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European signal processing conference

作者： Sina Jafarpour Guengor Polatkan Eugene Brevdo Shannon Hughes Andrei Brasoveanu Ingrid Daubechies Departments of Electrical Engineering Computer Science and Mathematics and the Program in Applied and Computational Mathematics Princeton NJ 08544

ISBN: (纸本)9781617388767

Wavelet transforms and machine learning tools can be used to assist art experts in the stylistic analysis of paintings. A dual-tree complex wavelet transform, Hidden Markov Tree modeling and Random Forest classifiers are used here for a stylistic analysis of Vincent van Gogh's paintings with results on two stylometry challenges that concern "dating, resp. extracting distinguishing features".

关键词： Support vector machines Abstracts Image resolution Radio frequency

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Inertial Hegselmann-Krause systems

Inertial Hegselmann-Krause systems

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American Control Conference (ACC)

作者： Bernard Chazelle Chu Wang Department of Computer Science Princeton University Program in Applied and Computational Mathematics Princeton University

ISBN: (纸本)9781467386838

We derive an energy bound for inertial Hegselmann-Krause (HK) systems, which we define as a variant of the classic HK model in which the agents can change their weights arbitrarily at each step. We use the bound to prove the convergence of HK systems with closed-minded agents, which settles a conjecture of long standing. This paper also introduces anchored HK systems and show their equivalence to the symmetric heterogeneous model.

关键词： Convergence Communication networks Kinetic theory Protocols Nickel Mobile communication Turning

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A Flow Artist for High-Dimensional Cellular Data 33

A Flow Artist for High-Dimensional Cellular Data

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33rd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2023

作者： MacDonald, Kincaid Bhaskar, Dhananjay Thampakkul, Guy Nguyen, Nhi Zhang, Joia Perlmutter, Michael Adelstein, Ian Krishnaswamy, Smita Yale University Department of Mathematics United States Pomona College Department of Mathematics United States University of Washington Department of Statistics United States Boise State University Department of Mathematics United States Yale University Department of Computer Science United States Yale University Applied Mathematics Program United States Yale University Computational Biology and Bioinformatics Program United States

ISBN: (纸本)9798350324112

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data. © 2023 IEEE.

关键词： RNA

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Heart wall myofibers are arranged in minimal surfaces to optimize organ function (vol 109, pg 9253, 2012)

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PROCEEDINGS OF THE NATIONAL ACADEMY OF scienceS OF THE UNITED STATES OF AMERICA 2012年第49期109卷 20166-20166页

作者： Savadjiev, Peter Strijkers, Gustav J. Bakermans, Adrianus J. Piuze, Emmanuel Zucker, Steven W. Siddiqi, Kaleem [a]Psychiatry Neuroimaging Laboratory and Laboratory for Mathematics in Imaging Brigham and Women’s Hospital Harvard Medical School Boston MA 02215 [b]Department of Biomedical Engineering Eindhoven University of Technology 5600 MB Eindhoven The Netherlands [c]School of Computer Science and Centre for Intelligent Machines McGill University Montréal Canada H3A 2A7 and [d]Departments of Computer Science and Biomedical Engineering and Program in Applied Mathematics Yale University New Haven CT 06520-8285

Heart wall myofibers wind as helices around the ventricles, strengthening them in a manner analogous to the reinforcement of concrete cylindrical columns by spiral steel cables [Richart FE, et al. (1929) Univ of Illinois, Eng Exp Stn Bull 190]. A multitude of such fibers, arranged smoothly and regularly, contract and relax as an integrated functional unit as the heart beats. To orchestrate this motion, fiber tangling must be avoided and pumping should be efficient. Current models of myofiber orientation across the heart wall suggest groupings into sheets or bands, but the precise geometry of bundles of myofibers is unknown. Here we show that this arrangement takes the form of a special minimal surface, the generalized helicoid [Blair DE, Vanstone JR (1978) Minimal Submanifolds and Geodesics 13-16], closing the gap between individual myofibers and their collective wall structure. The model holds across species, with a smooth variation in its three curvature parameters within the myocardial wall providing tight fits to diffusion magnetic resonance images from the rat, the dog, and the human. Mathematically it explains how myofibers are bundled in the heart wall while economizing fiber length and optimizing ventricular ejection volume as they contract. The generalized helicoid provides a unique foundation for analyzing the fibrous composite of the heart wall and should therefore find applications in heart tissue engineering and in the study of heart muscle diseases. [PUBLICATION ABSTRACT]

关键词： myocardium myofiber geometry diffusion tensor MRI

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Extending discrete exterior calculus to a fractional derivative

arXiv

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arXiv 2019年

作者： Crum, Justin Levine, Joshua A. Gillette, Andrew Program in Applied Mathematics University of Arizona Department of Computer Science University of Arizona Department of Mathematics University of Arizona

Fractional partial differential equations (FDEs) are used to describe phenomena that involve a "non-local" or "long-range" interaction of some kind. Accurate and practical numerical approximation of their solutions is challenging due to the dense matrices arising from standard discretization procedures. In this paper, we begin to extend the well-established computational toolkit of Discrete Exterior Calculus (DEC) to the fractional setting, focusing on proper discretization of the fractional derivative. We define a Caputo-like fractional discrete derivative, in terms of the standard discrete exterior derivative operator from DEC, weighted by a measure of distance between p-simplices in a simplicial complex. We discuss key theoretical properties of the fractional discrete derivative and compare it to the continuous fractional derivative via a series of numerical experiments. Copyright © 2019, The Authors. All rights reserved.

关键词： Calculations

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An independent set approach for the communication network of the GPS III system

An independent set approach for the communication network of...

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作者： Brinkmann, Gunnar Crevals, Simon Frye, John Applied Mathematics and Computer Science Ghent University Krijgslaan 281 S9 9000 Ghent Belgium Lockheed Martin GPS III Program 100 Campus Drive Newtown PA 18940 United States

In this article, we describe an algorithm to find the optimal communication network for the new GPS III satellite system. Finding a possible network will be translated to a maximum clique problem and an efficient algorithm for finding all maximum cliques under these special circumstances is described. © 2011 Elsevier B.V. All rights reserved.

关键词： Network security

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Convolutional neural networks with low-rank regularization 4

Convolutional neural networks with low-rank regularization

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4th International Conference on Learning Representations, ICLR 2016

作者： Tai, Cheng Xiao, Tong Zhang, Yi Wang, Xiaogang Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Department of Electronic Engineering Chinese University of Hong Kong Hong Kong Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor United States

Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank tensor decomposition for removing the redundancy in the convolution kernels. The algorithm finds the exact global optimizer of the decomposition and is more effective than iterative methods. Based on the decomposition, we further propose a new method for training low-rank constrained CNNs from scratch. Interestingly, while achieving a significant speedup, sometimes the low-rank constrained CNNs delivers significantly better performance than their non-constrained counterparts. On the CIFAR-10 dataset, the proposed low-rank NIN model achieves 91.31% accuracy (without data augmentation), which also improves upon state-of-the-art result. We evaluated the proposed method on CIFAR-10 and ILSVRC12 datasets for a variety of modern CNNs, including AlexNet, NIN, VGG and GoogleNet with success. For example, the forward time of VGG-16 is reduced by half while the performance is still comparable. Empirical success suggests that low-rank tensor decompositions can be a very useful tool for speeding up large CNNs. © ICLR 2016: San Juan, Puerto Rico. All Rights Reserved.

关键词： Iterative methods

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TSP cuts which do not conform to the template paradigm 5th

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5th International Conference on Mobile Agents, MA 2001

作者： Applegate, David Bixby, Robert Chvátal, Vašek Cook, William Algorithms and Optimization Department AT and T Labs – Research Florham ParkNJ07932 United States Computational and Applied Mathematics Rice University HoustonTX77005 United States Department of Computer Science Rutgers University PiscatawayNJ08854 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

ISBN: (纸本)3540428771

The first computer implementation of the Dantzig-Fulkerson- Johnson cutting-plane method for solving the traveling salesman problem, written by Martin, used subtour inequalities as well as cutting planes of Gomory’s type. The practice of looking for and using cuts that match prescribed templates in conjunction with Gomory cuts was continued in computer codes of Miliotis, Land, and Fleischmann. Gr¨otschel, Padberg, and Hong advocated a different policy, where the template paradigm is the only source of cuts;furthermore, they argued for drawing the templates exclusively from the set of linear inequalities that induce facets of the TSP polytope. These policies were adopted in the work of Crowder and Padberg, in the work of Gr¨otschel and Holland, and in the work of Padberg and Rinaldi;their computer codes produced the most impressive computational TSP successes of the nineteen eighties. Eventually, the template paradigm became the standard frame of reference for cutting planes in the TSP. The purpose of this paper is to describe a technique for finding cuts that disdains all understanding of the TSP polytope and bashes on regardless of all prescribed templates. Combining this technique with the traditional template approach was a crucial step in our solutions of a 13,509-city TSP instance and a 15,112-city TSP instance. © Springer-Verlag Berlin Heidelberg 2001.

关键词： Traveling salesman problem

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COVID-19 Infected Lung Computed Tomography Segmentation and Supervised Classification Approach

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computers, Materials & Continua 2021年第7期68卷 391-407页

作者： Aqib Ali Wali Khan Mashwani Samreen Naeem Muhammad Irfan Uddin Wiyada Kumam Poom Kumam Hussam Alrabaiah Farrukh Jamal Christophe Chesneau Department of Computer Science Concordia College BahawalpurBahawalpur63100Pakistan Department of Computer Science&IT Glim Institute of Modern StudiesBahawalpur63100Pakistan Institute of Numerical Sciences Kohat University of Science&TechnologyKohat26000Pakistan Institute of Computing Kohat University of Science and TechnologyKohat26000Pakistan Program in Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiThanyaburi12110Thailand Departments of Mathematics Faculty of ScienceCenter of Excellence in Theoretical and Computational Science(TaCS-CoE)&KMUTT Fixed Point Research LaboratoryRoom SCL 802 Fixed Point LaboratoryScience Laboratory BuildingKing Mongkut’s University of Technology Thonburi(KMUTT)Bangkok10140Thailand Department of Medical Research China Medical University HospitalTaichung40402Taiwan College of Engineering Al Ain UniversityAl Ain64141United Arab Emirates Department of Mathematics Tafila Technical UniversityTafila66110Jordan Department of Statistics The Islamia University of BahawalpurBahawalpur63100Pakistan 11Department of MathematicsUniversitéde CaenLMNOCaen14032France

The purpose of this research is the segmentation of lungs computed tomography(CT)scan for the diagnosis of COVID-19 by using machine learning *** dataset contains data from patients who are prone to the *** contains three types of lungs CT images(Normal,Pneumonia,and COVID-19)collected from two different sources;the first one is the Radiology Department of Nishtar Hospital Multan and Civil Hospital Bahawalpur,Pakistan,and the second one is a publicly free available medical imaging database known as *** the preprocessing,a novel fuzzy c-mean automated region-growing segmentation approach is deployed to take an automated region of interest(ROIs)and acquire 52 hybrid statistical features for each ***,12 optimized statistical features are selected via the chi-square feature reduction *** the classification,five machine learning classifiers named as deep learning J4,multilayer perceptron,support vector machine,random forest,and naive Bayes are deployed to optimize the hybrid statistical features *** is observed that the deep learning J4 has promising results(sensitivity and specificity:0.987;accuracy:98.67%)among all the deployed *** a complementary study,a statistical work is devoted to the use of a new statistical model to fit the main datasets of COVID-19 collected in Pakistan.

关键词： COVID-19 machine learning fuzzy c-mean deep learning J4

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Positive photoresist process simulation over nonplanar substrates

Journal of Vacuum Science & Technology B: Microelectronics P...

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Journal of Vacuum science & Technology B: Microelectronics Processing and Phenomena 1990年第6期8卷 1432-1436页

作者： Eytan Barouch Brian Bradie Uwe Hollerbach Steven A. Orszag Department of Mathematics and Computer Science Clarkson University Potsdam New York 13676 Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544

A three‐dimensional computational simulator of nonplanar substrates coated with positive photoresists is presented. The model includes four major steps: projection printing, exposure, post‐exposure baking (PEB), and dissolution. Projection printing is based on Hopkins’ classical work. The exposure model employs the full nonlinear wave equation coupled with the photoactive compound (PAC) bleaching rate equation. These equations are solved using a spectral element iterative scheme. The PEB is treated as a material diffusion equation employing ideas introduced by Mack and the dissolution algorithm is our LEAD (least action dissolution) algorithm modified for nonplanar substrates. Several realistic examples are presented displaying final profiles at various dissolution times.

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