https://www.cs.rice.edu/~nakhleh/COMP571/Fall05/DatabaseSearch/blast.pdf

Basic Local Alignment Search Tool

The BLAST programs are widely used tools for searching protein and DNA databases for sequence similarities. For protein comparisons, a variety of definitional, algorithmic and statistical refinements described here permits the execution time of the BLAST programs to be decreased substantially while enhancing their sensitivity to weak similarities. A new criterion for triggering the extension of word hits, combined with a new heuristic for generating gapped alignments, yields a gapped BLAST program that runs at approximately three times the speed of the original. In addition, a method is introduced for automatically combining statistically significant alignments produced by BLAST into a position-specific score matrix, and searching the database using this matrix. The resulting Position-Specific Iterated BLAST (PSIBLAST) program runs at approximately the same speed per iteration as gapped BLAST, but in many cases is much more sensitive to weak but biologically relevant sequence similarities. PSI-BLAST is used to uncover several new and interesting members of the BRCT superfamily.

/pdf/gapped-blast-and-psi-blast-a-new-generation-of-protein-2ybl67x5yx.pdf

Gapped BLAST and PSI-BLAST: a new generation of protein database search programs.

There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This tutorial provides an overview of the basic theory of hidden Markov models (HMMs) as originated by L.E. Baum and T. Petrie (1966) and gives practical details on methods of implementation of the theory along with a description of selected applications of the theory to distinct problems in speech recognition. Results from a number of original sources are combined to provide a single source of acquiring the background required to pursue further this area of research. The author first reviews the theory of discrete Markov chains and shows how the concept of hidden states, where the observation is a probabilistic function of the state, can be used effectively. The theory is illustrated with two simple examples, namely coin-tossing, and the classic balls-in-urns system. Three fundamental problems of HMMs are noted and several practical techniques for solving these problems are given. The various types of HMMs that have been studied, including ergodic as well as left-right models, are described. >

/pdf/a-tutorial-on-hidden-markov-models-and-selected-applications-1vlzbxbk68.pdf

A tutorial on hidden Markov models and selected applications in speech recognition

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

We study the Langevin dynamics for the family of spherical p-spin disordered mean-field models of statistical physics. We prove that in the limit of system size N approaching infinity, the empirical state correlation and integrated response functions for these N-dimensional coupled diffusions converge almost surely and uniformly in time, to the non-random unique strong solution of a pair of explicit non-linear integro-differential equations intensively studied by Cugliandolo and Kurchan.

Cugliandolo-Kurchan equations for dynamics of spin-glasses

A new iterative approach for hidden Markov modeling of information sources which aims at minimizing the discrimination information (or the cross-entropy) between the source and the model is proposed. This approach does not require the commonly used assumption that the source to be modeled is a hidden Markov process. The algorithm is started from the model estimated by the traditional maximum likelihood (ML) approach and alternatively decreases the discrimination information over all probability distributions of the source which agree with the given measurements and all hidden Markov models. The proposed procedure generalizes the Baum algorithm for ML hidden Markov modeling. The procedure is shown to be a descent algorithm for the discrimination information measure and its local convergence is proved.

A minimum discrimination information approach for hidden Markov modeling

Nous considerons le theoreme de fluctuation-dissipation de la mechanique statistique dans une approche mathematique. Nous donnons un concept formel de la reponse lineaire dans le cadre general de la theorie des processus de Markov. Nous demontrons que pour un processus hors d'equilibre celle ci depend non seulement du processus de Markov X(s) mais aussi de la perturbation choisie. Nous characterisons l'ensemble de toutes les reponses possibles pour un processus de Markov donne et demontrons qu'a l'equilibre elles satisfassent toutes le theoreme de fluctuation-dissipation. C'est a dire, si une mesure ν est invariante pour un semigroupe markovien donne, alors pour tout temps s < t et functions regulieres f, g, la dissipation, definie comme la derivee en s de la covariance de g(X (t)) et de f (X(s)) est egale a la reponse infinitesimale au temps t en direction de g pour toute perturbation markovienne qui modifie la mesure invariante ν en direction de f au temps s. Ce resultat s'etend au regime proche de l'equilibre, c.-a.-d. dans la limite s → ∞ avec t - s fixe, en supposant que X (s) converge en loi vers sa mesure invariante. Nous donnons la reponse pour deux perturbations markoviennes generiques, que nous comparons ensuite pour des processus de sauts dans un espace discret, pour des diffusions a dimension finie et pour une dynamique stochastique de spins.

/pdf/markovian-perturbation-response-and-fluctuation-dissipation-50n38pb1o2.pdf

Markovian perturbation, response and fluctuation dissipation theorem

M. Pinsker and P. Ebert (Bell Syst. Tech. J., p.1705-1712, Oct.1970) proved that in channels with additive Gaussian noise, feedback at most doubles the capacity. Recently, T. Cover and S. Pombra (ibid., vol.35, no.1, p.37-43, Jan.1989) proved that feedback at most adds half a bit per transmission. Following their approach, the author proves that in the limit as signal power approaches either zero (very low SNR) or infinity (very high SNR), feedback does not increase the finite block-length capacity (which for nonstationary Gaussian channels replaces the standard notion of capacity that may not exist). Tighter upper bounds on the capacity are obtained in the process. Specializing these results to stationary channels, the author recovers some of the bounds recently obtained by L.H. Ozarow (to appear in IEEE Trans. Inf. Theory) using a different bounding technique. >

On Gaussian feedback capacity

Stein’s method is applied to study the rate of convergence in the normal approximation for sums of non-linear functionals of correlated Gaussian random variables, for the exceedances of r-scans of i.i.d. random variables, and in a multinomial setting.

Amir Dembo

Papers

Cugliandolo-Kurchan equations for dynamics of spin-glasses

A minimum discrimination information approach for hidden Markov modeling

Markovian perturbation, response and fluctuation dissipation theorem

On Gaussian feedback capacity

Some Examples of Normal Approximations by Stein’s Method