Function Matrix Research Articles

Specialized structure and function of the apical extracellular matrix at sense organs

Apical extracellular matrix (aECM) covers every surface of the body and exhibits tissue-specific structures that carry out specialized functions. This is particularly striking at sense organs, where aECM forms the interface between sensory neurons and the environment, and thus plays critical roles in how sensory stimuli are received. Here, we review the extraordinary adaptations of aECM across sense organs and discuss how differences in protein composition and matrix structure assist in sensing mechanical forces (tactile hairs, campaniform sensilla, and the tectorial membrane of the cochlea); tastes and smells (uniporous gustatory sensilla and multiporous olfactory sensilla in insects, and salivary and olfactory mucus in vertebrates); and light (cuticle-derived lenses in arthropods and mollusks). We summarize the power of using C. elegans, in which defined sense organs associate with distinct aECM, as a model for understanding the tissue-specific structural and functional specializations of aECM. Finally, we synthesize results from recent studies in C. elegans and Drosophila into a conceptual framework for aECM patterning, including mechanisms that involve transient cellular or matrix scaffolds, mechanical pulling or pushing forces, and localized secretion or endocytosis.

Mechanism study of BMSC-exosomes combined with hyaluronic acid gel in the treatment of posttraumatic osteoarthritis

ObjectiveTo explore the mechanism and efficacy of gel in the treatment of posttraumatic osteoarthritis (PTOA), combined with hyaluronic acid (HA) and bone marrow mesenchymal stem cell exosomes (BMSC-EXOs), and to explain its role in alleviating oxidative stress damage induced by mitochondrial reactive oxygen species (ROS). MethodsHow is the therapeutic potential of toa influenced by bone marrow mesenchymal stem cells-EXO to be evaluated both in vitro and in vivo. In vitro, BMSC-EXOs were extracted and characterized from rat specimens and labeled with Dil. Rat primary chondrocytes were then isolated to create a cellular PTOA model. BMSC-EXOs + HA group, BMSC-EXOs + HA + 740Y–P group, model group, BMSC-EXOs group, HA group, and control group were included in the cell group, and the function of cartilage matrix and the level of oxidative stress could be evaluated. Cartilage matrix integrity and oxidative stress can be assessed by grouping rats. At the same time, a rat model of ptosis can be established by excision of the anterior cruciate ligament, and joint rehabilitation, with pro-inflammatory and Enzyme-linked immunosorbent assay (ELISA) can be used to determine anti-inflammatory markers. ResultsThe combined use of BMSC-EXOs and HA gel was found to significantly reduce oxidative stress in chondrocytes and PTOA rat models, improving cartilage mechanical properties more effectively than BMSC-EXOs alone. ConclusionBMSC-EXOs combined with HA gel offer a promising treatment for PTOA by modulating damage caused by mitochondrial ROS-induced oxidative stress.

A knowledge-data integration framework for rolling element bearing RUL prediction across its life cycle

Prediction of Remaining Useful Life (RUL) for Rolling Element Bearings (REB) has attracted widespread attention from academia and industry. However, there are still several bottlenecks, including the effective utilization of multi-sensor data, the interpretability of prediction models, and the prediction across the entire life cycle, which limit prediction accuracy. In view of that, we propose a knowledge-based explainable life-cycle RUL prediction framework. First, considering the feature fusion of fast-changing signals, the Pearson correlation coefficient matrix and feature transformation objective function are incorporated to an Improved Graph Convolutional Autoencoder. Furthermore, to integrate the multi-source signals, a Cascaded Multi-head Self-attention Autoencoder with Characteristic Guidance is proposed to construct health indicators. Then, the whole life cycle of REB is divided into different stages based on the Continuous Gradient Recognition with Outlier Detection. With the development of Measurement-based Correction Life Formula and Bidirectional Recursive Gated Dual Attention Unit, accurate life-cycle RUL prediction is achieved. Data from self-designed test rig and PHM 2012 Prognostic challenge datasets are analyzed with the proposed framework and five existing prediction models. Compared with the strongest prediction model among the five, the proposed framework demonstrates significant improvements. For the data from self-designed test rig, there is a 1.66 % enhancement in Corrected Cumulative Relative Accuracy (CCRA) and a 49.00 % improvement in Coefficient of Determination (R2). For the PHM 2012 datasets, there is a 4.04 % increase in CCRA and a 120.72 % boost in R2.

Starlike and Convex functions associated with Hypergeometric Matrix functions

Starlike and Convex functions associated with Hypergeometric Matrix functions

S-Nodes, Factorisation of Spectral Matrix Functions and Corresponding Inequalities

S-Nodes, Factorisation of Spectral Matrix Functions and Corresponding Inequalities

Application of Dimension Extending Technique to Unified Hardening Model

This paper provides the process of incremental constitutive integration for the unified hardening model combined with the transformation stress method. The dimension-extending technique takes the hardening function of the hardening/softening model as the same position as the stress components, so that the constitutive integration of the plasticity can be reduced to an initial value problem of differential–complementarity equations, which is solved using the Gauss–Seidel algorithm-based Projection–Correction for the mixed complementarity problem. The Gauss–Seidel based Projection–Correction algorithm does not require the calculation of the Jacobean matrix of the potential function, making it relatively easy to implement in programming. The unified hardening model is proposed based on the modified Cam–Clay model and the sub-loading surface model, and the elastic properties are pressure-dependent. Two processing methods, backward Euler integration and exact elastic property, are used for the variable elasticity properties. The constitutive integration of the increased dimensional unified hardening model is reduced to a special mixed complementarity problem and solved by the proposed algorithm, which does not need to calculate the Jacobean matrix of the potential function, and greatly simplifies the derivation process. Several numerical examples are given to verify the feasibility of the incremental constitutive integration in the unified hardening model, including the single integral point and the boundary value problems. The research results have expanded the scope of use of the Gauss–Seidel based Projection–Correction algorithm.

Intelligent Text Mining for Ontological Knowledge Graph Refinement and Patent Portfolio Analysis—Case Study of Net-Zero Data Center Innovation Management

Ontological knowledge graph (OKG) is a well-formed visual representation that depicts knowledge organization in formal elements (e.g., entities and attributes) and their interrelationships. OKG is crucial for innovation management analysis as it provides a clear boundary to understand complex knowledge domain in detail. In the patent analysis field, it facilitates the definition of a well-defined patent portfolio, aiming for accurate and complete patent retrievals and subsequent analyses. In recent decade, the rapid growth of the information and communication technology (ICT) sector has rendered data centers (DCs) indispensable for data processing, storage, and cloud computing, while ensuring security and privacy during DC operations. However, their energy-intensive operations pose challenges to global efforts toward achieving net-zero emissions goals. In response, this research develops a formal OKG refinement process and uses DC net-zero technology OKG as case study for in-depth OKG refinement and application in patent portfolio analysis. The net-zero DC domain covers five sub-technologies. Utilizing the proposed OKG refinement and patent portfolio analysis framework, the 1801 most recent decade’s patents related to relevant “DC net-zero technologies” are retrieved and analyzed. Particularly in this case, DC colocation and server-as-a-service perspectives are the newly discovered sub-domains for OKG refinement. Furthermore, the research also adopts the technology function matrix and technology maturity to assess current and future technology development trends, providing crucial insights supporting strategic innovation management.

CTHRC1 is a prognostic biomarker correlated with immune infiltration in head and neck squamous cell carcinoma

BackgroundHead and neck squamous cell carcinoma (HNSCC) is the sixth most common malignancy worldwide, characterized by high morbidity, high mortality, and poor prognosis. Collagen triple helix repeat containing 1 (CTHRC1) has been shown to be highly expressed in various cancers. However, its biological functions, potential role as a biomarker, and its relationship with immune infiltrates in HNSCC remain unclear. Our principal objective was to analyze CTHRC1 expression, its prognostic implications, biological functions, and its effects on the immune system in HNSCC patients using bioinformatics analysis.MethodsThe expression matrix was obtained from The Cancer Genome Atlas (TCGA) and Gene Expression Omnibus (GEO). CTHRC1 expression in HNSCC was analyzed between tumor and adjacent normal tissues, different stages were compared, and its impact on clinical prognosis was assessed using Kaplan-Meier analysis. Gene Ontology (GO), Kyoto Encyclopedia of Genes and Genomes (KEGG), and Gene Set Variation Analysis (GSVA) were employed for enrichment analysis. The Search Tool for the Retrieval of Interacting Genes database (STRING) was used to analyze protein-protein interactions. Pearson correlation tests were used to investigate the association between CTHRC1 expression and immune checkpoints. The correlation between CTHRC1 and immune infiltration was investigated using CIBERSORT, TIMER, and ESTIMATE.ResultsCompared to adjacent normal tissues, CTHRC1 was found to be highly overexpressed in tumors. Increased expression of CTHRC1 was more evident in the advanced stage of HNSCC and predicted a poor prognosis. Most genes related to CTHRC1 in HNSCC were enriched in physiological functions of Extracellular matrix(ECM) and tumor. Furthermore, several immune checkpoints, such as TNFSF4 and CD276 have been shown to be associated with CTHRC1 expression. Notably, the level of CTHRC1 expression correlated significantly with immune infiltration levels, particularly activated macrophages in HNSCC.ConclusionsHigh expression of CTHRC1 predicts poor prognosis and is associated with immune infiltration in HNSCC, confirming its utility as a tumor marker for HNSCC.Trial registrationNot applicable. All data are from public databases and do not contain any clinical trials.

A numerical approach for solving nonlinear fractional Klein–Gordon equation with applications in quantum mechanics

Abstract In this paper, we propose a numerical approach for solving the nonlinear fractional Klein–Gordon equation (FKGE), a model of significant importance in simulating nonlinear waves in quantum mechanics. Our method combines the Bernoulli wavelet collocation scheme with a functional integration matrix to obtain approximate solutions for the proposed model. Initially, we transform the main problem into a system of algebraic equations, which we solve using the Newton–Raphson method to extract the unknown coefficients and achieve the desired approximate solution. To theoretically validate our method, we conduct a comprehensive convergence analysis, demonstrating its uniform convergence. We perform numerical experiments on various examples with different parameters, presenting the results through tables and figures. Our findings indicate that employing more terms in the utilized techniques enhances accuracy. Furthermore, we compare our approach with existing methods from the literature, showcasing its performance in terms of computational cost, convergence rate, and solution accuracy. These examples illustrate how our techniques yield better approximate solutions for the nonlinear model at a low computational cost, as evidenced by the calculated CPU time and absolute error. Additionally, our method consistently provides better accuracy than other methods from the literature, suggesting its potential for solving more complex problems in physics and other scientific disciplines.

Perineural Invasion Is Associated With Function-evoked Pain and Altered Extracellular Matrix in Patients With Head and Neck Squamous Cell Carcinoma

Head and neck squamous cell carcinoma (HNSCC) is painful, and perineural invasion (PNI) has been associated with the worst pain. Pain due to HNSCC is diverse and may vary based on clinicopathological factors. This study aims to characterize different pain patterns linked with PNI, its influence on daily functioning, and gain insights into molecular changes and pathways associated with PNI-related pain in HNSCC patients. We conducted a cross-sectional study across 3 medical centers (n = 114), assessing pain phenotypes and their impact on daily functioning using 2 self-reported pain questionnaires, given to patients prior to their cancer surgery. Furthermore, we conducted RNA-seq analysis utilizing the The Cancer Genome Atlas dataset of HNSCC tumor from patients (n = 192) to identify genes relevant to both PNI and pain. Upon adjusting for demographic and clinicopathological variables using linear regression models, we found that PNI independently predicted function-evoked pain according to the University of Calfornia San Francisco Oral Cancer Pain Questionnaire, as well as the worst pain intensity reported in the Brief Pain Inventory. Distinct pain patterns were observed to be associated with daily activities in varying manners. Our molecular analyses revealed significant disruptions in pathways associated with the extracellular matrix structure and organization. The top differentially expressed genes linked to the extracellular matrix are implicated in cancer development, pain, and neurodegenerative diseases. Our data underscore the importance of properly categorizing pain phenotypes in future studies aiming to uncover mechanistic underpinnings of pain. Additionally, we have compiled a list of genes of interest that could serve as targets for both cancer and cancer pain management. PerspectivePNI independently predicts function-evoked pain. Different pain phenotypes affect daily activities differently. We identified a list of candidate genes involved in the extracellular matrix structure and function that can be targeted for both cancer and cancer pain control.

Modal identification from turbulence response based on improved frequency domain decomposition

Turbulence excitation is an unavoidable form of excitation in flutter flight tests, and it is also a necessary and effective excitation method in high-speed flights, dives, other high-risk test, and high-frequency modal information mining. However, because the turbulence excitation signals are unmeasurable in the time domain, although the turbulence response contains rich and valuable flutter test information, the randomness and low quality of the data often cause difficulties in modal analysis. Therefore, an improved frequency domain decomposition algorithm for turbulence response processing is proposed in this paper. First, due to the irrelevancy of the atmospheric excitation, the power spectral density function matrix of the multi-channel turbulence response is subjected to singular value decomposition. There is a mathematical relationship between the maximum singular value curve and the system frequency response function. Second, the modal assurance criteria are used to calculate the maximum singular value of a single-degree-of-freedom system. Finally, an orthogonal polynomial method is applied to fit the maximum singular value curve, and the system identification is performed directly in the frequency domain. The simulated data and a certain type of aircraft flutter flight test data are used to verify the proposed method, and the results confirm the effectiveness and engineering applicability of the method developed in this work.

Sums of squares III: Hypoellipticity in the infinitely degenerate regime

This is the third paper in a series of three dealing with sums of squares and hypoellipticity in the infinitely degenerate regime. We establish a C^{2,\delta} generalization of M. Christ’s smooth sum of squares theorem, and then use a bootstrap argument with the sum of squares decomposition for matrix functions, obtained in our second paper of this series, to prove a hypoellipticity theorem that generalizes some cases of the results of Christ, Hoshiro, Koike, Kusuoka and Stroock and Morimoto for sums of squares, and of Fedĭi and Kohn for degeneracies not necessarily a sum of squares.

Neuroanatomical evidence and a mouse calcitonin gene-related peptide model in line with human functional magnetic resonance imaging data support the involvement of peptidergic Edinger-Westphal nucleus in migraine.

The urocortin 1 (UCN1)-expressing centrally projecting Edinger-Westphal (EWcp) nucleus is influenced by circadian rhythms, hormones, stress, and pain, all known migraine triggers. Our study investigated EWcp's potential involvement in migraine. Using RNAscope in situ hybridization and immunostaining, we examined the expression of calcitonin gene-related peptide (CGRP) receptor components in both mouse and human EWcp and dorsal raphe nucleus (DRN). Tracing study examined connection between EWcp and the spinal trigeminal nucleus (STN). The intraperitoneal CGRP injection model of migraine was applied and validated by light-dark box, and von Frey assays in mice, in situ hybridization combined with immunostaining, were used to assess the functional-morphological changes. The functional connectivity matrix of EW was examined using functional magnetic resonance imaging in control humans and interictal migraineurs. We proved the expression of CGRP receptor components in both murine and human DRN and EWcp. We identified a direct urocortinergic projection from EWcp to the STN. Photophobic behavior, periorbital hyperalgesia, increased c-fos gene-encoded protein immunoreactivity in the lateral periaqueductal gray matter and trigeminal ganglia, and phosphorylated c-AMP-responsive element binding protein in the STN supported the efficacy of CGRP-induced migraine-like state. Calcitonin gene-related peptide administration also increased c-fos gene-encoded protein expression, Ucn1 mRNA, and peptide content in EWcp/UCN1 neurons while reducing serotonin and tryptophan hydroxylase-2 levels in the DRN. Targeted ablation of EWcp/UCN1 neurons induced hyperalgesia. A positive functional connectivity between EW and STN as well as DRN has been identified by functional magnetic resonance imaging. The presented data strongly suggest the regulatory role of EWcp/UCN1 neurons in migraine through the STN and DRN with high translational value.

Low frequency load identification under high noise level using weighted total least squares

Load identification in structural dynamics is an ill-conditioned inverse problem, and the errors exist in both the transfer function matrix and the response vector, which have a great influence on the accuracy of the identification, especially at the low frequency and high noise. Although the Total Least Squares (TLS) method can consider the errors in the transfer function matrix and the response vector, the problem of unequal precision between them has not been properly solved. In this article, the Weighted Total Least Squares (WTLS) method for load identification is presented. First, the variance–covariance matrices are constructed using stochastic information, which can consider the unequal precision of the data and make the solution less biased and more precise. Then, Tikhonov regularization is used to regularize the WTLS method to reduce the ill-condition of the transfer function matrix. To validate the performance of the WTLS method under different noise levels, a load identification simulation with four excitation loads on a plate and a load identification experiment with three excitation loads on a steel plate were studied. The results show that when the noise levels of the transfer function and the response are different, the accuracy of the TLS solution is poor. Especially when the noise levels are high, the identification deviations are large. The WTLS method considers the unequal noise levels using the weight matrices, which provides more stable load estimates at different noise levels. And the identification deviations are greatly reduced compared to the TLS method.

On negative imaginariness and [formula omitted] control of descriptor systems with state–space symmetry

This paper studies negative imaginariness and the static output feedback H∞ control synthesis of descriptor systems based on the state–space symmetric model. First, under the assumption that the transfer function matrix is proper, necessary and sufficient conditions to determine negative imaginary properties are established for descriptor systems with state–space symmetry. Then, based on state–space symmetry, a sufficient condition is derived for the design of static output feedback controller, such that the resulting closed-loop system satisfies negative imaginary and H∞ performance. Finally, two circuit networks and a numerical example are provided to validate the main results of the paper.

An Efficient Algorithm for Basic Elementary Matrix Functions with Specified Accuracy and Application

If the matrix function f(At) posses the properties of f(At)=gf(tkA, then the recurrence formula fi−1=gfi,i=N,N−1,⋯,1,f(tA)=f0, can be established. Here, fN=f(AN)=∑j=0majANj,AN=tkNA. This provides an algorithm for computing the matrix function f(At). By specifying the calculation accuracy p, a method is presented to determine m and N in a way that minimizes the time of the above algorithm, thus providing a fast algorithm for f(At). It is important to note that m only depends on the calculation accuracy p and is independent of the matrix A and t. Therefore, f(AN) has a fixed calculation format that is easily computed. On the other hand, N depends not only on A, but also on t. This provides a means to select t such that N is equal to 0, a property of significance. In summary, the algorithm proposed in this article enables users to establish a desired level of accuracy and then utilize it to select the appropriate values for m and N to minimize computation time. This approach ensures that both accuracy and efficiency are addressed concurrently. We develop a general algorithm, then apply it to the exponential, trigonometric, and logarithmic matrix functions, and compare the performance with that of the internal system functions of Mathematica and Pade approximation. In the last section, an example is provided to illustrate the rapid computation of numerical solutions for linear differential equations.

Riemann-Hilbert problems, Toeplitz operators and ergosurfaces

The Riemann-Hilbert approach, in conjunction with the canonical Wiener-Hopf factorisation of certain matrix functions called monodromy matrices, enables one to obtain explicit solutions to the non-linear field equations of some gravitational theories. These solutions are encoded in the elements of a matrix M depending on the Weyl coordinates ρ and v, determined by that factorisation. We address here, for the first time, the underlying question of what happens when a canonical Wiener-Hopf factorisation does not exist, using the close connection of Wiener-Hopf factorisation with Toeplitz operators to study this question. For the case of rational monodromy matrices, we prove that the non-existence of a canonical Wiener-Hopf factorisation determines curves in the (ρ, v) plane on which some elements of M(ρ, v) tend to infinity, but where the space-time metric may still be well behaved. In the case of uncharged rotating black holes in four space-time dimensions and, for certain choices of coordinates, in five space-time dimensions, we show that these curves correspond to their ergosurfaces.

Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process

Under the effect of the Rosenblatt process, time-delay systems of nonlinear stochastic delay differential equations are considered. Utilizing the delayed matrix functions and exact solutions for these systems, the existence and Hyers–Ulam stability results are derived. First, depending on the fixed point theory, the existence and uniqueness of solutions are proven. Next, sufficient criteria for the Hyers–Ulam stability are established. Ultimately, to illustrate the importance of the results, an example is provided.

A lightweight, conservation-moment-based implicit gas kinetic Lax–Wendroff scheme for all Knudsen number isothermal gas flows

This work presents an efficient implicit gas kinetic Lax–Wendroff scheme for steady isothermal gas flows in all Knudsen number (Kn) regimes. In the scheme, the discrete velocity Bhatnagar–Gross–Krook model equations (DVE) and the associated conservation moment equations (CME) are coupled and solved by matrix-free implicit schemes. Thanks to obtaining the fluxes of the CME by multiplying the fluxes of the DVE with a projection matrix and utilizing the equilibrium distribution functions at the new time predicted by the CME, both the complicated macro fluxes reconstruction of the CME and the calculation of the Jacobian matrix of the equilibrium distribution functions are not needed in the scheme, which makes the scheme lightweight. Moreover, to enhance the accuracy of the predicted equilibrium distribution functions at the new time to improve the convergence, a symmetric Gauss–Seidel scheme with inner iterations is used to solve the CME system. Due to the coupling between the DVE and the CME, the highly efficient implicit scheme for the CME drives the DVE system to converge quickly for the continuum and near-continuum flows. Furthermore, to verify the accuracy and high efficiency of the proposed implicit scheme, comparison studies of several two-dimensional isothermal rarefied gas flow cases simulated by the present implicit scheme and the explicit gas kinetic Lax–Wendroff scheme are also provided. The numerical results show that the present implicit scheme can be as accurate as its explicit counterpart with one to two orders times speed-up in all Kn number flow regimes.

Synthesis of realistic non-homogeneous non-Gaussian turbulent wind fields

This paper presents a sequential method for generating synthetic non-homogeneous non-Gaussian turbulent wind fields with a prescribed time-space covariance structure. The proposed methodology is based on the optimisation of restricted multivariate autoregressive (VAR) models, and the quantile-to-quantile transform between statistical distributions. The considered case study is a non-homogeneous non-Gaussian turbulent wind field over the roof of a high rise building simulated with LES. Results show a notably good matching in terms of the reproduced wind statistical distributions, Covariance Matrix Function (CMF) and Cross Power Spectral Density Matrix (CPSDM). In addition, the synthetic wind field reproduced accurately the recirculation bubble close to the roof. The main advantages of the proposed method are that, once the VAR model is computed, the synthesis of several realisations is computationally very cheap, which is useful for performing several aeroelastic simulations of the same analysis case, as suggested by the standards. The critical point is that, to characterise the statistical features for a specific case study (such as wind turbine wakes or turbulence due to obstacles), an LES simulation of the wind field is required as input. The software employed in this work is open source and it is available on GitHub.