Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.

MosaicShape: Stochastic Region Grouping with Shape Prior

A novel method that combines shape-based object recognition and image segmentation is proposed for shape retrieval from images. Given a shape prior represented in a multi-scale curvature form, the proposed method identifies the target objects in images by grouping oversegmented image regions. The problem is formulated in a unified probabilistic framework and solved by a stochastic Markov Chain Monte Carlo (MCMC) mechanism. By this means, object segmentation and recognition are accomplished simultaneously. Within each sampling move during the simulation process,probabilistic region grouping operations are influenced by both the image information and the shape similarity constraint. The latter constraint is measured by a partial shape matching process. A generalized parallel algorithm by Barbu and Zhu,combined with a large sampling jump and other implementation improvements, greatly speeds up the overall stochastic process. The proposed method supports the segmentation and recognition of multiple occluded objects in images. Experimental results are provided for both synthetic and real images.

GreedyDual* Web Caching Algorithm: Exploiting the Two Sources of Temporal Locality in Web Request Streams

The relative importance of long-term popularity and short-term temporal correlation of references for Web cache replacement policies has not been studied thoroughly. This is partially due to the lack of accurate characterization of temporal locality that enables the identification of the relative strengths of these two sources of temporal locality in a reference stream. In [21], we have proposed such a metric and have shown that Web reference streams differ significantly in the prevalence of these two sources of temporal locality. These finding underscore the importance of a Web caching strategy that can adapt in a dynamic fashion to the prevalence of these two sources of temporal locality. In this paper, we propose a novel cache replacement algorithm, GreedyDual*, which is a generalization of GreedyDual-Size. GreedyDual* uses the metrics proposed in [21] to adjust the relative worth of long-term popularity versus short-term temporal correlation of references. Our trace-driven simulation experiments show the superior performance of GreedyDual* when compared to other Web cache replacement policies proposed in the literature.