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 develop a quantitative large deviations theory for random Bernoulli tensors. The large deviation principles rest on a decomposition theorem for arbitrary tensors outside a set of tiny measure, in terms of a novel family of norms generalizing the cut norm. Combined with associated counting lemmas, these yield sharp asymptotics for upper tails of homomorphism counts in the $r$-uniform Erdős--Renyi hypergraph for any fixed $r\ge 2$, generalizing and improving on previous results for the Erdős--Renyi graph ($r=2$). The theory is sufficiently quantitative to allow the density of the hypergraph to vanish at a polynomial rate, and additionally yields (joint) upper and lower tail asymptotics for other nonlinear functionals of interest.

Regularity method and large deviation principles for the Erd\H{o}s--R\'enyi hypergraph

. We study the line ensembles of non-crossing Brownian bridges above a hard wall, each tilted by the area of the region below it with geometrically growing pre-factors. This model, which mimics the level lines of the (2+1) d sos model above a hard wall, was studied in two works from 2019 by Caputo, Ioﬀe and Wachtel. In those works, the tightness of the law of the top k paths, for any ﬁxed k , was established under either zero or free boundary conditions, which in the former setting implied the existence of a limit via a monotonicity argument. Here we address the open problem of a limit under free boundary conditions: we prove that as the interval length, followed by the number of paths, go to ∞ , the top k paths converge to the same limit as in the zero boundary case, as conjectured by Caputo, Ioﬀe and Wachtel.

On the limiting law of line ensembles of Brownian polymers with geometric area tilts

A generalization of the conventional window method for the design of finite impulse response (FIR) digital filters is presented by including nonequal passband and stopband ripple specifications in the design process. Typically, this results in a savings of up to 30 percent in filter length in comparison to the conventional approach.

http://ieeexplore.ieee.org/iel6/29/26186/01164431.pdf

Generalization of the window method for FIR digital filter design

A class of high density associative memories is constructed, starting from a description of desired properties those should exhibit. These properties include high capacity, controllable basins of attraction and fast speed of convergence. Fortunately enough, the resulting memory is implementable by an artificial Neural Net.

/pdf/high-density-associative-memories-2ehon1r9y2.pdf

High density associative memories

Starting with the large deviation principle (LDP) for the Erdős-Renyi binomial random graph $\mathcal{G}(n,p)$ (edge indicators are i.i.d.), due to Chatterjee and Varadhan (2011), we derive the LDP for the uniform random graph $\mathcal{G}(n,m)$ (the uniform distribution over graphs with $n$ vertices and $m$ edges), at suitable $m=m_n$. Applying the latter LDP we find that tail decays for subgraph counts in $\mathcal{G}(n,m_n)$ are controlled by variational problems, which up to a constant shift, coincide with those studied by Kenyon et al. and Radin et al. in the context of constrained random graphs, e.g., the edge/triangle model.

Amir Dembo

Papers

Regularity method and large deviation principles for the Erd\H{o}s--R\'enyi hypergraph

On the limiting law of line ensembles of Brownian polymers with geometric area tilts

Generalization of the window method for FIR digital filter design

High density associative memories

A large deviation principle for the Erd\H{o}s-R\'enyi uniform random graph