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Journal articles on the topic 'Weight matrices'

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Published: 5 June 2025
Last updated: 24 June 2025

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1

Gross, Marco. "Estimating GVAR weight matrices." Spatial Economic Analysis 14, no. 2 (2018): 219–40. http://dx.doi.org/10.1080/17421772.2019.1556800.

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2

Pastur, L. "Eigenvalue distribution of large random matrices arising in deep neural networks: Orthogonal case." Journal of Mathematical Physics 63, no. 6 (2022): 063505. http://dx.doi.org/10.1063/5.0085204.

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This paper deals with the distribution of singular values of the input–output Jacobian of deep untrained neural networks in the limit of their infinite width. The Jacobian is the product of random matrices where the independent weight matrices alternate with diagonal matrices whose entries depend on the corresponding column of the nearest neighbor weight matrix. The problem has been considered in the several recent studies of the field for the Gaussian weights and biases and also for the weights that are Haar distributed orthogonal matrices and Gaussian biases. Based on a free probability argument, it was claimed in those papers that, in the limit of infinite width (matrix size), the singular value distribution of the Jacobian coincides with that of the analog of the Jacobian with special random but weight independent diagonal matrices, the case well known in random matrix theory. In this paper, we justify the claim for random Haar distributed weight matrices and Gaussian biases. This, in particular, justifies the validity of the mean field approximation in the infinite width limit for the deep untrained neural networks and extends the macroscopic universality of random matrix theory to this new class of random matrices.
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3

Alphonce, Christian B., and Cathal M. Brugha. "Extracting Consistent Weight Ratio Matrices from Inconsistent Judgment Matrices." Tanzania Journal of Engineering and Technology 22, no. 2 (1998): 247–58. http://dx.doi.org/10.52339/tjet.v22i2.282.

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4

Kyazhin, S. N. "Weight properties of primitive matrices." Prikladnaya diskretnaya matematika. Prilozhenie, no. 11 (September 1, 2018): 10–12. http://dx.doi.org/10.17223/2226308x/11/2.

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5

Giraud, Mathieu, and Jean-Stéphane Varré. "Parallel Position Weight Matrices algorithms." Parallel Computing 37, no. 8 (2011): 466–78. http://dx.doi.org/10.1016/j.parco.2010.10.001.

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6

Ermagun, Alireza, and David M. Levinson. "Development and application of the network weight matrix to predict traffic flow for congested and uncongested conditions." Environment and Planning B: Urban Analytics and City Science 46, no. 9 (2018): 1684–705. http://dx.doi.org/10.1177/2399808318763368.

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To capture network dependence between traffic links, we introduce two distinct network weight matrices ([Formula: see text]), which replace spatial weight matrices used in traffic forecasting methods. The first stands on the notion of betweenness centrality and link vulnerability in traffic networks. To derive this matrix, we use an unweighted betweenness method and assume all traffic flow is assigned to the shortest path. The other relies on flow rate change in traffic links. For forming this matrix, we use the flow information of traffic links and employ user equilibrium assignment and the method of successive averages algorithm to solve the network. The components of the network weight matrices are a function not simply of adjacency, but of network topology, network structure, and demand configuration. We test and compare the network weight matrices in different traffic conditions using the Nguyen–Dupuis network. The results lead to a conclusion that the network weight matrices operate better than traditional spatial weight matrices. Comparing the unweighted and flow-weighted network weight matrices, we also reveal that the assigned flow network weight matrices perform two times better than a betweenness network weight matrix, particularly in congested traffic conditions.
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7

Truong, S. N. "A Ternary Neural Network with Compressed Quantized Weight Matrix for Low Power Embedded Systems." Engineering, Technology & Applied Science Research 12, no. 2 (2022): 8311–15. http://dx.doi.org/10.48084/etasr.4758.

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In this paper, we propose a method of transforming a real-valued matrix to a ternary matrix with controllable sparsity. The sparsity of quantized weight matrices can be controlled by adjusting the threshold during the training and quantizing process. A 3-layer ternary neural network was trained with the MNIST dataset using the proposed adjustable dynamic threshold. The sparsity of the quantized weight matrices varied from 0.1 to 0.6 and the obtained recognition rate reduced from 91% to 88%. The sparse weight matrices were compressed by the compressed sparse row format to speed up the ternary neural network, which can be deployed on low-power embedded systems, such as the Raspberry Pi 3 board. The ternary neural network with the sparsity of quantized weight matrices of 0.1 is 4.24 times faster than the ternary neural network without compressing weight matrices. The ternary neural network is faster as the sparsity of quantized weight matrices increases. When the sparsity of the quantized weight matrices is as high as 0.6, the recognition rate degrades by 3%, however, the speed is 9.35 times the ternary neural network's without compressing quantized weight matrices. Ternary neural network work with compressed sparse matrices is feasible for low-cost, low-power embedded systems.
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8

Arasu, K. T., Ka Hin Leung, Siu Lun Ma, Ali Nabavi, and D. K. Ray-Chaudhuri. "Circulant weighing matrices of weight 22t." Designs, Codes and Cryptography 41, no. 1 (2006): 111–23. http://dx.doi.org/10.1007/s10623-006-0026-2.

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9

Teofanov, Nenad, and Filip Tomić. "Extended Gevrey Regularity via Weight Matrices." Axioms 11, no. 10 (2022): 576. http://dx.doi.org/10.3390/axioms11100576.

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The main aim of this paper is to compare two recent approaches for investigating the interspace between the union of Gevrey spaces Gt(U) and the space of smooth functions C∞(U). The first approach in the style of Komatsu is based on the properties of two parameter sequences Mp=pτpσ, τ>0, σ>1. The other one uses weight matrices defined by certain weight functions. We prove the equivalence of the corresponding spaces in the Beurling case by taking projective limits with respect to matrix parameters, while in the Roumieu case we need to consider a larger space than the one obtained as the inductive limit of extended Gevrey classes.
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10

Arasu, K. T., and Dina Torban. "New weighing matrices of weight 25." Journal of Combinatorial Designs 7, no. 1 (1999): 11–15. http://dx.doi.org/10.1002/(sici)1520-6610(1999)7:1<11::aid-jcd2>3.0.co;2-4.

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11

Meyer, K. "Covariance matrices for growth traits of Australian Polled Hereford cattle." Animal Science 57, no. 1 (1993): 37–45. http://dx.doi.org/10.1017/s0003356100006589.

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AbstractEstimates of covariance components due to direct and maternal effects among birth, weaning, yearling and final weight for Australian Polled Herefords were obtained by restricted maximum likelihood fitting an animal model. Data were obtained from commercial herds participating in the National Beef Recording Scheme and an across-herd genetic evaluation service. Analyses were carried out considering nine subsets of data, each comprising at least 3000 weaning, 1000 yearling and 500 final weight records which yielded a total of 30 506,17 105 and 9486 records for the three weights, respectively. Estimates of variances and genetic parameters varied considerably between data sets. Both genetic and permanent environmental effects were found to affect all traits except final weights significantly, with maternal environmental effects explaining proportionately more than 0·20 of the total variation in weaning weight. Estimates of the direct-maternal genetic correlation were consistently negative and moderate to strong, ranging from -0·34 to -0·82 for weaning weight. Maternal correlations between weaning and yearling weights were close to unity. Estimates of the direct genetic correlations among the three later weights were 0·8 or larger. Problems with this kind of analysis are discussed.
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12

Gupta, Abhimanyu. "ESTIMATION OF SPATIAL AUTOREGRESSIONS WITH STOCHASTIC WEIGHT MATRICES." Econometric Theory 35, no. 2 (2018): 417–63. http://dx.doi.org/10.1017/s0266466618000142.

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We examine a higher-order spatial autoregressive model with stochastic, but exogenous, spatial weight matrices. Allowing a general spatial linear process form for the disturbances that permits many common types of error specifications as well as potential ‘long memory’, we provide sufficient conditions for consistency and asymptotic normality of instrumental variables, ordinary least squares, and pseudo maximum likelihood estimates. The implications of popular weight matrix normalizations and structures for our theoretical conditions are discussed. A set of Monte Carlo simulations examines the behaviour of the estimates in a variety of situations. Our results are especially pertinent in situations where spatial weights are functions of stochastic economic variables, and this type of setting is also studied in our simulations.
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13

Tichavsky, P., and A. Yeredor. "Fast Approximate Joint Diagonalization Incorporating Weight Matrices." IEEE Transactions on Signal Processing 57, no. 3 (2009): 878–91. http://dx.doi.org/10.1109/tsp.2008.2009271.

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14

Olejnik, Jakub, and Alicja Olejnik. "QML estimation with non-summable weight matrices." Journal of Geographical Systems 22, no. 4 (2020): 469–95. http://dx.doi.org/10.1007/s10109-020-00326-2.

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Abstract This paper revisits the theory of asymptotic behaviour of the well-known Gaussian Quasi-Maximum Likelihood estimator of parameters in mixed regressive, high-order autoregressive spatial models. We generalise the approach previously published in the econometric literature by weakening the assumptions imposed on the spatial weight matrix. This allows consideration of interaction patterns with a potentially larger degree of spatial dependence. Moreover, we broaden the class of admissible distributions of model residuals. As an example application of our new asymptotic analysis we also consider the large sample behaviour of a general group effects design.
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15

Wang, Ying-Ming, Ying Luo, and Yi-Song Xu. "Cross-Weight Evaluation for Pairwise Comparison Matrices." Group Decision and Negotiation 22, no. 3 (2011): 483–97. http://dx.doi.org/10.1007/s10726-011-9279-x.

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16

Bozóki, Sándor, and János Fülöp. "Efficient weight vectors from pairwise comparison matrices." European Journal of Operational Research 264, no. 2 (2018): 419–27. http://dx.doi.org/10.1016/j.ejor.2017.06.033.

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17

Best, Darcy, Hadi Kharaghani, and Hugh Ramp. "On unit weighing matrices with small weight." Discrete Mathematics 313, no. 7 (2013): 855–64. http://dx.doi.org/10.1016/j.disc.2012.12.022.

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18

Hannenhalli, S., and L. S. Wang. "Enhanced position weight matrices using mixture models." Bioinformatics 21, Suppl 1 (2005): i204—i212. http://dx.doi.org/10.1093/bioinformatics/bti1001.

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19

Elhay, Sylvan, Gene H. Golub, and Jaroslav Kautsky. "Jacobi matrices for sums of weight functions." BIT 32, no. 1 (1992): 143–66. http://dx.doi.org/10.1007/bf01995114.

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20

Marada, Tomas, Radomil Matousek, and Daniel Zuth. "Design of Linear Quadratic Regulator (LQR) Based on Genetic Algorithm for Inverted Pendulum." MENDEL 23, no. 1 (2017): 149–56. http://dx.doi.org/10.13164/mendel.2017.1.149.

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One of the crucial problems in the dynamics and automatic control theory is balancing of an invertedpendulum robot by moving a cart along a horizontal path. This task is often used as a benchmark for di erentmethod comparison. In the practical use of the LQR method, the key problem is how to choose weight matricesQ and R correctly. To obtain satisfying results the experiments should be repeated many times with di erentparameters of weight matrices. These LQR parameters can be tuned by a Genetic Algorithm (GA) techniquefor getting better results. In our paper, the LQR parameters weight matrices Q and R which were tuned usingthe Genetic Algorithm. The simulations of the control problem are designed using MATLAB script code andMATLAB Simulink on an inverted pendulum model. The results show that the Genetic Algorithm is suitablefor tuning the parameters to give an optimal response. The control problem of the inverted pendulum was solvedsuccessfully.
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21

Li, Yan, and Yi Shen. "Preserving Global Exponential Stability of Hybrid BAM Neural Networks with Reaction Diffusion Terms in the Presence of Stochastic Noise and Connection Weight Matrices Uncertainty." Mathematical Problems in Engineering 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/486052.

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We study the impact of stochastic noise and connection weight matrices uncertainty on global exponential stability of hybrid BAM neural networks with reaction diffusion terms. Given globally exponentially stable hybrid BAM neural networks with reaction diffusion terms, the question to be addressed here is how much stochastic noise and connection weights matrices uncertainty the neural networks can tolerate while maintaining global exponential stability. The upper threshold of stochastic noise and connection weights matrices uncertainty is defined by using the transcendental equations. We find that the perturbed hybrid BAM neural networks with reaction diffusion terms preserve global exponential stability if the intensity of both stochastic noise and connection weights matrices uncertainty is smaller than the defined upper threshold. A numerical example is also provided to illustrate the theoretical conclusion.
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22

Firsanova, V. I. "A method for the dimensionality reduction of neural network weight matrices for natural language processing." Cherepovets State University Bulletin, no. 5(122) (October 15, 2024): 84–96. http://dx.doi.org/10.23859/1994-0637-2024-5-122-8.

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The growth in the number of parameters of neural network models for language modeling makes the question of reducing the dimensionality of the matrices storing the models' weights increasingly relevant. The study proposes a novel method to reducing the dimensionality of training weight matrices and an algorithm called Convolutional Weights Compression. The essence of the method is to apply the convolution operation to the analysis of matrices of neural network training weights to reduce their dimensionality. В связи с ростом количества параметров нейросетевых моделей для обработки естественного языка все более актуальным становится вопрос о том, как уменьшить размерность матриц, в которых хранятся веса таких моделей. Исследование предлагает новый метод уменьшения размерности матриц обучающих весов и алгоритм сжатия под названием «сверточная компрессия весов». Суть метода заключается в применении операции свертки к анализу матриц обучающих весов нейронных сетей для уменьшения их размерности.
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23

Boytsov, Alexandr, Sergey Abramov, Vsevolod J. Makeev, and Ivan V. Kulakovskiy. "Positional weight matrices have sufficient prediction power for analysis of noncoding variants." F1000Research 11 (January 12, 2022): 33. http://dx.doi.org/10.12688/f1000research.75471.1.

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The commonly accepted model to quantify the specificity of transcription factor binding to DNA is the position weight matrix, also called the position-specific scoring matrix. Position weight matrices are used in thousands of projects and computational tools in regulatory genomics, including prediction of the regulatory potential of single-nucleotide variants. Yet, recently Yan et al. presented new experimental method for analysis of regulatory variants and, based on its results, reported that "the position weight matrices of most transcription factors lack sufficient predictive power". Here, we re-analyze the rich experimental dataset obtained by Yan et al. and show that appropriately selected position weight matrices in fact can successfully quantify transcription factor binding to alternative alleles.
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24

Mimis, A. "3D WEIGHT MATRICES IN MODELING REAL ESTATE PRICES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W2 (October 6, 2016): 123–25. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w2-123-2016.

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Central role in spatial econometric models of real estate data has the definition of the weight matrix by which we capture the spatial dependence between the observations. The weight matrices presented in literature so far, treats space in a two dimensional manner leaving out the effect of the third dimension or in our case the difference in height where the property resides. To overcome this, we propose a new definition of the weight matrix including the third dimensional effect by using the Hadamard product. The results illustrated that the level effect can be absorbed into the new weight matrix.
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25

Pellegrini, Marco, and Massimiliano Sala. "Weight distribution of Hermitian codes and matrices rank." Finite Fields and Their Applications 60 (November 2019): 101578. http://dx.doi.org/10.1016/j.ffa.2019.101578.

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26

Leung, Ka Hin, and Siu Lun Ma. "Proper circulant weighing matrices of weight $$p^2$$." Designs, Codes and Cryptography 72, no. 3 (2012): 539–50. http://dx.doi.org/10.1007/s10623-012-9786-z.

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27

Claverie, Jean-Michel. "Some useful statistical properties of position-weight matrices." Computers & Chemistry 18, no. 3 (1994): 287–94. http://dx.doi.org/10.1016/0097-8485(94)85024-0.

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28

Kim, Chang‐Ho, Kee Yong Kim, W. S. l’Yi, Yongduk Kim, and Young‐Jai Park. "SU(m/n) weight systems and superprojection matrices." Journal of Mathematical Physics 27, no. 8 (1986): 2009–15. http://dx.doi.org/10.1063/1.527019.

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29

Delvaux, Steven, and Marc Van Barel. "A Givens-Weight Representation for Rank Structured Matrices." SIAM Journal on Matrix Analysis and Applications 29, no. 4 (2008): 1147–70. http://dx.doi.org/10.1137/060654967.

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30

Leung, Ka Hin, and Bernhard Schmidt. "Finiteness of circulant weighing matrices of fixed weight." Journal of Combinatorial Theory, Series A 118, no. 3 (2011): 908–19. http://dx.doi.org/10.1016/j.jcta.2010.10.004.

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31

Grisoni, Francesca, Viviana Consonni, Serena Nembri, and Roberto Todeschini. "How to weight Hasse matrices and reduce incomparabilities." Chemometrics and Intelligent Laboratory Systems 147 (October 2015): 95–104. http://dx.doi.org/10.1016/j.chemolab.2015.08.006.

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32

Schulze-Pillot, Rainer. "Ternary quadratic forms and Brandt matrices." Nagoya Mathematical Journal 102 (June 1986): 117–26. http://dx.doi.org/10.1017/s0027763000000465.

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In a recent paper [9] the author showed (among other results) estimates on the asymptotic behaviour of the representation numbers of positive definite integral ternary quadratic forms, in particular, that for n in a fixed square class tZ2 and lattices L, K in the same spinor genus one has . The main tool utilized for the proof was the theory of modular forms of weight 3/2, especially Shimura’s lifting from the space of cusp forms of weight 3/2 to the space of modular forms of weight 2.
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33

Strauss, Tobias, Welf Wustlich, and Roger Labahn. "Design Strategies for Weight Matrices of Echo State Networks." Neural Computation 24, no. 12 (2012): 3246–76. http://dx.doi.org/10.1162/neco_a_00374.

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This article develops approaches to generate dynamical reservoirs of echo state networks with desired properties reducing the amount of randomness. It is possible to create weight matrices with a predefined singular value spectrum. The procedure guarantees stability (echo state property). We prove the minimization of the impact of noise on the training process. The resulting reservoir types are strongly related to reservoirs already known in the literature. Our experiments show that well-chosen input weights can improve performance.
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34

Meng, Jie, Qingzhang Chen, and Ren He. "Research on Optimal Control for the Vehicle Suspension Based on the Simulated Annealing Algorithm." Journal of Applied Mathematics 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/420719.

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A method is designed to optimize the weight matrix of the LQR controller by using the simulated annealing algorithm. This method utilizes the random searching characteristics of the algorithm to optimize the weight matrices with the target function of suspension performance indexes. This method improves the design efficiency and control performance of the LQR control, and solves the problem of the LQR controller when defining the weight matrices. And a simulation is provided for vehicle active chassis control. The result shows that the active suspension using LQR optimized by the genetic algorithm compared to the chassis controlled by the normal LQR and the passive one, shows better performance. Meanwhile, the problem of defining the weight matrices is greatly solved.
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35

Boytsov, Alexandr, Sergey Abramov, Vsevolod J. Makeev, and Ivan V. Kulakovskiy. "Positional weight matrices have sufficient prediction power for analysis of noncoding variants." F1000Research 11 (June 23, 2022): 33. http://dx.doi.org/10.12688/f1000research.75471.2.

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The position weight matrix, also called the position-specific scoring matrix, is the commonly accepted model to quantify the specificity of transcription factor binding to DNA. Position weight matrices are used in thousands of projects and software tools in regulatory genomics, including computational prediction of the regulatory impact of single-nucleotide variants. Yet, recently Yan et al. reported that "the position weight matrices of most transcription factors lack sufficient predictive power" if applied to the analysis of regulatory variants studied with a newly developed experimental method, SNP-SELEX. Here, we re-analyze the rich experimental dataset obtained by Yan et al. and show that appropriately selected position weight matrices in fact can adequately quantify transcription factor binding to alternative alleles.
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36

Boytsov, Alexandr, Sergey Abramov, Vsevolod J. Makeev, and Ivan V. Kulakovskiy. "Positional weight matrices have sufficient prediction power for analysis of noncoding variants." F1000Research 11 (July 4, 2022): 33. http://dx.doi.org/10.12688/f1000research.75471.3.

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The position weight matrix, also called the position-specific scoring matrix, is the commonly accepted model to quantify the specificity of transcription factor binding to DNA. Position weight matrices are used in thousands of projects and software tools in regulatory genomics, including computational prediction of the regulatory impact of single-nucleotide variants. Yet, recently Yan et al. reported that "the position weight matrices of most transcription factors lack sufficient predictive power" if applied to the analysis of regulatory variants studied with a newly developed experimental method, SNP-SELEX. Here, we re-analyze the rich experimental dataset obtained by Yan et al. and show that appropriately selected position weight matrices in fact can adequately quantify transcription factor binding to alternative alleles.
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37

Gupta, Anjana, Aparna Mehra, and S. S. Appadoo. "Mixed Solution Strategy for MCGDM Problems Using Entropy/Cross Entropy in Interval-Valued Intuitionistic Fuzzy Environment." International Game Theory Review 17, no. 01 (2015): 1540007. http://dx.doi.org/10.1142/s0219198915400071.

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Although several weight determining methods have been studied for multiple criteria group decision making (MCGDM) problems under intuitionistic fuzzy environment, in the present study, besides the criteria values provided by the decision makers (DMs), we propose to also use the historical data of alternatives-criteria to compute the criteria weights. This is a reasonable thought as the past information may influence the decision makers' choice of entries in their respective alternatives-criteria decision matrices. To this aim, we introduce a novel mixed solution strategy to derive the criteria final weight vector. Initially, the alternatives-criteria decision matrices provided by the DMs are taken to involve interval-valued intuitionistic fuzzy numbers (IVIFNs). The entropy measure for IVIFNs, studied by Ye [2010a], is used to aggregate these decision matrices. We also introduce a new definition of cross entropy for IVIFNs and used it to rank the alternatives. Finally, an example is presented to illustrate the proposed approach.
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38

Witte, N. S., P. J. Forrester, and Christopher M. Cosgrove. "Integrability, random matrices and Painlevé transcendents." ANZIAM Journal 44, no. 1 (2002): 41–50. http://dx.doi.org/10.1017/s1446181100007896.

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AbstractThe probability that an interval I is free of eigenvalues in a matrix ensemble with unitary symmetry is given by a Fredholm determinant. When the weight function in the matrix ensemble is a classical weight function, and the interval I includes an endpoint of the support, Tracy and Widom have given a formalism which gives coupled differential equations for the required probability and some auxiliary quantities. We summarize and extend earlier work by expressing the probability and some of the auxiliary quantities in terms of Painlevé transcendents.
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39

Li, Jilong, Niuniu Kong, Shiping Lin, Jie Zeng, Yilin Ke, and Jiacheng Chen. "Spatial Nonlinear Effects of Street Vitality Constrained by Construction Intensity and Functional Diversity—A Case Study from the Streets of Shenzhen." ISPRS International Journal of Geo-Information 13, no. 7 (2024): 238. http://dx.doi.org/10.3390/ijgi13070238.

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As an important part of urban vitality, street vitality is an external manifestation of street economic prosperity and is affected by the built environment and the surrounding street vitality. However, existing research on the formation mechanism of street vitality focuses only on the built environment itself, ignoring the spatial spillover effect on street vitality. This study uses 5290 street segments in Shenzhen as examples. Utilizing geospatial and other multisource big data, this study creates spatial weight matrices at varying distances based on different living circle ranges. By combining the panel threshold model (PTM) and the spatial panel Durbin model (SPDM), this study constructs a spatial autoregressive threshold model to explore the spatial nonlinear effects of street vitality, considering various spatial weight matrices and thresholds of construction intensity and functional diversity. Our results show the following: (1) Street vitality exhibits significant spatial spillover effects, which gradually weaken as the living circle range expands (Moran indices are 0.178***, 0.160***, and 0.145*** for the 500 m, 1000 m, and 1500 m spatial weight matrices, respectively). (2) Construction intensity has a threshold, which is 0.1466 under spatial matrices of different distances. Functional diversity has two thresholds: 0.6832 and 2.2065 for the 500 m spatial weight matrix, and 0.6832 and 1.4325 for the 1000 m matrices, and 0.6832 and 1.2724 for 1500 m matrices. (3) As an international metropolis, street accessibility in Shenzhen has a significant and strong positive impact on its street vitality. This conclusion provides stakeholders with spatial patterns that influence street vitality, offering a theoretical foundation to further break down barriers to street vitality.
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40

Han, Er Dong, and Peng Guo. "Uncertain Linguistic Multi-Attribute Group Decision Making Method with Multi-Granularity Based on Projection and Dominance Degree." Applied Mechanics and Materials 722 (December 2014): 386–89. http://dx.doi.org/10.4028/www.scientific.net/amm.722.386.

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In order to solve multiple attribute group decision making problems with multi-granularity uncertain linguistic assessment information, where the information of attribute weights are incomplete, a group decision making method based on projection and dominance degree is proposed. Firstly, the uncertain linguistic evaluation matrices with multi-granularity are transformed to two-tuple decision matrices according to the continuous interval two-tuple ordered weighted harmonic (ITC-OWH) operator. By using projection method, a goal programming model is set up to determine the attribute weights vector of individual decision maker. Then, integrative attribute dominance degree between pairwise comparisons of arbitrary alternatives are computed, a group integrative dominance degree matrix is obtained based on integrative dominance degree matrices and expert weight vector. The priority-time matrix is given to calculate the general priority time of alternatives, consequently, the rank result of alternatives can be determined.
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41

Rahmalia, Dinita, Teguh Herlambang, Sigit Pancahayani, and Khozin Mu’tamar. "Optimization of Linear Quadratic Tracking (LQT) Weight Matrices Using Simulated Annealing Applied on Planar Arm Model." SPECTA Journal of Technology 4, no. 3 (2020): 22–35. http://dx.doi.org/10.35718/specta.v4i3.193.

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Optimal controls have been applied in this time. One of simple optimal control which will be analyzed in this research is planar arm model dynamic. The planar arm model dynamic consists of joint angles consisting of shoulder joint and elbow joint, angle velocities, and joint torquest due to passive muscle forces. There are control inputs from six muscles in the system. In this research, from planar arm model, it will be designed optimal control using Linear Quadratic Tracking (LQT). The objective function of planar arm model is we will minimimize two angles consisting of shoulder joint and elbow joint. In LQT, the value of performance index depends on the weight matrices so that we should optimize the weight matrices. In this research, the optimization of weight matrices in planar arm model will be applied by Simulated Annealing. The Simulated Annealing method is based on the simulation of thermal annealing of critically heated solids. Based on simulation results, Simulated Annealing can optimize the weight matrices in LQT so that it results optimal performance index with angle as state solution can follow the reference and we also obtain optimal controls from six muscle forces applied.
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42

Pace, R. Kelley, and James P. LeSage. "Chebyshev approximation of log-determinants of spatial weight matrices." Computational Statistics & Data Analysis 45, no. 2 (2004): 179–96. http://dx.doi.org/10.1016/s0167-9473(02)00321-3.

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43

Ang, Miin Huey, K. T. Arasu, Siu Lun Ma, and Yoseph Strassler. "Study of proper circulant weighing matrices with weight 9." Discrete Mathematics 308, no. 13 (2008): 2802–9. http://dx.doi.org/10.1016/j.disc.2004.12.029.

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44

Georgi, B., and A. Schliep. "Context-specific independence mixture modeling for positional weight matrices." Bioinformatics 22, no. 14 (2006): e166-e173. http://dx.doi.org/10.1093/bioinformatics/btl249.

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45

Wang, Chao, Liang Lin, and Jiajun Liu. "Uncertainty Weight Generation Approach Based on Uncertainty Comparison Matrices." Applied Mathematics 03, no. 05 (2012): 499–507. http://dx.doi.org/10.4236/am.2012.35075.

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Leung, Ka Hin, and Bernhard Schmidt. "Structure of group invariant weighing matrices of small weight." Journal of Combinatorial Theory, Series A 154 (February 2018): 114–28. http://dx.doi.org/10.1016/j.jcta.2017.08.016.

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47

Rubei, Elena. "Affine subspaces of matrices with rank in a range." Electronic Journal of Linear Algebra 40 (October 4, 2024): 621–35. http://dx.doi.org/10.13001/ela.2024.8817.

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The problem of finding the maximal dimension of linear or affine subspaces of matrices whose rank is constant, or bounded below, or bounded above, has attracted many mathematicians from the sixties to the present day. The problem has caught also the attention of algebraic geometers, since vector spaces of matrices of constant rank $r$ give rise to vector bundle maps whose images are vector bundles of rank $r$. Moreover, there is a link with the so-called "rank metric codes," since a constant rank $r$ subspace of $K^{n \times n}$ can be viewed as a constant weight $r$ rank metric code; it can be interesting to study also the maximal dimension of the subspaces of $K^{n \times n}$ whose elements have rank in a range $[s,r]$, since such subspaces obviously give rank metric codes with weights in $[s,r]$. In this paper, with the main purpose to get an organic result including the ones on spaces of matrices with constant rank, the ones on spaces of matrices with rank bounded below and the ones on spaces of matrices with rank bounded above and to generalize a previous result on real matrices with constant rank to matrices on a more general field, we study the maximal dimension of affine subspaces of matrices whose rank is between two numbers under mild assumptions on the field. We get also a result on antisymmetric matrices and on matrices in row echelon form.
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Siddharthan, Rahul. "Dinucleotide Weight Matrices for Predicting Transcription Factor Binding Sites: Generalizing the Position Weight Matrix." PLoS ONE 5, no. 3 (2010): e9722. http://dx.doi.org/10.1371/journal.pone.0009722.

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Luo, Zhi-Quan. "On the Convergence of the LMS Algorithm with Adaptive Learning Rate for Linear Feedforward Networks." Neural Computation 3, no. 2 (1991): 226–45. http://dx.doi.org/10.1162/neco.1991.3.2.226.

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We consider the problem of training a linear feedforward neural network by using a gradient descent-like LMS learning algorithm. The objective is to find a weight matrix for the network, by repeatedly presenting to it a finite set of examples, so that the sum of the squares of the errors is minimized. Kohonen showed that with a small but fixed learning rate (or stepsize) some subsequences of the weight matrices generated by the algorithm will converge to certain matrices close to the optimal weight matrix. In this paper, we show that, by dynamically decreasing the learning rate during each training cycle, the sequence of matrices generated by the algorithm will converge to the optimal weight matrix. We also show that for any given ∊ &gt; 0 the LMS algorithm, with decreasing learning rates, will generate an ∊-optimal weight matrix (i.e., a matrix of distance at most ∊ away from the optimal matrix) after O(1/∊) training cycles. This is in contrast to Ω(1/∊log 1/∊) training cycles needed to generate an ∊-optimal weight matrix when the learning rate is kept fixed. We also give a general condition for the learning rates under which the LMS learning algorithm is guaranteed to converge to the optimal weight matrix.
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BABKINA, N. V., L. O. VORONTSOVA, O. I. ANTONENKO, et al. "ULTRAVIOLET PROTECTION AND DAMPING ABILITY OF TRANSPARENT POLYURETHANE MATERIALS WITH THE COMPONENTS OF DIFFERENT CHEMICAL NATURE." Polymer journal 44, no. 3 (2022): 188–97. https://doi.org/10.15407/polymerj.44.03.188.

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This article is devoted to the study of the influence of the chemical nature of the components of polyurethane matrices (PU) on their optical and viscoelastic properties in order to obtain polymer materials that combine several different functional properties: high transparency, effective UV protection and high damping ability. PU matrices with different chemical structures of diisocyanate (aliphatic (hexamethylene diisocyanate) or aromatic (toluylene diisocyanate)) and oligodiol (oligoether (oligooxypropylene glycol) or oligoester (oligodiethylene glycol adipate)) blocks were synthesized. PU matrices with different molecular weights of ester (800 and 1500) were synthesized too. It was established that all PU matrices have a fairly high (~90 %) transmission coefficient in the range of visible wavelengths and UV blocking. However, the range of UV absorption significantly depends on the PU components. Matrices based on aliphatic diisocyanate absorb UV up to 250–280 nm. The UV absorption of PU matrices based on aromatic diisocyanate, regardless of the nature of their oligoester component and its molecular weight, undergoes a shift to the long-wavelength region – up to 300–400 nm, which is due to the presence of aromatic rings. For PUs with an aromatic component, the highest absorption in the UV region is observed for PUs based on oligoesters, which is explained by the greater absorption ability of ester groups relative to ether ones. It was found that PU matrix based on oligoester has better elastic properties, but the PU matrix based on oligoether is characterized by a wider temperature range of effective damping. The replacement of aliphatic diisocyanate with an aromatic one shifts the area of effective damping of PU material towards positive temperatures. Therefore, by changing the nature of PU components, as well as the molecular weight of the PU oligoester component, it is possible to obtain transparent materials with a wide temperature range of effective damping in combination with high protection against UV radiation.
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