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arXiv 2024年

作者： Borisiak, Kevin Visani, Gian Marco Nourmohammad, Armita Department of Physics University of Washington United States Paul G. Allen School of Computer Science and Engineering University of Washington United States Department of Applied Mathematics University of Washington United States Fred Hutch Cancer Research Center SeattleWA United States

Predicting protein functional characteristics from structure remains a central problem in protein science, with broad implications from understanding the mechanisms of disease to designing novel therapeutics. Unfortunately, current machine learning methods are limited by scarce and biased experimental data, and physics-based methods are either too slow to be useful, or too simplified to be accurate. In this work, we present Loop-Diffusion, an energy based diffusion model which leverages a dataset of general protein loops from the entire protein universe to learn an energy function that generalizes to functional prediction tasks. We evaluate Loop-Diffusion’s performance on scoring TCR-pMHC interfaces and demonstrate state-of-the-art results in recognizing binding-enhancing mutations. Copyright © 2024, The Authors. All rights reserved.

关键词： Learning systems

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Efficiently Escaping Saddle Points in Bilevel Optimization

arXiv

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arXiv 2022年

作者： Huang, Minhui Chen, Xuxing Ji, Kaiyi Ma, Shiqian Lai, Lifeng Department of Electrical and Computer Engineering University of California Davis United States Department of Mathematics University of California Davis United States Department of Computer Science and Engineering University at Buffalo United States Department of Computational Applied Mathematics and Operations Research Rice University United States

Bilevel optimization is one of the fundamental problems in machine learning and optimization. Recent theoretical developments in bilevel optimization focus on finding the first-order stationary points for nonconvex-strongly-convex cases. In this paper, we analyze algorithms that can escape saddle points in nonconvex-strongly-convex bilevel optimization. Specifically, we show that the perturbed approximate implicit differentiation (AID) with a warm start strategy finds ∊-approximate local minimum of bilevel optimization in O͂(∊−2) iterations with high probability. Moreover, we propose an inexact NEgative-curvature-Originated-from-Noise Algorithm (iNEON), a pure first-order algorithm that can escape saddle point and find local minimum of stochastic bilevel optimization. As a by-product, we provide the first nonasymptotic analysis of perturbed multi-step gradient descent ascent (GDmax) algorithm that converges to local minimax point for minimax problems. Copyright © 2022, The Authors. All rights reserved.

关键词： Optimization

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Thermal-Aware Channel Capacity

Thermal-Aware Channel Capacity

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IEEE International Symposium on Information Theory

作者： Yeow Meng Chee Tuvi Etzion Kees A. Schouhamer Immink Tuan Thanh Nguyen Van Khu Vu Jos H. Weber Eitan Yaakobi Department of Industrial Systems Engineering and Management National University of Singapore Singapore Department of Computer Science Technion — Israel Institute of Technology Haifa Israel Turing Machines Inc. Rotterdam The Netherlands Science Mathematics and Technology Cluster Singapore University of Technology and Design Singapore Department of Applied Mathematics Delft University of Technology Delft The Netherlands

High temperatures in electronic devices have a negative effect on their performance. Various techniques have been proposed and studied to address and combat this thermal challenge. To guarantee that the peak temperature of the devices will be bounded by some maximum temperature, the transmitted signal has to satisfy some *** this motivation, we study the constrained channel that only accepts sequences that satisfy prescribed thermal constraints. The main goal in this paper is to compute the capacity of this channel. We provide the exact capacity of the channel with some certain parameters and we also present some bounds on the capacity in various ***, we consider the model that multiple wires are available to use and find out the smallest number of wires required to satisfy the thermal constraints.

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Extremal Chemical Graphs for the Arithmetic-Geometric Index

arXiv

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arXiv 2024年

作者： Hertz, Alain Bonte, Sébastien Devillez, Gauvain Dusollier, Valentin Mélot, Hadrien Schindl, David Department of Mathematics and Industrial Engineering Polytechnique Montréal - Gerad Montréal Canada Computer Science Department - Algorithms Lab University of Mons Mons Belgium Faculty of Mathematics and Physics University of Ljubljana Ljubljana Slovenia Haute école de gestion de Genève University of Applied Sciences Western Switzerland Genève Switzerland

The arithmetic-geometric index is a newly proposed degree-based graph invariant in mathematical chemistry. We give a sharp upper bound on the value of this invariant for connected chemical graphs of given order and size and characterize the connected chemical graphs that reach the bound. We also prove that the removal of the constraint that extremal chemical graphs must be connected does not allow to increase the upper bound. © 2024, CC BY.

关键词： Graphic methods

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Invariants and Reversibility In Polynomial Systems of Ode

SSRN

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SSRN 2024年

作者： Grašič, Mateja Jarrah, Abdul Salam Romanovski, Valery G. Faculty of Natural Science and Mathematics University of Maribor Koroška Cesta 160 MariborSI-2000 Slovenia Institute of Mathematics Physics and Mechanics Jadranska 19 LjubljanaSI-1000 Slovenia Department of Mathematics and Statistics American University of Sharjah Sharjah United Arab Emirates Faculty of Electrical Engineering and Computer Science University of Maribor Koroška cesta 46 MariborSI-2000 Slovenia Center for Applied Mathematics and Theoretical Physics Mladinska 3 MariborSI-2000 Slovenia

This paper explores a relationship between invariants of certain group actions and the time-reversibility of two-dimensional polynomial differential systems exhibiting a $1:-1$ resonant singularity. We focus on the connection of time-reversibility with the Sibirsky subvariety of the center variety, which encompasses systems possessing a local analytic first integral near the origin. An algorithm for generating the Sibirsky ideal for these systems is proposed and the algebraic properties of the ideal are examined. Furthermore, using a generalization of the concept of time-reversibility we study $n$-dimensional systems with a $1:\zeta:\zeta^2:\dots:\zeta^{n-1}$ resonant singularity, where $n$ is prime and $\zeta$ is a primitive $n$-th root of unity. We study the invariants of a Lie group action on the parameter space of the system, leveraging the theory of binomial ideals as a fundamental tool for the analysis. Our study reveals intriguing connections between generalized reversibility, invariants, and binomial ideals, shedding light on their complex interrelations. © 2024, The Authors. All rights reserved.

关键词： Choquet integral

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Gym Exercise Recognition Using Deep Convolutional and LSTM Neural Network Based on IMU Sensor Data

Gym Exercise Recognition Using Deep Convolutional and LSTM N...

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International Technical Conference o Circuits/Systems, computers and Communications (ITC-CSCC)

作者： Sakorn Mekruksavanich Datchakorn Tancharoen Anuchit Jitpattanakul Department of Computer Engineering School of Information and Communication Technology University of Phayao Phayao Thailand Faculty of Engineering and Technology Panyapiwat Institute of Management Nonthaburi Thailand Department of Mathematics Faculty of Applied Science Intelligent and Nonlinear Dynamic Innovations Research Center King Mongkut's University of Technology North Bangkok Bangkok Thailand

ISBN: (数字)9798350379051

ISBN: (纸本)9798350379068

This study delves into the utilization of wearable devices equipped with inertial measurement units (IMUs) to gather data for human activity recognition. It explores the application of deep neural networks for automatically identifying gym workouts using IMU sensors. Our methodology involves developing a framework that integrates convolutional neural networks (CNNs) to extract features from raw sensor data, followed by using long short-term memory (LSTM) recurrent neural networks to classify sequences. IMU data from accelerometers and gyroscopes are collected from 10 individuals performing 30 standard gym routines. The CNN-LSTM pipeline is supervised on a comprehensive dataset comprising multiple sensors and subjects to distinguish between different workouts accurately. During the evaluation, the CNN-LSTM model achieved an accuracy of 93.81 % in categorizing 30 workout categories based solely on accelerometer data. Through augmentation, this accuracy is further improved to 95.75 %. This solution outperforms independently utilized CNN and LSTM models and traditional machine learning approaches. Detailed assessments offer valuable insights into the benefits of combining diverse sensor types and model architectures for robust exercise classification. This research raises a precise and dependable wearable system for identifying gym exercises using deep neural networks. The findings suggest promising avenues for future exploration in human activity recognition, mainly focusing on utilizing on-body sensors and deep learning to analyze more complex human movements.

关键词： Accelerometers Accuracy Sensor phenomena and characterization Feature extraction Sensors Convolutional neural networks Human activity recognition

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Coupled heat and fluid transport in pulled extrusion of cylinders

arXiv

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arXiv 2024年

作者： Yuwono, Eunice B. Stokes, Yvonne M. Tronnolone, Hayden Wylie, Jonathan J. School of Computer and Mathematical Sciences Institute of Photonics and Advanced Sensing The University of Adelaide SA5005 Australia College of Science and Engineering Flinders University SA5042 Australia Department of Mathematics City University of Hong Kong Kowloon Hong Kong Center for Applied Mathematics and Statistics New Jersey Institute of Technology NewarkNJ07102 United States

In the fabrication of optical fibres, the viscosity of the glass varies dramatically with temperature so that heat transfer plays an important role in the deformation of the fibre geometry. Surprisingly, for quasi-steady drawing, with measurement of pulling tension, the applied heat can be adjusted to control the tension and temperature modelling is not needed. However, when pulling tension is not measured, a coupled heat and fluid flow model is needed to determine the inputs required for a desired output. In the fast process of drawing a preform to a fibre, heat advection dominates conduction so that heat conduction may be neglected. By contrast, in the slow process of extruding a preform, heat conduction is important. This means that solving the coupled flow and temperature modelling is essential for prediction of preform geometry. In this paper we derive such a model that incorporates heat conduction for the extensional flow of fibres. The dramatic variations in viscosity with temperature means that this problem is extremely challenging to solve via standard numerical techniques and we therefore develop a novel finite-difference numerical solution method that proves to be highly robust. We use this method to show that conduction significantly affects the size of internal holes at the exit of the *** Codes 76D08, 80A19, 80-10 Copyright © 2024, The Authors. All rights reserved.

关键词： Heat conduction

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Decentralized Upper Confidence Bound Algorithms for Homogeneous Multi-Agent Multi-Armed Bandits

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IEEE Transactions on Automatic Control 2025年

作者： Zhu, Jingxuan Mulle, Ethan Smith, Christopher S. Koppel, Alec Liu, Ji E-Surfing Digital Life Technology Co. Ltd. Hangzhou311100 China Stony Brook University Department of Applied Mathematics and Statistics Stony BrookNY11794 United States University of California Santa Cruz Department of Applied Mathematics Santa CruzCA95064 United States Stony Brook University Department of Computer Science Stony Brook11794 United States J.P. Morgan Ai Research New YorkNY10017 United States Stony Brook University Department of Electrical and Computer Engineering Stony BrookNY11794 United States

This paper studies a decentralized homogeneous multi-armed bandit problem in a multi-agent network. The problem is simultaneously solved by N agents assuming they face a common set of M arms and share the same arms' reward distributions. Each agent can receive information only from its neighbors, where the neighbor relationships among the agents are described by a fixed graph. Two fully decentralized upper confidence bound (UCB) algorithms are proposed for undirected graphs, respectively based on the classic UCB1 algorithm and the state-of-the-art Kullback-Leibler upper confidence bound (KL-UCB) algorithm. The proposed decentralized UCB1 and KL-UCB algorithms permit each agent in the network to achieve a better logarithmic asymptotic regret than their single-agent counterparts, provided that the agent has at least one neighbor, and the more neighbors an agent has, the better regret it will have, meaning that the sum is more than its component parts. The same algorithm design framework is also extended to directed graphs through the design of a variant of the decentralized UCB1 algorithm, which outperforms the single-agent UCB1 algorithm. © 1963-2012 IEEE.

关键词： Undirected graphs

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Reliable Extrapolation of Deep Neural Operators Informed by Physics or Sparse Observations

SSRN

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SSRN 2023年

作者： Zhu, Min Zhang, Handi Jiao, Anran Karniadakis, George Em Lu, Lu Department of Chemical and Biomolecular Engineering University of Pennsylvania PhiladelphiaPA19104 United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Computer and Information Science University of Pennsylvania PhiladelphiaPA19104 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States School of Engineering Brown University ProvidenceRI02912 United States

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity via the 2-Wasserstein distance between two function spaces and propose a new strategy of bias-variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information-the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed. © 2023, The Authors. All rights reserved.

关键词： Extrapolation

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Tianji’s horse racing optimization (THRO): a new metaheuristic inspired by ancient wisdom and its engineering optimization applications

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Artificial Intelligence Review 2025年第9期58卷 1-111页

作者： Wang, Liying Du, Haiping Zhang, Zhenxing Hu, Gang Mirjalili, Seyedali Khodadadi, Nima Hussien, Abdelazim G. Liao, Yingying Zhao, Weiguo School of Water Conservancy and Hydropower Hebei University of Engineering Handan China School of Electrical Computer and Telecommunications Engineering University of Wollongong Wollongong Australia Prairie Research Institute University of Illinois at Urbana-Champaign Champaign USA Department of Applied Mathematics Xi’an University of Technology Xi’an China Centre for Artificial Intelligence Research and Optimisation Torrens University Australia Brisbane Australia Faculty of Electrical Engineering and Computer Science VSB-Technical University of Ostrava Ostrava Czech Republic University Research and Innovation Center Obuda University Budapest Hungary Department of Civil and Environmental Engineering Pacific Earthquake Engineering Research (PEER) Center University of California Berkeley USA Faculty of Science Fayoum University Fayoum Egypt School of Civil Engineering Shijiazhuang Tiedao University Shijiazhuang China

In this study, we introduce a novel metaheuristic algorithm named Tianji’s horse racing optimization (THRO), inspired by the Chinese historical story of Tianji’s horse racing. The story illustrates how Tianji leveraged his strengths to counteract his opponent’s weaknesses, ultimately leading to his victory in the competition. This strategic principle, which led to Tianji’s victory, forms the foundation of THRO’s design. The need for such a proposal arises from the limitations of existing optimization algorithms, which often struggle with convergence speed and solution accuracy when solving complex problems. THRO addresses these challenges by employing a unique dynamic individual matching strategy that enhances the algorithm’s convergence rate and solution precision. In this algorithm, an effective greedy strategy is employed to maximize benefits by selecting individuals from its population and matching them with individuals from the opponent’s population, thereby facilitating individual updates. This paper provides mathematically grounded explanations and analysis of how the algorithm converges to the global optimum with probability 1. To validate the efficacy of THRO, comparative experiments with 12 popular algorithms are conducted on 23 classical benchmark functions and the CEC2017 test suite. For the 29 CEC2017 functions across 10, 30, 50, and 100 dimensions, THRO achieves the slowest Friedman average ranking values among all competing methods, which are 2.052, 2.500, 2.293, and 2.259, respectively. Additionally, we conduct a comprehensive comparison with several advanced algorithms, including high-performance hybrid optimizers and the CEC winners, across the CEC2014, CEC2017, CEC2020, and CEC2022 suites, where THRO again achieves the slowest Friedman average ranking value of 1.729. Furthermore, six engineering design problems are employed to comprehensively check the applicability of THRO. Eventually, THRO’s proficiency extends to the application of identifying

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