Coefficient Matrix Research Articles

Leveraging relationships between species abundances to improve predictions and inform conservation

Abstract Many management and conservation contexts can benefit from understanding relationships between species abundances, which can be used to improve predictions of species occurrence and abundance. We present conditional prediction as a tool to capture information about species abundances via residual covariance between species. From a fitted joint species distribution model, this framework produces a species coefficient matrix that contains relationships between species abundances. The species coefficients allow co‐observed species to be treated as a second set of predictors supplementing covariates in the model to improve prediction. We use simulations to demonstrate the potential benefits and limitations of conditional prediction across data types and species covariance before applying conditional prediction to two management contexts with real data. Simulations demonstrate that conditional prediction provides the largest benefits to continuous data and when there is residual covariance between many species. In our first application, we show that conditioning on other species improves in‐sample and out‐of‐sample predictions of fish and invertebrate species, including Atlantic cod. In our second application, we show that the species coefficient matrix can be used to identify bird species at risk of nest parasitism by Brown‐headed Cowbirds. Synthesis and applications. We present guidelines for using conditional prediction, which can help understand relationships between species abundances, improve predictions and inform conservation in a variety of contexts.

On the Bloch eigenvalues, band functions and bands of the differential operator of odd order with the periodic matrix coefficients

On the Bloch eigenvalues, band functions and bands of the differential operator of odd order with the periodic matrix coefficients

Solvability and Stability of Switched Discrete-time Singular Systems with the Same Switching Rules in Coefficient Matrices

The aim of this paper is to study the problem of solvability and stability for switched discrete-time linear singular (SDLS) systems with the same switching rules in coefficient matrices under Lipschitz perturbation. Firstly, we prove the unique existence of the solution, as well as describe the solution manifold. Secondly, by utilizing a Lyapunov function, we derive certain conditions that guarantee the stability of these systems. Finally, we illustrate our results with an example.

A novel numerical algorithm for solving linear systems with periodic pentadiagonal Toeplitz coefficient matrices

A novel numerical algorithm for solving linear systems with periodic pentadiagonal Toeplitz coefficient matrices

Total Least Squares Estimation in Hedonic House Price Models

In real estate valuation using the Hedonic Price Model (HPM) estimated via Ordinary Least Squares (OLS) regression, subjectivity and measurement errors in the independent variables violate the Gauss–Markov theorem assumption of a non-random coefficient matrix, leading to biased parameter estimates and incorrect precision assessments. In this contribution, the Errors-in-Variables model equipped with Total Least Squares (TLS) estimation is proposed to address these issues. It fully considers random errors in both dependent and independent variables. An iterative algorithm is provided, and posterior accuracy estimates are provided to validate its effectiveness. Monte Carlo simulations demonstrate that TLS provides more accurate solutions than OLS, significantly improving the root mean square error by over 70%. Empirical experiments on datasets from Boston and Wuhan further confirm the superior performance of TLS, which consistently yields a higher coefficient of determination and a lower posterior variance factor, which shows its more substantial explanatory power for the data. Moreover, TLS shows comparable or slightly superior performance in terms of prediction accuracy. These results make it a compelling and practical method to enhance the HPM.

Exact closed forms for the transmittance of electromagnetic waves in one-dimensional anisotropic periodic media

In this work, we obtain closed expressions for the transfer matrix and the transmittance of electromagnetic waves propagating in finite one-dimensional anisotropic periodic stratified media with an arbitrary number of cells. By invoking the Cayley–Hamilton theorem on the transfer matrix for the electromagnetic field in a periodic stratified media formed by N cells, we obtain a fourth-order recursive relation for the matrix coefficients that defines the so-called Tetranacci polynomials (TPs). In the symmetric case, corresponding to a unit-cell transfer matrix with a characteristic polynomial where the coefficients of the linear and cubic terms are equal, closed expressions for the solutions to the recursive relation, known as symmetric TPs, have recently been derived, allowing us to write the transfer matrix and transmittance in a closed form. We show as sufficient conditions that the 4×4 differential propagation matrix of each layer in the binary unit cell, Δ , a) has eigenvalues of the form ±p1 , ±p2 , with p1≠p2 , and b) its off-diagonal 2×2 block matrices possess the same symmetric structure in both layers. Otherwise, the recursive relations are still solvable for any 4×4 matrix and provide an algorithm to compute the Nth power of the transfer matrix without carrying out explicitly the matrix multiplication of N matrices. We obtain analytical expressions for the dispersion relation and transmittance, in closed form, for two finite periodic systems: the first one consists of two birefringent uniaxial media with their optical axis perpendicular to the z-axis, and the second consists of two isotropic media subject to an external magnetic field oriented along the z-axis and exhibiting the Faraday effect. Our formalism applies also to lossy media, magnetic anisotropy or optical activity.

The general algebraic solution of dual fuzzy linear systems and fuzzy Stein matrix equations

In this paper, we present a new method for solving a dual fuzzy linear system (DFLS), AX˜+C˜=BX˜+D˜, where the coefficient matrices A and B are arbitrary real m×n matrices and C˜ and D˜ are given fuzzy number vectors. A necessary and sufficient condition for the R-consistency of the associated system of linear equations is obtained. The straightforward method for solving m×n DFLS based on an arbitrary {1}-inverse of A−B is introduced. Also, as an application, we present the first algorithm for solving the fuzzy Stein matrix equations, based on {1}-inverses. Finally, these results are illustrated by examples.

Stiffness of reinforced concrete structures under bending considering shear and axial forces (part 2)

The paper presents a physical and computational model for determining the parameters of limit states of reinforced concrete structures under complex stressed state - bending with axial and shear forces. Based on the adopted scheme of cross-section discretization and A.R. Rzhanitsyn's theorem of duality between force and deformation parameters, the forward and backward transfer for determining the coefficients of the stiffness matrix of reinforced concrete rod structures with inclined and normal cracks have been constructed. Stiffness of structures in the zone of inclined cracks is determined using the model of composite strips which separate the zone with inclined cracks. The hypothesis about the character of deformation distribution in a complex-stressed reinforced concrete element with inclined cracks is accepted.For this model the conditional shear modulus is obtained, which allows to determine the average relative linear and angular strains of concrete and reinforcement at the point adjacent to the shear joint between inclined cracks. Based on this model and using the experimentally obtained value of the relative shear in the inclined crack, the dowel forces in the reinforcing bar intersected by the inclined crack were determined. The application of the obtained analytical relationships in the practice of designing reinforced concrete structures allows not only to clarify significantly the definition of displacements and width of opening of inclined and normal cracks, but also to maximize the convergence of the design and physical model based on experimental data.

The neural network approach for estimation of heat transfer coefficient in heat exchangers considering the fouling formation dynamic

Routine maintenance for plate heat exchanger (PHE) cleaning improves the effectiveness of heat exchange network operation. Until recently, complex mathematical modelling was used to predict the value of the heat transfer coefficient after a certain period of operation of the heat exchanger, as well as the point in time when the coefficient reached the allowable limit. The applied mathematical tools included the systems of differential equations, matrices of heuristic coefficients, which needed a lot of computer resources. This paper offers an artificial neural network (ANN) technique for forecasting the following values: heat transfer coefficient at any time points during the operating period of PHEs; the time point, when the heat transfer coefficient reaches its lower permitted value. In this method, ANN uses the fuzzy logic techniques to expand the set of training parameters for the model, working with data of industrial measurements and data obtained from the mathematical modelling of the process. It allowed to train the developed feed-forward neural network (FFNN) with the coefficient of determination R2 equal to 0.99 and can predict the thermal resistance in PHE based on measurement data. To adequately predict the time-point to reach the limiting value of the heat transfer coefficient, it was proposed a recurrent neural network (RNN) with a hidden layer of long short-term memory (LSTM), where R2 value came up to 0.89.

Application of optimized sparse encoding algorithm in data compression

Data transmission is crucial in the process of equipment monitoring. The compression algorithms are adopted to reduce the amount of data transmission. When sparse encoding algorithms are used for this purpose, despite extensive attempts to improve their performance, some problems still remain. The main issues pertain to: (1) Dictionary construction − As practical dictionary better matches the input signal, such a dictionary must be efficiently established; 2) The setting of sparsity value − It is difficult to determine the size of sparsity values when prior knowledge is insufficient (when the parameter settings are too large, the cost of data transmission increases considerably, while excessively small values can result in poor reconstruction accuracy); and (3) How to implement engineering applications of data compression based on sparse encoding. To address these issues, in this work, an optimized sparse encoding algorithm is proposed by combining the non-negative Online Dictionary Learning (ODL) with the optimized Orthogonal Matching Pursuit (OMP) algorithm. First, a non-negative ODL algorithm is adopted for dictionary learning based on the training dataset to obtain an effective dictionary. Next, the optimized OMP algorithm is used to obtain the sparsity and the sparse coefficient matrix. Further analyses confirm that the reconstructed signal has a small reconstruction error. Finally, A lossy compression framework is proposed for the compressing equipment condition monitoring data using sparse encoding algorithms. Compared with the compression algorithms based on compressive sensing and DCT, the average compression ratio can reach 42.7 when the reconstruction accuracy is similar. In terms of comprehensive compression performance, the quality score is also higher compared to other algorithms.

Multivariate Meixner polynomials related to holomorphic discrete series representations of [formula omitted]

We show that Griffiths’ multivariate Meixner polynomials occur as matrix coefficients of holomorphic discrete series representations of the group SU(1,d). Using this interpretation we derive several fundamental properties of the multivariate Meixner polynomials, such as orthogonality relations and difference equations. Furthermore, we also show that matrix coefficients for specific group elements lead to degenerate versions of the multivariate Meixner polynomials and their properties.

Approximation of reliabilities for random-regression single-step genomic best linear unbiased predictor models

Random-regression models (RRM) are used in national genetic evaluations for longitudinal traits. The outputs of RRM are an index based on random regression coefficients and its reliability. The reliabilities are obtained from the inverse of the coefficient matrix of mixed model equations (MME). The reliabilities must be approximated for large data sets because it is impossible to invert the MME. There is no extensive literature on methods to approximate the reliabilities of RRM when genomic information is included by single-step GBLUP. We developed an algorithm to approximate such reliabilities. Our method combines the reliability of the index without genomic information with the reliability of a GBLUP model in terms of effective record contributions. We tested our algorithm in the 3-lactation model for milk yield from the Czech Republic. The data had 30 million test-day records, 2.5 million animals in the pedigree, and 54,000 genotyped animals. The correlation between our approximation and the reliabilities obtained from the inversion of the MME was 0.98, and the slope and intercept of the regression were 0.91 and 0.02, respectively. The elapsed time to approximate the reliabilities for the Czech data was 21 min.

[formula omitted] output tracking control for polynomial parameter-varying systems via homogeneous Lyapunov methods

This paper investigates the H∞ output tracking control for polynomial parameter-varying systems—a class of nonlinear parameter-varying systems. Based on the homogeneous polynomial Lyapunov function (HPLF), a state feedback controller is presented to make the augmented system (composed of the original system and the tracking error system) robust exponentially stable, so that the output of the original system can track the reference signal and satisfy the H∞ output tracking performance. The conservativeness of the theoretical results is reduced due to the following facts: (1) the HPLF can depend on the full states and time-varying parameters; and (2) there are no constraints on the input coefficient matrix and the inverse of the Lyapunov matrix. In particular, when the system states and time-varying parameters are confined to a compact set, local results are obtained based on the generalized S-procedure. The solvable conditions are given in terms of state-and-parameter-dependent linear matrix inequalities, which can be solved by sum of squares (SOS) techniques. Finally, the feasibility and effectiveness of the proposed method are verified by a numerical example and the heading control of unmanned surface vehicle.

Characters of [formula omitted] and vertex operators

In this paper, we present a vertex operator approach to construct and compute all complex irreducible characters of the general linear group GLn(Fq). Green's theory of GLn(Fq) is recovered and enhanced under the realization of the Grothendieck ring of representations RG=⨁n≥0R(GLn(Fq)) as two isomorphic Fock spaces associated to two infinite-dimensional F-equivariant Heisenberg Lie algebras hˆF‾ˆq and hˆF‾q, where F is the Frobenius automorphism of the algebraically closed field F‾q. Under this picture, the irreducible characters are realized by the Bernstein vertex operators for Schur functions, the characteristic functions of the conjugacy classes are realized by the vertex operators for the Hall-Littlewood functions, and the character table is completely given by matrix coefficients of vertex operators of these two types. One of the features of the current approach is a simpler identification of the Fock space RG as the Hall algebra of symmetric functions via vertex operator calculus, and another is that we are able to compute in general the character table, where Green's degree formula is demonstrated as an example.

Prediction Model of Coal Gas Permeability Based on Improved DBO Optimized BP Neural Network.

Accurate measurement of coal gas permeability helps prevent coal gas safety accidents effectively. To predict permeability more accurately, we propose the IDBO-BPNN coal body gas permeability prediction model. This model combines the Improved Dung Beetle algorithm (IDBO) with the BP neural network (BPNN). First, the Sine chaotic mapping, Osprey optimization algorithm, and adaptive T-distribution dynamic selection strategy are integrated to enhance the DBO algorithm and improve its global search capability. Then, IDBO is utilized to optimize the weights and thresholds in BPNN to enhance its prediction accuracy and mitigate the risk of overfitting to some extent. Secondly, based on the influencing factors of gas permeability, effective stress, gas pressure, temperature, and compressive strength, they are chosen as the coupling indicators. The SPSS 27 software is used to analyze the correlation among the indicators using the Pearson correlation coefficient matrix. Additionally, the Kernel Principal Component Analysis (KPCA) is employed to extract the original data. Then, the original data is divided into principal component data for the model input. The prediction results of the IDBO-BPNN model are compared with those of the PSO-BPNN, PSO-LSSVM, PSO-SVM, MPA-BPNN, WOA-SVM, BES-SVM, and DPO-BPNN models. This comparison assesses the capability of KPCA to enhance the accuracy of model predictions and the performance of the IDBO-BPNN model. Finally, the IDBO-BPNN model is tested using data from a coal mine in Shanxi. The results indicate that the predicted outcome closely aligns with the actual value, confirming the reliability and stability of the model. Therefore, the IDBO-BPNN model is better suited for predicting coal gas permeability in academic research writing.

ИНДЕКС ФОНДООТДАЧИ: СОВРЕМЕННОЕ СОСТОЯНИЕ И ФАКТОРЫ РОСТА

The scientific article contains an analysis of scientific literature on ensuring the efficient use of fixed assets in enterprises, research on capital productivity and capital intensity, and the development of main directions for the efficient use of fixed capital. The dynamics of the coefficients of renewal and disposal of fixed assets in the economy are presented in graphical form. The information base for the study was data from the official website of the Federal State Statistics Service. The maximum values of the renewal coefficient were observed in 2018, 2019 and 2022, and the minimum in 2015, 2020 and 2021. The maximum values of the retirement rate are presented in 2014, 2015 and 2016, and the minimum in 2019, 2020 and 2021. An econometric study of the capital productivity index showed an inverse and very weak relationship with the value of gross domestic product and the cost of fixed assets (the value of the correlation coefficient (index) (-0.1)): with an increase in the value of gross domestic product and the value of fixed assets in the period under study, no growth was observed capital productivity index. The value of the gross domestic product and the cost of fixed assets have a direct and close relationship (the value of the correlation coefficient (index) is 0.9): the annual growth of the gross domestic product is accompanied by an increase in the cost of fixed assets. A matrix of correlation coefficients (indices) was constructed to calculate the total correlation coefficient (index). The result of calculating the total correlation coefficient (index) (its value is 0.4) showed that there is a direct and weak connection between the capital productivity index, the value of the gross domestic product and the cost of fixed assets: the growth of the capital productivity index is weakly related to the growth of the gross domestic product and the cost of fixed assets funds.

Properties of spectral characteristics of quasi-stationary electron states in an open multi-cascade nanostructure

The exact expressions for scattering matrix and transmission coefficient in open multi-cascade nanostructure are obtained. The theory of spectral characteristics of electron quasi-stationary states is developed in two approaches. For the nanostructure with GaAs wells and AlGaAs barriers, it is established that resonance bands appear in the N-cascade structure. Each one is formed by the energies of N states. Only the scattering matrix allows to unambiguously determine the resonance energies and resonance widths of all electron states in the multi-cascade structure. The approach of transmission coefficient, due to the collapse of resonances, gives the incomplete information about the spectral characteristics.

The Potential of Multi-Task Learning in CFDST Design: Load-Bearing Capacity Design with Three MTL Models.

Concrete-filled double steel tubes (CFDSTs) are a load-bearing structure of composite materials. By combining concrete and steel pipes in a nested structure, the performance of the column will be greatly improved. The performance of CFDSTs is closely related to their design. However, existing codes for CFDST design often focus on how to verify the reliability of a design, but specific design parameters cannot be directly provided. As a machine learning technique that can simultaneously learn multiple related tasks, multi-task learning (MTL) has great potential in the structural design of CFDSTs. Based on 227 uniaxial compression cases of CFDSTs collected from the literature, this paper utilized three multi-task models (multi-task Lasso, VSTG, and MLS-SVR) separately to provide multiple parameters for CFDST design. To evaluate the accuracy of models, four statistical indicators were adopted (R2, RMSE, RRMSE, and ρ). The experimental results indicated that there was a non-linear relationship among the parameters of CFDSTs. Nevertheless, MLS-SVR was still able to provide an accurate set of design parameters. The coefficient matrices of two linear models, multi-task Lasso and VSTG, revealed the potential connection among CFDST parameters. The latent-task matrix V in VSTG divided the prediction tasks of inner tube diameter, thickness, strength, and concrete strength into three groups. In addition, the limitations of this study and future work are also summarized. This paper provides new ideas for the design of CFDSTs and the study of related codes.

On the boundary conditions for a thin circular plate conjugated to a massive body

The problem of deformation under the action of uniform pressure of a circular plate coupled with a massive base is considered, while the condition for the coupling of the plate with the base is modeled using boundary conditions of the generalized elastic embedding type, i.e. the relationship between the bending moment and forces at the edge of the plate with displacements and rotation angles through the compliance matrix. The main goal of the work is to study the influence of the elasticity of the embedding on the elastic response of the plate. The solution to the problem was obtained in the formulation of the linear theory of plates, the theory of membranes in the approximation of homogeneity of longitudinal forces, and the Foppl — von Karman theory, also in the approximation of the assumption of homogeneity of longitudinal forces. The values of the coefficients of the compliance matrix were obtained using the finite element method for the auxiliary problem and compared with the values of the coefficients obtained for related problems by analytical methods. Numerical results were obtained for an aluminum wafer on a silicon base. The obtained solution was compared with the solution obtained for the rigid embedment condition for all three models used. It is shown that in the case of large deflections (several plate thicknesses), taking into account the compliance of the embedment becomes essential.

ПАКЕТ GAP ДЛЯ РОЗЩЕПЛЕННЯ ЛІНІЙНИХ СИСТЕМ

There are a number of problems, the solution of which requires the breakdown of the initial system of equations using algebraic decoupling methods. This means reducing the matrix of coefficients to block-diagonal (or block-triangular) form by means of substitution of variables. The main computational tasks when using such methods are finding the centralizer of several matrices or compiling the algebra generated by these matrices. For calculations, it is convenient to use the GAP computer algebra system because the system itself is designed for discrete algebra calculations. The problem is that the GAP program does not support calculations with real numbers. For practical problems you can try to replace them (with some accuracy) by rational numbers. At the same time, the decision may turn out to be excessively cumbersome. On the other hand, the advantage of GAP is the complete absence of rounding errors.