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Slow Mixing (slow + mixing)

Distribution by Scientific Domains

Mathematics and Statistics	60%

Selected Abstracts

Steering of Liquid Mixing Speed in Interdigital Micro Mixers , From Very Fast to Deliberately Slow Mixing

CHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 3 2004
P. Löb
Abstract Very fast mixing in the range of milliseconds as well as deliberately slow mixing was realized by specially adjusted interdigital micro mixers made of glass or stainless steel. The corresponding micro mixers are presented including experimental and theoretical investigations of the respective mixing process. Fast mixing was realized by combination of flow multilamination by interdigital microstructured feeding structures with geometric focusing. Details on the microfabrication, achievable throughputs and hydrodynamics are discussed. To prevent clogging of microsized feeding structures in the case of precipitation reactions, mixing was deliberately slowed down by separating the reactant solutions at the outlet by additional layers of inert liquids. [source]

Slow mixing of Glauber dynamics for the hard-core model on regular bipartite graphs

RANDOM STRUCTURES AND ALGORITHMS, Issue 4 2006
David Galvin
Abstract Let , = (V,E) be a finite, d -regular bipartite graph. For any , > 0 let ,, be the probability measure on the independent sets of , in which the set I is chosen with probability proportional to ,|I| (,, is the hard-core measure with activity , on ,). We study the Glauber dynamics, or single-site update Markov chain, whose stationary distribution is ,,. We show that when , is large enough (as a function of d and the expansion of subsets of single-parity of V) then the convergence to stationarity is exponentially slow in |V(,)|. In particular, if , is the d -dimensional hypercube {0,1}d we show that for values of , tending to 0 as d grows, the convergence to stationarity is exponentially slow in the volume of the cube. The proof combines a conductance argument with combinatorial enumeration methods. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006 [source]

Sampling independent sets in the discrete torus,

RANDOM STRUCTURES AND ALGORITHMS, Issue 3 2008
David GalvinArticle first published online: 27 MAY 200
Abstract The even discrete torus is the graph TL,d on vertex set {0,,,L , 1}d (with L even) in which two vertices are adjacent if they differ on exactly one coordinate and differ by 1(modL) on that coordinate. The hard-core measure with activity , on TL,d is the probability distribution ,, on the independent sets (sets of vertices spanning no edges) of TL,d in which an independent set I is chosen with probability proportional to ,|I|. This distribution occurs naturally in problems from statistical physics and the study of communication networks. We study Glauber dynamics, a single-site update Markov chain on the set of independent sets of TL,d whose stationary distribution is ,,. We show that for , = ,(d,1/4 log 3/4d) and d sufficiently large the convergence to stationarity is (essentially) exponentially slow in Ld,1. This improves a result of Borgs, Chayes, Frieze, Kim, Tetali, Vigoda, and Vu (Proceedings of the IEEE FOCS (1999), 218,229) 5 who had shown slow mixing of Glauber dynamics for , growing exponentially with d. Our proof, which extends to ,-local chains (chains which alter the state of at most a proportion , of the vertices in each step) for suitable ,, closely follows the conductance argument of Borgs et al., 5 adding to it some combinatorial enumeration methods that are modifications of those used by Galvin and Kahn (Combinatorics, Probability and Computing 13 (2004), 137,164) 12 to show that the hard-core model with parameter , on the integer lattice ,d exhibits phase coexistence for , = ,(d,1/4 log 3/4d). The discrete even torus is a bipartite graph, with partition classes , (consisting of those vertices the sum of whose coordinates is even) and . Our result can be expressed combinatorially as the statement that for each sufficiently large ,, there is a ,(,) > 0 such that if I is an independent set chosen according to ,,, then the probability that ,I ,,|,|I ,, is at most ,(,)Ld is exponentially small in Ld,1. In particular, we obtain the combinatorial result that for all , > 0 the probability that a uniformly chosen independent set from TL,d satisfies ,I ,,|,|I ,,, (.25 - ,)Ld is exponentially small in Ld,1. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 [source]

A Bayesian Hierarchical Model for Classification with Selection of Functional Predictors

BIOMETRICS, Issue 2 2010
Hongxiao Zhu
Summary In functional data classification, functional observations are often contaminated by various systematic effects, such as random batch effects caused by device artifacts, or fixed effects caused by sample-related factors. These effects may lead to classification bias and thus should not be neglected. Another issue of concern is the selection of functions when predictors consist of multiple functions, some of which may be redundant. The above issues arise in a real data application where we use fluorescence spectroscopy to detect cervical precancer. In this article, we propose a Bayesian hierarchical model that takes into account random batch effects and selects effective functions among multiple functional predictors. Fixed effects or predictors in nonfunctional form are also included in the model. The dimension of the functional data is reduced through orthonormal basis expansion or functional principal components. For posterior sampling, we use a hybrid Metropolis,Hastings/Gibbs sampler, which suffers slow mixing. An evolutionary Monte Carlo algorithm is applied to improve the mixing. Simulation and real data application show that the proposed model provides accurate selection of functional predictors as well as good classification. [source]