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arXiv 2024年

作者： Ruzayqat, Hamza Knio, Omar Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

This paper presents a new data assimilation (DA) scheme based on a sequential Markov Chain Monte Carlo (SMCMC) DA technique [36] which is provably convergent and has been recently used for filtering, particularly for high-dimensional non-linear, and potentially, non-Gaussian state-space models. Unlike particle filters, which can be considered exact methods and can be used for filtering non-linear, non-Gaussian models, SMCMC does not assign weights to the samples/particles, and therefore, the method does not suffer from the issue of weight-degeneracy when a relatively small number of samples is used. We design a localization approach within the SMCMC framework that focuses on regions where observations are located and restricts the transition densities included in the filtering distribution of the state to these regions. This results in immensely reducing the effective degrees of freedom and thus improving the efficiency. We test the new technique on high-dimensional (d ∼ 104 − 105) linear Gaussian model and non-linear shallow water models with Gaussian noise with real and synthetic observations. For two of the numerical examples, the observations mimic the data generated by the Surface Water and Ocean Topography (SWOT) mission led by NASA, which is a swath of ocean height observations that changes location at every assimilation time step. We also use a set of ocean drifters' real observations in which the drifters are moving according the ocean kinematics and assumed to have uncertain locations at the time of assimilation. We show that when higher accuracy is required, the proposed algorithm is superior in terms of efficiency and accuracy over competing ensemble methods and the original SMCMC *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2024, CC BY.

关键词： Markov chains

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SURREAL-GAN:SEMI-SUPERVISED REPRESENTATION LEARNING VIA GAN FOR UNCOVERING HETEROGENEOUS DISEASE-RELATED IMAGING PATTERNS

arXiv

引用

arXiv 2022年

作者： Yang, Zhijian Wen, Junhao Davatzikos, Christos Center for Biomedical Image Computing and Analytics University of Pennsylvania United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States

A plethora of machine learning methods have been applied to imaging data, enabling the construction of clinically relevant imaging signatures of neurological and neuropsychiatric diseases. Oftentimes, such methods do not explicitly model the heterogeneity of disease effects, or approach it via nonlinear models that are not interpretable. Moreover, unsupervised methods may parse heterogeneity that is driven by nuisance confounding factors that affect global brain structure or function, rather than heterogeneity relevant to a pathology of interest. On the other hand, semi-supervised clustering methods seek to derive a pathology-related dichotomous subtypes, ignoring the truth that disease heterogeneity spatially and temporally extends along a continuum. To address the aforementioned limitations, herein, we propose a novel method, termed Surreal-GAN (Semi-SUpeRvised ReprEsentAtion Learning via GAN). Using cross-sectional imaging data, Surreal-GAN dissects underlying disease-related heterogeneity under the principle of semi-supervised clustering [cluster mappings from the normal control (CN) to patient (PT) domain], proposes a continuously dimensional representation, and infers the disease severity of patients at individual level along each dimension. The model first learns a transformation function from the CN domain to the PT domain with latent variables controlling transformation directions. An inverse mapping function together with regularization on function continuity, pattern orthogonality and monotonicity was also imposed to make sure that the transformation function captures necessarily meaningful imaging patterns with clinical significance. We first validated the model through semi-synthetic experiments, and then demonstrated its potential in capturing biologically plausible imaging patterns in Alzheimer's disease (AD). © 2022, CC BY.

关键词： Pathology

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Risk-Aware Stochastic Control of a Sailboat

Risk-Aware Stochastic Control of a Sailboat

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American Control Conference (ACC)

作者： MingYi Wang Natasha Patnaik Anne Somalwar Jingyi Wu Alexander Vladimirsky The Center for Applied Mathematics Cornell University Ithaca NY USA The Department of Computational Applied Mathematics and Operations Research Rice University Houston TX USA The graduate group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA USA The Center for Data Science New York University New York City NY USA Department of Mathematics Cornell University Ithaca NY USA

ISBN: (数字)9798350382655

ISBN: (纸本)9798350382662

Sailboat path-planning is a natural hybrid control problem (due to continuous steering and occasional “tack-switching” maneuvers), with the actual path-to-target greatly affected by stochastically evolving wind conditions. Previous studies have focused on finding risk-neutral policies that minimize the expected time of arrival. In contrast, we present a robust control approach, which maximizes the probability of arriving before a specified deadline/threshold. Our numerical method recovers the optimal risk-aware (and threshold-specific) policies for all initial sailboat positions and a broad range of thresholds simultaneously. This is accomplished by solving two quasi-variational inequalities based on second-order Hamilton-Jacobi-Bellman (HJB) PDEs with degenerate parabolicity. Monte-Carlo simulations show that risk-awareness in sailing is particularly useful when a carefully calculated bet on the evolving wind direction might yield a reduction in the number of tack-switches.

关键词： Robust control Geometry Monte Carlo methods Shape Stochastic processes Boats Differential games

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WONDER: Weighted one-shot distributed ridge regression in high dimensions

arXiv

引用

arXiv 2019年

作者： Dobriban, Edgar Sheng, Yue Wharton Statistics Department University of Pennsylvania 3730Walnut Street PhiladelphiaPA United States Graduate Group in Applied Mathematics and Computational Science Department of Mathematics University of Pennsylvania

In many areas, practitioners need to analyze large datasets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental and highly important problem in this area: How to do ridge regression in a distributed computing environment? Ridge regression is an extremely popular method for supervised learning, and has several optimality properties, thus it is important to study. We study one-shot methods that construct weighted combinations of ridge regression estimators computed on each machine. By analyzing the mean squared error in a high dimensional random-effects model where each predictor has a small effect, we discover several new phenomena. Infinite-worker limit: The distributed estimator works well for very large numbers of machines, a phenomenon we call "infinite-worker limit". Optimal weights: The optimal weights for combining local estimators sum to more than unity, due to the downward bias of ridge. Thus, all averaging methods are suboptimal. We also propose a new Weighted ONe-shot DistributEd Ridge regression (WONDER) algorithm. We test WONDER in simulation studies and using the Million Song Dataset as an example. There it can save at least 100x in computation time, while nearly preserving test accuracy. Copyright © 2019, The Authors. All rights reserved.

关键词： Regression analysis

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Antithetic Multilevel Particle Filters

arXiv

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arXiv 2023年

作者： Jasra, Ajay Maama, Mohamed Ombao, Hernando Applied Mathematics and Computational Science Program United States Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon time-discretization of the diffusion process and then the application of particle filters. Perhaps the state-of-the-art method for moderate dimensional problems is the multilevel particle filter of [12]. This is a method that combines multilevel Monte Carlo and particle filters. The approach in that article is based intrinsically upon an Euler discretization method. We develop a new particle filter based upon the antithetic truncated Milstein scheme of [10]. We show that for a class of diffusion problems, for ϵ > 0 given, that the cost to produce a mean square error (MSE) in estimation of the filter, of O(ϵ2) is O(ϵ−2 log(ϵ)2). In the case of multidimensional diffusions with non-constant diffusion coefficient, the method of [12] has a cost of O(ϵ−2.5) to achieve the same MSE. We support our theory with numerical results in several examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean square error

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Noise-like pulse generation from a thulium-doped fiber laser using nonlinear polarization rotation with different net anomalous dispersion

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Photonics Research 2016年第6期4卷 318-321页

作者： Shuo Liu Fengping Yan Yang Li Luna Zhang Zhuoya Bai Hong Zhou Yafei Hou Key Laboratory of All Optical Network & Advanced Telecommunication of EMC Institute of Lightwave TechnologyBeijing Jiaotong University Institute of Applied Physics and Computational Mathematics Department of Electronics Information and Communication Engineering Osaka Institute of Technology Graduate School of Information Science Nara Institute of Science and Technology

A mode-locked thulium-doped fiber laser(TDFL) based on nonlinear polarization rotation(NPR) with different net anomalous dispersion is demonstrated. When the cavity dispersion is-1.425 ps^2, the noise-like(NL) pulse with coherence spike width of 406 fs and pulse energy of 12.342 nJ is generated at a center wavelength of 2003.2 nm with 3 dB spectral bandwidth of 23.20 nm. In the experimental period of 400 min, the 3 dB spectral bandwidth variation, the output power fluctuation, and the central wavelength shift are less than 0.06 nm, 0.04 d B, and0.4 nm, respectively, indicating that the NPR-based TDFL operating in the NL regime holds good long-term stability.

关键词： NPR net Noise-like pulse generation from a thulium-doped fiber laser using nonlinear polarization rotation with different net anomalous dispersion mode

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TWO-SAMPLE TEST OF COMMUNITY MEMBERSHIPS OF WEIGHTED STOCHASTIC BLOCK MODELS

arXiv

引用

arXiv 2018年

作者： Li, Yezheng Li, Hongzhe Program in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States University of Pennsylvania PhiladelphiaPA19104 United States

Suppose two networks are observed for the same set of nodes, where each network is assumed to be generated from a weighted stochastic block model. This paper considers the problem of testing whether the community memberships of the two networks are the same. A test statistic based on singular subspace distance is developed. Under the weighted stochastic block models with dense graphs, the limiting distribution of the proposed test statistic is developed. Simulation results show that the test has correct empirical type 1 errors under the dense graphs. The test also behaves as expected in empirical power, showing gradual changes when the intra-block and inter-block distributions are close and achieving 1 when the two distributions are not so close, where the closeness of the two distributions is characterized by Renyi divergence of order 1/2. The Enron email networks are used to demonstrate the proposed *** Codes 62E20, 62F03, 62H15, 91D30, 62F05 Copyright © 2018, The Authors. All rights reserved.

关键词： Clustering algorithms

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Cloaking the underlying long-range order of randomly perturbed lattices

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Physical Review E 2020年第3期101卷 032118-032118页

作者： Michael A. Klatt Jaeuk Kim Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a diffuse contribution, the scattering intensity from the the resulting point pattern typically inherits the Bragg peaks (long-range order) of the original lattice. Here we demonstrate how these Bragg peaks can be hidden in the effective diffraction pattern of independent and identically distributed perturbations. All Bragg peaks vanish if and only if the sum of all probability densities of the positions of the shifted lattice points is a constant at all positions. The underlying long-range order is then “cloaked” in the sense that it cannot be reconstructed from the pair correlation function alone. On the one hand, density fluctuations increase monotonically with the strength of perturbations a, as measured by the hyperuniformity order metric Λ¯. On the other hand, the disappearance and reemergence of long-range order, depending on whether the system is cloaked as the perturbation strength increases, is manifestly captured by the τ order metric. Therefore, while the perturbation strength a may seem to be a natural choice for an order metric of perturbed lattices, the τ order metric is a superior choice. It is noteworthy that cloaked perturbed lattices allow one to easily simulate very large samples (with at least 106 particles) of disordered hyperuniform point patterns without Bragg peaks.

关键词： Classical statistical mechanics

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An Efficient Three-Factor Authenticated Key Agreement Technique Using FCM Under HC-IoT Architectures

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Computers, Materials & Continua 2022年第7期72卷 1373-1389页

作者： Chandrashekhar Meshram Agbotiname Lucky Imoize Sajjad Shaukat Jamal Parkash Tambare Adel R.Alharbi Iqtadar Hussain Department of Post Graduate Studies and Research in Mathematics Jayawanti Haksar Government Post-Graduation CollegeCollege of Chhindwara UniversityBetul460001M.P.India Department of Electrical and Electronics Engineering Faculty of EngineeringUniversity of LagosAkokaLagos100213Nigeria Department of Electrical Engineering and Information Technology Institute of Digital CommunicationRuhr University44801BochumGermany Department of Mathematics College of ScienceKing Khalid UniversityAbhaSaudi Arabia Water Resources&Applied Mathematics Research Lab Nagpur440027India College of Computing and Information Technology University of TabukTabuk71491Saudi Arabia Mathematics Program Department of MathematicsStatistics and PhysicsCollege of Arts and SciencesQatar University2713DohaQatar

The Human-Centered Internet of Things(HC-IoT)is fast becoming a hotbed of security and privacy *** users can establish a common session key through a trusted server over an open communication channel using a three-party authenticated key *** of the early authenticated key agreement systems relied on pairing,hashing,or modular exponentiation processes that are computationally intensive and *** order to address this problem,this paper offers a new three-party authenticated key agreement technique based on fractional chaotic *** new scheme uses fractional chaotic maps and supports the dynamic sensing of HC-IoT devices in the network architecture without a password *** projected security scheme utilized a hash function,which works well for the resource-limited HC-IoT *** results show that our new technique is resistant to password guessing attacks since it does not use a ***,our approach provides users with comprehensive privacy protection,ensuring that a user forgery attack causes no ***,our new technique offers better security features than the techniques currently available in the literature.

关键词： Three-party authenticated key agreement anonymity fractional chaotic maps Chebyshev polynomial password table human-centered internet of things(HC-IoT)

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BPS2025 - Structural basis of potassium selectivity in kalium channelrhodopsins

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Biophysical Journal 2025年第3期124卷 64a-65a页

作者： Seiya Tajima Yoon Seok Kim YoungJu Jo Peter Y. Wang Joseph M. Paggi Charu Ramakrishnan Shunki Takaramoto Takashi Nagata Masae Konno Kota Katayama Hideki Kandori Ron O. Dror Keiichi Inoue Karl Deisseroth Hideaki Kato Research Center for Advanced Science and Technology The University of Tokyo Tokyo Japan Department of Bioengineering Stanford University Stanford CA USA Department of Computer Science Stanford University Stanford CA USA Cracking the Neural Code Program Stanford University Stanford CA USA The Institute for Solid State Physics The University of Tokyo Kashiwa Japan PRESTO Japan Science and Technology Agency Kawaguchi Japan Department of Life Science and Applied Chemistry Nagoya Institute of Technology Nagoya Japan OptoBioTechnology Research Center Nagoya Institute of Technology Nagoya Japan Institute for Computational and Mathematical Engineering Stanford University Stanford CA USA Howard Hughes Medical Institute Stanford University Stanford CA USA Graduate School of Arts and Sciences The University of Tokyo Tokyo Japan

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