Fast mixing for independent sets,colorings, and other models on trees

We study the mixing time of the Glauber dynamics for general spin systems on the regular tree, including the Ising model, the hard‐core model (independent sets), and the antiferromagnetic Potts model at zero temperature (colorings). We generalize a framework, developed in our recent paper (Martinelli, Sinclair, and Weitz, Tech. Report UCB//CSD‐03‐1256, Dept. of EECS, UC Berkeley, July 2003) in the context of the Ising model, for establishing mixing time O(nlog n), which ties this property closely to phase transitions in the underlying model. We use this framework to obtain rapid mixing results for several models over a significantly wider range of parameter values than previously known, including situations in which the mixing time is strongly dependent on the boundary condition. We also discuss applications of our framework to reconstruction problems on trees. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

Embedology

Mathematical formulations of the embedding methods commonly used for the reconstruction of attractors from data series are discussed. Embedding theorems, based on previous work by H. Whitney and F. Takens, are established for compact subsetsA of Euclidean space R^k. Ifn is an integer larger than twice the box-counting dimension ofA, then almost every map fromR ^k toR ⁿ , in the sense of prevalence, is one-to-one onA, and moreover is an embedding on smooth manifolds contained withinA. IfA is a chaotic attractor of a typical dynamical system, then the same is true for almost everydelay-coordinate map fromR ^k toR ⁿ . These results are extended in two other directions. Similar results are proved in the more general case of reconstructions which use moving averages of delay coordinates. Second, information is given on the self-intersection set that exists whenn is less than or equal to twice the box-counting dimension ofA.     

The CuGaSe2(0 0 1) surface: A (4 × 1) reconstruction

We report on the formation of a stable (4 × 1) reconstruction of the chalcopyrite CuGaSe₂(0 0 1) surface. Using Ar⁺ ion-bombardment and annealing of epitaxial CuGaSe₂ films grown on GaAs(0 0 1) substrates it was possible to obtain flat, well-ordered surfaces showing a clear (4 × 1) reconstruction. The cleanliness and structure were analyzed in situ by AES and LEED. AES data suggest a slight Se-enrichment and Cu-depletion upon surface preparation. Our results demonstrate that (0 0 1) surfaces of the Cu-III-VI₂(0 0 1) material can show stable, unfacetted surfaces.     

Fourier transforms of stationary processes

We consider the asymptotic behavior of Fourier transforms of stationary and ergodic sequences. Under sufficiently mild conditions, central limit theorems are established for almost all frequencies as well as for a given frequency. Applications to the widely used linear processes and iterated random functions are discussed. Our results shed new light on the foundation of spectral analysis in that the asymptotic distribution of the periodogram, the fundamental quantity in the frequency-domain analysis, is obtained.

     

公理A自同态的统计性结果（英文）

本文对公理A自同态建立了中心极限定理和大偏差估计，并且复习了已知的有关统计性结果。     

A measure of rotatability for second order response surface designs

The concept of rotatability introduced by Box and Hunter (1957,Ann. Math. Statist.,28, 195–241) is an important design criterion for response surface design. Recently, a few measures of rotatability that enable us to assess the degree of rotatability for a given response surface design have been introduced. In this paper, a new measure of rotatability for second order response surface designs is suggested, and illustrated for 3 ^k factorial design and central composite design. Also a short comparison is made between the proposed measure with the previously suggested measures.     

有限超特殊p-群的一个注记

本文获得了以下结果：设G为有限超特殊P-群．则下列条件等价：（1）G的非平凡特征子群的阶相同；（2）G的非平凡特征子群唯一；（3）当p〉2时，exp G=p；当P=2时，G≠D8．     

On Central-Path Proximity Measures in Interior-Point Methods

One of the main ingredients of interior-point methods is the generation of iterates in a neighborhood of the central path. Measuring how close the iterates are to the central path is an important aspect of such methods and it is accomplished by using proximity measure functions. In this paper, we propose a unified presentation of the proximity measures and a study of their relationships and computational role when using a generic primal-dual interior-point method for computing the analytic center for a standard linear optimization problem. We demonstrate that the choice of the proximity measure can affect greatly the performance of the method. It is shown that we may be able to choose the algorithmic parameters and the central-path neighborhood radius (size) in such a way to obtain comparable results for several measures. We discuss briefly how to relate some of these results to nonlinear programming problems. The first author was partially supported by Simón Bolívar University, Venezuelan National Council for Sciences and Technology (CONICIT) Grant PG97-000592, Center for Research on Parallel Computing of Rice University, and TU Delft. The authors thank Amr El Bakry, Richard Tapia, Adolfo Quiroz, and Pedro Berrizbeitia for discussions and suggestions. They acknowledge the observations and comments of the editors and an anonymous referee.