Genomics and proteomics: a signal processor's tour

The theory and methods of signal processing are becoming increasingly important in molecular biology. Digital filtering techniques, transform domain methods, and Markov models have played important roles in gene identification, biological sequence analysis, and alignment. This paper contains a brief review of molecular biology, followed by a review of the applications of signal processing theory. This includes the problem of gene finding using digital filtering, and the use of transform domain methods in the study of protein binding spots. The relatively new topic of noncoding genes, and the associated problem of identifying ncRNA buried in DNA sequences are also described. This includes a discussion of hidden Markov models and context free grammars. Several new directions in genomic signal processing are briefly outlined in the end

Comparing Degenerate Strings

Uncertain sequences are compact representations of sets of similar strings. They highlight common segments by collapsing them, and explicitly represent varying segments by listing all possible options. A generalized degenerate string (GD string) is a type of uncertain sequence. Formally, a GD string S is a sequence of n sets of strings of total size N, where the ith set contains strings of the same length ki but this length can vary between different sets. We denote by W the sum of these lengths k0, k1,... , kn-1. Our main result is an (N + M)-time algorithm for deciding whether two GD strings of total sizes N and M, respectively, over an integer alphabet, have a non-empty intersection. This result is based on a combinatorial result of independent interest: although the intersection of two GD strings can be exponential in the total size of the two strings, it can be represented in linear space. We then apply our string comparison tool to devise a simple algorithm for computing all palindromes in S in (min{W, n2}N)-time. We complement this upper bound by showing a similar conditional lower bound for computing maximal palindromes in S. We also show that a result, which is essentially the same as our string comparison linear-time algorithm, can be obtained by employing an automata-based approach

Faster Queries for Longest Substring Palindrome After Block Edit

Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. Manacher [J. ACM 1975] proposed a seminal algorithm that computes the longest substring palindromes (LSPals) of a given string in O(n) time, where n is the length of the string. In this paper, we consider the problem of finding the LSPal after the string is edited. We present an algorithm that uses O(n) time and space for preprocessing, and answers the length of the LSPals in O(l + log log n) time, after a substring in T is replaced by a string of arbitrary length l. This outperforms the query algorithm proposed in our previous work [CPM 2018] that uses O(l + log n) time for each query

A Bayesian Search for Transcriptional Motifs

Identifying transcription factor (TF) binding sites (TFBSs) is an important step towards understanding transcriptional regulation. A common approach is to use gaplessly aligned, experimentally supported TFBSs for a particular TF, and algorithmically search for more occurrences of the same TFBSs. The largest publicly available databases of TF binding specificities contain models which are represented as position weight matrices (PWM). There are other methods using more sophisticated representations, but these have more limited databases, or aren't publicly available. Therefore, this paper focuses on methods that search using one PWM per TF. An algorithm, MATCHTM, for identifying TFBSs corresponding to a particular PWM is available, but is not based on a rigorous statistical model of TF binding, making it difficult to interpret or adjust the parameters and output of the algorithm. Furthermore, there is no public description of the algorithm sufficient to exactly reproduce it. Another algorithm, MAST, computes a p-value for the presence of a TFBS using true probabilities of finding each base at each offset from that position. We developed a statistical model, BaSeTraM, for the binding of TFs to TFBSs, taking into account random variation in the base present at each position within a TFBS. Treating the counts in the matrices and the sequences of sites as random variables, we combine this TFBS composition model with a background model to obtain a Bayesian classifier. We implemented our classifier in a package (SBaSeTraM). We tested SBaSeTraM against a MATCHTM implementation by searching all probes used in an experimental Saccharomyces cerevisiae TF binding dataset, and comparing our predictions to the data. We found no statistically significant differences in sensitivity between the algorithms (at fixed selectivity), indicating that SBaSeTraM's performance is at least comparable to the leading currently available algorithm. Our software is freely available at: http://wiki.github.com/A1kmm/sbasetram/building-the-tools

Hunter-gatherers in a howling wilderness: Neoliberal capitalism as a language that speaks itself

The 'self-referential' character of evolutionary process noted by Goldenfeld and Woese (2010) can be restated in the context of a generalized Darwinian theory applied to economic process through a 'language' model: The underlying inherited and learned culture of the firm, the short-time cognitive response of the firm to patterns of threat and opportunity that is sculpted by that culture, and the embedding socioeconomic environment, are represented as interacting information sources constrained by the asymptotic limit theorems of information theory. If unregulated, the larger, compound, source that characterizes high probability evolutionary paths of this composite then becomes, literally, a self-dynamic language that speaks itself. Such a structure is, for those enmeshed in it, more akin to a primitive hunter-gatherer society at the mercy of internal ecological dynamics than to, say, a neolithic agricultural community in which a highly ordered, deliberately adapted, ecosystem is consciously farmed so as to match its productivity to human needs

Dynamic and Internal Longest Common Substring

Given two strings S and T, each of length at most n, the longest common substring (LCS) problem is to find a longest substring common to S and T. This is a classical problem in computer science with an O(n) -time solution. In the fully dynamic setting, edit operations are allowed in either of the two strings, and the problem is to find an LCS after each edit. We present the first solution to the fully dynamic LCS problem requiring sublinear time in n per edit operation. In particular, we show how to find an LCS after each edit operation in O~ (n2 / 3) time, after O~ (n) -time and space preprocessing. This line of research has been recently initiated in a somewhat restricted dynamic variant by Amir et al. [SPIRE 2017]. More specifically, the authors presented an O~ (n) -sized data structure that returns an LCS of the two strings after a single edit operation (that is reverted afterwards) in O~ (1) time. At CPM 2018, three papers (Abedin et al., Funakoshi et al., and Urabe et al.) studied analogously restricted dynamic variants of problems on strings; specifically, computing the longest palindrome and the Lyndon factorization of a string after a single edit operation. We develop dynamic sublinear-time algorithms for both of these problems as well. We also consider internal LCS queries, that is, queries in which we are to return an LCS of a pair of substrings of S and T. We show that answering such queries is hard in general and propose efficient data structures for several restricted cases

Longest common substring made fully dynamic

Given two strings S and T, each of length at most n, the longest common substring (LCS) problem is to find a longest substring common to S and T. This is a classical problem in computer science with an O(n)-time solution. In the fully dynamic setting, edit operations are allowed in either of the two strings, and the problem is to find an LCS after each edit. We present the first solution to this problem requiring sublinear time in n per edit operation. In particular, we show how to find an LCS after each edit operation in Õ(n2/3) time, after Õ(n)-time and space preprocessing. 1 This line of research has been recently initiated in a somewhat restricted dynamic variant by Amir et al. [SPIRE 2017]. More specifically, they presented an Õ(n)-sized data structure that returns an LCS of the two strings after a single edit operation (that is reverted afterwards) in Õ(1) time. At CPM 2018, three papers (Abedin et al., Funakoshi et al., and Urabe et al.) studied analogously restricted dynamic variants of problems on strings. We show that the techniques we develop can be applied to obtain fully dynamic algorithms for all of these variants. The only previously known sublinear-time dynamic algorithms for problems on strings were for maintaining a dynamic collection of strings for comparison queries and for pattern matching, with the most recent advances made by Gawrychowski et al. [SODA 2018] and by Clifford et al. [STACS 2018]. As an intermediate problem we consider computing the solution for a string with a given set of k edits, which leads us, in particular, to answering internal queries on a string. The input to such a query is specified by a substring (or substrings) of a given string. Data structures for answering internal string queries that were proposed by Kociumaka et al. [SODA 2015] and by Gagie et al. [CCCG 2013] are used, along with new ones, based on ingredients such as the suffix tree, heavy-path decomposition, orthogonal range queries, difference covers, and string periodicity