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arXiv 2022年

作者： Ablowitz, Mark J. Cole, Justin T. El, Gennady A. Hoefer, Mark A. Luo, Xu-Dan Department of Applied Mathematics University of Colorado Boulder United States Department of Mathematics University of Colorado Colorado Springs United States Department of Mathematics Physics and Electrical Engineering Northumbria University United Kingdom Chinese Academy of Sciences China

The propagation of localized solitons in the presence of large-scale waves is a fundamental problem, both physically and mathematically, with applications in fluid dynamics, nonlinear optics and condensed matter physics. Here, the evolution of a soliton as it interacts with a rarefaction wave or a dispersive shock wave, examples of slowly varying and rapidly oscillating dispersive mean fields, for the Korteweg-de Vries equation is studied. Step boundary conditions give rise to either a rarefaction wave (step up) or a dispersive shock wave (step down). When a soliton interacts with one of these mean fields, it can either transmit through (tunnel) or become embedded (trapped) inside, depending on its initial amplitude and position. A comprehensive review of three separate analytical approaches is undertaken to describe these interactions. First, a basic soliton perturbation theory is introduced that is found to capture the solution dynamics for soliton-rarefaction wave interaction in the small dispersion limit. Next, multiphase Whitham modulation theory and its finite-gap description are used to describe soliton-rarefaction wave and soliton-dispersive shock wave interactions. Lastly, a spectral description and an exact solution of the initial value problem is obtained through the Inverse Scattering Transform. For transmitted solitons, far-field asymptotics reveal the soliton phase shift through either type of wave mentioned above. In the trapped case, there is no proper eigenvalue in the spectral description, implying that the evolution does not involve a proper soliton solution. These approaches are consistent, agree with direct numerical simulation, and accurately describe different aspects of solitary wave-mean field interaction. Copyright © 2022, The Authors. All rights reserved.

关键词： Solitons

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Integrability of polynomial vector fields and a dual problem

arXiv

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arXiv 2024年

作者： Petek, Tatjana Romanovski, Valery G. Faculty of Electrical Engineering and Computer Science University of Maribor Koroska cesta 46 MariborSI-2000 Slovenia Institute of Mathematics Physics and Mechanics Jadranska 19 LjubljanaSI-1000 Slovenia Faculty of Natural Science and Mathematics University of Maribor Koroska cesta 160 MariborSI-2000 Slovenia Center for Applied Mathematics and Theoretical Physics Mladinska 3 MariborSI-2000 Slovenia

We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability variety in relation to the invariants of the associated Lie group. Our study extends to differential operators on affine algebraic varieties, highlighting the intrinsic connection between these operators and local analytic first integrals. To illustrate the duality the case of quadratic vector fields is considered in detail. © 2024, CC BY.

关键词： Choquet integral

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A New Strategy for Designing Dual-band Antennas Based on Double-layer Metasurfaces

arXiv

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arXiv 2023年

作者： Hecht, Kristy Chahat, Nacer Chattopadhyay, Goutam Martini, Enrica Mencagli, Mario Junior Department of Electrical and Computer Engineering University of North Carolina at Charlotte CharlotteNC28223 United States California Institute of Technology PasadenaCA91109 United States University of Siena Department of Information Engineering and Mathematics Siena53100 Italy

We present a new strategy for the design of dual-band planar antennas based on metasurfaces (MTSs) in the microwave and millimeter-wave regimes. It is based on a double-layer structure obtained by cascading two subwavelength patterned metallic claddings supported by a grounded dielectric slab. Each metallic layer is responsible for controlling radiation at one frequency, and it is engineered to be transparent at the other frequency. Hence, the two metallic layers can be designed independently using the well-established techniques for the design of single-layered MTS antennas. Layers decoupling is achieved by suitably exploiting Foster’s reactance theorem, which regulates the frequency response of the impedance sheet modeling the metallic layer. By using the proposed strategy, a dual-band double-layered MTS antenna radiating a circularly polarized broadside beam in two popular frequency bands for climate science applications is designed and numerically verified. © 2023, CC BY.

关键词： Frequency response

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Reinforcement Learning-Based Optimal Control for Multiplicative-Noise Systems with Input Delay

arXiv

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arXiv 2023年

作者： Wang, Hongxia Zhao, Fuyu Zhang, Zhaorong Xu, Juanjuan Li, Xun The School of Electrical and Automation Engineering Shandong University of Science and Technology Qingdao30332 China The Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong Shandong University Jinan250061 China

In this paper, the reinforcement learning (RL)-based optimal control problem is studied for multiplicative-noise systems, where input delay is involved and partial system dynamics is unknown. To solve a variant of Riccati-ZXL equations, which is a counterpart of standard Riccati equation and determines the optimal controller, we first develop a necessary and sufficient stabilizing condition in form of several Lyapunov-type equations, a parallelism of the classical Lyapunov theory. Based on the condition, we provide an offline and convergent algorithm for the variant of Riccati-ZXL equations. According to the convergent algorithm, we propose a RL-based optimal control design approach for solving linear quadratic regulation problem with partially unknown system dynamics. Finally, a numerical example is used to evaluate the proposed algorithm. Copyright © 2023, The Authors. All rights reserved.

关键词： Stochastic systems

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Inverse Kalman Filtering for Systems with Correlated Noises

Inverse Kalman Filtering for Systems with Correlated Noises

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IEEE Conference on Decision and Control

作者： Yibei Li Xiaoming Hu Bo Wahlberg Lihua Xie School of Electrical and Electronic Engineering Nanyang Technological University Singapore Department of Mathematics Division of Optimization and Systems Theory KTH Royal Institute of Technology Sweden Division of Decision and Control Systems School of Electrical Engineering and Computer Sciencem KTH Royal Institute of Technology Sweden

This paper focuses on two inverse problems of the Kalman filter in which the process and measurement noises are correlated. The unknown covariance matrix in a stochastic system is reconstructed from observations of its posterior beliefs. For the standard inverse Kalman filtering problem, a novel duality-based formulation is proposed, where a well-defined inverse optimal control (IOC) problem is solved instead. Identifiability of the underlying model is proved, and a least squares estimator is designed that is statistically consistent. The time-invariant case using the steady-state Kalman gain is further studied. Since this inverse problem is ill-posed, a canonical class of covariance matrices is constructed, which can be uniquely identified from the dataset with asymptotic convergence. Finally, the performances of the proposed methods are illustrated by numerical examples.

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Correction of Italian under-reporting in the first COVID-19 wave via age-specific deconvolution of hospital admissions

arXiv

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arXiv 2023年

作者： Milanesi, Simone De Nicolao, Giuseppe Department of Mathematics University of Pavia Pavia Italy Department of Electrical Computer and Biomedical Engineering University of Pavia Pavia Italy Division of Infectious Diseases I Fondazione IRCCS Policlinico San Matteo Pavia Italy

When the COVID-19 pandemic first emerged in early 2020, healthcare and bureaucratic systems worldwide were caught off guard and largely unprepared to deal with the scale and severity of the outbreak. In Italy, this led to a severe underreporting of infections during the first wave of the spread. The lack of accurate data is critical as it hampers the retrospective assessment of nonpharmacological interventions, the comparison with the following waves, and the estimation and validation of epidemiological models. In particular, during the first wave, reported cases of new infections were strikingly low if compared with their effects in terms of deaths, hospitalizations and intensive care admissions. In this paper, we observe that the hospital admissions during the second wave were very well explained by the convolution of the reported daily infections with an exponential kernel. By formulating the estimation of the actual infections during the first wave as an inverse problem, its solution by a regularization approach is proposed and validated. In this way, it was possible to computed corrected time series of daily infections for each age class. The new estimates are consistent with the serological survey published in June 2020 by the National Institute of Statistics (ISTAT) and can be used to speculate on the total number of infections occurring in Italy during 2020, which appears to be about double the number officially recorded. © 2023, CC BY.

关键词： Inverse problems

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Energy-Efficient Respiratory Anomaly Detection in Premature Newborn Infants

arXiv

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arXiv 2022年

作者： Paul, Ankita Tajin, Md Abu Saleh Das, Anup Mongan, William Dandekar, Kapil Department of Electrical and Computer Engineering Drexel University PhiladelphiaPA19104 United States Department of Mathematics and Computer Science Ursinus College CollegevillePA19426 United States

Precise monitoring of respiratory rate in premature newborn infants is essential to initiating medical interventions as required. Wired technologies can be invasive and obtrusive to the patients. We propose a Deep Learning enabled wearable monitoring system for premature newborn infants, where respiratory cessation is predicted using signals that are collected wirelessly from a non-invasive wearable Bellypatch put on the infant's body. We propose a five-stage design pipeline involving data collection and labeling, feature scaling, deep learning model selection with hyper parameter tuning, model training and validation, and model testing and deployment. The machine learning model used is a 1-D Convolutional Neural Network (1DCNN) architecture with 1 convolution layer, 1 pooling layer, and 3 fully-connected layers, achieving 97.15% classification accuracy. To address energy limitations of wearable processing, several quantization techniques are explored and their performance and energy consumption are analyzed for the respiratory classification task. Results demonstrate a reduction of energy footprints and model storage overhead with a considerable degradation of the classification accuracy, meaning that quantization and other model compression techniques are not the best solution for respiratory classification problem on wearable devices. Hence,to improve classification accuracy, yet reduce the energy consumption we propose a novel Spiking Neural Network (SNN)-based respiratory classification solution, which can be implemented on event-driven neuromorphic hardware platforms. To this end, we propose an approach to convert the analog operations of our baseline trained 1DCNN to their spiking equivalent. We perform a design-space exploration using the parameters of the converted SNN to generate inference solutions having different accuracy and energy footprints. We select a solution that achieves an accuracy of 93.33% with 18x lower energy compared to the baseline 1DCNN

关键词： Energy utilization

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Application of Machine Learning in Mental Diseases Diagnosis

Application of Machine Learning in Mental Diseases Diagnosis

引用

Information Technology (ACIT)

作者： Rahaf Alsawi Raed Alazaidah Ghassan Samara Haneen Alzoui Omar Alidmat Esraa Abu Elsoud Mohammed Talat Khouj Anwar Katrawi Mo’Ath Alluwaici Department of Data Science and AI Faculty of Information Technology Zarqa University Zarqa Jordan Department of Computer Science Faculty of Information Technology Applied Science Private University Amman Jordan Department of Computer Science Faculty of Information Technology Zarqa University Zarqa Jordan Department of Electrical Engineering University of Business and Technology Jeddah Saudi Arabia Department of Computer Science Faculty of IT Zarqa University Zarqa Jordan

ISBN: (数字)9798331540012

ISBN: (纸本)9798331540029

Mental diseases, mental disorders, or psychological disorders is a large group of symptoms which causes changes to the state of mood and reflect this on the behavior of the person with the mental disorder. It affects the patient’s way of thinking, which limits his ability to perform his simple daily needs, and thus, becomes a burden on the individual, and on the surrounding society as well. There are common types of mental disorders such as depression, anxiety disorders, schizophrenia, and bipolar disorder. In this research, two main objectives are considered. The first objective is determining which is the best classifier for predicting a person’s mental disorder among six well-known classifiers. The second objective is determining what is the best feature selection technique to use with mental disorders datasets considering six popular techniques, and with respect to several evaluation metrics. The results revealed that Logistic Regression and Naïve Bayes are the two best classification models, while Info Gain Ratio is the best feature selection method.

关键词： Measurement Logistic regression Mood Machine learning Schizophrenia Feature extraction Depression Bayes methods Medical diagnosis Information technology

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Machine Learning-Assisted Screening of Heterogeneous N-Heterocyclic Carbenes Supported Single-Atom Catalysts for Nitrogen Fixation

SSRN

引用

SSRN 2023年

作者： Sun, Jingchao Zheng, Dian Deng, Fei Liu, Sitong Xie, Yunhao Liu, Ying Xu, Jing Liu, Wei Department of Optical Engineering College of Optical Mechanical and Electrical Engineering Zhejiang A&F University Zhejiang Hangzhou311300 China College of Mathematics and Computer Science Zhejiang A & F University Zhejiang Hangzhou311300 China

Electrocatalytic nitrogen reduction reaction (NRR) has emerged as a sustainable and eco-friendly alternative for ammonia production at ambient conditions. Exploring highly efficient and selective electrocatalysts for NRR continues to gain significant attention, but remains a challenge. In this work, we conducted a series of single-atom catalysts (SACs) by embedding 29 kinds of transition metal (TM) atoms on the two-dimensional heterogeneous N-heterocyclic carbene, and systematically investigated their catalytic performance for NRR using density functional theory, high-throughput screening, and machine learning. Two promising candidates (TM = Mn and Ta) with high catalytic activity and selectivity were identified, with limiting potentials of [[EQUATION]]0.51 and [[EQUATION]]0.53 V, respectively. Moreover, considering solvation effects, the limiting potential for Mn was further reduced to [[EQUATION]]V. Machine learning (ML) analysis revealed that the adsorption energy of N2 emerged as an efficient descriptor for NRR activity, and transition metal atomic Mendeleev number (Nm), the molar volume of TM atoms (Vm) and the 1st ionization energy of TM atoms (Im) were primary descriptors featuring the intrinsic difference in NRR performance of these SACs. Our findings demonstrate a novel class of efficient SACs based on heterogeneous N-heterocyclic carbene, offering valuable insights for further design of NRR electrocatalysts with exceptional catalytic performance. © 2023, The Authors. All rights reserved.

关键词： Electrocatalysts

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Open set label noise learning with robust sample selection and margin-guided module

arXiv

引用

arXiv 2025年

作者： Zhao, Yuandi Xia, Qianxi Sun, Yang Wen, Zhijie Ma, Liyan Ying, Shihui College of Air Traffic Management Civil Aviation University of China Tianjin300300 China Department of Mathematics College of Sciences Shanghai University Shanghai200444 China School of Computer Engineering and Science Shanghai University Shanghai200444 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai200072 China

In recent years, the remarkable success of deep neural networks (DNNs) in computer vision is largely due to large-scale, high-quality labeled datasets. Training directly on real-world datasets with label noise may result in overfitting. The traditional method is limited to deal with closed set label noise, where noisy training data has true class labels within the known label space. However, there are some real-world datasets containing open set label noise, which means that some samples belong to an unknown class outside the known label space. To address the open set label noise problem, we introduce a method based on Robust Sample Selection and Margin-Guided Module (RSS-MGM). Firstly, unlike the prior clean sample selection approach, which only select a limited number of clean samples, a robust sample selection module combines small loss selection or high-confidence sample selection to obtain more clean samples. Secondly, to efficiently distinguish open set label noise and closed set ones, margin functions are designed to filter open-set data and closed set data. Thirdly, different processing methods are selected for different types of samples in order to fully utilize the data's prior information and optimize the whole model. Furthermore, extensive experimental results with noisy labeled data from benchmark datasets and real-world datasets, such as CIFAR-100N-C, CIFAR80N-O, WebFG-469, and Food101N, indicate that our approach outperforms many state-of-the-art label noise learning methods. Especially, it can more accurately divide open set label noise samples and closed set ones. Copyright © 2025, The Authors. All rights reserved.

关键词： Deep neural networks

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