁺ ion 1 and Ca²⁺ ion 1. Ca²⁺ ion 2 diffuses freely away from its crystallographically defined binding site. Zn²⁺ ion 2 plays a minor role in conformational stability of the catalytic domain while Ca²⁺ ion 3 is strongly attracted to the highly electronegative sidechains of the Asp residues around the central β-sheet core of the hemopexin domain.

Additive manufacturing (AM) techniques are widely investigated for the cost-effective use of titanium (Ti) alloys in various aerospace applications. One of the AM techniques developed for such applications is plasma transferred arc solid free-form fabrication (PTA-SFFF). Materials manufactured through AM techniques often exhibit anisotropies in mechanical properties due to the layer-by-layer material build. In this regard, the present study investigates the isothermal directional fatigue of Ti-TiB metal matrix composite (MMC) manufactured by PTA-SFFF. This investigation includes rotating beam fatigue test, electron microscopy, and fatigue calculations. The fatigue experiments were performed at 350 ºC using specimen with the test axis oriented diagonally (45º) and parallel (90º) to the AM builds directions. The fatigue values from the current experiments along with literature data find that Ti MMC manufactured via PTA-SFFF exhibit fatigue anisotropy reporting highest strength in 90º and lowest in perpendicular (0º) AM build directions. Further, the electron microscopy investigations on 0º, 45º, and 90º AM build specimens reveal frequent TiB clusters in all three AM build directions and suggest that the spread of these TiB clusters play a role in fatigue anisotropy. Moreover, the fatigue calculations were performed using both the Paris’ and recently reported modified Paris’ equations. Comparison of R^2 values for these calculations show that modified Paris’ equation predicts the fatigue life of AM Ti-TiB MMC more accurately than the Paris’ equation.

Hydrotalcites (HTlc) represents a class of nanostructured layered materials that may be employed in a variety of applications, from green to bio technologies. In this paper, we report an investigation on HTlc made of Mg and Fe, recently employed to improve the growth in vitro of osteoblasts within a keratin sponge. We have carried out an analysis of powder materials and of HTlc dispersed in keratin and spin-coated on a Si/SiO2 substrate at different temperatures. A DC magnetic study of the powders has been carried out with a Quantum Design Physical Property Measurement System, equipped with a Vibrating Sample Magnetometer. The data gathered prove that these HTlc are fully paramagnetic, and keratin shows a very small magnetic response. Optical and Atomic Force Microscopy analyses of the thin films provide a detailed picture of clusters randomly dispersed in the films with various dimensions. The magnetic properties of these films have been characterized using the Nano Magneto Optical Kerr Effect (NanoMOKE) down to 7.5K. The data collected show that the local magnetic properties can be mapped with a micrometric resolution distinguishing HTlc regions from keratin ones. This approach opens new perspectives in the characterization of these composite materials.

Given a square matrix $A$, we are able to construct numerous equalities that involve reasonable mixed operations of $A$ and its conjugate transpose $A^{\ast}$, Moore--Penrose inverse $A^{\dag}$, and group inverse $A^{\#}$. Such kind of equalities can be generally represented in the equation form $f(A, \, A^{\ast}, A^{\dag}, A^{\#}) =0$. In this article, the author constructs a series of simple or complicated matrix equalities, as well as matrix rank equalities involving the mixed operations of the four matrices. As applications, we give a sequence of necessary and sufficient conditions for a square matrix to be range-Hermitian.

The neuroglial extracellular matrix (ECM) provides critical support and physiological cues for the proper growth, differentiation, and function of neuronal cells in the brain. However, in most in vitro settings that study neural physiology, cells are grown as monolayers on stiff surfaces that maximize adhesion and proliferation, and therefore lack the physiological cues that ECM in native neuronal tissues provides. Macromolecular crowding (MMC) is a biophysical phenomenon based on the principle of excluded volume that can be harnessed to induce native ECM deposition by cells in culture. Here, we show that MMC using two species of Ficoll with vitamin C supplementation significantly boosts deposition of relevant brain ECM by cultured human astrocytes. Dopaminergic neurons co-cultured on this astrocyte-ECM bed prepared under MMC treatment showed longer and denser neuronal extensions, a higher number of pre ad post synaptic contacts, and increased physiological activity as evidenced by higher frequency calcium oscillation, compared to standard co-culture conditions. When the pharmacological activity of various compounds was tested on MMC-treated co-cultures, their responses were enhanced, and for apomorphine, a D2-receptor agonist, it was inverted in comparison to control cell culture conditions, thus emulating responses observed in in vivo settings. These results indicate that macromolecular crowding can harness the ECM-building potential of human astrocytes in vitro forming an ultra-flat 3D microenvironment that makes neural cultures more physiological and pharmacological relevant.

Complex proteomic and physiological approaches to study cold and heat stress responses in plant mitochondria are still limited. Variations in the mitochondrial proteome of cauliflower (Brassica oleracea var. botrytis) curds after cold and heat and after stress recovery were assayed by 2D PAGE in relation to respiratory parameters. Quantitative analysis of the mitochondrial proteome revealed numerous stress-affected protein spots. In cold alternative oxidase isoforms were extensively upregulated; major downregulations in the level of photorespiratory enzymes, porine isoforms, oxidative phosphorylation (OXPHOS) and some low-abundant proteins were observed. On the contrary, distinct proteins, including carbohydrate metabolism enzymes, heat-shock proteins, translation, protein import, and OXPHOS components were involved in heat response and recovery. Few metabolic regulations were suggested. Cauliflower plants appeared less susceptible to heat; closed stomata in heat stress resulted in moderate photosynthetic, but only minor respiratory impairments, however photosystem II performance was unaffected. Decreased photorespiration corresponded with proteomic alterations in cold. Our results show that cold and heat stress not only operate in diverse mode (exemplified by cold-specific accumulation of some heat shock proteins), but exert some associations on molecular and physiological levels. This implies more complex model of action of investigated stresses on plant mitochondria.

This study investigated the inhibitory effect of Siegesbeckia orientalis ethanolic extract (SOE) on growth and metastasis of hepatic tumors in C57BL/6JNarl mice, which is the model of tumor-igenesis induced by subcutaneous injection of Hepa1-6 murine hepatoma cells on the back of mice. Feeding 25 mg SOE/kg BW daily for 14 days effectively reduced the hepatoma weight in tu-mor-bearing mice by 59.7%. SOE intervention reduced the expression of anti-apoptotic Bcl-2 gene in tumor tissue by 48.5% and down-regulated the antioxidant system, by reducing the gene ex-pression of catalase (48.0%), glutathione peroxidase (46.3%), and superoxide dismutase (32.0%). In addition, SOE intervention increased the production of ROS by 21.4%, and the gene expression of pro-inflammatory cytokines TNF-α, IL-1β, and IL-6 by 135.3%, 179.3% and 91.7%, respectively, indicating that SOE intervention promoted the acute inflammatory response. Results of H&E staining analysis showed that SOE had the ability to inhibit angiogenesis in tumor tissue. Fur-thermore, SOE treatment inhibited the expression of migration-related genes, such as MMP-2, MMP-7, MMP-9 and β-catenin, and the inhibition rates were 24.8%, 27.4%, 10.4% and 21.9%, respectively. These results imply that SOE had the ability to suppress tumor metastasis. On the other hand, SOE intervention decreased the serum contents of inflammatory cytokines, such as TNF-α, IL-1β and IL-6 by 27.4%, 30.4%, and 30.7%, respectively, indicating that SOE intervention has an anti-inflammatory effect on normal tissues of mice. Since SOE intervention had no signif-icant effect on liver and kidney weights, and no mice died throughout the experiment, it shows that it is safe to feed SOE under this experimental condition. Based on the above results, SOE has a great potential to be used in the treatment of hepatoma.