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On the particle approximation of lagged Feynman–Kac formulae

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 Thuwal23955-6900 Saudi Arabia University of Toulouse CNRS-Lab. de Chimie et Physique Quantiques Toulouse31062 France Centre de Recherche Inria Bordeaux Sud-Ouest Talence33405 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： Iterative methods

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Identification of potential plant secondary metabolites targeting begomovirus-associated betasatellite virulence factor βC1 protein through molecular docking, simulation and MM-PBSA studies

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Discover Plants 2025年第1期2卷 1-21页

作者： Hiremath, Shridhar Bharath, M. Muttappagol, Mantesh Kumar, H. D. Vinay Kumar, T. L. Mohan Shankarappa, K. S. Venkataravanappa, V. Basha, C. R. Jahir Reddy, C. N. Lakshminarayana Department of Plant Pathology College of Agriculture University of Agricultural Sciences GKVK Bangalore India Centre for Infectious Diseases CSIR-North East Institute of Science and Technology Jorhat India Department of Agricultural Statistics Applied Mathematics and Computer Science College of Agriculture University of Agricultural Sciences GKVK Bangalore India Department of Plant Pathology College of Horticulture University of Horticultural Sciences Bengaluru India Division of Crop Protection ICAR-Indian Institute of Horticultural Research Bangalore India

The βC1 protein encoded by begomoviruses plays a key role in counteracting plant defense mechanisms, making it a prime target for antiviral compounds. Here, we investigated the role of plant secondary metabolites for their antiviral potential. Initially, the tertiary structure of βC1 protein was predicted and docked to 2851 plant secondary metabolites along with positive controls ribavirin and ningnanmycin. Additionally, 43 analogues of the ligand with highest dock score were created and assessed against the βC1 protein to see if they offered better binding energy than the initial compound. To check the protein–ligand complex's stability, we performed a 100 ns molecular dynamics (MD) simulation, then measured the change in Gibbs free energy (ΔG) using the molecular mechanics/Poisson-Boltzmann surface area (MM-PBSA) approach. Our study found that Anonaine, a bioactive compound, had a high binding score of − 6.0 kcal/mol, with its analogues a33 and a41 scoring − 6.8 kcal/mol and − 6.6 kcal/mol, respectively. Molecular dynamics simulations for these complexes showed stable interactions, with minimal changes in root mean square deviation (RMSD) and root mean square fluctuation (RMSF) values. Additionally, the protein–ligand complexes showed consistent hydrogen bond formation, with negligible changes in the radius of gyration (Rg) and solvent-accessible surface area (SASA). The binding free energy (ΔG) calculations revealed estimated values of − 16.99 ± 2.16, − 18.29 ± 1.91, and − 27.26 ± 2.11 for the βC1-Anonaine, βC1-a33, and βC1-a44 protein–ligand complexes, respectively. In silico toxicity predictions suggest top ligands are less toxic, making them ideal for biopesticide development. Overall, these findings reveal the potential of plant secondary metabolites as promising agents in controlling begomovirus infections.

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Quantum Fisher Information and the Curvature of Entanglement

arXiv

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arXiv 2025年

作者： Saleem, Zain H. Shaji, Anil Babu, Anjala M. Luo, Da-Wei Langfitt, Quinn Yu, Ting Gray, Stephen K. Mathematics and Computer Science Division Argonne National Laboratory LemontIL United States School of Physics IISER Thiruvananthapuram Kerala 695551 India School of Physics and Applied Physics Southern Illinois University CarbondaleIL United States Center for Quantum Science and Engineering Department of Physics Stevens Institute of Technology HobokenNJ07030 United States Department of Computer Science Northwestern University EvanstonIL United States Center for Nanoscale Materials Argonne National Laboratory LemontIL United States

We explore the relationship between quantum Fisher information (QFI) and the second derivative of concurrence with respect to the coupling between two qubits, referred to as the curvature of entanglement (CoE). For a two-qubit quantum probe used to estimate the coupling constant appearing in a simple interaction Hamiltonian, we show that at certain times CoE = −QFI;these times can be associated with the concurrence, viewed as a function of the coupling parameter, being a maximum. We examine the time evolution of the concurrence of the eigenstates of the symmetric logarithmic derivative and show that, for both initially separable and initially entangled states, simple product measurements suffice to saturate the quantum Cramér-Rao bound when CoE = −QFI, while otherwise, in general, entangled measurements are required giving an operational significance to the points in time when CoE = −QFI. Copyright © 2025, The Authors. All rights reserved.

关键词： Quantum entanglement

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Significance of slip velocity and viscosity variation on squeezed film couple-stress properties between a rough plate and a cylinder

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Partial Differential Equations in applied mathematics 2025年 14卷

作者： K, Arshiya Kousar A, Salma Althobaiti, Saja Abdulrahman BN, Hanumagowda Tawade, Jagadish V Abduvalieva, Dilsora Waqas, M. Saeed, Mohammed Azeez Gupta, Manish Department of Mathematics School of Applied Science REVA University India Department of Chemistry College of Sciences & Humanities Prince Sattam Bin Abdulaziz University Saudi Arabia Department of Mathematics Vishwakarma University Pune 411048 India Department of Mathematics and Information Technologies Tashkent State Pedagogical University Bunyodkor avenue 27 Tashkent 100070 Uzbekistan Department of Computer Science National University of Technology Islamabad 44000 Pakistan Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Department of Environmental Engineering College of Engineering Knowlwdge University Erbil 44001 Iraq Division of Research and Development Lovely Professional University Phagwara India

This study examines the impact of surface roughness and viscosity variation on the couple stress squeeze film characteristics between a cylinder and a rough plate with slip velocity. Two distinct one-dimensional roughness patterns—longitudinal and transverse—are considered. Using Christensen's theory, the stochastic modified Reynolds equation is derived for Stokes couple stress fluid, incorporating viscosity variation with pressure. The standard perturbation technique is applied to solve the average Reynolds equation, yielding closed-form expressions for the mean fluid film pressure, load-carrying capacity, and squeeze film time. Various parameters are varied, and the results are discussed through graphical representations in 2D and 3D. This study highlights the importance of viscosity variation, couple stresses, and surface roughness in optimizing squeeze film performance. While increased viscosity and couple stresses enhance load-bearing capacity and film time, slip velocity detracts from these properties. Additionally, surface roughness has a significant impact, with transverse roughness improving, and longitudinal roughness reducing, the squeeze film characteristics. Applications of this study include improving the design and performance of bearing systems, lubrication in mechanical seals, and hydraulic systems where surface roughness and viscosity variation play a significant role in operational efficiency. © 2025

关键词： Couple stress fluid Rough surface Slip velocity Squeeze-film Viscosity variation

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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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COMPUTATION OF KRONECKERS CANONICAL FORM OF A SINGULAR PENCIL

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LINEAR ALGEBRA AND ITS APPLICATIONS 1979年第OCT期27卷 103-140页

作者： VANDOOREN, P Division of Applied Mathematics and Computer Science Katholieke Universiteit te Leuven Louvain Belgium

We develop stable algorithms for the computation of the Kronecker structure of an arbitrary pencil. This problem can be viewed as a generalization of the well-known eigenvalue problem of pencils of the type λ I − A . We first show that the elementary divisors ( λ − α ) i of a regular pencil λ B − A can be retrieved with a deflation algorithm acting on the expansion ( λ − α ) B − ( A − αB ). This method is a straightforward generalization of Kublanovskaya's algorithm for the determination of the Jordan structure of a constant matrix. We also show how to use this method to determine the structure of the infinite elementary divisors of λ B − A . In the case of singular pencils, the occurrence of Kronecker indices—containing the singularity of the pencil—somewhat complicates the problem. Yet our algorithm retrieves these indices with no additional effort, when determining the elementary divisors of the pencil. The present ideas can also be used to separate from an arbitrary pencil a smaller regular pencil containing only the finite elementary divisors of the original one. This is shown to be an effective tool when used together with the QZ algorithm.

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Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

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computer Modeling in Engineering & sciences 2024年第3期138卷 2471-2495页

作者： Wimonmas Bamrungsetthapong Pramote Charongrattanasakul Division of Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiPathum Thani12110Thailand Division of Mathematics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology KrungthepBangkok10120Thailand

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull *** control chart developed supports the examination of the mean lifespan variation for a particular product in the process of *** control limit levels are used:the warning control limit,inner control limit,and outer control ***,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control *** control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control ***,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

关键词： Modified DS np chart generalizedmultiple dependent state sampling time truncated life test Weibull distribution average run length average sample size

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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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Certified randomness using a trapped-ion quantum processor

arXiv

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arXiv 2025年

作者： Liu, Minzhao Shaydulin, Ruslan Niroula, Pradeep DeCross, Matthew Hung, Shih-Han Kon, Wen Yu Cervero-Martín, Enrique Chakraborty, Kaushik Amer, Omar Aaronson, Scott Acharya, Atithi Alexeev, Yuri Berg, K. Jordan Chakrabarti, Shouvanik Curchod, Florian J. Dreiling, Joan M. Erickson, Neal Foltz, Cameron Foss-Feig, Michael Hayes, David Humble, Travis S. Kumar, Niraj Larson, Jeffrey Lykov, Danylo Mills, Michael Moses, Steven A. Neyenhuis, Brian Eloul, Shaltiel Siegfried, Peter Walker, James Lim, Charles Pistoia, Marco Global Technology Applied Research JPMorganChase New YorkNY10017 United States Quantinuum BroomfieldCO80021 United States Computational Science Division Argonne National Laboratory LemontIL60439 United States Department of Physics The University of Chicago ChicagoIL60637 United States Department of Computer Science The University of Texas at Austin AustinTX78712 United States Department of Electrical Engineering National Taiwan University Taipei City10617 Taiwan Quantinuum Terrington House 13–15 Hills Road CambridgeCB2 1NL United Kingdom Quantum Science Center Oak Ridge National Laboratory Oak RidgeTN37831 United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL60439 United States

While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers [1, 2], realizing this potential remains a challenge. One such task is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy [3]. Certified randomness has many applications [4] but is fundamentally impossible to achieve solely by classical computation. In this work, we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations [5, 6]: a client generates quantum "challenge" circuits using a small randomness seed, sends them to an untrusted quantum server to execute, and verifies the server’s results. We analyze the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of 1.1 × 1018 floating-point operations per second across multiple supercomputers, we certify 71, 313 bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of today’s quantum computers. Copyright © 2025, The Authors. All rights reserved.

关键词： Quantum computers

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