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Publications related to Matrices (10,000)
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In this paper, we propose a generalized Lucas matrix (a recursive matrix of higher order) obtained from the generalized Fibonacci sequences. We obtain their algebraic properties such as direct inverse calculation, recursive nature, etc. Then, we propose a modified public key cryptography using the generalized Lucas matrices as a key element that op...
This paper addresses the challenge of estimating the orientation, position, and velocity of a vehicle operating in three-dimensional (3D) space with six degrees of freedom (6-DoF). A Deep Learning-based Adaptation Mechanism (DLAM) is proposed to adaptively tune the noise covariance matrices of Kalman-type filters for the Visual-Inertial Navigation...
Recent advancements in machine learning have opened new avenues for preventing fatal ventricular arrhyth-mia by accurately measuring and analyzing QT intervals. This paper presents virtual sensor based on an expert system designed to prevent the risk of fatal ventricular arrhythmias associated with QT-prolonging treatments. The expert system catego...
This paper describes how to propagate wavefields for arbitrary numbers of traditional time steps in a single step, called a superstep. We show how to construct operators that accomplish this task for finite-difference time domain schemes, including temporal first-order schemes in isotropic, anisotropic and elastic media, as well as temporal second-...
Background: Psychosis-proneness (PP) is identified as the subclinical aspect of the psychosis continuum. Previous research suggests that PP has multimodal substrates. However, no studies have explored these factors together in a comprehensive manner. In this study, we present the first model that simultaneously examines environmental influences on...
Recycled fine aggregates (RFA) are often prohibited in new construction applications because of their poor physical properties. This paper assesses the feasibility of incorporating steel fibers, silica fume, and latex polymers to mitigate the drop in mechanical properties and durability of RFA-modified cementitious matrices. Testing was conducted o...
Sequences of structured matrices of increasing size, such as generalized locally Toeplitz sequences, arise in many scientific applications and especially in the numerical discretization of linear differential problems. We assume that the eigenvalues of a matrix X_n , belonging to a sequence of such kind, are given by a regular expansion. Under this...
Composites for ballistic armor generally use high-performance synthetic fibers due to their excellent properties,
but they have a high cost and environmental impact. Natural lignocellulosic fibers emerge as a more sustainable
alternative, although they face challenges. Hybrid composites, which combine natural and synthetic fibers, were
developed to...
Quantization stands as a pivotal technique for large language model (LLM) serving, yet it poses significant challenges particularly in achieving effective low-bit quantization. The limited numerical mapping makes the quantized model produce a non-trivial error, bringing out intolerable performance degration. This paper is anchored in the basic idea...
Knowledge of the force time history of a structure is essential to assess its behaviour, ensure safety and maintain reliability. However, direct measurement of external forces is often challenging due to sensor limitations, unknown force characteristics, or inaccessible load points. This paper presents an efficient dynamic load reconstruction metho...
Algorithms based on linear approximation are the primary methods for fast online image reconstruction in electrical capacitance tomography (ECT). One-step reconstruction algorithms use certain inverse matrix approximations , such as the normalized transpose matrix or the Moore-Penrose pseudoinverse matrix used in the linear back-projection (LBP) al...
The objective of the study is to reconstruct the bathymetry of a shallow river using the Structure-from-Motion algorithm and to evaluate the robustness of the approach by exploring its repeatability and reproducibility. To address this issue, the multi-UAV experimental campaign was organized in SW Poland/N Czechia, and focused on the smoothly flowi...
This paper presents a novel equilibrium-based approach to the linear homogenization of shear-deformable beams and plates with periodic heterogeneity. The proposed approach leverages the fact that, under equilibrium, the stress resultants and sectional strains in beams and plates vary at most linearly with respect to the axial or in-plane coordinate...
Select electron-propagator (EP) methods agree as closely with experimental standards for molecular vertical ionization energies as they do with computational data of nearly full-configuration-interaction quality. Several EP methods consistently attain higher accuracy than alternatives with equal arithmetic bottlenecks expressed in terms of occupied...
Background
In the rapidly evolving field of molecular diagnostics, identifying a suitable extraction method is crucial in determining the applicability of the point‐of‐need device. Extraction, which serves as the initial and important step in the diagnostic process, plays a vital role in the accuracy, reliability, and speed of detecting pathogens....
Based on density functional theory (DFT), we conducted an in‐depth evaluation of the protonation energies of matrix molecules in matrix‐assisted laser desorption/ionization (MALDI) technology. Various error analysis strategies were employed to explore the discrepancies between theoretical calculations and experimental data. The results showed that,...
Ensembles of complex symmetric, and complex self dual random matrices are known to exhibit local statistical properties distinct from those of the non-Hermitian Ginibre ensembles. On the other hand, in distinction to the latter, the joint eigenvalue probability density function of these two ensembles are not known. Nonetheless, as carried out in th...
We study amorphous solids with strong elastic disorder and find an unjamming instability that exists, in a harmonic model built using Euclidean random matrices (ERMs). Employing the Zwanzig-Mori projection operator formalism and Gaussian factorization approximations, we develop a first-principles, self-consistent theory of transverse momentum corre...
Grape-derived phenolic compounds possess many health benefits, but their biological effectiveness and their effects on human health depend directly on bioaccessibility. Different physiological conditions, interactions with food compounds (proteins, lipids, and carbohydrates), and/or microbial transformations affect the solubilization and stability...
Rapid advancements in science and technology have allowed medical providers to treat wider ranges of diseases with safer and more effective therapies than ever before. One of the areas of health that has been consistently understudied, however, is one that affects us all: environmental health or the effects that the chemicals we are exposed to ever...
An analytical method for calculating the dynamic stiffness of rubber isolator with multi-rigid-flexible bodies and various coupling deformation modes is proposed. The three-dimensional transfer matrices are reduced to two-dimensional representation for calculations, based on the excitation direction of the isolator and the deformation modes of the...
This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and measurement coordinate systems. For these problems, a procedure is developed for mapping the observed measurements and...
We present a new method for estimating high-dimensional sparse partial correlation and inverse covariance matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation method wherein each individual feature is regressed on all other features while positive semi-definiteness...
Critiqueu
The aim of this study is to evaluate GPT-4's reasoning ability to interpret oral mucosal disease photos and generate structured reports from free-text inputs, while exploring the role of prompt engineering in enhancing its performance. Prompt received by utilizing automatic prompt engineering and knowledge of oral physicians, was provided to GPT-4...
Accurate metro passenger flow prediction can provide data support for vehicle scheduling and personnel allocation by metro operation departments, ensuring the efficient utilization of related resources. In recent years, Graph Convolutional Networks (GCNs) have demonstrated excellent performance in spatial processing, making them an effective method...
We shown among other inequalities that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A_{1}$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepa...
Super sample covariance (SSC) is important when estimating covariance matrices using a set of mock catalogues for galaxy surveys. If the underlying cosmological simulations do not include the variation in background parameters appropriate for the simulation sizes, then the scatter between mocks will be missing the SSC component. The coupling betwee...
Polymeric membranes offer an appealing solution for sustainable CO 2 capture, with potential for large-scale deployment. However, balancing high permeability and selectivity is an inherent challenge for pristine membranes. To address this challenge, the development of mixed matrix membranes (MMMs) is a promising strategy. MMMs are obtained by caref...
The article presents experimental data on the study of heterocyclic aromatic amines formation in model matrices consisting of amino acids (8 essential, glutamic acid and aspartic acid), carbohydrates (sucrose, lactose) and creatine. The results of the studies showed that carbohydrates in the reaction of MeIQx and PhIP formation can exhibit both inh...
Per- and poly-fluoroalkyl substances (PFAS) have received significant attention due to their persistence in the environment. Because of their accumulative nature, even trace amounts can adversely impact human health and ecosystems. Here, we present Molecule-Probed Raman Spectroscopy (MPRS), an ultra-sensitive, low-cost, and fast method that can ach...
The modulation of the light field by metasurfaces in near-field remains constrained by the coupling of cross-polarization components. This limits the storage space for ciphertexts with orthogonal polarization states. Our proposal introduces a transmission model with layered-control theory, which realizes decoupled states of anti-diagonal entries of...
Accurate and reliable vehicle state information is essential for ensuring vehicle safety and stability. While Interactive Multiple Model Square Root Cubature Kalman Filtering (IMM-SRCKF) has shown promise in state estimation, this work specifically addresses the unique challenges of achieving high-accuracy and real-time state estimation for commerc...
In the big data era, images serve as essential carriers of visual information, widely utilized across fields such as commerce, healthcare, education, and the military. To ensure the security of digital images, image encryption has been widely concerned. In this paper, we propose an image encryption algorithm using a novel two-dimensional (2D) chaot...
Nahm sums are specific q-hypergeometric series associated with symmetric positive definite matrices. In this paper we study Nahm sums associated with symmetrizable matrices. We show that one direction of Nahm’s conjecture, which was proven by Calegari, Garoufalidis, and Zagier for the symmetric case, also holds for the symmetrizable case. This asse...
Laser patterning of perovskite is a novel technology with the advantages of high speed, programmability, and maskless, which is ideal for fabricating micro light‐emitting diodes (micro‐LED) color conversion layers (CCL). This work reports a method for laser in situ synthesis of wide bandgap tunable perovskite with an emission spectrum from 475 to 6...
Using spin-1/2 state (qubit state) description by the conditional probability distributions of dichotomic random variables, we construct the irreducible Lie su(2) algebra representations by means of the probability distribution functions. We obtain explicit 2×2-matrices of the Lie algebra elements and express them in terms of Pauli matrices. Then w...
The optical properties of Mn5+ ions, which are responsible for the intense green–turquoise–blue coloration of Mn5+-based pigments and the near-infrared emission of phosphors, are the focus of this article. Mn5+ ions enter crystalline matrices in four-fold coordinated positions and can maintain their 5+ valence state when crystalline hosts meet the...
In recent studies of emotional EEG classification, connectivity matrices have been successfully employed as input to convolutional neural networks (CNNs), which can effectively consider inter-regional interaction patterns in EEG. However, we find that such an approach has a limitation that important patterns in connectivity matrices may be lost dur...
Unsupervised cross-modal hashing, due to its independence from heavy label information, is more convenient for application to other fields. In recent years, this area has gained widespread attention and achieved great success. However, existing unsupervised cross-modal hashing methods still face some issues, such as simple fusion after feature extr...
Pure states correspond to one-dimensional subspaces of $\mathbb{C}^n$ represented by unit vectors. In this paper, we develop the theory of perfect state transfer (PST) between real pure states with emphasis on the adjacency and Laplacian matrices as Hamiltonians of a graph representing a quantum spin network. We characterize PST between real pure s...
Objective
One of the primary goals of treatments received by elderly individuals (≥ 75 years) with lumbar spine diseases is to improve their quality of life and obtain favorable outcomes (FOs). Predicting the risk of unfavorable outcomes (UFOs, defining as being unable to obtain functional independence and simultaneously being dissatisfied with the...
In this paper, we introduce the Wigner parametrization of unitary matrices and then apply it to the full description of canonical seesaw models, which extend the Standard Model with three right-handed neutrino singlets and account simultaneously for tiny Majorana neutrino masses and the baryon number asymmetry in the Universe. In the Wigner paramet...
Modern large language models (LLMs) often encounter communication bottlenecks on current hardware, rather than purely computational constraints. Multi-head Latent Attention (MLA) tackles this challenge by using low-rank matrices in the key-value (KV) layers, thereby allowing compressed latent KV states to be cached. This approach significantly redu...
This article designs a new timer-related sampled-data fuzzy observer, and proposes a novel aperiodic-sampling-dependent free-matrix approach, to estimate the state of nonlinear chaotic systems. The nonlinear systems are approximated by the Takagi-Sugeno (T-S) fuzzy model. Different from the traditional one, the designed observer incorporates the sa...
An empirical stochastic analysis of high-frequency, tick-by-tick order data of NASDAQ100 listed stocks is conducted using a first-order discrete-time Markov chain model to explore intraday order transition dynamics. This analysis focuses on three market cap categories: High, Medium, and Low. Time-homogeneous transition probability matrices are esti...
Sobol’ sensitivity index estimators for stochastic models are functions of nested
Monte Carlo estimators, which are estimators built from two nested Monte Carlo
loops. The outer loop explores the input space and, for each of the explorations,
the inner loop repeats model runs to estimate conditional expectations. Although
the optimal allocation bet...
Open quantum systems are powerful effective descriptions of quantum systems interacting with their environments. Studying changes of Fock states probabilities can be intricate in this context since the prevailing description of open quantum dynamics is by master equations of the systems' reduced density matrices, which usually requires finding solu...
Many machine learning algorithms use Euclidean distance as a common metric to calculate similarities between data. However, Euclidean distance is not valid when data lie on a manifold with non-zero curvatures. Therefore, we propose a new non-parametric approach that uses curvatures to calculate distances. Curvature is an appealing feature for this...
Problems attempted to be evaluated using the fundamentals of Mathematics include Goldbach's Conjecture, The Riemann Hypothesis, the Collatz Conjecture, the theory of Dates, Complexity, the Twin Primes Conjecture, Fermat's Conjecture and Beal's Conjecture. A Beal's Conjecture Proof was found to also involve matrices which meant once it and the other...
While self-attention has been instrumental in the success of Transformers, it can lead to over-concentration on a few tokens during training, resulting in suboptimal information flow. Enforcing doubly-stochastic constraints in attention matrices has been shown to improve structure and balance in attention distributions. However, existing methods re...
We consider products of matrices of the form A n = O n + ϵ N n where ( O n ) n ⩾ 1 is a sequence of d × d orthogonal matrices, N n has independent standard normal entries and where the ( N n ) n ⩾ 1 are mutually independent. We study the Lyapunov exponents of the cocycle as a function of ε , giving an exact expression for the j th Lyapunov exponent...
This research paper titled Comparison Of African Indigenous And Western Intelligence Tests
Using Validation Processes Of Bakare Progressive Matrix And Wechsler Adult Intelligence Tests,
was written by Taiwo, Adebukola Kabir and Ojuolape, Mumud Olabode.
In the oceans, ecological analyses of pelagic amphipods have mainly focused on the epipelagic zone with few studies in the deep waters. In this study, a coarse-scale vertical analysis, between 0 and 1000 m depth, was performed in the southern Gulf of Mexico during summer and winter. We hypothesize greater differences between the epi-and mesopelagic...
Recent studies highlight the growing appeal of multi-view learning due to its enhanced generalization. Semi-supervised classification, using few labeled samples to classify the unlabeled majority, is gaining popularity for its time and cost efficiency, particularly with high-dimensional and large-scale multi-view data. Existing graph-based methods...
Drone-based synthetic aperture radar (SAR) systems have increasingly gained attention due to their potential for rapid surveillance in localized areas. This paper presents a novel approach to SAR processing for subsurface target detection from a lightweight drone platform. The limited processing capacity and memory resources of small SAR platforms...
We study the $\ell^\infty \to \ell^\infty$ operator norm of products of independent random matrices with independent and identically distributed entries. For $n$-by-$n$ matrices whose entries are centered, have unit variance, and have a finite moment of order $4\alpha$ for some $\alpha > 1$, we find that the operator norm of the product of $p$ matr...
In this paper, we explore the least-norm solution to the classical matrix equation AXB=C over the dual quaternion algebra, where A, B, and C are given matrices, while X remains the unknown matrix. We begin by transforming the definition of the Frobenius norm for dual quaternion matrices into an equivalent form. Using this new expression, we investi...
Obtaining the inverse of a large symmetric positive definite matrix $\mathcal{A}\in\mathbb{R}^{p\times p}$ is a continual challenge across many mathematical disciplines. The computational complexity associated with direct methods can be prohibitively expensive, making it infeasible to compute the inverse. In this paper, we present a novel iterative...
El modelado computacional multiescala permite diseñar matrices fibrosas sintéticas para reproducir el comportamiento mecánico de tejidos biológicos. El objetivo de este trabajo es desarrollar un método para obtener diseños CAD de tejidos artificiales (scaffolds) para ensayos uniaxiales in-silico automatizados. Se desarrolló un software para generar...
In this study, we address the challenge of low-rank model compression in the context of in-memory computing (IMC) architectures. Traditional pruning approaches, while effective in model size reduction, necessitate additional peripheral circuitry to manage complex dataflows and mitigate dislocation issues, leading to increased area and energy overhe...
We investigate structural properties of the binary rank of Kronecker powers of binary matrices, equivalently, the biclique partition numbers of the corresponding bipartite graphs. To this end, we engineer a Column Generation approach to solve linear optimization problems for the fractional biclique partition number of bipartite graphs, specifically...
In the case of the circular unitary ensemble of Haar distributed unitary matrices, the large $N$ form of the moments of the absolute value of the characteristic polynomial is known to be of relevance to the moments of the Riemann zeta function on the critical line, and further to relate to Fisher-Hartwig asymptotics in the theory of Toeplitz determ...
Previously, methods for learning marginally stable linear dynamical systems either required the transition matrix to be symmetric or incurred regret bounds that scale polynomially with the system's hidden dimension. In this work, we introduce a novel method that overcomes this trade-off, achieving dimension-free regret despite the presence of asymm...
A novel unsupervised learning method is proposed in this paper for biclustering large-dimensional matrix-valued time series based on an entirely new latent two-way factor structure. Each block cluster is characterized by its own row and column cluster-specific factors in addition to some common matrix factors which impact on all the matrix time ser...
Asphalt performance improves with the incorporation of various additives and with the time factor. In this study, the effect of time on asphalt mixtures (AM) containing styrene–butadiene–styrene (SBS) and sargassum particles (SGP) is analyzed. The
composites were prepared by the melt method, using five part hundred rubber (phr) of SGP and polymeric...
Introducción: Con el objetivo de dignificar el patrimonio escrito y conservar la memoria divino-humana, surge el proyecto de salvaguarda de importantes documentos históricos parroquiales del archipiélago portugués, albergados en la catedral de Angra do Heroísmo y en las iglesias matrices de Ponta Delgada y Horta. Metodología: La investigación, desa...
This short method note presents a systematic framework for constructing Markov chains with transition matrices (or kernels) that achieve specific stationary distributions, including the Gaussian, heavy-tailed Cauchy, extreme-value Gumbel, and Bose–Einstein (Planck’s law) distributions.
Using the Metropolis–Hastings algorithm, we derive detailed b...
Background
Healthcare professionals in plastic and reconstructive surgery (PRS) face unique stressors that contribute to burnout, increasing the risk of errors and compromising patient care. Despite this, there is limited research on PRS burnout in the United States. This study aimed to measure burnout rates and identify high-impact improvement tar...
Fuzzy matrices play a crucial role in fuzzy logic and fuzzy systems. This paper investigates the problem of supervised learning fuzzy matrices through sample pairs of input–output fuzzy vectors, where the fuzzy matrix inference mechanism is based on the max–min composition method. We propose an optimization approach based on stochastic gradient des...
Melanoma is a very dangerous type of skin cancer that needs new ways to be found so that it can be treated quickly. The goal of this study is to create better ways to find melanoma by combining mixed Convolutional Neural Networks (CNN) and Autoencoder models with in-depth data analysis. This will make melanoma identification more accurate and relia...
Let $X$ be an $N$-dimensional random vector which describes the ordered eigenvalues of a $\beta$-Hermite ensemble, and let $z$ the vector containing the ordered zeros of the Hermite poynomial $H_N$. We present an explicit estimate for $P(\|X-z\|_2\ge\epsilon)$ for small $\epsilon>0$ and large parameters $\beta$. The proof is based on a central limi...