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LSTM new gate for computing the efficiency on inputdata

Knowledge-Based Systems 2025年 322卷

作者： García Cabello, Julia Carbó-García, Santiago Department of Applied Mathematics Andalusian Research Institute in Data Science and Computational Intelligence University of Granada Granada Spain Department of Computer Science and Artificial Intelligence Andalusian Research Institute in Data Science and Computational Intelligence University of Granada Granada Spain

The recognized learning ability of neural networks (NNs) is determined by their training process. The NN data-dependent nature makes that their success depends to a large extent on the quality of the training data sets. This paper addresses the selection of the best training sets for Long Short Time Models (LSTMs) in real-life contexts. If such selection from a theoretical standpoint is already complex, it becomes challenging when addressed for real scenarios, where effectiveness should be replaced by efficiency (i.e., effectiveness in the shortest possible time and without increasing the computational cost). Our proposal revolves around the introduction, definition and structuring of a new LSTM gate: the efficiency gate, that applies to those inputs that have passed the forget gate. The efficiency gate is responsible for ensuring that training advances only with the best inputs in the sense that the corresponding outputs match as closely as possible with a target value (best estimators). For this purpose, new mathematical results will be demonstrated here in order to prove that our efficiency gate is mathematically feasible. We also fully describe how the new gate joins the LSTM operation, blending in with it. The consequence of such natural integration is that the computational effort is practically unchanged. Our methodology also allows the user to set the admissible error thresholds (which are different in each real scenario) as part of the setting options. © 2025 The Authors

关键词： Efficiency gate New LSTM gate Selection of training data sets Real-life contexts

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On Approximations to the Ruin Probability for the Classical Risk Process

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Journal of Mathematical sciences (United States) 2022年第1期267卷 57-63页

作者： Gavrilenko, S.V. Korolev, V.Yu. Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University Moscow Russian Federation Moscow Center for Fundamental and Applied Mathematics Moscow Russian Federation Federal Research Center “Computer Science and Control” Russian Academy of Sciences Moscow Russian Federation

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On the convergence of the pseudospectral approximation of reproduction numbers for age-structured models

arXiv

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arXiv 2024年

作者： De Reggi, Simone Scarabel, Francesca Vermiglio, Rossana CDLAb - Computational Dynamics Laboratory University of Udine Italy Department of Mathematics Computer Science and Physics University of Udine Italy Department of Applied Mathematics University of Leeds United Kingdom

We rigorously investigate the convergence of a new numerical method, recently proposed by the authors, to approximate the reproduction numbers of a large class of age-structured population models with finite age span. The method consists in reformulating the problem on a space of absolutely continuous functions via an integral mapping. For any chosen splitting into birth and transition processes, we first define an operator that maps a generation to the next one (corresponding to the Next Generation Operator in the case of R0). Then, we approximate the infinite-dimensional operator with a matrix using pseudospectral discretization. In this paper, we prove that the spectral radius of the resulting matrix converges to the true reproduction number, and the (interpolation of the) corresponding eigenvector converges to the associated eigenfunction, with convergence order that depends on the regularity of the model coefficients. Results are confirmed experimentally and applications to epidemiology are *** Codes 34L16, 47B07, 65L15, 65L60, 65N12, 92D25 © 2024, CC BY.

关键词： Eigenvalues and eigenfunctions

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Local Sequential MCMC for Data Assimilation with Applications in Geoscience

arXiv

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arXiv 2024年

作者： Ruzayqat, Hamza Knio, Omar Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

This paper presents a new data assimilation (DA) scheme based on a sequential Markov Chain Monte Carlo (SMCMC) DA technique [36] which is provably convergent and has been recently used for filtering, particularly for high-dimensional non-linear, and potentially, non-Gaussian state-space models. Unlike particle filters, which can be considered exact methods and can be used for filtering non-linear, non-Gaussian models, SMCMC does not assign weights to the samples/particles, and therefore, the method does not suffer from the issue of weight-degeneracy when a relatively small number of samples is used. We design a localization approach within the SMCMC framework that focuses on regions where observations are located and restricts the transition densities included in the filtering distribution of the state to these regions. This results in immensely reducing the effective degrees of freedom and thus improving the efficiency. We test the new technique on high-dimensional (d ∼ 104 − 105) linear Gaussian model and non-linear shallow water models with Gaussian noise with real and synthetic observations. For two of the numerical examples, the observations mimic the data generated by the Surface Water and Ocean Topography (SWOT) mission led by NASA, which is a swath of ocean height observations that changes location at every assimilation time step. We also use a set of ocean drifters' real observations in which the drifters are moving according the ocean kinematics and assumed to have uncertain locations at the time of assimilation. We show that when higher accuracy is required, the proposed algorithm is superior in terms of efficiency and accuracy over competing ensemble methods and the original SMCMC *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2024, CC BY.

关键词： Markov chains

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A Flow Artist for High-Dimensional Cellular Data 33

A Flow Artist for High-Dimensional Cellular Data

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33rd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2023

作者： MacDonald, Kincaid Bhaskar, Dhananjay Thampakkul, Guy Nguyen, Nhi Zhang, Joia Perlmutter, Michael Adelstein, Ian Krishnaswamy, Smita Yale University Department of Mathematics United States Pomona College Department of Mathematics United States University of Washington Department of Statistics United States Boise State University Department of Mathematics United States Yale University Department of Computer Science United States Yale University Applied Mathematics Program United States Yale University Computational Biology and Bioinformatics Program United States

ISBN: (纸本)9798350324112

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data. © 2023 IEEE.

关键词： RNA

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Firefly Algorithm Approach for Recovering the Mathematical Structure of One-Dimensional Chaotic Maps from Time Series Data

Firefly Algorithm Approach for Recovering the Mathematical S...

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computer Technologies (ICCTech), International Conference on

作者： Akemi Gálvez Iztok Fister Andrés Iglesias Dept. of Applied Mathematics & Computational Sciences University of Cantabria Santander Spain Faculty of Electrical Engineering & Computer Science University of Maribor Maribor Slovenia

ISBN: (数字)9798350395419

ISBN: (纸本)9798350395426

Uncovering the mathematical structure of unknown chaotic systems from limited time series data poses a significant challenge in the field of dynamical systems, with broad applications across various domains. In this paper, we propose a swarm intelligence approach to tackle this issue, specifically focusing on one-dimensional discrete maps. Our approach leverages the firefly algorithm, a popular nature-inspired metaheuristic, known for its optimization capabilities. We assess the performance of the method by applying it to two illustrative examples of time series derived from one-dimensional maps: the Hénon map and the Burger map. The results show that this approach is promising for recovering the equations of motion of one-dimensional chaotic maps, even in situations where no additional information is available beyond the provided data points.

关键词： Heuristic algorithms Time series analysis Metaheuristics Focusing Particle swarm optimization Dynamical systems

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Solutions of fractional differential models by using Sumudu transform method and its hybrid

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Partial Differential Equations in applied mathematics 2024年 11卷

作者： Aibinu, Mathew O. Mahomed, Fazal M. Jorgensen, Palle E. School of Computer Science and Applied Mathematics University of the Witwatersrand Department of Mathematics University of Iowa Mathematics and Statistics University of Regina National Institute for Theoretical and Computational Sciences (NITheCS)

This paper presents the Sumudu transform method and its hybrid for the construction of solutions of differential equations, both with integer-order and fractional derivatives. The paper discusses the construction of solutions of fractional differential equations with varying delay proportional to the independent variable by using two methods. The paper considers the mathematical model for the decay of Iodine 135 as an application of fractional differential equations in nuclear physics. The application indicates that fractional differential equations with variable delay proportional to the independent variable are a useful tool for the modeling of many anomalous phenomena in nature and in the theory of complex systems. © 2024 The Author(s)

关键词： Decay Delay Fractional derivatives Model Sumudu transform

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Surrogate-based multilevel Monte Carlo methods for uncertainty quantification in the Grad-Shafranov free boundary problem

arXiv

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arXiv 2025年

作者： Elman, Howard C. Liang, Jiaxing Sánchez-Vizuet, Tonatiuh Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Department of Computational Applied Mathematics & Operations Research Rice University United States Department of Mathematics The University of Arizona United States

We explore a hybrid technique to quantify the variability in the numerical solutions to a free boundary problem associated with magnetic equilibrium in axisymmetric fusion reactors amidst parameter uncertainties. The method aims at reducing computational costs by integrating a surrogate model into a multilevel Monte Carlo method. The resulting surrogate-enhanced multilevel Monte Carlo methods reduce the cost of simulation by factors as large as 104 compared to standard Monte Carlo simulations involving direct numerical solutions of the associated Grad-Shafranov partial differential equation. Accuracy assessments also show that surrogate-based sampling closely aligns with the results of direct computation, confirming its effectiveness in capturing the behavior of plasma boundary and geometric *** Codes 65Z05, 65C05, 62P35, 35R35, 35R60 Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

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A Pseudo-Spectral Scheme for Systems of Two-Point Boundary Value Problems with Left and Right Sided Fractional Derivatives and Related Integral Equations

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computer Modeling in Engineering & sciences 2021年第7期128卷 21-41页

作者： I.G.Ameen N.A.Elkot M.A.Zaky A.S.Hendy E.H.Doha Department of Mathematics Faculty of ScienceAl-Azhar UniversityCairoEgypt Department of Mathematics Faculty of ScienceCairo UniversityGiza12613Egypt Department of Applied Mathematics Physics DivisionNational Research CentreDokkiCairo12622Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and MathematicsUral Federal UniversityYekaterinburg620002Russia Department of Mathematics Faculty of ScienceBenha UniversityBenha13511Egypt

We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional *** main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral ***,a Legendre-based spectral collocation method is developed for solving the transformed ***,we can make good use of the advantages of the Gauss quadrature *** present the construction and analysis of the collocation *** results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange *** numerical examples are given to confirm the convergence analysis and robustness of the scheme.

关键词： Spectral collocation method weakly singular integral equations two-point boundary value problems convergence analysis

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NEURAL ENTROPIC GROMOV-WASSERSTEIN ALIGNMENT

arXiv

引用

arXiv 2023年

作者： Wang, Tao Goldfeld, Ziv Applied Mathematics and Computational Science University of Pennsylvania United States School of Electrical and Computer Engineering Cornell University United States

The Gromov-Wasserstein (GW) distance, rooted in optimal transport (OT) theory, provides a natural framework for aligning heterogeneous datasets. Alas, statistical estimation of the GW distance suffers from the curse of dimensionality and its exact computation is NP hard. To circumvent these issues, entropic regularization has emerged as a remedy that enables parametric estimation rates via plug-in and efficient computation using Sinkhorn iterations. Motivated by further scaling up entropic GW (EGW) alignment methods to data dimensions and sample sizes that appear in modern machine learning applications, we propose a novel neural estimation approach. Our estimator parametrizes a minimax semi-dual representation of the EGW distance by a neural network, approximates expectations by sample means, and optimizes the resulting empirical objective over parameter space. We establish non-asymptotic error bounds on the EGW neural estimator of the alignment cost and optimal plan. Our bounds characterize the effective error in terms of neural network (NN) size and the number of samples, revealing optimal scaling laws that guarantee parametric convergence. The bounds hold for compactly supported distributions, and imply that the proposed estimator is minimax-rate optimal over that class. Numerical experiments validating our theory are also provided. Copyright © 2023, The Authors. All rights reserved.

关键词： Alignment

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