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A Discrete Perspective Towards the Construction of Sparse Probabilistic Boolean Networks

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arXiv 2024年

作者： Fok, Christopher H. Wong, Chi-Wing Ching, Wai-Ki Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong

Boolean Network (BN) and its extension Probabilistic Boolean Network (PBN) are popular mathematical models for studying genetic regulatory networks. BNs and PBNs are also applied to model manufacturing systems, financial risk and healthcare service systems. In this paper, we propose a novel Greedy Entry Removal (GER) algorithm for constructing sparse PBNs. We derive theoretical upper bounds for both existing algorithms and the GER algorithm. Furthermore, we are the first to study the lower bound problem of the construction of sparse PBNs, and to derive a series of related theoretical results. In our numerical experiments based on both synthetic and practical data, GER gives the best performance among state-of-the-art sparse PBN construction algorithms and outputs sparsest possible decompositions on most of the transition probability matrices being tested. Copyright © 2024, The Authors. All rights reserved.

关键词： Approximation algorithms

The positive mass theorem for asymptotically flat manifolds with isolated conical singularities

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Science China mathematics 2024年

作者： Xianzhe Dai Yukai Sun Changliang Wang Department of Mathematics University of California Santa Barbara Key Laboratory of Pure and Applied Mathematics School of Mathematical SciencesPeking University School of Mathematical Sciences and Institute for Advanced Study Key Laboratory of Intelligent Computing and Applications (Ministry of Education)Tongji University

We prove the positive mass theorem for asymptotically flat(AF for short) manifolds with finitely many isolated conical singularities. We do not impose the spin condition. Instead, we use the conformal blow-up techniqu...

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Adaptive energy-preserving algorithms for guiding center system

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Plasma Science and Technology 2023年第4期25卷 11-22页

作者：朱贝贝刘健张嘉炜祝爱卿唐贻发 Department of Applied Mathematics School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijing 100083Peopleʼs Republic of China School of Nuclear Science and Technology University of Science and Technology of ChinaHefei 230026Peopleʼs Republic of China Advanced algorithm Joint Lab Shandong Computer Science CenterQilu University of TechnologyJinan 250014Peopleʼs Republic of China The State Key Laboratory of Scientific and Engineering Computing The Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190Peopleʼs Republic of China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049Peopleʼs Republic of China

We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized *** adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving *** new adaptive algorithms are second order,and their algebraic order is carefully *** results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.

关键词： guiding center system energy-preserving methods adaptive energy conservation

Machine learning algorithm partially reconfigured on FPGA for an image edge detection system

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Journal of Electronic Science and Technology 2024年第2期22卷 48-68页

作者： Gracieth Cavalcanti Batista Johnny Oberg Osamu Saotome Haroldo F.de Campos Velho Elcio Hideiti Shiguemori Ingemar Soderquist Division of Electronic and Embedded Systems KTH Royal Institute of TechnologyStockholm 16440Sweden Electronic Engineering Division Aeronautics Institute of TechnologySao Josédos Campos SP 12228-900Brazil Laboratory of Applied Computing and Mathematics National Institute for Space ResearchSao Josédos Campos SP 12227-900Brazil Department of C4ISR Institute of Advanced StudiesSao Josédos Campos SP 12228-001Brazil Saab AB Linkoping 58188Sweden

Unmanned aerial vehicles(UAVs)have been widely used in military,medical,wireless communications,aerial surveillance,*** key topic involving UAVs is pose estimation in autonomous navigation.A standard procedure for this process is to combine inertial navigation system sensor information with the global navigation satellite system(GNSS)***,some factors can interfere with the GNSS signal,such as ionospheric scintillation,jamming,or *** alternative method to avoid using the GNSS signal is to apply an image processing approach by matching UAV images with georeferenced *** a high effort is required for image edge *** a support vector regression(SVR)model is proposed to reduce this computational load and processing *** dynamic partial reconfiguration(DPR)of part of the SVR datapath is implemented to accelerate the process,reduce the area,and analyze its granularity by increasing the grain size of the reconfigurable *** show that the implementation in hardware is 68 times faster than that in *** architecture with DPR also facilitates the low power consumption of 4 mW,leading to a reduction of 57%than that without *** is also the lowest power consumption in current machine learning hardware ***,the circuitry area is 41 times *** with Gaussian kernel shows a success rate of 99.18%and minimum square error of 0.0146 for testing with the planning *** system is useful for adaptive applications where the user/designer can modify/reconfigure the hardware layout during its application,thus contributing to lower power consumption,smaller hardware area,and shorter execution time.

关键词： Dynamic partial reconfiguration(DPR) Field programmable gate array(FPGA)implementation Image edge detection Support vector regression(SVR) Unmanned aerial vehicle(UAV) pose estimation

Memristive feature and mechanism induced by laser-doping in defect-free 2D semiconductor materials

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Journal of Semiconductors 2024年第7期45卷 85-91页

作者： Xiaoshan Du Shu Wang Qiaoxuan Zhang Shengyao Chen Fengyou Yang Zhenzhou Liu Zhengwei Fan Lijun Ma Lei Wang Lena Du Zhongchang Wang Cong Wang Bing Chen Qian Liu College of Electronic and Information Engineering Shandong University of Science and TechnologyQingdao 266590China National Center for Nanoscience and Technology&University of Chinese Academy of Sciences Beijing 100190China Hebei University of Water Resources and Electric Engineering Electrical Automation Department Cangzhou 061001China The MOE Key Laboratory of Weak-Light Nonlinear Photonics and International Sino-Slovenian Join Re-search Center on Liquid Crystal Pho-tonics TEDA Institute of Applied Physics and School of PhysicsNankai UniversityTianjin 300457China College of Mathematics and Physics Shandong Advanced Optoelectronic Materials and Technologies Engineering LaboratoryQingdao Uni-versity of Science and TechnologyQingdao 266061China Department of Physics Capital Normal UniversityBeijing 100048China Department of Advanced Materials and Computing International Iberian Nanotechnology Laboratory(INL)4715-330 BragaPortugal College of Mathematics and Physics Beijing University of Chemical TechnologyBeijing 100029China

Memristors as non-volatile memory devices have gained numerous attentions owing to their advantages in storage,in-memory computing, synaptic applications, etc. In recent years, two-dimensional(2D) materials with moderate defects have been discovered to exist memristive feature. However, it is very difficult to obtain moderate defect degree in 2D materials, and studied on modulation means and mechanism becomes urgent and essential. In this work, we realized memristive feature with a bipolar switching and a configurable on/off ratio in a two-terminal MoS_(2) device(on/off ratio ~100), for the first time, from absent to present using laser-modulation to few-layer defect-free MoS_(2)(about 10 layers), and its retention time in both high resistance state and low resistance state can reach 2×10^(4) s. The mechanism of the laser-induced memristive feature has been cleared by dynamic Monte Carlo simulations and first-principles calculations. Furthermore, we verified the universality of the laser-modulation by investigating other 2D materials of TMDs. Our work will open a route to modulate and optimize the performance of 2D semiconductor memristive devices.

关键词： 2D-material memristor laser doping laser direct writing memristive mechanism

A discrete perspective towards the construction of sparse probabilistic Boolean networks

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Information Sciences 2025年 718卷

作者： Fok, Christopher H. Wong, Chi-Wing Ching, Wai-Ki Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Pokfulam Hong Kong

The construction problem of sparse probabilistic Boolean networks (PBNs) has important applications in areas such as gene regulatory network inference and financial risk modeling. Many of the existing methods for solving this problem do not output sparse decompositions or are associated with high time complexity. We propose a new Entry-Removal-Type (ERT) algorithm called the Greedy Entry Removal algorithm (GER) for solving the construction problem. The key idea behind GER is to maximize the reduction in the number of positive entries in the residue matrix at each iteration, resulting in fewer iterations needed for the residue matrix to become the zero matrix and allowing GER to output sparse decompositions. We establish new upper bounds for two existing ERT algorithms and GER, providing theoretical guarantees for their performance. In numerical experiments based on both synthetic and real-world data, GER outperforms state-of-the-art sparse PBN construction algorithms by producing the sparsest decompositions for most of the tested transition probability matrices. Additionally, we are the first to study the lower bound problem related to sparse PBN construction and derive a series of theoretical results, which can inform future algorithm design and set realistic expectations for the sparsity achievable in practical scenarios. © 2025 Elsevier Inc.

关键词： Digital arithmetic

Advancing Simulations of Coupled Electron and Phonon Nonequilibrium Dynamics Using Adaptive and Multirate Time Integration

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arXiv 2024年

作者： Yao, Jia Maliyov, Ivan Gardner, David J. Woodward, Carol S. Bernardi, Marco Department of Applied Physics and Materials Science Department of Physics California Institute of Technology PasadenaCA91125 United States Mathematics for Materials Modeling Institute of Mathematics Institute of Materials EPFL LausanneCH-1015 Switzerland Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States

Electronic structure calculations in the time domain provide a deeper understanding of nonequilibrium dynamics in materials. The real-time Boltzmann equation (rt-BTE), used in conjunction with accurate interactions computed from first principles, has enabled reliable predictions of coupled electron and lattice dynamics. However, the timescales and system sizes accessible with this approach are still limited, with two main challenges being the different timescales of electron and phonon interactions and the cost of computing collision integrals. As a result, only a few examples of these calculations exist, mainly for two-dimensional (2D) materials. Here we leverage adaptive and multirate time integration methods to achieve a major step forward in solving the coupled rt-BTEs for electrons and phonons. Relative to conventional (non-adaptive) time-stepping, our approach achieves a 10x speedup for a given target accuracy, or greater accuracy by 3–6 orders of magnitude for the same computational cost, enabling efficient calculations in both 2D and bulk materials. This efficiency is showcased by computing the coupled electron and lattice dynamics in graphene up to ∼100 ps, as well as modeling ultrafast lattice dynamics and thermal diffuse scattering maps in a bulk material (silicon). These results open new opportunities for quantitative studies of nonequilibrium physics in materials. Copyright © 2024, The Authors. All rights reserved.

关键词： Boltzmann equation

VITO: VISION TRANSFORMER-OPERATOR

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arXiv 2023年

作者： Ovadia, Oded Turkel, Eli Kahana, Adar Karniadakis, George Em Stinis, Panos Department of Applied Mathematics Tel Aviv University Tel Aviv Israel Division of Applied Mathematics Brown University ProvidenceRI United States Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA United States

We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs). Our approach, named ViTO, combines a U-Net based architecture with a vision transformer. We apply ViTO to solve inverse PDE problems of increasing complexity, namely for the wave equation, the Navier-Stokes equations and the Darcy equation. We focus on the more challenging case of super-resolution, where the input dataset for the inverse problem is at a significantly coarser resolution than the output. The results we obtain are comparable or exceed the leading operator network benchmarks in terms of accuracy. Furthermore, ViTO’s architecture has a small number of trainable parameters (less than 10% of the leading competitor), resulting in a performance speed-up of over 5x when averaged over the various test cases. © 2023, CC BY.

关键词： Inverse problems

Group Projected Subspace Pursuit for Block Sparse Signal Reconstruction: Convergence Analysis and Applications

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arXiv 2024年

作者： He, Roy Y. Liu, Haixia Liu, Hao Department of Mathematics City University of Hong Kong Kowloon Tong Hong Kong School of Mathematics and Statistics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong

In this paper, we present a convergence analysis of the Group Projected Subspace Pursuit (GPSP) algorithm proposed by He et al. [HKL+23] (Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT), Journal of Computational Physics, 494, 112526) and extend its application to general tasks of block sparse signal recovery. We prove that when the sampling matrix satisfies the Block Restricted Isometry Property (BRIP) with a sufficiently small Block Restricted Isometry Constant (BRIC), GPSP exactly recovers the true block sparse signals. When the observations are noisy, this convergence property of GPSP remains valid if the magnitude of the true signal is sufficiently large. GPSP selects the features by subspace projection criterion (SPC) for candidate inclusion and response magnitude criterion (RMC) for candidate exclusion. We compare these criteria with counterparts of other state-of-the-art greedy algorithms. Our theoretical analysis and numerical ablation studies reveal that SPC is critical to the superior performances of GPSP, and that RMC can enhance the robustness of feature identification when observations contain noises. We test and compare GPSP with other methods in diverse settings, including heterogeneous random block matrices, inexact observations, face recognition, and PDE identification. We find that GPSP outperforms the other algorithms in most cases for various levels of block sparsity and block sizes, justifying its effectiveness for general applications. © 2024, CC BY.

关键词： Face recognition