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 consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We study the probability that the random walk travels slower than its typical speed and determine its decay rate asymptotic.

Slowdown estimates for one-dimensional random walks in random environment with holding times

Absolute stability and optimal training for dynamic neural networks

Precise analytical asymptotic exponential rates of error, and bounds on those rates, for differential multiplephase-shift keying (DMPSK) systems that include post-detection integration are provided. Easily computed bounds on these rates are provided, both in the case of floor bit error probability (i.e., with no additive noise) and in the case of weak additive noise. The derivation uses the theory of large deviations and illustrates its applicability to the analysis of communications systems. >

Exponential rates for error probabilities in DMPSK systems

We show that the total-variation mixing time of the lamplighter random walk on fractal graphs exhibit sharp cutoff when the underlying graph is transient (namely of spectral dimension greater than two). In contrast, we show that such cutoff can not occur for strongly recurrent underlying graphs (i.e. of spectral dimension less than two).

/pdf/cutoff-for-lamplighter-chains-on-fractals-155lbnsn5u.pdf

Cutoff for lamplighter chains on fractals

Nakamoto invented the longest chain protocol, and claimed its security by analyzing the private double-spend attack, a race between the adversary and the honest nodes to grow a longer chain. But is it the worst attack? We answer the question in the affirmative for three classes of longest chain protocols, designed for different consensus models: 1) Nakamoto's original Proof-of-Work protocol; 2) Ouroboros and SnowWhite Proof-of-Stake protocols; 3) Chia Proof-of-Space protocol. As a consequence, exact characterization of the maximum tolerable adversary power is obtained for each protocol as a function of the average block time normalized by the network delay. The security analysis of these protocols is performed in a unified manner by a novel method of reducing all attacks to a race between the adversary and the honest nodes.

Amir Dembo

Papers

Slowdown estimates for one-dimensional random walks in random environment with holding times

Absolute stability and optimal training for dynamic neural networks

Exponential rates for error probabilities in DMPSK systems

Cutoff for lamplighter chains on fractals

Everything is a Race and Nakamoto Always Wins