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Improved error estimates for a modified exponential Euler method for the semilinear stochastic heat equation with rough initial data

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science China mathematics 2024年第12期67卷 2873-2898页

作者： Xinping Gui Buyang Li Jilu Wang Beijing Computational Science Research Center Beijing 100193China Department of Applied Mathematics The Hong Kong Polytechnic UniversityHong KongChina School of Science Harbin Institute of TechnologyShenzhen 518055China

A class of stochastic Besov spaces BpL^(2)(Ω;˙H^(α)(O)),1≤p≤∞andα∈[−2,2],is introduced to characterize the regularity of the noise in the semilinear stochastic heat equation du−Δudt=f(u)dt+dW(t),under the following conditions for someα∈(0,1]:||∫_(0)^(t)e−(t−s)^(A)dW(s)||L^(2)(Ω;L^(2)(O))≤C^(t^(α/2))and||∫_(0)^(t)e−(t−s)^(A)dW(s)||_B^(∞)L^(2)(Ω:H^(α)(O))≤C..The conditions above are shown to be satisfied by both trace-class noises(withα=1)and one-dimensional space-time white noises(withα=1/2).The latter would fail to satisfy the conditions withα=1/2 if the stochastic Besov norm||·||B∞L^(2)(Ω;˙H^(α)(O))is replaced by the classical Sobolev norm||·||L^(2)(Ω;˙Hα(O)),and this often causes reduction of the convergence order in the numerical analysis of the semilinear stochastic heat *** this paper,the convergence of a modified exponential Euler method,with a spectral method for spatial discretization,is proved to have orderαin both the time and space for possibly nonsmooth initial data in L^(4)(Ω;˙H^(β)(O))withβ>−1,by utilizing the real interpolation properties of the stochastic Besov spaces and a class of locally refined stepsizes to resolve the singularity of the solution at t=0.

关键词： semilinear stochastic heat equation additive noise space-time white noise exponential Euler method spectral method strong convergence stochastic Besov space real interpolation

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Phase-field simulations of the effect of temperature and interface for zirconiumδ-hydrides

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Chinese Physics B 2024年第4期33卷 701-710页

作者：陈子航盛杰刘瑜施小明黄厚兵许可王越超武帅孙博刘海风宋海峰 School of Materials Science and Engineering Beijing Institute of TechnologyBeijing 100081China Advanced Research Institute of Multidisciplinary Science Beijing Institute of TechnologyBeijing 100081China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Department of Physics University of Science and Technology BeijingBeijing 100083China

Hydride precipitation in zirconium cladding materials can damage their integrity and *** temperature and material defects have a significant effect on the dynamic growth of *** this study,we have developed a phasefield model based on the assumption of elastic behaviour within a specific temperature range(613 K-653 K).This model allows us to study the influence of temperature and interfacial effects on the morphology,stress,and average growth rate of zirconium *** results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride *** ultimate determinant of hydride orientation is the loss of interfacial coherency,primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree *** escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical,accompanied by the onset of redirection ***,redirection occurs at a critical mismatch level,denoted as qc,and remains unaffected by variations in temperature and interfacial ***,this redirection leads to an increase in the maximum stress,which may influence the direction of hydride crack *** research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.

关键词： zirconium hydride phase-field method temperature effect mismatch degree

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Detection of Mobile LoRa Jammers

Detection of Mobile LoRa Jammers

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2023 IEEE Virtual Conference on Communications, VCC 2023

作者： Bleszynski, Bartlomiej Jozef Orfanidis, Charalampos Fafoutis, Xenofon Department of Applied Mathematics and Computer Science Denmark

ISBN: (纸本)9798350318807

Low Power Wide Area Networks (LPWANs) plat-forms (LoRa, NB-IoT, Sigfox) came to add a missing piece to the Internet of Things (IoT) ecosystem, namely long range communication in low power. LPWAN platforms are characterized by low data rate and long transmission time. LoRa specifically, has a data rate from 27 to 0.3 kbps and the transmission time of a single packet might be more than 1.5 seconds for some cases. These characteristics render LPWANs vulnerable to jamming attacks as a malicious user can perform a jamming attack from long range and the long transmission time is allowing a large time window to perform the attack. Moreover, if the jamming node is mobile (i.e., attached on a vehicle or an Unmanned Aerial Vehicle (UAV)), the current countermeasures proposed by the literature will not be relevant anymore. In this paper we investigate if it is possible to detect a mobile LoRa jammer based on the impact of the Doppler effect and based on a combination of signal strength and the entropy of the transmitted data. The results, obtained by utilizing commercial hardware, reveal that we could detect a potential mobile jammer that follows a deceptive jamming strategy with random payload, but further investigation is required for more sophisticated jamming attacks. © 2023 IEEE.

关键词： Internet of things

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Continuous-Time Graph Representation with Sequential Survival Process 38

Continuous-Time Graph Representation with Sequential Surviva...

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38th AAAI Conference on Artificial Intelligence, AAAI 2024

作者： Çelikkanat, Abdulkadir Nakis, Nikolaos Mørup, Morten Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark

ISBN: (纸本)1577358872

Over the past two decades, there has been a tremendous increase in the growth of representation learning methods for graphs, with numerous applications across various fields, including bioinformatics, chemistry, and the social sciences. However, current dynamic network approaches focus on discrete-time networks or treat links in continuous-time networks as instantaneous events. Therefore, these approaches have limitations in capturing the persistence or absence of links that continuously emerge and disappear over time for particular durations. To address this, we propose a novel stochastic process relying on survival functions to model the durations of links and their absences over time. This forms a generic new likelihood specification explicitly accounting for intermittent edge-persistent networks, namely GRAS2P: Graph Representation with Sequential Survival Process. We apply the developed framework to a recent continuous time dynamic latent distance model characterizing network dynamics in terms of a sequence of piecewise linear movements of nodes in latent space. We quantitatively assess the developed framework in various downstream tasks, such as link prediction and network completion, demonstrating that the developed modeling framework accounting for link persistence and absence well tracks the intrinsic trajectories of nodes in a latent space and captures the underlying characteristics of evolving network structure. Copyright © 2024, Association for the Advancement of Artificial Intelligence (***). All rights reserved.

关键词： Random processes

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Decoder ensembling for learned latent geometries 1

Decoder ensembling for learned latent geometries

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1st Geometry-Grounded Representation Learning and Generative Modeling Workshop, GRaM 2024 at the 41st International Conference on Machine Learning, ICML 2024

作者： Syrota, Stas Moreno-Muñoz, Pablo Hauberg, Søren Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric, allowing for a standard differential geometric analysis of the latent space. Unfortunately, data manifolds are generally compact and easily disconnected or filled with holes, suggesting a topological mismatch to the Euclidean latent space. The most established solution to this mismatch is to let uncertainty be a proxy for topology, but in neural network models, this is often realized through crude heuristics that lack principle and generally do not scale to high-dimensional representations. We propose using ensembles of decoders to capture model uncertainty and show how to easily compute geodesics on the associated expected manifold. Empirically, we find this simple and reliable, thereby coming one step closer to easy-to-use latent geometries. Copyright 2024 by the author(s).

关键词： Topology

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Caching in a Mixed-Criticality 5G Radio Base Station 3

Caching in a Mixed-Criticality 5G Radio Base Station

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3rd International Workshop on Resource AWareness of Systems and Society, RAW 2024

作者： Maroun, Emad Jacob Pezzarossa, Luca Schoeberl, Martin Technical University of Denmark Department of Applied Mathematics and Computer Science Denmark

Telecommunication is a critical driver of economic and social development. 5G technologies are state-of-the-art in telecommunication, setting strong and open-ended requirements for implementing systems. Current systems for implementing baseband technologies in 5G depend on hardware separation to ensure high- and low-criticality tasks do not interfere in such a way as to violate guarantees. To increase performance and lower costs, this paper sets the research direction into future mixed-criticality systems that can handle both the high- and low-criticality tasks of the baseband unit. We analyze the 5G requirements and the common systems that currently implement them. We propose using T-CREST as the research platform with a specific architecture targeting mixed-criticality workloads. We present two cache proposals to reduce the interference of low-criticality tasks on high-criticality tasks but ensure high cache utilization and efficiency. The first cache proposal uses timeouts to automatically free cache lines reserved for high-criticality tasks. The second proposal uses contention tracking to limit how much low-criticality tasks may influence high-criticality tasks. Lastly, we propose a third cache architecture to unify the method and stack caches unique to T-CREST into a single level-2 cache. © 2024 Copyright © 2024 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

关键词： 5G mobile communication systems

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Brief Announcement: Distributed Maximum Flow in Planar Graphs 38

Brief Announcement: Distributed Maximum Flow in Planar Graph...

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38th International Symposium on Distributed Computing, DISC 2024

作者： Abd-Elhaleem, Yaseen Dory, Michal Parter, Merav Weimann, Oren Department of Computer Science University of Haifa Israel Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel

ISBN: (纸本)9783959773522

The dual of a planar graph G is a planar graph G∗ that has a vertex for each face of G and an edge for each pair of adjacent faces of G. The profound relationship between a planar graph and its dual has been the algorithmic basis for solving numerous (centralized) classical problems on planar graphs involving distances, flows, and cuts. In the distributed setting however, the only use of planar duality is for finding a recursive decomposition of G [DISC 2017, STOC 2019]. In this paper, we extend the distributed algorithmic toolkit (such as recursive decompositions and minor-aggregations) to work on the dual graph G∗. These tools can then facilitate various algorithms on G by solving a suitable dual problem on G∗. Given a directed planar graph G with hop-diameter D, our key result is an Õ(D2)-round algorithm1 for Single Source Shortest Paths on G∗, which then implies an Õ(D2)-round algorithm for Maximum st-Flow on G. Prior to our work, no Õ(Poly(D))-round algorithm was known for Maximum st-Flow. We further obtain a D·no(1)-rounds (1 + ϵ)-approximation algorithm for Maximum st-Flow on G when G is undirected and s and t lie on the same face. Finally, we give a near optimal Õ(D)-round algorithm for computing the weighted girth of G. The main challenges in our work are that G∗ is not the communication graph (e.g., a vertex of G is mapped to multiple vertices of G∗), and that the diameter of G∗ can be much larger than D (i.e., possibly by a linear factor). We overcome these challenges by carefully defining and maintaining subgraphs of the dual graph G∗ while applying the recursive decomposition on the primal graph G. The main technical difficulty, is that along the recursive decomposition, a face of G gets shattered into (disconnected) components yet we still need to treat it as a dual node. © Yaseen Abd-Elhaleem, Michal Dory, Merav Parter, and Oren Weimann.

关键词： Approximation algorithms

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Approximate Analytical Solutions for a Heat Transfer in a Slab with Internal Heat Generation

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Defect and Diffusion Forum 2023年 424卷 45-57页

作者： Nkwanazana, Mpho Moitsheki, Raseelo Joel Department of Mathematics and Applied Mathematics Sefako Makgatho Health Science University Molotlegi Street Ga-Rankuwa0204 South Africa School of Computer Science and Applied Mathematics University of the Witwatersrand Private Bag 3 Braamfontien Johannesburg South Africa

In this article we consider heat transfer models prescribed by reaction-diffusion equations. The diffusivity term and internal heat generator are given by the power law. The differential transform method (DTM) is utilized to construct the approximate analytical solutions. These solutions are generated using one- and two-dimensional DTM for the steady state and the transient problem, respectively. The effects of parameters appearing in the our model are presented and explained. © 2023 Trans Tech Publications Ltd, Switzerland.

关键词： Heat transfer

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Entropy approach of hydromagnetic Williamson nanofluid flow with Joule heating

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International Journal of Ambient Energy 2023年第1期44卷 1106-1118页

作者： Yaseen Khan, Amir Oyelakin, Ibukun S. Mondal, Sabyasachi Dey, Sharadia Department of Mathematics Amity University Kolkata India School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa Kolkata India

The current investigation, the flow of a hydromagnetic Nanofluid Williamson over an unsteady via a porous medium while stretching a sheet is being analysed along with the impact of thermal radiation and magnetic field on its flow properties. Slip condition between the nanofluid and stretching sheet is also considered. Appropriate similarity transformations are used for converting into a dimensionless form the governing equations with boundary conditions. The derived conventional differential equation was solved using the method of spectral local linearisation. After completing the numerical simulation, the outcomes are presented through different graphs and tables. The momentum conservation equation used in research papers on Williamson nanofluids, hitherto, was corrected. The effect of Joule heating has been considered in the temperature and entropy generation equations for Nanofluid flow over a stretched sheet by Williamson. The growth in the Weissenburg parameter (We) decreases the velocity profile. However, it increases the concentration and temperature distributions. Higher values of the temperature difference parameter ((Formula presented.)) are seen to decrease the entropy generated in the nanofluid system. The Reynolds number (Re) and the Brinkman number show the opposite tendency. The results have been validated with existing research and our results are found to be in great agreement. © 2022 Informa UK Limited, trading as Taylor & Francis Group.

关键词： Porous materials

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Automated soccer event detection and highlight generation for short and long views

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Multimedia Tools and Applications 2024年 1-21页

作者： Afzal, Maira Shah, Jamal Hussain ur Rehman, Saeed Khokhar, Fahad Ahmed Yasmin, Mussarat Kadry, Seifedine Department of Computer Science COMSATS University Islamabad Wah Campus Rawalpindi Pakistan Department of Mathematics and Information University of Florence Florence Italy Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Department of Applied Data Science Noroff University College Kristiansand Norway

The computer vision field has wide applications in various areas, including sports. Almost all sports events have been exploiting the best features. Sports videos are structure-based, and due to this characteristic, these videos can be categorized into interesting and non-interesting events. Identifying the view of the video and separating important events from non-interesting events is challenging. However, correct view detection can lead to correct event detection. Various researchers have proposed many strategies for detecting events in sports videos. Significant research shows some gaps while generating highlights due to limited work available in the long or short view;there is still a need for some automated methods. The main purpose of this research work is to detect key events by normalizing the data, extracting features, fusing those features, and classifying them. In this research, events are detected by classification. A new dataset is created for research purposes. The benchmark dataset is divided into two subsets, which can be used separately or as part of a larger dataset. A proposed novel approach for event highlight generation in long and short view is presented using a fusion of AlexNet and VGGNet architectures to explore the model's efficiency in the context of accurate highlight generation deep learning models fused with handcrafted. AlexNet and VGG16 pre-trained deep CNN models are applied to extract deep prior features, which are then combined with HOG to improve the results. The proposed methodology undergoes evaluation on a dataset that we created, resulting in an accuracy of 99.6%. © The Author(s), under exclusive licence to Springer science+Business Media, LLC, part of Springer Nature 2024.

关键词： Feature extraction

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