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CONVERGENCE SPEED AND APPROXIMATION ACCURACY OF NUMERICAL MCMC

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arXiv 2022年

作者： Cui, Tiangang Dong, Jing Jasra, Ajay Tong, Xin T. School of Mathematics Monash University Australia Graduate School of Business Columbia University United States Applied Mathematics and Computational Science Program Computer Electrical Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Mathematics National University of Singapore Singapore

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has similar convergence speed and high approximation accuracy as well. We discuss two different analysis frameworks: ergodicity and spectral gap, both are widely used in the literature. Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators. We also demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis and Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally we present some simple numerical examples to verify our theoretical claims. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

Machine Learning Techniques for Improving Multiclass Anomaly Detection on Conveyor Belts

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Machine Learning Techniques for Improving Multiclass Anomaly...

IEEE Instrumentation and Measurement technology Conference

作者： Saulo N. Matos Otávio F. Coletti Rafael Zimmer Fernando U. Filho Ricardo C.C. L. de Carvalho Victor R. da Silva Jorge L. Franco Thomas V. B. Pinto Luiz G. D. de Barros Caetano M. Ranieri Bruno E. Lopes Diego F. Silva Jó Ueyama Gustavo Pessin Institute of Mathematics and Computer Science University of Sã o Paulo Brazil São Carlos School of Engineering University of São Paulo Brazil Vale Institute of Technology Ouro Preto Brazil Graduate Program in Electrical Engineering Universidade Federal of Minas Gerais Belo Horizonte MG Brazil Vale SA Vitória Brazil

ISBN: (数字)9798350380903

ISBN: (纸本)9798350380910

Industrial conveyor belt systems are an efficient means of transport due to their adaptability and extension. Nonetheless, such systems are prone to various failures, including but not limited to: idler anomalies; belt tears; and pin misalignment which can cause significant disruptions in the production process. Preemptive maintenance and health monitoring of these conveyor belts is a common practice for avoiding these failures, but a challenging task due to the rarity of comprehensive anomaly detection datasets in the area, with current works aimed at evaluating the belt's immediate condition at fixed points. This study addresses this research gap by comparing multiple machine learning techniques, such as a proposed Hybrid Neural Network (HNN) tailored for classification of multiple anomaly classes, as well as machine learning approaches for time series based on feature extraction, Catch22, Minirocket Arsenal, and Time Series Forest. Our proposed HNN architecture performed better in classifying and distinguishing between different types of anomalies, with an accuracy of 95.55%. The obtained results suggest a promising approach for the area of predictive maintenance for industrial conveyor systems, as well as gives insights on possible improvements on the model and future research.

关键词： Machine learning algorithms Accuracy Time series analysis Machine learning Belts Transformers Feature extraction

On Time Uniform Wong-Zakai Approximation Theorems

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arXiv 2023年

作者： Del Moral, Pierre Hu, Shulan Jasra, Ajay Ruzayqat, Hamza Wang, Xinyu Institut de Mathematiques de Bordeaux Bordeaux33405 France School of Statistics and Mathematics Zhongnan University of Economics and Law 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 Wenlan School of Business Zhongnan University of Economics and Law China

We consider the long time behavior of Wong-Zakai approximations of stochastic differential equations. These piecewise smooth diffusion approximations are of great importance in many areas, such as those with ordinary differential equations associated to random smooth fluctuations;e.g. robust filtering problems. In many examples, the mean error estimate bounds that have been derived in the literature can grow exponentially with respect to the time horizon. We show in a simple example that indeed mean error estimates do explode exponentially in the time parameter, i.e. in that case a Wong-Zakai approximation is only useful for extremely short time intervals. Under spectral conditions, we present some quantitative time-uniform convergence theorems, i.e. time-uniform mean error bounds, yielding what seems to be the first results of this type for Wong-Zakai diffusion *** Codes 60H35(Primary), 65C30(Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： Brownian movement

Transferable Learning of Reaction Pathways from Geometric Priors

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arXiv 2025年

作者： Nam, Juno Steiner, Miguel Misterka, Max Yang, Soojung Singhal, Avni Gómez-Bombarelli, Rafael Department of Materials Science and Engineering Massachusetts Institute of Technology CambridgeMA02139 United States Energy Storage Research Alliance Argonne National Laboratory 9700 South Cass Avenue LemontIL60439 United States Department of Mathematics Massachusetts Institute of Technology CambridgeMA02139 United States Computational and Systems Biology Program Massachusetts Institute of Technology CambridgeMA02139 United States

Identifying minimum-energy paths (MEPs) is crucial for understanding chemical reaction mechanisms but remains computationally demanding. We introduce MEPIN, a scalable machine-learning method for efficiently predicting MEPs from reactant and product configurations, without relying on transition-state geometries or pre-optimized reaction paths during training. The task is defined as predicting deviations from geometric interpolations along reaction coordinates. We address this task with a continuous reaction path model based on a symmetry-broken equivariant neural network that generates a flexible number of intermediate structures. The model is trained using an energy-based objective, with efficiency enhanced by incorporating geometric priors from geodesic interpolation as initial interpolations or pre-training objectives. Our approach generalizes across diverse chemical reactions and achieves accurate alignment with reference intrinsic reaction coordinates, as demonstrated on various small molecule reactions and [3+2] cycloadditions. Our method enables the exploration of large chemical reaction spaces with efficient, data-driven predictions of reaction pathways. Copyright © 2025, The Authors. All rights reserved.

关键词： Reaction intermediates

Modern extreme value statistics for Utopian extremes

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arXiv 2023年

作者： Richards, Jordan Alotaibi, Noura Cisneros, Daniela Gong, Yan Guerrero, Matheus B. Redondo, Paolo Shao, Xuanjie School of Mathematics University of Edinburgh United Kingdom Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal Saudi Arabia Harvard School of Public Health BostonMA United States Department of Mathematics California State University FullertonCA United States

Capturing the extremal behaviour of data often requires bespoke marginal and dependence models which are grounded in rigorous asymptotic theory, and hence provide reliable extrapolation into the upper tails of the data-generating distribution. We present a toolbox of four methodological frameworks, motivated by modern extreme value theory, that can be used to accurately estimate extreme exceedance probabilities or the corresponding level in either a univariate or multivariate setting. Our frameworks were used to facilitate the winning contribution of Team Yalla to the EVA (2023) Conference Data Challenge, which was organised for the 13th International Conference on Extreme Value Analysis. This competition comprised seven teams competing across four separate sub-challenges, with each requiring the modelling of data simulated from known, yet highly complex, statistical distributions, and extrapolation far beyond the range of the available samples in order to predict probabilities of extreme events. Data were constructed to be representative of real environmental data, sampled from the fantasy country of "Utopia". © 2023, CC BY.

关键词： Extrapolation

Species diversity and dominance of Oligochaeta in copper and cadmium polluted soil 10

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Species diversity and dominance of Oligochaeta in copper and...

10th International Seminar on New Paradigm and Innovation of Natural sciences and itsApplication, ISNPINSA 2020

作者： Ulfah, M. Anggoro, S. Soeprobowati, T.R. Syafrudin, S. Department of Biology Faculty of Mathematics Science and Information Technology Universitas PGRI Semarang Semarang Indonesia Doctorate Program of Environmental Science School of Postgraduate Studies Univesitas Diponegoro Semarang Indonesia Faculty of Fisheries and Marine Science Universitas Diponegoro Semarang Indonesia Department of Biology Faculty of Science and Mathematics Universitas Diponegoro Semarang Indonesia Department of Enviromental Engineering Faculty of Engineering Universitas Diponegoro Semarang Indonesia School of Postgraduate Studies Universitas Diponegoro Semarang Indonesia

The aim of this study was to determine the dominance and species diversity of oligochaeta were studied incopper and cadmium polluted soil. This location is used for the garbage disposal of Jatibarang Landfill Semarang City residents, Central Java. Oligochaeta were collected from 5 research sites. The research method used is field experiment. Oligochaeta sampling was carried out based on a random sampling method. Oligochaeta sampling in Jatibarang Landfill was carried out at a depth of 25 cm. Analysis of oligochaeta diversity includes species diversity using the index formula Shannon-Wienner and dominance with the index formula Simpson. The species diversity (Shannon-Weiner Index) showed value of 0.191 (site 1), 0.411 (site 2), 0.539 (site 3), 0.137 (site 4), 0.443 (site 5) and the dominance calculated was 0.207 (site 1), 0.024 (site 2), 0.279 (site 3), 0.045 (site 4), 0.031 (site 5) which indicates that the diversity and the dominance were inversely related. The population density (individuals/m2) of the Oligochaeta species at 5 research sites showed variations. The total density of L. terrestris recorded was 280.66 (site 1), 59.66 (site 2), 130.33 (site 3), 136.66 (site 4), 62 (site 5), and the total density of Pheretrima sp 14 (site 1), 10 (site 2), 39 (site 3), 4.33 (site 4), 12 (site 5). Two species of Oligochaeta showed high richness whereas some were sparsely populated. © Published under licence by IOP Publishing Ltd.

关键词： Biodiversity

Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations

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arXiv 2023年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas 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 Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is high-dimensional, but the model for the signal yields longer-range time dependencies through the observation locations. Motivated by this model we revisit a lesser-known and provably convergent computational methodology from [4, 11, 28] that uses sequential Markov Chain Monte Carlo (MCMC) chains. We extend this methodology for data filtering problems with unknown observation locations. We benchmark our algorithms on Linear Gaussian state space models against competing ensemble methods and demonstrate a significant improvement in both execution speed and accuracy. Finally, we implement a realistic case study on a high-dimensional rotating shallow water model (of about 104 - 105 dimensions) with real and synthetic data. The data is provided by the National Oceanic and Atmospheric Administration (NOAA) and contains observations from ocean drifters in a domain of the Atlantic Ocean restricted to the longitude and latitude intervals [-51◦,-41◦], [17◦,27◦] *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2023, CC BY.

关键词： Location

Role of deep learning in cognitive healthcare: Wearable signal analysis, algorithms, benefits, and challenges

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Digital Communications and Networks 2025年第3期 642-670页

作者： Md.Sakib Bin Alam Aiman Lameesa Senzuti Sharmin Shaila Afrin Shams Forruque Ahmed Mohammad Reza Nikoo Amir H.Gandomi Department of Information Technology University of Information Technology and Sciences (UITS) Department of Computer Science American International University-Bangladesh (AIUB) Science and Math Program Asian University for Women School of Mathematical Sciences Sunway University Department of Mathematics and Physics North South University Department of Civil and Architectural Engineering Sultan Qaboos University Faculty of Engineering and Information Technology University of Technology Sydney University Research and Innovation Center (EKIK) óbuda University Department of Computer Science Khazar University

Deep Learning(DL) offers promising solutions for analyzing wearable signals and gaining valuable insights into cognitive disorders. While previous review studies have explored various aspects of DL in cognitive healthcare, there remains a lack of comprehensive analysis that integrates wearable signals, data processing techniques, and the broader applications, benefits, and challenges of DL methods. Addressing this limitation, our study provides an extensive review of DL's role in cognitive healthcare, with a particular emphasis on wearables, data processing, and the inherent challenges in this field. This review also highlights the considerable promise of DL approaches in addressing a broad spectrum of cognitive issues. By enhancing the understanding and analysis of wearable signal modalities, DL models can achieve remarkable accuracy in cognitive healthcare. Convolutional Neural Network(CNN), Recurrent Neural Network(RNN), and Long Short-term Memory(LSTM) networks have demonstrated improved performance and effectiveness in the early diagnosis and progression monitoring of neurological disorders. Beyond cognitive impairment detection, DL has been applied to emotion recognition, sleep analysis, stress monitoring, and neurofeedback. These applications lead to advanced diagnosis, personalized treatment, early intervention, assistive technologies, remote monitoring, and reduced healthcare costs. Nevertheless, the integration of DL and wearable technologies presents several challenges, such as data quality, privacy, interpretability, model generalizability, ethical concerns, and clinical adoption. These challenges emphasize the importance of conducting future research in areas such as multimodal signal analysis and explainable AI. The findings of this review aim to benefit clinicians, healthcare professionals, and society by facilitating better patient outcomes in cognitive healthcare.

关键词：

Polyelectrolyte nanoparticles derived from durian seed gum modified with chitosan for selective targeting in cancer cells

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International Journal of Biological Macromolecules 2025年 315卷 144625页

作者： Putro, Jindrayani Nyoo Bintang Ilhami, Fasih Cheng, Chih-Chia Imanuela, Keziah Janice Mangindaan, Dave Irawaty, Wenny Rahmawati, Astrid Shimomura, Osamu Ismadji, Suryadi Chemical Engineering Master Program Faculty of Engineering Widya Mandala Surabaya Catholic University Kalijudan 37 Surabaya60114 Indonesia Collaborative Research Center for Sustainable and Zero Waste Industries Jl. Kalijudan 37 East Java Surabaya60114 Indonesia Department of Natural Science Faculty of Mathematics and Natural Science Universitas Negeri Surabaya Surabaya60231 Indonesia Graduate Institute of Applied Science and Technology National Taiwan University of Science and Technology Taipei10607 Taiwan Department of Chemical Engineering Widya Mandala Surabaya Catholic University Kalijudan 37 Surabaya60114 Indonesia Professional Engineer Program Department Faculty of Engineering Bina Nusantara University K.H. Syahdan No. 9 Jakarta11480 Indonesia Waste-Food-Environmental Nexus Research Interest Group Bina Nusantara University K.H. Syahdan No. 9 Jakarta11480 Indonesia Department of Applied Chemistry Osaka Institute of Technology 5-16-1 Omiya Ashahi-ku Osaka535-8585 Japan

The synthesis of natural polysaccharides from durian seed gum-modified chitosan as complex nanoparticles was successfully developed. The complex formation of nanoparticles was confirmed by 1H NMR, indicating the interpenetrating polymer network between the durian seed gum and chitosan. The material's physical properties were analyzed using ZETA potential, SEM, FTIR, swelling assay, and spectrofluorometer. The material showed a pH-responsive behavior as evidenced by the swelling assay, in which the complex nanoparticle has a smaller swelling index in pH 5.5 and 7.4 than pH 2.1. The stability of the material was tested by checking the hydrodynamic diameter, which resulted in the modification of chitosan having higher kinetic stability than the durian seed gum under a diameter smaller than 1 μm. The chitosan-modified durian seed gum's hemolytic activity indicates blood compatibility with 4 % hemolytic activity under high nanoparticle concentration (400 μg/mL). More importantly, the cytotoxicity test of complex nanoparticles showed biocompatibility with NIH/3 T3 cells, whereas complex nanoparticles exhibited high toxicity towards HeLa cells. Moreover, complex nanoparticles showed strong intracellular blue fluorescence with selective activity towards cancer cells. Hence, this newly developed green synthesis of polyelectrolyte nanoparticles derived from durian seed gum modified with chitosan improved selectivity and intracellular fluorescence in tracking cancer cells. © 2025 Elsevier B.V.

关键词： Chitosan