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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)

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)

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)

Using a direct counting argument, we derive lower and upper bounds for the number of nodes enumerated by linear programming-based branch-and-bound (B&B) method to prove the infeasibility of an integer knapsack problem. We prove by example that the size of the B&B tree could be exponential in the worst case. 1 Introduction Linear programming-based… (More)

We study the multiscale simplicial flat norm (MSFN) problem, which computes flat norm at various scales of sets defined as oriented subcomplexes of finite simplicial complexes in arbitrary dimensions. We show that the multiscale simplicial flat norm is NP-complete when homology is defined over integers. We cast the multiscale simplicial flat norm as an… (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)

We present a new method for exploring cancer gene expression data based on tools from algebraic topology. Our method selects a small relevant subset from tens of thousands of genes while simultaneously identifying nontrivial higher order topological features, i.e., holes, in the data. We first circumvent the problem of high dimensionality by dualizing the… (More)

We had recently shown that every positive integer can be represented uniquely using a recurrence sequence , when certain restrictions on the digit strings are satisfied. We present the details of how such representations can be used to build a knapsack-like public key cryptosystem. We also present new disguising methods, and provide arguments for the… (More)