In the theory of worst case complexity, NP completeness is used to establish that, for all practical purposes, the given NP problem is not decidable in polynomial time. In the theory of average case complexity, average case completeness is supposed to play the role of NP completeness. However, the average case reduction theory is still at an early stage, and only a few average case complete pro...

The first algebraic average-case complete problem is presented. It is arguably the simplest natural average-case complete problem to date.

We present new algorithms for computing the log-determinant of symmetric, diagonally dominant matrices. Existing algorithms run with cubic complexity with respect to the size of the matrix in the worst case. Our algorithm computes an approximation of the log-determinant in time near-linear with respect to the number of non-zero entries and with high probability. This algorithm builds upon the u...

We consider the problem of recovering a symmetric, positive semidefinite (SPSD) matrix from a subset of its entries, possibly corrupted by noise. In contrast to previous matrix recovery work, we drop the assumption of a random sampling of entries in favor of a deterministic sampling of principal submatrices of the matrix. We develop a set of sufficient conditions for the recovery of a SPSD matr...

The Gibbs Centroid Sampler is a software package designed for locating conserved elements in biopolymer sequences. The Gibbs Centroid Sampler reports a centroid alignment, i.e. an alignment that has the minimum total distance to the set of samples chosen from the a posteriori probability distribution of transcription factor binding-site alignments. In so doing, it garners information from the f...

This study investigates acoustic characteristics of Aymara ejectives. Acoustic measurements of the Aymara ejectives were conducted in terms of the durations of the release burst, the vowel, and the intervening gap (VOT), the intensity and spectral centroid of the release burst, and H1-H2 of the initial part of the vowel. Results showed that ejectives vary with place of articulation in the durat...

It is well-known that orthogonalization of column vectors in a rectangular matrix B with respect to the bilinear form induced by a nonsingular symmetric indefinite matrix A can be seen as its factorization B = QR that is equivalent to the Cholesky-like factorization in the form BTAB = RTΩR, where Ω is some signature matrix. Under the assumption of nonzero principal minors of the matrix M = BTAB...

We extend the classical problem of predicting a sequence of outcomes from a finite alphabet to the matrix domain. In this extension, the alphabet of n outcomes is replaced by the set of all dyads, i.e. outer products uu> where u is a vector in R of unit length. Whereas in the classical case the goal is to learn (i.e. sequentially predict as well as) the best multinomial distribution, in the mat...