Ostwald Ripening in Two Dimensions: Treatment with Pairwise Interactions

We present a systematic extension of mean field models for Ostwald ripening in two dimensions. We derived, using a mean field type approximation, an analytic expression for pairwise interactions between the minority phase droplets. These interactions appear in dynamic equations for the droplets' radii and positions, which are solved numerically for systems of tens of thousands of droplets, yielding very good agreement with recent experiments.Comment: 4 pages, RevTex, 3 eps figure

Recovery of Protein Structure from Contact Maps

We present an efficient algorithm to recover the three dimensional structure of a protein from its contact map representation. First we show that when a physically realizable map is used as target, our method generates a structure whose contact map is essentially similar to the target. Furthermore, the reconstructed and original structures are similar up to the resolution of the contact map representation. Next we use non-physical target maps, obtained by corrupting a physical one; in this case our method essentially recovers the underlying physical map and structure. Hence our algorithm will help to fold proteins, using dynamics in the space of contact maps. Finally we investigate the manner in which the quality of the recovered structure degrades when the number of contacts is reduced.Comment: 27 pages, RevTex, 12 figures include

Data clustering using a model granular magnet

We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors. This magnetic system exhibits three phases. At very low temperatures it is completely ordered; all spins are aligned. At very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered, whereas different clusters remain uncorrelated. This intermediate phase is identified by a jump in the order parameters. The spin-spin correlation function is used to partition the spins and the corresponding data points into clusters. We demonstrate on three synthetic and three real data sets how the method works. Detailed comparison to the performance of other techniques clearly indicates the relative success of our method.Comment: 46 pages, postscript, 15 ps figures include