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arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN Shenzhen China 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

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

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Effective Dimension Aware Fractional-Order Stochastic Gradient Descent for Convex Optimization Problems

arXiv

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arXiv 2025年

作者： Partohaghighi, Mohammad Marcia, Roummel Chen, YangQuan Electrical Engineering and Computer Science graduate program University of California Merced United States Department of Applied Mathematics University of California Merced MercedCA United States Lab Department of Mechanical Engineering School of Engineering University of California MercedCA95343 United States

Fractional-order stochastic gradient descent (FOSGD) leverages a fractional exponent to capture long-memory effects in optimization, yet its practical impact is often constrained by the difficulty of tuning and stabilizing this exponent. In this work, we introduce 2SED Fractional-Order Stochastic Gradient Descent (2SEDFOSGD), a novel method that synergistically combines the Two-Scale Effective Dimension (2SED) algorithm with FOSGD to automatically calibrate the fractional exponent in a data-driven manner. By continuously gauging model sensitivity and effective dimensionality, 2SED dynamically adjusts the exponent to curb erratic oscillations and enhance convergence rates. Theoretically, we demonstrate how this dimension-aware adaptation retains the benefits of fractional memory while averting the sluggish or unstable behaviors frequently observed in naive fractional SGD. Empirical evaluations across multiple benchmarks confirm that our 2SED-driven fractional exponent approach not only converges faster but also achieves more robust final performance, suggesting broad applicability for fractional-order methodologies in large-scale machine learning and related domains. © 2025, CC BY.

关键词： Convex optimization

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A Deep Learning Approach for Nerve Injury Classification in Brachial Plexopathies Using Magnetic Resonance Neurography with Modified Hiking Optimization Algorithm

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Academic Radiology 2025年

作者： Dahou, Abdelghani Elaziz, Mohamed Abd Khattap, Mohamed G. Hassan, Hend Galal Eldeen Mohamed Ali School of Computer Science and Technology Zhejiang Normal University Jinhua 321004 China Mathematics and Computer Science department University of Ahmed DRAIA Adrar 01000 Algeria Department of Mathematics Faculty of Science Zagazig University Zagazig 44519 Egypt Faculty of Computer Science and Engineering Galala University Suez 435611 Egypt Artificial Intelligence Research Center (AIRC) Ajman University Ajman 346 United Arab Emirates Department of Diagnostic Interventional Radiology and Molecular Imaging Faculty of Medicine Ain Shams University Cairo 11591 Egypt Technology of Radiology and Medical Imaging Program Faculty of Applied Health Sciences Technology Galala University Suez 435611 Egypt

Rationale and Objectives: Brachial plexopathies (BPs) encompass a complex spectrum of nerve injuries affecting motor and sensory function in the upper extremities. Diagnosis is challenging due to the intricate anatomy and symptom overlap with other neuropathies. Magnetic Resonance Neurography (MRN) provides advanced imaging but requires specialized interpretation. This study proposes an AI-based framework that combines deep learning (DL) with the modified Hiking Optimization Algorithm (MHOA) enhanced by a Comprehensive Learning (CL) technique to improve the classification of nerve injuries (neuropraxia, axonotmesis, neurotmesis) using MRN data. Materials and Methods: The framework utilizes MobileNetV4 for feature extraction and MHOA for optimized feature selection across different MRI sequences (STIR, T2, T1, and DWI). A dataset of 39 patients diagnosed with BP was used. The framework classifies injuries based on Seddon's criteria, distinguishing between normal and abnormal conditions as well as injury severity. Results: The model achieved excellent performance, with 1.0000 accuracy in distinguishing normal from abnormal conditions using STIR and T2 sequences. For injury severity classification, accuracy was 0.9820 in STIR, outperforming the original HOA and other metaheuristic algorithms. Additionally, high classification accuracy (0.9667) was observed in DWI. The proposed framework outperformed traditional methods and demonstrated high sensitivity and specificity. Conclusion: The proposed AI-based framework significantly improves the diagnosis of BP by accurately classifying nerve injury types. By integrating DL and optimization techniques, it reduces diagnostic variability, making it a valuable tool for clinical settings with limited specialized neuroimaging expertise. This framework has the potential to enhance clinical decision-making and optimize patient outcomes through precise and timely diagnoses. © 2025 The Association of University Radiologists

关键词： Brachial Plexopathy (BP) Comprehensive Learning (CL) Deep Learning (DL) Feature Selection (FS) Hiking Optimization Algorithm (HOA) Magnetic Resonance Neurography (MRN) MobileNetV4

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HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

arXiv

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arXiv 2025年

作者： Viswanath, Siddharth Madhu, Hiren Bhaskar, Dhananjay Kovalic, Jake Johnson, Dave Ying, Rex Tape, Christopher Adelstein, Ian Perlmutter, Michael Krishnaswamy, Smita Department of Computer Science Yale University New Haven United States Department of Genetics Yale University New Haven United States Department of Applied Physics Yale University New Haven United States Program in Computing Boise State University Idaho United States Cell Communication Lab Department of Oncology University College London Cancer Institute London United Kingdom Department of Mathematics Yale University New Haven United States Department of Mathematics Boise State University Idaho United States Computational Biology and Bioinformatics Program Yale University New Haven United States Wu-Tsai Institute Yale University New Haven United States Program for Applied Math Yale University New Haven United States

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods for point clouds which are tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multiscale features—capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis. © 2025, CC BY.

关键词： Network topology

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Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems

arXiv

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arXiv 2025年

作者： Wei, Lu Jia, Zhian Wang, Yufeng Kaszlikowski, Dagomir Ling, Haibin Department of Applied Mathematics & Statistics Stony Brook University Stony BrookNY11794 United States Program of Data Science Stony Brook University Stony BrookNY11794 United States Centre for Quantum Technologies National University of Singapore SG 117543 Singapore Department of Physics National University of Singapore SG 117543 Singapore Department of Computer Science Stony Brook University Stony BrookNY11794 United States

The transformer architecture, known for capturing long-range dependencies and intricate patterns, has extended beyond natural language processing. Recently, it has attracted significant attention in quantum information and condensed matter physics. In this work, we propose the transformer density operator ansatz for determining the steady states of dissipative quantum many-body systems. By vectorizing the density operator as a many-body state in a doubled Hilbert space, the transformer encodes the amplitude and phase of the state’s coefficients, with its parameters serving as variational variables. Our design preserves translation invariance while leveraging attention mechanisms to capture diverse long-range correlations. We demonstrate the effectiveness of our approach by numerically calculating the steady states of dissipative Ising and Heisenberg spin chain models, showing that our method achieves excellent accuracy in predicting steady states. © 2025, CC BY.

关键词： Hilbert spaces

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PERMUTATION GENERATION METHODS

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COMPUTING SURVEYS 1977年第2期9卷 137-164页

作者： SEDGEWICK, R Program in Computer Science and Division of Applied Mathematics Brown University Providence Rhode Island

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On the particle approximation of lagged Feynman–Kac formulae

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Stochastic Processes and their Applications 2025年 188卷

作者： Awadelkarim, Elsiddig Caffarel, Michel Del Moral, Pierre Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal 23955-6900 Saudi Arabia University of Toulouse CNRS-Lab. de Chimie et Physique Quantiques Toulouse 31062 France Centre de Recherche Inria Bordeaux Sud-Ouest Talence 33405 France School of Data Science The Chinese University of Hong Kong Shenzhen Shenzhen China

In this paper we examine the numerical approximation of the limiting invariant measure associated with Feynman–Kac formulae. These are expressed in a discrete time formulation and are associated with a Markov chain and a potential function. The typical application considered here is the computation of eigenvalues associated with non-negative operators as found, for example, in physics or particle simulation of rare-events. We focus on a novel lagged approximation of this invariant measure, based upon the introduction of a ratio of time-averaged Feynman–Kac marginals associated with a positive operator iterated l∈N times;a lagged Feynman–Kac formula. This estimator and its approximation using Diffusion Monte Carlo (DMC) are commonly used in the physics literature. In short, DMC is an iterative algorithm involving N∈N particles or walkers simulated in parallel, that undergo sampling and resampling operations. In this work, it is shown that for the DMC approximation of the lagged Feynman–Kac formula, one has an almost sure characterization of the L₁-error as the time parameter (iteration) goes to infinity and this is at most of O(exp{−κl}/N), for κ>0. In addition a non-asymptotic in time, and time uniform L₁−bound is proved which is O(l/N). We also prove a novel central limit theorem to give a characterization of the exact asymptotic in time variance. This analysis demonstrates that the strategy used in physics, namely, to run DMC with N and l small and, for long time enough, is mathematically justified. Our results also suggest how one should choose N and l in practice. We emphasize that these results are not restricted to physical applications;they have broad relevance to the general problem of particle simulation of the Feynman–Kac formula, which is utilized in a great variety of scientific and engineering fields. © 2025 Elsevier B.V.

关键词： Diffusion Monte Carlo Eigenvalue approximation Feynman–Kac formula

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Absolute change pivot rule for the simplex algorithm

Absolute change pivot rule for the simplex algorithm

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International MultiConference of Engineers and computer Scientists, IMECS 2014

作者： Chankong, Kittiphong Intiyot, Boonyarit Sinapiromsaran, Krung Applied Mathematics and Computational Science Program Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok Thailand

ISBN: (纸本)9789881925336

The simplex algorithm is a widely used method for solving a linear programming problem (LP) which is first presented by George B. Dantzig. One of the important steps of the simplex algorithm is applying an appropriate pivot rule, the rule to select the entering variable. An effective pivot rule can lead to the optimal solution of LP with the small number of iterations. In a minimization problem, Dantzig's pivot rule selects an entering variable corresponding to the most negative reduced cost. The concept is to have the maximum improvement in the objective value per unit step of the entering variable. However, in some problems, Dantzig's rule may visit a large number of extreme points before reaching the optimal solution. In this paper, we propose a pivot rule that could reduce the number of such iterations over the Dantzig's pivot rule. The idea is to have the maximum improvement in the objective value function by trying to block a leaving variable that makes a little change in the objective function value as much as possible. Then we test and compare the efficacy of this rule with Dantzig' original rule.

关键词： Linear programming

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The differential geometry of shape from shading: Biology reveals curvature structure

The differential geometry of shape from shading: Biology rev...

引用

2012 IEEE computer Society Conference on computer Vision and Pattern Recognition Workshops, CVPRW 2012

作者： Kunsberg, Benjamin Zucker, Steven W. Applied Mathematics Program Yale University United States Departments of Computer Science and Applied Mathematics Yale University United States

ISBN: (纸本)9781467316118

Shape from shading is a classical inverse problem in computer vision. We introduce a novel mathematical formulation for calculating local surface shape based on covariant derivatives, rather than the customary integral minimization or P.D.E approaches. Motivated by neurobiology, we introduce the shading flow field (the tangent map to the image isophotes) between the image and the surface levels. Just as in the perceptual organization of texture, we use the parallel transport of our shading flow field to move the isophote field at different points on the unknown surface to a single point, amassing restrictions on our surface curvatures. Under simplifying assumptions we solve exactly for the light source/surface pairs needed for a local image patch to have a given shading flow. The magnitude of the brightness gradient then restricts this family to a single light source and surface estimate pair, up to the concave/convex ambiguity and an additional elliptical/saddle ambiguity. Example calculations illustrate our approach. © 2012 IEEE.

关键词： Flow fields

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A NEAR-OPTIMAL MANHATTAN CHANNEL ROUTER FOR A CLASS OF NETS WITH THE SHIFT-RIGHT-ONE PATTERN

引用

applied mathematics LETTERS 1993年第6期6卷 65-69页

作者： TUAN, TC Institute of Applied Mathematics (Computer Science Program) National Sun Yat-sen University Kaohsiung Taiwan 80424 People's Republic of China

The Manhattan channel routing problem of providing a one-to-one rectilinear wire connection (horizontal segments on one layer, while vertical segments are on the other) between two sets of terminals which lie on two horizontal lines, with the smallest width, is NP-hard. In this paper, it is studied for m consecutive shift-right-one nets, and a near-optimal router which produces a layout with width at most 2 more than the theoretical lower bound given in [1] is presented.

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