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The Journal of Machine Learning Research 2022年第1期23卷 8621-8643页

作者： Pedro Felzenszwalb Caroline Klivans Alice Paul School of Engineering and Department of Computer Science Brown University Providence RI Division of Applied Mathematics Brown University Providence RI Department of Biostatistics Brown University Providence RI

We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP relaxation using iterated linear optimization. We show the vertices of the Max k-Cut relaxation correspond to partitions of the data into at most k sets. We also show the vertices are attractive fixed points of iterated linear optimization. Each step of this iterative process solves a relaxation of the closest vertex problem and leads to a new clustering problem where the underlying clusters are more clearly defined. Our experiments show that using fixed point iteration for rounding the Max k-Cut SDP relaxation leads to significantly better results when compared to randomized rounding.

关键词： clustering semidefinite programming optimization

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RANDOMLY PERTURBED ERGODIC AVERAGES

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Proceedings of the American Mathematical Society, Series B 2021年第19期8卷 224-244页

作者： Choi, Jaeyong Reinhold-Larsson, Karin DIVISION OF MATHEMATICS AND COMPUTER SCIENCE (DMACS) COLLEGE OF NATURAL AND APPLIED SCIENCES (CNAS) UNIVERSITY OF GUAM (UOG) ALS 319 UOG STATION MANGILAO 96923 Guam DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY AT ALBANY SUNY ALBANY 12222 NY United States

We consider a class of random ergodic averages, containing averages along random non–integer sequences. For such averages, Cohen & Cuny obtained ∫ uniform universal pointwise convergence for functions in L² with max(1, log(1 + |t|))dμf < ∞ via a uniform estimation of trigonometric poly-nomials. ∫ We extend this result to L² functions satisfying the weaker condition max(1, log log(1+|t|))dμf < ∞. We also prove that uniform universal point-wise convergence in L² holds for the corresponding smoothed random averages or for random averages whose kernels exhibit sufficient decay at infinity. © 2021 by the authors under Creative Commons Attribution-Nonommerial 3.0 Liense (CC BY NC 3.0).

关键词： Random ergodic averages universal convergence

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Dimensionless machine learning: imposing exact units equivariance

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2023年第1期24卷 4923-4954页

作者： Soledad Villar Weichi Yao David W. Hogg Ben Blum-Smith Bianca Dumitrascu Department of Applied Mathematics and Statistics Mathematical Institute for Data Science Johns Hopkins University Department of Technology Operations and Statistics New York University Center for Cosmology and Particle Physics Department of Physics New York University Max-Planck-Institut für Astronomie Flatiron Institute a Division of the Simons Foundation Department of Applied Mathematics and Statistics Johns Hopkins University Department of Computer Science and Technology Cambridge University

Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional scalings. Here, we express this symmetry in terms of a (non-compact) group action, and we employ dimensional analysis and ideas from equivariant machine learning to provide a methodology for exactly units-equivariant machine learning: For any given learning task, we first construct a dimensionless version of its inputs using classic results from dimensional analysis and then perform inference in the dimensionless space. Our approach can be used to impose units equivariance across a broad range of machine learning methods that are equivariant to rotations and other groups. We discuss the in-sample and out-of-sample prediction accuracy gains one can obtain in contexts like symbolic regression and emulation, where symmetry is important. We illustrate our approach with simple numerical examples involving dynamical systems in physics and ecology.

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Heterogeneous Network Propagation with Optimal Similarity Measure for Drug-Target Associations 25

Heterogeneous Network Propagation with Optimal Similarity Me...

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25th International computer science and Engineering Conference, ICSEC 2021

作者： Tangmanussukum, Piyanut Kawichai, Thitipong Suratanee, Apichat Plaimas, Kitiporn Chulalongkorn University Faculty of Science Department of Mathematics and Computer Science Bangkok Thailand Chulachomklao Royal Military Academy Academic Division Department of Mathematics and Computer Science Nakhon Nayok Thailand Faculty of Applied Science Intelligent and Nonlinear Dynamic Innovations Research Center Sci. and Technol. Res. Inst. King Mongkut's Univ. of Technol. N. Bangkok Department of Mathematics Bangkok Thailand Center Faculty of Science Department of Mathematics and Computer Science Bangkok Thailand

ISBN: (纸本)9781665411974

Identification of drug target proteins is an important process in drug discovery and development. To perform predictions of large-scale drug-Target interactions, many computational methods have been proposed using the information of target-Target and drug-drug similarities into a network. In this work, we propose an enhanced heterogeneous network model with various biological aspects of target-Target and drug-drug similarities to predict drug-Target associations. Network propagation was performed through the heterogeneous network to predict new potential targets of a certain drug. Cross-validation and the Area Under the Receiver Operating Characteristic curve (AUROC) were then used to qualify the best model in the drug-Target association prediction. The result shows that the model using the similarity measures based on drug-disease associations and target protein sequences significantly outperforms the other models and the original model. Overall, our best model yields an accuracy of 93.5%. In conclusion, the heterogeneous model with optimal similarity measures is a well-suited approach to predict a new target for a certain drug. © 2021 IEEE.

关键词： Heterogeneous networks

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Characteristic Mode Analysis of Nanostructures using Hydrodynamic Volume Integral Equation

Characteristic Mode Analysis of Nanostructures using Hydrody...

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Antennas and Propagation & USNC/URSI National Radio science Meeting

作者： Meruyert Khamitova Ran Zhao Doolos Aibek uulu Hakan Bagci Electrical and Computer Engineering (ECE) Program Computer Electrical and Mathematical Science and Engineering (CEMSE) Division King Abdullah University of Science and Technology (KAUST) Thuwal Kingdom of Saudi Arabia School of Electronic Science and Engineering University of Electronic Science and Technology of China (UESTC) Chengdu Sichuan China Department of Mathematics and Natural Sciences University of Central Asia (UCA) Naryn Kyrgyzstan

ISBN: (数字)9798350369908

ISBN: (纸本)9798350369915

The characteristic mode analysis (CMA) is formulated and implemented for the hydrodynamic volume integral equation (HDVIE) that is used to mathematically model electromagnetic field interactions and conduction current dynamics on nanoantennas and nanoscatterers. The proposed method produces excitation-independent characteristic hydrodynamic currents and the corresponding modal significance curves, providing useful information that can be used to optimize the performance of a nanoantenna. Numerical results demonstrate the reliability and the applicability of the proposed approach.

关键词： Solid modeling Nanoantennas Integral equations Hydrodynamics Mathematical models Characteristic mode analysis Numerical models

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Detecting Bone Lesions in X-Ray Under Diverse Acquisition Conditions

arXiv

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arXiv 2022年

作者： Zimbalist, Tal Rosen, Ronnie Peri-Hanania, Keren Caspi, Yaron Rinott, Bar Zeltser-Dekel, Carmel Bercovich, Eyal Eldar, Yonina C. Bagon, Shai Department of Computer Science & Applied Mathematics Weizmann Institute of Science Rehovot Israel Medical Imaging Division Rambam Health Care Campus Haifa Israel

The diagnosis of primary bone tumors is challenging, as the initial complaints are often non-specific. Early detection of bone cancer is crucial for a favorable prognosis. Incidentally, lesions may be found on radiographs obtained for other reasons. However, these early indications are often missed. In this work, we propose an automatic algorithm to detect bone lesions in conventional radiographs to facilitate early diagnosis. Detecting lesions in such radiographs is challenging: first, the prevalence of bone cancer is very low;any method must show high precision to avoid a prohibitive number of false alarms. Second, radiographs taken in health maintenance organizations (HMOs) or emergency departments (EDs) suffer from inherent diversity due to different X-ray machines, technicians and imaging protocols. This diversity poses a major challenge to any automatic analysis method. We propose to train an off-the-shelf object detection algorithm to detect lesions in radiographs. The novelty of our approach stems from a dedicated preprocessing stage that directly addresses the diversity of the data. The preprocessing consists of self-supervised region-of-interest detection using vision transformer (ViT), and a foreground-based histogram equalization for contrast enhancement to relevant regions only. We evaluate our method via a retrospective study that analyzes bone tumors on radiographs acquired from January 2003 to December 2018 under diverse acquisition protocols. Our method obtains 82.43% sensitivity at 1.5% false-positive rate and surpasses existing preprocessing methods. For lesion detection, our method achieves 82.5% accuracy and an IoU of 0.69. The proposed preprocessing method enables to effectively cope with the inherent diversity of radiographs acquired in HMOs and EDs. © 2022, CC BY-NC-ND.

关键词： Tumors

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An Assessment of the Supremizer and Aggregation Methods of Stabilization for Reduced-Order Models

arXiv

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arXiv 2023年

作者： Davie, Kayla D. Elman, Howard C. Applied Mathematics & Statistics Scientific Computation Program University of Maryland College ParkMD20742 United States Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States

MSC Codes 65N22, 65K10, 65F45We explore the features of two methods of stabilization, aggregation and supremizer methods, for reduced-order modeling of parametrized optimal control problems. In both methods, the reduced basis spaces are augmented to guarantee stability. For the aggregation method, the reduced basis approximation spaces for the state and adjoint variables are augmented in such a way that the spaces are identical. For the supremizer method, the reduced basis approximation space for the state-control product space is augmented with the solutions of a supremizer equation. We implement both of these methods for solving several parametrized control problems and assess their performance. Results indicate that the number of reduced basis vectors needed to approximate the solution space to some tolerance with the supremizer method is much larger, possibly double, that for aggregation. There are also some cases where the supremizer method fails to produce a converged solution. We present results to compare the accuracy, efficiency, and computational costs associated with both methods of stabilization which suggest that stabilization by aggregation is a superior stabilization method for control problems. © 2023, CC BY.

关键词： Stabilization

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SOCIO-SPATIAL SEGREGATION AND HUMAN MOBILITY: A REVIEW OF EMPIRICAL EVIDENCE

arXiv

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arXiv 2024年

作者： Liao, Yuan Gil, Jorge Yeh, Sonia Pereira, Rafael H.M. Alessandretti, Laura Department of Space Earth and Environment Chalmers University of Technology Gothenburg Sweden Department of Architecture and Civil Engineering Chalmers University of Technology Gothenburg Sweden - Brazil Data Science Division Brazil Department of Applied Mathematics and Computer Science Technical University of Denmark Lyngby Denmark

Socio-spatial segregation is the physical separation of different social, economic, or demographic groups within a geographic space, often resulting in unequal access to resources, services, and opportunities. The literature has traditionally focused on residential segregation, examining how individuals' residential locations are distributed differently across neighborhoods based on various social attributes, e.g., race, ethnicity, and income. However, this approach overlooks the complexity of spatial segregation in people's daily activities, which often extend far beyond residential areas. Since the 2010s, emerging mobility data sources have enabled a new understanding of socio-spatial segregation by considering daily activities such as work, school, shopping, and leisure visits. From traditional surveys to GPS trajectories, diverse data sources reveal that daily mobility can result in spatial segregation levels that differ from those observed in residential segregation. This literature review focuses on three critical questions: (a) What are the strengths and limitations of segregation research incorporating extensive mobility data? (b) How do human mobility patterns relate to individuals' residential vs. experienced segregation levels? and (c) What key factors explain the relationship between one's mobility patterns and experienced segregation? Our literature review enhances the understanding of socio-spatial segregation at the individual level and clarifies core concepts and methodological challenges in the field. Our review explores studies of key themes: segregation, activity space, co-presence, and the built environment. By synthesizing their findings, we aim to offer actionable insights for reducing segregation. © 2024, CC BY-SA.

关键词： Leisure

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An Optimal Framework for SDN Based on Deep Neural Network

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computers, Materials & Continua 2022年第10期73卷 1125-1140页

作者： Abdallah Abdallah Mohamad Khairi Ishak Nor Samsiah Sani Imran Khan Fahad RAlbogamy Hirofumi Amano Samih M.Mostafa Department of Industrial Engineering School of Applied Technical Sciences German Jordanian UniversityAmman35247Jordan School of Electrical and Electronic Engineering Universiti Sains MalaysiaNibong Tebal14300Malaysia Center for Artificial Intelligence Technology Faculty of Information Science and TechnologyThe National University of Malaysia(UKM)Bangi43600SelangorMalaysia Department of Electrical Engineering University of Engineering and TechnologyPeshawar814Pakistan Turabah University College Computer Sciences ProgramTaif UniversityTaif21944Saudi Arabia Research Institute for Information Technology Kyushu UniversityFukuoka819-0395Japan Computer Science-Mathematics Department Faculty of ScienceSouth Valley UniversityQena83523Egypt

Software-defined networking(SDN)is a new paradigm that promises to change by breaking vertical integration,decoupling network control logic from the underlying routers and switches,promoting(logical)network control centralization,and introducing network ***,the controller is similarly vulnerable to a“single point of failure”,an attacker can execute a distributed denial of service(DDoS)attack that invalidates the controller and compromises the network security in *** address the problem of DDoS traffic detection in SDN,a novel detection approach based on information entropy and deep neural network(DNN)is *** approach contains a DNN-based DDoS traffic detection module and an information-based entropy initial inspection *** initial inspection module detects the suspicious network traffic by computing the information entropy value of the data packet’s source and destination Internet Protocol(IP)addresses,and then identifies it using the DDoS detection module based on *** assaults were found when suspected irregular traffic was *** reveal that the algorithm recognizes DDoS activity at a rate of more than 99%,with a much better accuracy *** false alarm rate(FAR)is much lower than that of the information entropy-based detection ***,the proposed framework can shorten the detection time and improve the resource utilization efficiency.

关键词： Deep neural network computer networks data security optimization

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Global-Local Active Contour for Segmenting Images with Simultaneous Inhomogeneity and Texture

SSRN

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SSRN 2024年

作者： Shao, Pei-Chiang Department of Applied Mathematics Chung Yuan Christian University Zhongli District Taoyuan City320314 Taiwan Undergraduate Program in College of Electrical Engineering and Computer Science Chung Yuan Christian University Zhongli District Taoyuan City320314 Taiwan

Severe intensity inhomogeneity (InH) and complex real-world textures cause great difficulties and become two important issues in image segmentation and object extraction applications. Plenty of methods are proposed to tackle these issues, however, they usually perform poorly on images possess both InH and texture. In this paper, we propose a region-based active contour model for segmenting images with simultaneous inhomogeneity and texture. A new bias field possesses both global and local smoothness properties is proposed to handle the InH issue, and a pixel inhomogeneity factor (PIF) is employed to jointly deal with InH and textured images. We also employ the total variation (TV) regularization to further smooth and denoise the transformed PIF image, making the segmentation process to have the nice properties of global convergence and independence of contour initialization. A large number of numerical experiments and comparisons are conducted to demonstrate the effective performance of the newly proposed method. © 2024, The Authors. All rights reserved.

关键词： Textures

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