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History of a stochastic growth model

6th International Workshop on Digital Image Processing and Computer Graphics (DIP-97) - Applications in Humanities and Natural Sciences

作者： Eden, M Thevenaz, P NIH Off Res Serv Bethesda MD 20892 USA

ISBN: (纸本)0819427934

One of the earliest models of stochastic growth was originally developed for simulating the appearance of various biological patterns;in particular, bacterial colonies. Although it received little attention from biologists, some twenty years later it was adopted by crystallographers, solid state researchers, other physicists and chemists. Because of the model's flexibility it is being used by them after modifications appropriate to the application, in order to simulate their physical study objects under a variety of conditions. Only within the last few years has there been any interest in using this and similar digital models to represent the possible products of biological processes. It is also worth noting that aside from its relevance to probabilistically influenced pattern formation, the model has possible use in image processing for image compression and as an information-lossless way to code, regions, contours, or line segments.

关键词： stochastic algorithms discrete growth processes information-lossless image coding Eden model

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Brief Announcement: A Local stochastic Algorithm for Separation in Heterogeneous Self-Organizing Particle Systems 18

Brief Announcement: A Local Stochastic Algorithm for Separat...

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37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC)

作者： Cannon, Sarah Daymude, Joshua J. Gokmen, Cem Randall, Dana Richa, Andrea W. Georgia Inst Technol Atlanta GA 30332 USA Arizona State Univ Tempe AZ USA

ISBN: (纸本)9781450357951

We investigate stochastic, distributed algorithms that can accomplish separation and integration behaviors in self-organizing particle systems, an abstraction of programmable matter. These particle systems are composed of individual computational units known as particles that have limited memory, strictly local communication abilities, and modest computational power, and which collectively solve system-wide problems of movement and coordination. In this work, we extend the usual notion of a particle system to treat heterogeneous systems by considering particles of different colors. We present a fully distributed, asynchronous, stochastic algorithm for separation, where the particle system self-organizes into segregated color classes using only local information about each particle's preference for being near others of the same color. Conversely, by simply changing the particles' preferences, the color classes become well-integrated. We rigorously analyze the convergence of our distributed, stochastic algorithm and prove that under certain conditions separation occurs. We also present simulations demonstrating our algorithm achieves both separation and integration.

关键词： Programmable matter self-organization separation distributed algorithms stochastic algorithms

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stochastic BIAS-ACCELERATED SUBSET SELECTION ALGORITHM FOR JOINT LEARNING OF SAMPLING PATTERN AND RECONSTRUCTION IN ACCELERATED MRI 20

STOCHASTIC BIAS-ACCELERATED SUBSET SELECTION ALGORITHM FOR J...

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20th IEEE International Symposium on Biomedical Imaging (ISBI)

作者： Zibetti, Marcelo V. W. Regatte, Ravinder R. NYU Grossman Sch Med New York NY 10003 USA

ISBN: (纸本)9781665473583

This work proposes and illustrates a stochastic version of the bias-accelerated subset selection (BASS) algorithm used to learn the sampling pattern (SP) in accelerated Cartesian MRI problems. Recently, BASS was combined with ADAM for joint learning of the SP and deep learning reconstruction. However, BASS originally uses all the data in each iteration, taking a long processing time when the training dataset is large. Here, we illustrate that BASS is also very stable when only a small fraction of the dataset is used at each iteration. This version, called stochastic BASS (SBASS), can substantially reduce the SP training time for large datasets, obtaining similar quality measurements of the learned pair of SP and reconstruction.

关键词： MRI learning deep learning sampling pattern stochastic algorithms

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stochastic, analytic and numerical aspects of coagulation processes

Stochastic, analytic and numerical aspects of coagulation pr...

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3rd IMACS Seminar on Monte Carlo Methods (MCM 2001)

作者： Wagner, W Weierstrass Inst Appl Anal & Stochast D-10117 Berlin Germany

In this paper, we review recent results concerning stochastic models for coagulation processes and their relationship to deterministic equations. Open problems related to the gelation effect are discussed. Finally, we present some new conjectures based on numerical experiments performed with stochastic algorithms. (C) 2003 IMACS. Published by Elsevier Science B.V. All rights reserved.

关键词： coagulation gelation effect stochastic algorithms

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stochastic techniques for global optimization: A survey of recent advances

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Journal of Global Optimization 1991年第3期1卷 207-228页

作者： Schoen, Fabio Dept. Information Sciences University of Milano Milano I-20133 via Moretto da Brescia 9 Italy

In this paper stochastic algorithms for global optimization are reviewed. After a brief introduction on random-search techniques, a more detailed analysis is carried out on the application of simulated annealing to continuous global optimization. The aim of such an analysis is mainly that of presenting recent papers on the subject, which have received only scarce attention in the most recent published surveys. Finally a very brief presentation of clustering techniques is given. © 1991 Kluwer Academic Publishers.

关键词： clustering simulated annealing stochastic algorithms

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stochastic ANALYSIS OF THE LMS ALGORITHM FOR NON-STATIONARY WHITE GAUSSIAN INPUTS

STOCHASTIC ANALYSIS OF THE LMS ALGORITHM FOR NON-STATIONARY ...

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IEEE Statistical Signal Processing Workshop (SSP)

作者： Bershad, Neil J. Bermudez, Jose C. M. Univ Calif Irvine Dept Elect Eng & Comp Sci Irvine CA 92717 USA Univ Fed Santa Catarina Dept Elect Engn BR-88040900 Florianopolis SC Brazil

ISBN: (纸本)9781457705700

This paper studies the stochastic behavior of the LMS algorithm for a system identification framework when the input signal is a non-stationary white Gaussian process. The unknown system is modeled by the standard random walk model. An approximate theory is developed which is based upon the instantaneous average power in the adaptive filter taps. The stability of the algorithm is investigated using this model. Monte Carlo simulations of the algorithm provides strong support for the theoretical approximation.

关键词： Adaptive filters Analysis LMS Algorithm stochastic algorithms

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stochastic QUANTUM INFORMATION PROCESSING, WITH APPLICATIONS TO BLIND QUANTUM SYSTEM IDENTIFICATION AND SOURCE SEPARATION 28

STOCHASTIC QUANTUM INFORMATION PROCESSING, WITH APPLICATIONS...

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IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP)

作者： Deville, Y. Deville, A. Univ Toulouse UPS CNRS CNESOMPIRAP F-31400 Toulouse France Aix Marseille Univ IM2NP CNRS UMR 7334 F-13397 Marseille France

ISBN: (纸本)9781538654774

Many methods for processing classical or quantum data are based on estimating some parameters, e.g. those of adaptive filters, artificial neural networks (including deep learning approaches), blind source separation systems or quantum gates. For classical signals, these methods include stochastic algorithms, such as stochastic gradient descent. We here first introduce a partly related, general, type of stochastic algorithms for quantum data and we prove the asymptotic efficiency of the proposed estimator. We then show the attractiveness of this stochastic approach for the quantum version of blind multiple-input multiple-output system identification and blind source separation: the resulting model estimation methods can operate with a single copy of each considered quantum state, whereas the previous methods require many copies of the same (unknown) states to be available and are thus "less blind". Numerical tests show that good performance is obtained with 10(4) such quantum states.

关键词： stochastic algorithms blind adaptation blind MIMO system identification / process tomography and inversion blind source separation quantum information processing

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Asynchronous stochastic Convex Optimization over Random Networks: Error Bounds

Asynchronous Stochastic Convex Optimization over Random Netw...

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Information Theory and Applications Workshop (ITA)

作者： Touri, B. Nedic, A. Ram, S. Sundhar Univ Illinois IESE Dept Urbana IL 61801 USA Univ Illinois ECE Dept Urbana IL 61801 USA

ISBN: (纸本)9781424470143

We consider a distributed multi-agent network system where the goal is to minimize the sum of convex functions, each of which is known (with stochastic errors) to a specific network agent. We are interested in asynchronous algorithms for solving the problem over a connected network where the communications among the agent are random. At each time, a random set of agents communicate and update their information. When updating, an agent uses the (sub) gradient of its individual objective function and its own stepsize value. The algorithm is completely asynchronous as it neither requires the coordination of agent actions nor the coordination of the stepsize values. We investigate the asymptotic error bounds of the algorithm with a constant stepsize for strongly convex and just convex functions. Our error bounds capture the effects of agent stepsize choices and the structure of the agent connectivity graph. The error bound scales at best as m in the number m of agents when the agent objective functions are strongly convex.

关键词： convex optimization networked system stochastic algorithms asynchronous algorithms random consensus

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stochastic Methods for Solving High-Dimensional Partial Differential Equations 13th

Stochastic Methods for Solving High-Dimensional Partial Diff...

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13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC)

作者： Billaud-Friess, Marie Macherey, Arthur Nouy, Anthony Prieur, Clementine Cent Nantes LMJL UMR CNRS 6629 1 Rue Noe F-44321 Nantes France Univ Grenoble Alpes INRIA CNRS Grenoble INP Inst EngnLJK F-38000 Grenoble France

ISBN: (纸本)9783030434656;9783030434649

We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Two different algorithms are proposed, combining in different ways the sequential control variates algorithm and adaptive sparse interpolation. Numerical examples will illustrate the behavior of these algorithms.

关键词： stochastic algorithms High dimensional PDEs Adaptive sparse interpolation

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Discretization of processes at stopping times and Uncertainty quantification of stochastic approximation limits

Discretization of processes at stopping times and Uncertaint...

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作者： Uladzislau Stazhynski Ecole Polytechnique

学位级别：博士

This thesis consists of two parts. The first part is devoted to the problems of Brow- nian semimartingales discretization based on stop- ping times. We start with the study of the optimal discretization for stochastic integrals. In this context we establish an almost sure lower bound on the renormalized quadra- tic variation of the error and provide a sequence of stopping times which are asymptotically optimal, wi- thout the non-degeneracy assumption. Also we esta- blish an optimal discretization strategy which is com- pletely adaptive to the model. Further we study statistical fluctuations of the discreti- zation errors by showing Central Limit Theorems for general sequences of stopping times. The class of discretization grids is quite large and the limit distri- bution is given explicitly. The results are proved in the multidimensional case both for the process and for the discretization error. We apply these results to the problem of parametric statistical inference for diffusion processes based on observations at general stopping times. The second part is devoted to the problem of un- certainty quantification for stochastic approximation li- mits. In our framework the limit is defined as the zero of a function given by an expectation and typically re- presents the solution to some stochastic optimization problem. The expectation is related to a random va- riable for which the distribution is supposed to depend on an uncertain parameter (Bayesian point of view). Thereby the limit of the algorithm depends on this pa- rameter and is also uncertain. We introduce an algo- rithm called USA (Uncertainty for stochastic Approxi- mation) to efficiently calculate the chaos expansion coefficients of the limit as a function of the uncertain parameter. The convergence and the L 2 -convergence rate of the USA are analysed.

关键词： stochastic processes discretization optimization stopping times uncertainty quantification stochastic algorithms

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