Matrix Model Research Articles

Laboratory and numerical investigations on land-sourced solute transport in coastal fractured aquifers

Land-based pollutants threaten coastal aquifers, highlighting the need to protect groundwater and nearshore marine ecosystems. While aquifer heterogeneity has been recognized as a significant factor affecting solute behavior, the impact of fractures on land-sourced solute transport in coastal aquifers remains unclear. This study attempted to address this issue through laboratory experiments and discrete fracture matrix (DFM) models. The impact of horizontal fractures on the temporal and spatial characteristics of solute transport, spreading, and discharge under seawater intrusion was analyzed based on variations in fracture position and length. The results show that fractures/low-velocity zones (LVZ) can accelerate/delay solutes, dividing them into different transport modes and enhancing/prolonging their spreading/discharge duration. Changes in fracture position and length also affect its transport acceleration and path deviation abilities, which ultimately determine when solute discharge occurs. The mixing zone and unsaturated zone, in addition to the LVZ, hinder solute transport, reducing the rate and delaying the end of solute discharge. Meanwhile, fractures facilitate solute transport into the saltwater wedge, expanding the solute discharge zone. However, if solutes are initially within the LVZ, their entry into the fracture rely on their distance from the fracture's near-land edge and the size of the fracture's convergence zone.

Detection Problems in the Spiked Random Matrix Models

Detection Problems in the Spiked Random Matrix Models

Multiport Square Law Detectors: Responsivity Matrix Model and Direct Determination of the Optimum Injection Regime

Multiport Square Law Detectors: Responsivity Matrix Model and Direct Determination of the Optimum Injection Regime

Двоїстий алгоритм пошуку простих чисел на відрізках великих розмірностей

A matrix model of subsequence of natural numbers with a multiplicative basis from the first prime numbers is proposed. The matrix model is a square matrix, where vector columns are arithmetic progressions with difference and number of progressions equal to product of base elements. By crossing out arithmetic progressions with first terms which are multiples of base elements, we obtain a symmetric sparse matrix that contains all the prime numbers of subsequence of natural numbers, except for the base ones, which increases the density of prime numbers in sparse matrices. Sparse matrices are not formed clearly, only the vector of first terms of arithmetic progressions is formed. Properties of sparse matrices have been proven. Formulas that speed up the calculation of compound numbers in arithmetic progressions have been derived, the structures of vector elements of first terms of arithmetic progressions have been determined, the connectivity of symmetric parts of sparse matrices has been investigated. With the expansion of the base the number of pairs of elements with the difference equal to the power of two («twins», «fours», etc.) increases in the vector of first terms. This is a necessary condition for the existence of constants for which linear equations of two variables can have an infinite set of solutions in prime numbers. The irregularity of distribution of prime numbers in subsequences of natural numbers is related to the structure of elements of the vector of first terms. An algorithm for finding prime numbers on segments of large dimensions with a parallel calculation process has been built. The proposed algorithm is binary to algorithms for sifting subsequences of natural numbers by prime divisors. In these algorithms, it is not possible to parallelize the calculation process, since screening procedure requires storing the numerical information from the preceding steps (vector model of array processing). The binary algorithm calculates compound numbers in each pair of arithmetic progressions with symmetric first terms simultaneously, using only vector of the first terms of arithmetic progressions, which makes possible processing of large-dimensional arrays

Connectedness and Shock Propagation in South African Equity Sectors during Extreme Market Conditions

This study examined the connectedness and propagation of risk in the South African equity sectors during the Global Financial Crisis (GFC), the European Debt Crisis (EDC), the US–China trade war, and the COVID-19 pandemic. Daily returns of nine Johannesburg Stock Exchange (JSE) super sectors were examined from 3 January 2006 to 31 December 2021. Applying the connectedness matrix and time-varying parameter vector autoregressive (TVP-VAR) model, in full sample and sub-periods, the study showed that dynamic total connectedness of the super sectors is high in absolute form (62%). Furthermore, it was found that the highest volatility connectedness was during the EDC (68.83%) and during the COVID-19 pandemic (68.57%), followed by the GFC (63.16%) and lastly the US–China trade war (42.09%), respectively. This suggests that the tendency for a systemic risk is highest during the EDC, COVID-19, and GFC periods, and lowest during the US–China trade war. The financial sector was the primary net-transmitter of shocks during the COVID-19 period, while the automobile and parts sector was the strongest net-transmitter of shocks during the GFC, EDC, and US–China trade war. Similarly, the strongest net recipient of shocks during GFC, EDC, and COVID-19 is the chemical super sector. The study concludes that there is a significant volatility connectedness among JSE super sectors. In addition, the JSE super sectors exhibit time-varying connectedness during extreme events. Moreover, the net-transmitter and net-receiver of shock do not change significantly during different crisis periods. The policy implications of the findings are highlighted in the concluding section.

Effect of Corporate Social Performance and Dividend Payout on Value of Firms An Evidence of Non-Financial Firms Listed on Pakistan Stock Exchange

The relationship between corporate social performance, Dividend Payout and Value of Firm has been an important topic of literature and the subject of comprehensive empirical literature. However, the current literature is characterized by a lack of consistent and general research studies about the nature and direction of this unique nexus. This research study aims to contribute to the literature by reviewing the comprehensive literature on this subject related to the Pakistani corporate market. The research study used a sample size of 50 non-financial firms in Pakistan for the period of ten years from 2013-2022. The data was collected from the annual reports of non-financial firms. Regression, descriptive statistics and Correlation matrix were used to establish the relationship between corporate social performance, Dividend Payout and Value of Firm. Results were computed by using “E-views” software for the data analysis. The results of the research study revealed that there is a highly significant and positive relationship between Dividend Payout and the Value of Firm while also a significant and positive relationship between Corporate Social Performance and Value of Firm.

Deep learning in standard least-squares theory of linear models: Perspective, development and vision

Inspired by the attractive features of least-squares theory in many practical applications, this contribution introduces least-squares-based deep learning (LSBDL). Least-squares theory connects explanatory variables to predicted variables, called observations, through a linear(ized) model in which the unknown parameters of this relation are estimated using the principle of least-squares. Conversely, deep learning (DL) methods establish nonlinear relationships for applications where predicted variables are unknown (nonlinear) functions of explanatory variables. This contribution presents the DL formulation based on least-squares theory in linear models. As a data-driven method, a network is trained to construct an appropriate design matrix of which its entries are estimated using two descent optimization methods: steepest descent and Gauss–Newton. In conjunction with interpretable and explainable artificial intelligence, LSBDL leverages the well-established least-squares theory for DL applications through the following three-fold objectives: (i) Quality control measures such as covariance matrix of predicted outcome can directly be determined. (ii) Available least-squares reliability theory and hypothesis testing can be established to identify mis-specification and outlying observations. (iii) Observations’ covariance matrix can be exploited to train a network with inconsistent, heterogeneous and statistically correlated data. Three examples are presented to demonstrate the theory. The first example uses LSBDL to train coordinate basis functions for a surface fitting problem. The second example applies LSBDL to time series forecasting. The third example showcases a real-world application of LSBDL to downscale groundwater storage anomaly data. LSBDL offers opportunities in many fields of geoscience, aviation, time series analysis, data assimilation and data fusion of multiple sensors.

Reinforcement structure design and matrix model establishment of tubular 3D weaving based on ordinary loom

In order to optimize the design of three-dimensional tubular woven (3DTW), a design method and matrix model of 3DTW were proposed based on normal loom, where 3D woven was used as tube wall and the weaving method of tubular fabric was applied. Herein, 3D woven was used as the tube wall to obtain the face weave diagram, and the back weave diagram was subsequently obtained by the “negative flip” method. According to the method of layering weaving, the structure diagram of 3DTW could be determined. In order to obtain back weave matrix, the elements in the face weave matrix were replaced and reordered by MATLAB function, and Kronecker product operation was used to achieve the proportional embedding of the face and the back weave matrix and the assignment of the face warp by lifting point elements when weaving the back weft. Finally, the weave matrix of 3DTW was obtained. The proposed design method and matrix model can improve the design efficiency and reduce weaving cost of 3DTW, which could provide a reference for the design and preparation of 3DTW.

Commutative families in DIM algebra, integrable many-body systems and q, t matrix models

We extend our consideration of commutative subalgebras (rays) in different representations of the W1+∞ algebra to the elliptic Hall algebra (or, equivalently, to the Ding-Iohara-Miki (DIM) algebra Uq,tgl̂̂1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {U}_{q,t}\\left({\\hat{\\hat{\\mathfrak{gl}}}}_1\\right) $$\\end{document}). Its advantage is that it possesses the Miki automorphism, which makes all commutative rays equivalent. Integrable systems associated with these rays become finite-difference and, apart from the trigonometric Ruijsenaars system not too much familiar. We concentrate on the simplest many-body and Fock representations, and derive explicit formulas for all generators of the elliptic Hall algebra en,m. In the one-body representation, they differ just by normalization from znqmD̂\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {z}^n{q}^{m\\hat{D}} $$\\end{document} of the W1+∞ Lie algebra, and, in the N -body case, they are non-trivially generalized to monomials of the Cherednik operators with action restricted to symmetric polynomials. In the Fock representation, the resulting operators are expressed through auxiliary polynomials of n variables, which define weights in the residues formulas. We also discuss q, t-deformation of matrix models associated with constructed commutative subalgebras.

Decomposition of official population projections in Brazil

Brazil’s population has continually changed over time. However, the effects of each demographic component on official population projections are still unclear. In this research, we replicate the Population Projections Revision 2018 of the Brazilian Institute of Geography and Statistics using a projection matrix model and the cohort-component method by sex, age and geographic regions. Thereafter, we established four alternative scenarios to decompose the official benchmark scenario into four demographic effects (fertility, age structure, mortality, and migration) and one residual effect. The results reveal that fertility and age structure effects have been the main drivers of the population dynamics between 2010 and 2060. On the one hand, the negative effect of fertility below replacement level has been mostly offset by the still positive effect of the age structure, even across regions in the country. On the other hand, age structure effect has been decreasing over time. By 2048, the effects of age structure, mortality and migration will no longer counterbalance fertility effects, resulting in a population decline.

Interactions in the IKKT matrix model on covariant quantum spacetime

We study the interactions of the higher-spin gauge theory arising from the IKKT matrix model on a covariant quantum FLRW quantum space-time MJ1,3, denoted as HS-IKKT. In particular, we elaborate some of the vertices and observe that they are not manifestly Lorentz invariant in the unitary formulation. We argue that Lorentz invariance of HS-IKKT can be recovered since Lorentz transformations are part of the gauge invariance in the covariant formulation. This statement is verified for some vertices with lowest number of derivatives. The lowest-derivative sector of this theory is expected to be governed by an “almost”-Lorentz-invariant Yang-Mills theory coupled to emergent gravity.

Retrodiction of forest demography: Backward simulation with reverse matrix models

Abstract Reconstructing past ecological population dynamics and demographic events is crucial for understanding the dynamics of ecological processes, evaluating the impact of environmental changes and making informed conservation decisions. In forest ecosystems, retrodiction (i.e. the backward projection of ecological populations) plays a pivotal role in understanding historical forest carbon levels and the factors that have influenced their variation over time, because forest demography is a major determinant of the amount of carbon stored in forest ecosystems. The persistent lack of quantitative methods has been a significant obstacle in retrodicting forest demography, especially in applications of a broad geographical scale. While there is a wealth of models for predicting future forest conditions, models that can project these conditions backward in time are scarce. This study presents reverse matrix model (RMM), an innovative retrodiction modelling approach grounded in the principles of transition matrix models. RMM is designed to deduce past demographic characteristics of ecological populations using current data, making it one of the first models capable of projecting the fine‐scale dynamics of forest demography into the past. We assessed the retrodictive performance of RMM by fitting it to a dataset of a disturbed tropical rainforest in French Guiana in 2001–2023, then comparing the retrodictions to observations back to 1983 when the disturbance occurred. We further empirically evaluated the viability of retrodiction over a defined duration by inverting the density‐dependent matrix model by Lin et al. (1996), which predicts the dynamics of northern hardwoods in the United States. The case studies demonstrate significant potential for RMM application in various domains of forestry and conservation, including ecosystem management and conservation planning, global change impact assessment and biodiversity monitoring.

The interface dewetting process of particulate filled polymer composite

AbstractDewetting is one of the most common damage modes in particulate filled polymer composite, which greatly damages the structural integrity of the composite and leads to the deterioration of its mechanical properties. Studying the dewetting evolution process of composite is of great significance for evaluating the meso damage degree of composite and suppressing the development of dewetting damage. This article constructs an axisymmetric cylindrical cell model of a single particle inclusion matrix, derives the interface dewetting evolution process of the model under uniaxial tensile loading condition, and analyzes the influence of model geometric parameters and external loading conditions on the dewetting process. Subsequently, numerical models were constructed at both micro and meso scales, and dynamic tensile calculations were performed to analyze the correlation between the dewetting rate, porosity, and mechanical performance. Finally, a cylindrical cell specimen was designed to observe the interface dewetting evolution under uniaxial tensile conditions, confirming the conclusions of theoretical analysis and numerical simulation.Highlights Constructed a theoretical model for the dewetting process of interface. Conducted numerical analysis of dewetting process at both meso and micro scales. Designed interface dewetting experiment and analyzed the dewetting process.

A novel approach for enhancing the mechanical behavior of additively manufactured metal matrix composite structures: Preliminary investigation

Additive Manufacturing is a promising technique for expanding the boundaries of Metal Matrix Composites. In this study, Powder Bed Fusion (PBF) technique, employing Electron Beam as the heat source, was used to print Ti6Al4V metal matrix in different geometric shapes with a new approach for MMC fabrication. Yttria Stabilized Zirconia (YSZ) powder was then incorporated into these pattern shapes, compacted, and sintered to bind the powder particles together. The findings showed that successful sintering was achieved, resulting in the formation of a flexible interface region, with the circular design achieving the best interface region among all pattern designs. Regarding the mechanical performance evaluation of the developed Metal Matrix Composites, it was found that the mechanical strength was significantly increased with the hexagonal and circular patterns achieving the best results. Future research should pay more attention to further design development for the metal matrix model to achieve outstanding performance and create a new field for Metal Matrix Composites using the developed method.

Living on the edge: identifying demographic bottlenecks in an isolated sage‐grouse population

The greater sage‐grouse (Centrocercus urophasianus: hereafter sage‐grouse) population in Modoc County California is geographically isolated and contains a single lek (from 56 leks in the 1940s), despite significant efforts to increase the population through translocations and habitat improvement. Repeated wildfire within the landscape has led to an increase in invasive annual grasses and a decrease in sagebrush (Artemisia sp.) cover in important nesting and brood‐rearing habitat. We estimated survival for adult females, nests, and chicks and assessed biotic characteristics that may influence these survival estimates to identify factors that may be limiting population growth. We monitored 37 female sage‐grouse marked with GPS PTTS, 39 nests, and 8 broods for 3 years (2019–2021). We measured vegetation characteristics for nests at the microsite and landscape scale to evaluate effects on daily nest survival (DNS). We used survival rates from all life stages to parameterize matrix models and estimate population growth rate. Mean nest success over 3 years was 29% (95% CI: 17.1–44.8) across a 29‐day incubation period and DNS declined as the proportion of both medusahead Taeniatherum caput‐medusae and Japanese brome Bromus japonicus around the nest increased. Across all three years, mean chick survival across a 54‐day period was 44% (95% CI: 0.9–72.3) and mean annual survival for adult females was 29% (95% CI: 17.8–43.7). Our estimated vital rates were 45–55% lower than distribution‐wide estimates and the projected population growth rate was strongly declining (0.411, 95% CI: 0.30–0.52). Our results suggested recent cover changes associated with wildfire on the study area may have had a detrimental effect on this population across all life stages, and if attention is not given to preventing the transition from sagebrush communities into invasive grasslands, this population and others in degraded landscapes may not persist.

Family Concept Representation in English and Chinese Media: A Cognitive Matrix Modelling Approach

This article examines the representation of the FAMILY concept in English and Chinese newspapers. The research material was gathered from ten information sources and included 200 news articles, selected through continuous sampling using the keyword FAMILY / 家庭. The articles were analyzed to identify relevant issues and categorized based on their thematic content. In each article, key content elements—words and phrases that carry significant semantic meaning—were identified and used for cognitive matrix modeling. The findings reveal cognitive asymmetry in how the FAMILY concept is portrayed in English and Chinese media. In English-language media, the concept is centered on fundamental semantic components that form the cognitive core of the FAMILY concept, such as family members and their relationships. The representation also extends to areas like family activities, children, finances, employment, family pets, and legal issues. In contrast, Chinese media emphasizes the government’s role in educating the younger generation on family behavior, fostering a new generation of families that adhere to the country’s ethical norms, traditional cultural values, and moral standards. The central aspect of the FAMILY concept in Chinese media is the significant governmental support and societal focus on family needs and moral education, with family being viewed within the broader context of societal relations. The observed asymmetry is attributed to cultural, economic, social, and political differences. In capital-oriented social systems, the family is seen as an independent unit capable of self-sufficiency without substantial government intervention. This study is particularly relevant for understanding the role of professional discourse in shaping public perceptions of family across different cultures, highlighting how media narratives reflect and influence broader societal values and professional communication practices.

Family Concept Representation in English and Chinese Media: A Cognitive Matrix Modelling Approach

This article examines the representation of the FAMILY concept in English and Chinese newspapers. The research material was gathered from ten information sources and included 200 news articles, selected through continuous sampling using the keyword FAMILY / 家庭. The articles were analyzed to identify relevant issues and categorized based on their thematic content. In each article, key content elements—words and phrases that carry significant semantic meaning—were identified and used for cognitive matrix modeling. The findings reveal cognitive asymmetry in how the FAMILY concept is portrayed in English and Chinese media. In English-language media, the concept is centered on fundamental semantic components that form the cognitive core of the FAMILY concept, such as family members and their relationships. The representation also extends to areas like family activities, children, finances, employment, family pets, and legal issues. In contrast, Chinese media emphasizes the government’s role in educating the younger generation on family behavior, fostering a new generation of families that adhere to the country’s ethical norms, traditional cultural values, and moral standards. The central aspect of the FAMILY concept in Chinese media is the significant governmental support and societal focus on family needs and moral education, with family being viewed within the broader context of societal relations. The observed asymmetry is attributed to cultural, economic, social, and political differences. In capital-oriented social systems, the family is seen as an independent unit capable of self-sufficiency without substantial government intervention. This study is particularly relevant for understanding the role of professional discourse in shaping public perceptions of family across different cultures, highlighting how media narratives reflect and influence broader societal values and professional communication practices.

MXene-Fiber Composite Membranes for Permeable and Biocompatible Skin-Interfaced Iontronic Mechanosensing.

Artificial ionic sensory systems, bridging the divide between biological systems and electronics, mimic human skin functions but face critical challenges with biocompatibility, comfort, signal stability, and simplifying packaging. Here, we present a simple and permeable skin-interfaced iontronic mechanosensing (SIIM) architecture that integrates human skin as natural ionic material and hierarchically porous MXene-fiber composite membranes as sensing electrodes. The SIIM system eliminates complex ionic material design and multilayer matrix, exhibiting ultrahigh pressure sensitivities (5.4 kPa-1, <75 Pa), a low detection limit (6 Pa), excellent output stability along with high permeability to minimize the impact of sweating on sensing. The noncytotoxic nature of SIIM electrodes ensures excellent biocompatibility (>97% cell coincubational viability), facilitating long-term wearability and high biosafety. Furthermore, the scalable SIIM configuration integrated with matrix smart gloves, effectively monitors human physical movements. This SIIM-based sensor with marked sensing capabilities, structural simplicity, and scalability, holds promising potential in diverse wearable applications.

Supersymmetric Virasoro minimal strings

A random matrix model definition of a family of N=1 supersymmetric extensions of the Virasoro minimal string of Collier, Eberhardt, Mühlmann, and Rodriguez is presented. An analysis of the defining string equations shows that the models all naturally have unambiguous nonperturbative completions, which are explicitly supplied by the double-scaled orthogonal polynomial techniques employed. Perturbatively, the multiloop correlation functions of the model define a special supersymmetric class of “quantum volumes,” generalizing the prototype case, some of which are computed. Published by the American Physical Society 2024

Random matrix model of the Virasoro minimal string

The model of two dimensional quantum gravity defining the Virasoro minimal string, presented recently by Collier, Eberhardt, Mühlmann, and Rodriguez, was also shown to be perturbatively (in topology) equivalent to a random matrix model. An alternative definition is presented here, in terms of double-scaled orthogonal polynomials, thereby allowing direct access to nonperturbative physics. Already at leading order, the defining string equation’s properties yield valuable information about the nonperturbative fate of the model, confirming that the case (c=25,c^=1) (central charges of spacelike and timelike Liouville sectors) is special, by virtue of sharing certain key features of the N=1 supersymmetric JT gravity string equation. Solutions of the full string equation are constructed using a special limit, and the (Cardy) spectral density is completed to all genus and beyond. The distributions of the underlying discrete spectra are readily accessible too, as is the spectral form factor. Some examples of these are exhibited. Published by the American Physical Society 2024