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2022 International Conference on computational Science and computational Intelligence, CSCI 2022

作者： Quan Ngoc Nguyen, Dong Dong Tan Le, Phuong Xing, Lin Lin, Lizhen Yanqi Lake Beijing Institute of Mathematical Sciences and Applications Beijing101408 China University of Waterloo Department of Applied Mathematics Waterloo Canada University of Notre Dame Department of Applied and Computational Mathematics and Statistics Notre Dame United States

ISBN: (纸本)9798350320282

Methods for analyzing similarities among DNA sequences play a fundamental role in computational biology, and have a variety of applications in public health, and in the field of genome analysis. In this paper, a novel geometric and topological method for analyzing similarities among DNA sequences is developed, based on persistent homology from algebraic topology, in combination with chaos geometry in 4-dimensional space as a graphical representation of DNA sequences. Our topological framework for DNA similarity analysis is general, alignment-free, and can deal with DNA sequences of various lengths, while proving first-of-the-kind visualization features for visual inspection of DNA sequences directly, based on topological features of point clouds that represent DNA sequences. As an application, we test our methods on three datasets including genome sequences of different types of Hantavirus, Influenza A viruses, and Human Papillomavirus. © 2022 IEEE.

关键词： Geometry

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Mapping the Invisible: Face-GPS for Facial Muscle Dynamics in Videos 1

Mapping the Invisible: Face-GPS for Facial Muscle Dynamics i...

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1st IEEE International Conference on Artificial Intelligence for Medicine, Health and Care, AIMHC 2024

作者： Dong, Zhikang Kim, Juni Polak, Pawel Department of Applied Mathematics and Statistics Stony Brook University New York United States Stanford Online High School Redwood CityCA United States Department of Applied Mathematics and Statistics Institute for Advanced Computational Science Stony Brook University New York United States

ISBN: (纸本)9798350371987

We introduce a novel approach for analyzing facial muscle movement using commonly available video sources, such as smartphone recordings. Our method employs face detection, frame-to-frame tracking, and curvature estimation techniques to quantify the dynamics of local facial muscle movements. An attention-based deep learning network architecture is utilized to generate emotion probability distributions for each video frame. We integrate these probabilities with local kernel smoothing techniques to significantly enhance the precision of muscle movement measurements. Our adaptive kernel method visualizes the facial muscle movements and provides medical professionals with a valuable, interpretable alternative to deep learning models. It also serves as a non-invasive alternative to conventional equipment such as facial electromyography. Our proposed method has applications across various sectors, including neurosurgery, plastic surgery, and remote health monitoring for conditions like stroke, Bell’s palsy, and acoustic neuroma, as well as in emotion detection. ©2024 IEEE.

关键词： Neurosurgery

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Conditional random fields, planted constraint satisfaction and entropy concentration

Conditional random fields, planted constraint satisfaction a...

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16th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2013 and the 17th International Workshop on Randomization and Computation, RANDOM 2013

作者： Abbe, Emmanuel Montanari, Andrea Department of Electrical Engineering Program in Applied and Computational Mathematics Princeton University United States Departments of Electrical Engineering and Statistics Stanford University United States

ISBN: (纸本)9783642403279

This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted constraint satisfaction problems (CSPs), as well as more general structures motivated by coding and community clustering problems. It is shown that under mild assumptions on the kernel and for sparse random graphs, the conditional entropy of the node variables given the edge variables concentrates around a deterministic threshold. This implies in particular the concentration of the number of solutions in a broad class of planted CSPs, the existence of a threshold function for the disassortative stochastic block model, and the proof of a conjecture on parity check codes. It also establishes new connections among coding, clustering and satisfiability. © 2013 Springer-Verlag.

关键词： Entropy

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STUDY OF CRYSTAL GROWTH AND SOLUTE PRECIPITATION THROUGH FRONT TRACKING METHOD

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Acta Mathematica Scientia 2010年第2期30卷 377-390页

作者： Xiaolin Li James Glimmi Xiangmin Jiao Charles Peyser Yanhong Zhao Department of Applied Mathematics and Statistics Stony Brook University Stony Brook NY 11794 USA Computational Science Center Brookhaven National Laboratory Upton NY 11793 USA North Shore Hebrew Academy High School Great Neck NY 11020 USA

Crystal growth and solute precipitation is a Stefan problem. It is a free boundary problem for a parabolic partial differential equation with a time-dependent phase interface. The velocity of the moving interface between solute and crystal is a local function. The dendritic structure of the crystal interface, which develops dynamically, requires high resolution of the interface geometry. These facts make the Lagrangian front tracking method well suited for the problem. In this paper, we introduce an upgraded version of the front tracking code and its associated algorithms for the numerical study of crystal formation. We compare our results with the smoothed particle hydrodynamics method （SPH） in terms of the crystal fractal dimension with its dependence on the Damkohler number and density ratio.

关键词： front tracking crystal formation fractal dimension

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Topological Equatorial Waves and Violation (or not) of the Bulk Edge Correspondence

arXiv

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arXiv 2024年

作者： Bal, Guillaume Yu, Jiming Departments of Statistics and Mathematics Committee on Computational and Applied Mathematics University of Chicago ChicagoIL60637 United States Committee on Computational and Applied Mathematics University of Chicago ChicagoIL60637 United States

Atmospheric and oceanic mass transport near the equator display a well-studied asymmetry characterized by two modes moving eastward. This asymmetric edge transport is characteristic of interfaces separating two-dimensional topological insulators. The northern and southern hemispheres are insulating because of the presence of a Coriolis force parameter that vanishes only in the vicinity of the equator. A central tenet of topological insulators, the bulk edge correspondence, relates the quantized edge asymmetry to bulk properties of the insulating phases, which makes it independent of the Coriolis force profile near the equator. We show that for a natural differential Hamiltonian model of the atmospheric and oceanic transport, the bulk-edge correspondence does not always apply. In fact, an arbitrary quantized asymmetry can be obtained for specific, discontinuous, such profiles. The results are based on a careful analysis of the spectral flow of the branches of absolutely continuous spectrum of a shallow-water Hamiltonian. Numerical simulations validate our theoretical findings. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

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Bright Soliton Solutions in Degenerate Femi Gas near Feshbach Resonance

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Chinese Physics Letters 2009年第12期26卷 39-41页

作者：刘红何岱海楼森岳贺贤土 Logistics School Beijing Wuzi University Beijing 101149 Department of Mathematics and Statistics McMaster University Hamilton Ontario L8S 4K1 Canada Department of Physics Ningbo University Ningbo 315211 Institute of Applied Physics and Computational Mathematics Beijing PO Box 8009 Beijing 100088

For molecular and standard Bose-Einstein condensates and Fermi gases near Feshbach resonances, the general polytropic equation of states is P∝n γ＋1. According to the effective power γ≈0.5~1.3, we resolve the time-dependent nonlinear Schrodinger equation and find series bright solitons. The analysis could help in the search for matter-wave soliton trains in degenerate Femi gas.

关键词： Atomic and molecular physics Quantum gases liquids and solids Statistical physics and nonlinear systems

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Efficiency of single SNP analysis and sequence kernel association test in genome-wide association analysis

Efficiency of single SNP analysis and sequence kernel associ...

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2018 International MultiConference of Engineers and Computer Scientists, IMECS 2018

作者： Sookkhee, Sirikanlaya Fazil Baksh, M. Kirdwichai, Pianpool Department of Applied Statistics Faculty of Applied Science King Mongkut's University of Technology North Bangkok Bangkok10800 Thailand Department of Mathematics and Statistics School of Mathematical Physical and Computational Sciences University of Reading United Kingdom Department of Applied Statistics Faculty of Applied Science King Mongkut's University of Technology North Bangkok Bangkok10800 Thailand

ISBN: (纸本)9789881404787

This research compares the efficiency of the commonly used single SNP analysis and SNP-set analysis based on the recently proposed Sequence Kernel Association Test (SKAT) in the analysis of genome-wide studies of disease-gene association. False positive (FP) and true positive (TP) rates are evaluated for different genetic models of disease with significance thresholds adjusted for multiple testing based on the permutation method. Simulation results shows that although SKAT tends to be slightly more efficient in identifying true associations, this comes at the cost of a substantial increase in the false positive findings over the single SNP method and that this efficiency gain is also highly dependent on choosing an appropriate weight and correlation for the SNP sets in SKAT. © 2018 Newswood Limited. All rights reserved.

关键词： Efficiency

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Algorithmic stability implies training-conditional coverage for distribution-free prediction methods

arXiv

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arXiv 2023年

作者： Liang, Ruiting Barber, Rina Foygel Committee on Computational and Applied Mathematics University of Chicago United States Department of Statistics University of Chicago United States

In a supervised learning problem, given a predicted value that is the output of some trained model, how can we quantify our uncertainty around this prediction? Distribution-free predictive inference aims to construct prediction intervals around this output, with valid coverage that does not rely on assumptions on the distribution of the data or the nature of the model training algorithm. Existing methods in this area, including conformal prediction and jackknife+, offer theoretical guarantees that hold marginally (i.e., on average over a draw of training and test data). In contrast, training-conditional coverage is a stronger notion of validity that ensures predictive coverage of the test point for most draws of the training data, and is thus a more desirable property in practice. Training-conditional coverage was shown by Vovk [2012] to hold for the split conformal method, but recent work by Bian and Barber [2023] proves that such validity guarantees are not possible for the full conformal and jackknife+ methods without further assumptions. In this paper, we show that an assumption of algorithmic stability ensures that the training-conditional coverage property holds for the full conformal and jackknife+ methods. Copyright © 2023, The Authors. All rights reserved.

关键词： Forecasting

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Batched Nonparametric Contextual Bandits

arXiv

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arXiv 2024年

作者： Jiang, Rong Ma, Cong Committee on Computational and Applied Mathematics University of Chicago United States Department of Statistics University of Chicago United States

We study nonparametric contextual bandits under batch constraints, where the expected reward for each action is modeled as a smooth function of covariates, and the policy updates are made at the end of each batch of observations. We establish a minimax regret lower bound for this setting and propose a novel batch learning algorithm that achieves the optimal regret (up to logarithmic factors). In essence, our procedure dynamically splits the covariate space into smaller bins, carefully aligning their widths with the batch size. Our theoretical results suggest that for nonparametric contextual bandits, a nearly constant number of policy updates can attain optimal regret in the fully online setting. © 2024, CC BY.

关键词： Optimization

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Curve cognate constructions made easy

Curve cognate constructions made easy

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ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020

作者： Sherman, Samantha N. Hauenstein, Jonathan D. Wampler, Charles W. Department of Applied and Computational Mathematics and Statistics Co University of Notre Dame Notre Dame Indiana46556 United States nal Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre Dame Indiana46556 United States Chemical and Materials System Lab General Motors Global R&D Warren Michigan48092 United States

ISBN: (纸本)9780791883990

Cognate linkages are mechanisms that share the same motion, a property that can be useful in mechanical design. This paper treats planar curve cognates, that is, planar mechanisms whose tracing point draws the same curve. While Roberts cognates for planar four-bars are relatively simple to understand from a geometric drawing, the same cannot be said for planar six-bar cognates, especially the intricate diagrams Dijksman presented in cataloging all the known six-bar curve cognates. The purpose of this article is to show how the six-bar cognates can be easily understood using kinematic equations written using complex vectors, giving a simple method for generating these cognates as alternatives in a mechanical design. The simplicity of the approach enables the derivation of cognates for eight-bars and possibly beyond. Copyright © 2020 ASME.

关键词： Equations of motion Design engineering Linkages

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