Center for Discrete Mathematics and Theoretical Computer Science

Abstract: A computational method has been developed for the assignment of a protein sequence to a folding class in the Structural Classification of Proteins (SCOP). This method uses global descriptors of a primary protein sequence in terms of the physical, chemical, and structural properties of the constituent amino acids. Neural networks are utilized to combine these descriptors in a way to discriminate members of a given fold from members of all other folds. An extensive testing of the method has been performed to evaluate its prediction accuracy. The method is applicable for the fold assignment of any protein sequence with or without significant sequence homology to known proteins. A WWW page for predicting protein folds is available at URL http://cbcg.lbl.gov/. Proteins 1999;35:401–407.

Abstract: LetP be a set ofn points on the euclidean plane. LetL s(P) andL m (P) denote the lengths of the Steiner minimum tree and the minimum spanning tree onP, respectively. In 1968, Gilbert and Pollak conjectured that for anyP,L s (P)≥(√3/2)L m (P). We provide a proof for their conjecture in this paper.

Abstract: Aravind Srinivasant Several important NP-hard combinatorial optimization problems can be posed as packing\couerirag integer pragramq the rarzrfomized rouradingtechnique of Raghavan & Thompson is a powerful tool to approximate them well. We present one elementary unifying property of all these integer programs (IPs), and use the FKG correlation inequality to derive an improved analysis of randomized rounding on them. Thk also yields a pessimistic estimator, thus presenting deter-ministic polynomial-time algorithms for them with approximation guarantees significantly better than those known.

Abstract: We present a simple I/O-efficient k-clustering algorithm that was designed with the goal of enabling a privacy-preserving version of the algorithm. Our experiments show that this algorithm produces cluster centers that are, on average, more accurate than the ones produced by the well known iterative k-means algorithm. We use our new algorithm as the basis for a communication-efficient privacy-preservingk-clustering protocol for databases that are horizontally partitioned between two parties. Unlike existing privacy-preserving protocols based on the k-means algorithm, this protocol does not reveal intermediate candidate cluster centers.

Abstract: The recent rapid growth of protein sequence databases is outpacing the capacity of researchers to biochemically and structurally characterize new proteins. Accordingly, new methods for recognition of motifs and homologies in protein primary sequences may be useful in determining how these proteins might function. We have applied such a method, an iterative learning algorithm, to analyze possible coiled coil domains in histidine kinase receptors. The potential coiled coils have not yet been structurally characterized in any histidine kinase, and they appear outside previously noted kinase homology regions. The learning algorithm uses a combination of established sequence patterns in known coiled coil proteins and histidine kinase sequence data to learn to recognize efficiently this coiled coil-like motif in the histidine kinases. The common appearance of the structural motif in a functionally important part of the receptors suggests hypotheses for kinase regulation and signal transduction.