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MOTIVATION Most scoring functions used in protein fold recognition employ two-body (pseudo) potential energies. The use of higher-order terms may improve the performance of current algorithms. METHODS Proteins are represented by the side chain centroids of amino acids. Delaunay tessellation of this representation defines all sets of nearest neighbor(More)
MOTIVATION There is a need for an efficient and accurate computational method to identify the effects of single- and multiple-residue mutations on the stability and reactivity of proteins. Such a method should ideally be consistent and yet applicable in a widespread manner, i.e. it should be applied to various proteins under the same parameter settings, and(More)
Given a simplicial complex with weights on its simplices, and a nontrivial cycle on it, we are interested in finding the cycle with minimal weight which is homologous to the given one. Assuming that the homology is defined with integer (Z) coefficients, we show the following: <i>For a finite simplicial complex K of dimension greater than p, the boundary(More)
We propose a very simple preconditioning method for integer programming feasibility problems: replacing the problem b ′ ≤ Ax ≤ b x ∈ Z n with b ′ ≤ (AU)y ≤ b y ∈ Z n , where U is a unimodular matrix computed via basis reduction, to make the columns of AU short (i.e. have small Euclidean norm), and nearly orthogonal (see e.g. [20], [17]). Our approach is(More)
We develop an objective characterization of protein structure based entirely on the geometry of its parts. The three-dimensional alpha complex filtration of the protein represented as a union of balls (one per residue) captures all the relevant information about the geometry and topology of the molecule. The neighborhood of a strand of contiguous alpha(More)
Mutagenesis is commonly used to engineer proteins with desirable properties not present in the wild type (WT) protein, such as increased or decreased stability, reactivity, or solubility. Experimentalists often have to choose a small subset of mutations from a large number of candidates to obtain the desired change, and computational techniques are(More)
We study the effect of edge contractions on simplicial homology because these contractions have turned out to be useful in various applications involving topology. It was observed previously that contracting edges that satisfy the so called link condition preserves homeomorphism in low dimensional complexes, and homotopy in general. But, checking the link(More)
Currents represent generalized surfaces studied in geometric measure theory. They range from relatively tame integral currents representing oriented compact manifolds with boundary and integer multi-plicities, to arbitrary elements of the dual space of differential forms. The flat norm provides a natural distance in the space of currents, and works by(More)