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A Bayesian mixture model for clustering on the stiefel manifold

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arXiv 2017年

作者： Sengupta, Subhajit Pal, Subhadip Mitra, Riten Guo, Ying Banerjee, Arunava Ji, Yuan Program for Computational Genomics and Medicine NorthShore University HealthSystem Department of Bioinformatics and Biostatistics University of Louisville Department of Biostatistics and Bioinformatics Emory University Department of Computer and Information Science and Engineering University of Florida Department of Public Health Sciences University of Chicago

Analysis of a Bayesian mixture model for the Matrix Langevin distribution on the Stiefel manifold is presented. The model exploits a particular parametrization of the Matrix Langevin distribution, various aspects of which are elaborated on. A general, and novel, family of conjugate priors, and an efficient Markov chain Monte Carlo (MCMC) sampling scheme for the corresponding posteriors is then developed for the mixture model. Theoretical properties of the prior and posterior distributions, including posterior consistency, are explored in detail. Extensive simulation experiments are presented to validate the efficacy of the framework. Real-world examples, including a large scale neuroimaging dataset, are analyzed to demonstrate the computational tractability of the approach. Copyright © 2017, The Authors. All rights reserved.

关键词： Mixtures

To Trust or Not to Trust: Evolutionary Dynamics of an Asymmetric N-player Trust Game

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arXiv 2023年

作者： Soo Lim, Ik. Masuda, Naoki School of Computing and Mathematical Sciences University of Greenwich LondonSE10 9LS United Kingdom Department of Mathematics and Computational and Data-Enabled Science and Engineering Program State University of New York Buffalo United States

Trusting others and reciprocating the received trust with trustworthy actions are fundaments of economic and social interactions. The trust game (TG) is widely used for studying trust and trustworthiness and entails a sequential interaction between two players, an investor and a trustee. It requires at least two strategies or options for an investor (e.g. to trust versus not to trust a trustee). According to the evolutionary game theory, the antisocial strategies (e.g. not to trust) evolve such that the investor and trustee end up with lower payoffs than those that they would get with the prosocial strategies (e.g. to trust). A generalisation of the TG to a multiplayer (i.e. more than two players) TG was recently proposed. However, its outcomes hinge upon two assumptions that various real situations may substantially deviate from: (i) investors are forced to trust trustees and (ii) investors can turn into trustees by imitation and vice versa. We propose an asymmetric multiplayer TG that allows investors not to trust and prohibits the imitation between players of different roles;instead, investors learn from other investors and the same for trustees. We show that the evolutionary game dynamics of the proposed TG qualitatively depends on the nonlinearity of the payoff function and the amount of incentives collected from and distributed to players through an institution. We also show that incentives given to trustees can be useful and sufficient to cost-effectively promote trust and trustworthiness among self-interested players. © 2023, CC BY.

关键词： Dynamics

A Multi-phase Deep Learning Approach for Predicting HCC Response to TACE using Complete Computed Tomography

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A Multi-phase Deep Learning Approach for Predicting HCC Resp...

Data science and engineering in Healthcare, Medicine and Biology, IEEE EMBS Special Topic Conference on

作者： Shun Cheng Chang Chien Fu Liu Marta Misztal Yi Hsien Hsieh Che Lin Graduate Institute of Communication Engineering National Taiwan University (NTU) Taiwan School of Electronic Engineering and Computer Science Queen Mary University of London UK Department of Electrical Engineering NTU Taiwan Center for Computational and Systems Biology and Center for Biotechnology NTU Taiwan Smart Medicine and Health Informatics Program NTU Taiwan

In this research study, we compare the predictive performance of two advanced deep learning-based models in order to provide a solution to TACE (Transarterial Chemoembolization) response prediction in HCC (Hepatocellular Carcinoma) patients. Using entire abdominal CT scans enabled a broader perspective available for the model, eliminating the need for segmentation during the preprocessing. Making use of both single-phase and multi-phase CT imaging, we have used DenseNet121 and have obtained an accuracy of 80% for the multi-phase *** Relevance: The ability to predict the effectiveness of TACE treatment prior to its administration makes it possible to provide a better decision-making aid for physicians and patients.

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Secure state estimation and control for cyber security of AC microgirds

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arXiv 2019年

作者： Fooladivanda, Dariush Hu, Qie Chang, Young Hwan Sauer, Peter W. Department of Mechanical and Aerospace Engineering University of California San Diego United States Department of Electrical Engineering and Computer Sciences University of California Berkeley United States Department of Biomedical Engineering and Computational Biology Program Oregon Health and Science University United States Department of Electrical and Computer Engineering University of Illinois Urbana-Champaign United States

A timely, accurate, and secure dynamic state estimation is needed for reliable monitoring and efficient control of microgrids. The synchrophasor technology enables us to obtain synchronized measurements in real-time and to develop dynamic state estimators for real-time monitoring and control of microgrids. In this study, we consider an AC microgrid comprising several synchronous generators and inverter-interface power supplies, and focus on securely estimating the dynamic states of the microgrid from a set of corrupted data. We propose a dynamic state estimator which enables the microgrid operator to reconstruct the dynamic states of the microgrid from a set of corrupted data. Finally, we consider an AC microgrid with the same topology as the IEEE 33-bus distribution system, and numerically show that the proposed secure estimation algorithm can accurately reconstruct the attack signals. Copyright © 2019, The Authors. All rights reserved.

关键词： State estimation

Parameter Estimation for Partially Observed McKean-Vlasov Diffusions

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arXiv 2024年

作者： Jasra, Ajay Maama, Mohamed Tempone, Raul School of Data Science The Chinese University of Hong Kong CN Shenzhen China 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 Chair of Mathematics for Uncertainty Quantification RWTH Aachen University Aachen52062 Germany

In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the framework of [5] we develop a new randomized multilevel Monte Carlo method for estimating the parameters, based upon Markovian stochastic approximation methodology. New Markov chain Monte Carlo algorithms for the POMV model are introduced facilitating the application of [5]. We prove, under assumptions, that the expectation of our estimator is biased, but with expected small and controllable bias. Our approach is implemented on several examples. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

Gillespie algorithms for stochastic multiagent dynamics in populations and networks

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arXiv 2021年

作者： Masuda, Naoki Vestergaard, Christian L. Department of Mathematics State University of New York at Buffalo NY United States Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo NY United States Decision and Bayesian Computation Department of Neuroscience Cnrs Umr 3571 Department of Computational Biology Cnrs Usr 3756 Institut Pasteur Paris France

Many multiagent dynamics, including various collective dynamics occurring on networks, can be modeled as a stochastic process in which the agents in the system change their state over time in interaction with each other. The Gillespie algorithms are popular algorithms that exactly simulate such stochastic multiagent dynamics when each state change is driven by a discrete event, the dynamics is defined in continuous time, and the stochastic law of event occurrence is governed by independent Poisson processes. In the first main part of this volume, we provide a tutorial on the Gillespie algorithms focusing on simulation of social multiagent dynamics occurring in populations and networks. We do not assume advanced knowledge of mathematics (or computer science or physics). We clarify why one should use the continuous-time models and the Gillespie algorithms in many cases, instead of easier-to-understand discrete-time models. In the remainder of this volume, we review recent extensions of the Gillespie algorithms aiming to add more reality to the model (i.e., non-Poissonian cases) or to speed up the simulations. © 2021, CC BY.

关键词： Stochastic systems

Numerical Study of the Effective Combination of Microbubbles and Ultrasound in HIFU Therapy

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AIP Conference Proceedings 2011年第1期1359卷 437-442页

作者： Kohei Okita Kazuyasu Sugiyama Kenji Ono Shu Takagi Yoichiro Matsumoto aFunctionality Simulation and Information Team VCAD System Research Program RIKEN 2‐1 Hirosawa Wako Saitama 351‐0198 Japan bDepartment of Mechanical Engineering The University of Tokyo 7‐3‐1 Hongo Bunkyo Tokyo 113‐8656 Japan cOrgan and Body Scale Simulation Team Computational Science Research Program RIKEN 2‐1 Hirosawa Wako Saitama 351‐0198 Japan

The effective combination of microbubbles and ultrasound in HIFU therapy has been investigated through a numerical simulation. The equations for conservation of mass, momentum and energy are solved for a microbubble‐infused mixture, and model HIFU therapy in the presence of microbubbles. The bubbles follow Rayleigh‐Plesset equation, and are coupled with the mixture using the Euler‐Lagrange method. The impacts of both the volume fraction due to the microbubbles and the amplitude of the ultrasound on the heat distribution are analyzed by using a two dimensional cylindrical simulation of the propagation of focused ultrasound (1 MHz) through a mixture of bubbles 1.3 μm in diameter. As the initial void fraction increased, the shape of the high temperature region was observed to change from cigar shape, to tadpole shaped, to cone shape. It was numerically confirmed that the temperature dramatically increased by means of inertial cavitation. The results show that the effectiveness of HIFU therapy increases with increased initial void fraction, as well as an input ultrasound amplitude above the threshold required for inertial cavitation.

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CONVERGENCE SPEED AND APPROXIMATION ACCURACY OF NUMERICAL MCMC

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arXiv 2022年

作者： Cui, Tiangang Dong, Jing Jasra, Ajay Tong, Xin T. School of Mathematics Monash University Australia Graduate School of Business Columbia University United States Applied Mathematics and Computational Science Program Computer Electrical Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Mathematics National University of Singapore Singapore

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has similar convergence speed and high approximation accuracy as well. We discuss two different analysis frameworks: ergodicity and spectral gap, both are widely used in the literature. Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators. We also demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis and Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally we present some simple numerical examples to verify our theoretical claims. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

A multi-protease, multi-dissociation, bottom-up-to-top-down proteomic view of the Loxosceles intermedia venom

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Scientific Data 2017年第1期4卷 170090-170096页

作者： Trevisan-Silva, Dilza Bednaski, Aline V. Fischer, Juliana S.G. Veiga, Silvio S. Bandeira, Nuno Guthals, Adrian Marchini, Fabricio K. Leprevost, Felipe V. Barbosa, Valmir C. Senff-Ribeiro, Andrea Carvalho, Paulo C. Department of Cell Biology Federal University of Paraná Curitiba 81531-980 Brazil Computational Mass Spectrometry and Proteomics Group Carlos Chagas Institute Fiocruz Curitiba 81.350-010 Brazil Center for Computational Mass Spectrometry University of California San Diego 92093-0404 United States Functional Genomics Laboratory Carlos Chagas Institute Fiocruz Curitiba 81.350-010 Brazil Mass Spectrometry Facility RPT02H Carlos Chagas Institute Fiocruz Curitiba 81.350-010 Brazil Systems Engineering and Computer Science Program COPPE Federal University of Rio de Janeiro Rio de Janeiro 21941-914 Brazil Laboratory of Toxinology Fiocruz Rio de Janeiro 21040-900 Brazil

Venoms are a rich source for the discovery of molecules with biotechnological applications, but their analysis is challenging even for state-of-the-art proteomics. Here we report on a large-scale proteomic assessment of the venom of Loxosceles intermedia, the so-called brown spider. Venom was extracted from 200 spiders and fractioned into two aliquots relative to a 10 kDa cutoff mass. Each of these was further fractioned and digested with trypsin (4 h), trypsin (18 h), pepsin (18 h), and chymotrypsin (18 h), then analyzed by MudPIT on an LTQ-Orbitrap XL ETD mass spectrometer fragmenting precursors by CID, HCD, and ETD. Aliquots of undigested samples were also analyzed. Our experimental design allowed us to apply spectral networks, thus enabling us to obtain meta-contig assemblies, and consequently de novo sequencing of practically complete proteins, culminating in a deep proteome assessment of the venom. Data are available via ProteomeXchange, with identifier PXD005523.

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