This is a report about Hidden Markov Models, a data structure used to model the probabilities of sequences, and the three algorithms associated with it. The algorithms are the forward algorithm and the Viterbi algorithm, both used to calculate the probability of a sequence, and the forward-backward algorithm, used to train a Hidden Markov Model on a set of sequences, raising the propabilites of...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

We examine the renormalizability problem of spontaneously broken non-Abelian gauge theory on noncommutative spacetime. We show by an explicit analysis of the U(2) case that ultraviolet divergences can be removed at one loop level with the same limited number of renormalization constants as required on commutative spacetime. We thus push forward the efforts towards constructing realistic models ...

We examine the renormalizability problem of spontaneously broken non-Abelian gauge theory on noncommutative spacetime. We show by an explicit analysis of the U(2) case that ultraviolet divergences can be removed at one loop level with the same limited number of renormalization constants as required on commutative spacetime. We thus push forward the efforts towards constructing realistic models ...

We show how to use the elements of a sharply k-transitive permutation group of degree n to form error-correcting codes, as suggested by Blake [1], presenting suitable decoding algorithms for these codes. In particular, we concentrate on using the Mathieu group M12 to form a (12,95040,8)-code to correct three errors. The algorithm we give for this code differs from that given by Cohen and Deza [2].

The classical Viterbi algorithm (ML sequence estimation) can be computed using a forward-backward structure, similar to that of the classical hidden Markov model forward-backward algorithm (MAP state estimation). This similarity is exploited to develop a hybrid algorithm which provides a mathematical connection between ML sequence estimation and MAP state estimation.

GATK HaplotypeCaller (HC) is a popular variant caller, which is widely used to identify variants in complex genomes. However, due to its high variants detection accuracy, it suffers from long execution time. In GATK HC, the pair-HMMs forward algorithm accounts for a large percentage of the total execution time. This article proposes to accelerate the pair-HMMs forward algorithm on graphics proc...