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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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Accelerating Medical Knowledge Discovery through Automated Knowledge Graph Generation and Enrichment

arXiv

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arXiv 2024年

作者： Khalid, Mutahira Rahman, Raihana Abbas, Asim Kumari, Sushama Wajahat, Iram Bukhari, Syed Ahmad Chan TIB - Leibniz Information Centre for Science and Technology Lower Saxony Hannover Germany Department of Statistics Harvard University CambridgeMA United States School of Computer Science University of Birmingham Edgbaston BirminghamB15 2TT United Kingdom Sr Technical Program Manager Routing and Planning Amazon BellevueWA United States Institute for Biotechnology St. John's University New YorkNY United States Division of Computer Science Mathematics and Science St. John's University New YorkNY United States

Knowledge graphs (KGs) serve as powerful tools for organizing and representing structured knowledge. While their utility is widely recognized, challenges persist in their automation and completeness. Despite efforts in automation and the utilization of expert-created ontologies, gaps in connectivity remain prevalent within KGs. In response to these challenges, we propose an innovative approach termed "Medical Knowledge Graph Automation (M-KGA)". M-KGA leverages user-provided medical concepts and enriches them semantically using BioPortal ontologies, thereby enhancing the completeness of knowledge graphs through the integration of pre-trained embeddings. Our approach introduces two distinct methodologies for uncovering hidden connections within the knowledge graph: a cluster-based approach and a node-based approach. Through rigorous testing involving 100 frequently occurring medical concepts in Electronic Health Records (EHRs), our M-KGA framework demonstrates promising results, indicating its potential to address the limitations of existing knowledge graph automation techniques. © 2024, CC BY-NC-ND.

关键词： Knowledge graph

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Development of e-tracer study at faculty of mathematics and natural science, State University of Jakarta, Indonesia

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AIP Conference Proceedings 2024年第1期2982卷

作者： Ellis Salsabila Fariani Hermin Agus Agung Permana Mathematics Education Study Program Faculty of Mathematics and Natural Sciences Universitas Negeri Jakarta Jakarta Indonesia Computer Science Study Program Faculty of Mathematics and Natural Sciences Universitas Negeri Jakarta Jakarta Indonesia

Alumni or college graduates have an essential role in their respective universities in establishing cooperation with various agencies. Therefore, the role of alumni can be optimized if the university has alumni data on an ongoing basis. Alumni data tracing is a Tracer Study conducted in the Faculty of mathematics and Natural sciences, State University of Jakarta, Indonesia, which provides information on an alumnus data. Data collecting has been done using the online form method, namely Microsoft Forms. However, in reality, it is less effective because the data cannot be updated and the data management cannot be appropriately managed. This research is an innovation in searching and managing the alumni data in the form of a Tracer Study information system. The system development model uses the Spiral Model since it is flexible and possible to make changes throughout the software development life cycle to accommodate any needed alterations.

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On the Particle Approximation of Lagged Feynman-Kac Formulae

arXiv

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arXiv 2024年

作者： Awadelkarim, Elsiddig Caffarel, Michel Moral, Pierre Del 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 Hong Kong 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) have been extensively employed 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. © 2024, CC BY.

关键词： Eigenvalues and eigenfunctions

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Hybrid descriptor definition for content based image classification using fusion of handcrafted features to convolutional neural network features

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International Journal of Information Technology (Singapore) 2021年第4期13卷 1365-1374页

作者： Das, Rik Kumari, Khusbu De, Sourav Manjhi, P.K. Thepade, Sudeep Department of Post Graduate Program in Information Technology Xavier Institute of Social Service Ranchi Jharkhand India Department of Computer Applications Yogoda Satsanga Mahavidyalaya Ranchi Jharkhand India Department of Computer Science & Engineering Cooch Behar Government Engineering College Cooch Behar India Department of Mathematics Vinoba Bhave University Hazaribag Jharkhand India Department of Computer Engineering Pimpri Chinchwad College of Engineering Pune India

The efficacy of content-based image classification is dependent on the richness of the feature vectors extracted from the image data. Traditional feature extraction techniques highlight single low level image characteristics like shape, size, texture, color etc. for feature generation. The process often fails to extract meaningful descriptors since considering a single image characteristic will ignore other rich properties of image contents. Mass adoption of Convolutional Neural Network (CNN) has significantly improved classification performances for content-based image data. Recent literature has documented high level of precision for image classification by carrying out transfer learning with open source pre trained Convolutional Neural Network (CNN). However, the concept of transfer learning experiences major setback in case of limited training data due to overfitting of training instances during finetuning. This work has identified this challenge and has attempted to capture probability distribution of input images to a pre trained Convolution Neural Network by utilizing it as a fixed weight feature extractor. The proposed approach has addressed the overfitting problem by removing the finetuning step involved in transfer learning. Further investigation on robust descriptor definition is carried out by concatenating the pre-trained CNN features to handcrafted features. The hybrid architecture has encouraging outcomes that have outclassed the classification accuracies of state-of-the-art handcrafted techniques. © 2021, Bharati Vidyapeeth's Institute of computer Applications and Management.

关键词： Augmented feature learning Feature fusion Handcrafted features Image classification Pre trained Convolutional Neural Network (CNN) Representation learning

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Harnessing small projectors and multiple views for efficient vision pretraining 24

Harnessing small projectors and multiple views for efficient...

引用

Proceedings of the 38th International Conference on Neural Information Processing Systems

作者： Arna Ghosh Kumar Krishna Agrawal Shagun Sodhani Adam M. Oberman Blake A. Richards Mila - Quebec AI Institute & Computer Science McGill University Montréal QC Canada UC Berkeley CA USA Meta FAIR Toronto ON Canada and Mila - Quebec AI Institute & Mathematics and Statistics McGill University Montréal QC Canada Mila - Quebec AI Institute & Computer Science McGill University Montréal QC Canada and Neurology & Neurosurgery and Montreal Neurological Institute McGill University Montréal QC Canada and CIFAR Learning in Machines & Brains Program Toronto ON Canada

ISBN: (纸本)9798331314385

Recent progress in self-supervised (SSL) visual representation learning has led to the development of several different proposed frameworks that rely on augmentations of images but use different loss functions. However, there are few theoretically grounded principles to guide practice, so practical implementation of each SSL framework requires several heuristics to achieve competitive performance. In this work, we build on recent analytical results to design practical recommendations for competitive and efficient SSL that are grounded in theory. Specifically, recent theory tells us that existing SSL frameworks are actually minimizing the same idealized loss, which is to learn features that best match the data similarity kernel defined by the augmentations used. We show how this idealized loss can be reformulated to a functionally equivalent loss that is more efficient to compute. We study the implicit bias of using gradient descent to minimize our reformulated loss function, and find that using a stronger orthogonalization constraint with a reduced projector dimensionality should yield good representations. Furthermore, the theory tells us that approximating the reformulated loss should be improved by increasing the number of augmentations, and as such using multiple augmentations should lead to improved convergence. We empirically verify our findings on CIFAR, STL and Imagenet datasets, wherein we demonstrate an improved linear readout performance when training a ResNet-backbone using our theoretically grounded recommendations. Remarkably, we also demonstrate that by leveraging these insights, we can reduce the pretraining dataset size by up to 2 × while maintaining downstream accuracy simply by using more data augmentations. Taken together, our work provides theoretically grounded recommendations that can be used to improve SSL convergence and efficiency.

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More Efficient Identifiability Verification in ODE Models by Reducing Non-Identifiability

arXiv

引用

arXiv 2022年

作者： Ilmer, Ilia Ovchinnikov, Alexey Soto, Pedro Pogudin, Gleb Program in Computer Science Graduate Center CUNY New YorkNY United States Program in Mathematics CUNY Queens College New YorkNY United States LIX CNRS École Polytechnique Institute Polytechnique de Paris Paris France

Structural global parameter identifiability indicates whether one can determine a parameter’s value from given inputs and outputs in the absence of noise. If a given model has parameters for which there may be infinitely many values, such parameters are called non-identifiable. We present a procedure for accelerating a global identifiability query by eliminating algebraically independent non-identifiable parameters. Our proposed approach significantly improves performance across different computer algebra frameworks. © 2022, CC BY-SA.

关键词： Algebra

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The Smart Analysis of Performing Scalable Inference for Big Data Analytics

The Smart Analysis of Performing Scalable Inference for Big ...

引用

2023 International Conference on Power Energy, Environment and Intelligent Control, PEEIC 2023

作者： Bhandarkar, Vishakha D. Rongali, Aruna Sri Shamout, Mohamed Dawood Pund, Sachin Nama, Gigih Forda Patil, Shrishailappa Yeshwantrao Chavan College of Engineering Applied Mathematics and Humanities India University of the Cumberlands Graduate Doctoral Information Technology Information Technology Emphasis/Information Technology United States College of Business Administration University of Sharjah Department of Management Sharjah United Arab Emirates Shri Ramdeobaba College of Engineering and Management Department of Industrial Engineering Maharashtra Nagpur India Doctoral Program of Environtmental Science University of Lampung Department of Informatics Bandar Lampung Indonesia Vishwakarma Institute of Technology Computer Engineering Pune India

ISBN: (纸本)9798350357769

This paper examines the reproducibility of massive information analytics under particular factors. The paper proposes the 'performing Scalable Inference' technique to cope with scalability troubles and to exploit current big statistics platforms for efficient computing and statistics garage of the statistics. In particular, the paper describes how to perform leak-free, parallelizable visible analytics over massive datasets using present extensive records analytics frameworks such as Apache Flink. This method presents an automated manner to execute analytics that preserves reproducibility and the ability to make adjustments without re-running the entire technique. The paper also demonstrates how these analytics may help several real-world use instances, explore affected person cohorts for studies, and develop stratified patient cohorts for hospital therapy. In the end, the paper observes how the proposed method may be exercised within the real world. Actively scalable inference for massive information analytics is pivotal in optimizing decision-making and allocation of assets. Typically, such inferences are made based on information accumulated from numerous sources, databases, unstructured data, and different digital sources. So one can ensure scalability, a complete cloud-primarily based platform has to be hired. This solution will permit the ***, deploying the essential records series and evaluation algorithms are prime here. It could permit the platform to recognize the styles inside the statistics and discover any ability correlations or traits. Additionally, predictive analytics and system mastering strategies may be incorporated to provide insights into the results of the information. In the long run, by leveraging those techniques, the platform can draw efficient inferences and appropriately compare situations in an agile and green way.. © 2023 IEEE.

关键词： adjustments an a lytics automated preserves statistics

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Intrusion Detection using Deep Neural Network Algorithm on the Internet of Things

Intrusion Detection using Deep Neural Network Algorithm on t...

引用

IEEE International Conference on Communication, Networks and Satellite (ComNetSat)

作者： Syariful Ikhwan Adi Wibowo Budi Warsito Doctoral Program of Information System School of Postgraduate Studies Diponegoro University Semarang Indonesia D3 Telecommunication Engineering Institut Teknologi Telkom Purwokerto Banyumas Indonesia Computer Science Informatics Department of Science and Mathematics Faculty Diponegoro University Semarang Indonesia Statistics Department of Science and Mathematics Faculty Diponegoro University Semarang Indonesia

ISBN: (数字)9781665460309

ISBN: (纸本)9781665460316

The increasing use of IoT devices on future networks is very helpful for humans in their lives. However, the increase in devices connected to IoT networks also increases the potential for attacks against those networks. Vulnerabilities in Internet of Things (IoT) networks can be exposed at any time. Artificial intelligence can be used to protect the IoT network by being able to detect attacks on the network so that they can be prevented. In this study, network detection was carried out using the Deep Neural Network (DNN) algorithm. The test was carried out using the UNSW Bot-IoT dataset with a comparison of training data of 75% of the overall data. The results obtained show the ability of the algorithm to detect attacks on average with 99.999% accuracy. The validation loss and training loss look very small. In this study, there is a validation loss that still occurs in overfitting, but the difference is very small.

关键词： Deep learning Training Satellites Neural networks Intrusion detection Training data Feature extraction

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Exploring 3D Reconstruction with Drone Images: Advances and Challenges in Urban Environments

Exploring 3D Reconstruction with Drone Images: Advances and ...

引用

Annual Conference of Industrial Electronics Society

作者： Thiago João Miranda Baldivieso Taise Grazielle Da Silva Batista Fabio Suim Chagas Luiz Carlos Pacheco Rodrigues Velho Paulo Fernando Ferreira Rosa Defense Engineering Graduate Program Military Institute of Engineering Rio de Janeiro Brazil State Institute of the Environment Inea/RJ Rio de Janeiro Brazil Department of Science and Industry Systems University of South-Eastern Norway Kongsberg Norway Department of Computer Graphics Institute for Pure and Applied Mathematics Rio de Janeiro Brazil Electrical Engineering Graduate Program Military Institute of Engineering Rio de Janeiro Brazil

ISBN: (数字)9781665464543

ISBN: (纸本)9781665464550

This working-in-progress paper aims to present a three-dimensional reconstruction using aerial images in different environments. The experiments were conducted with aircraft in both external and internal settings, starting with image acquisition, followed by the application of specific photogrammetry software—both commercial and open-source—and concluding with a qualitative evaluation of the results.

关键词： Industrial electronics Three-dimensional displays Urban areas Aircraft Image reconstruction Photogrammetry Drones

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