Average-Case Optimal Approximate Circular String Matching

Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that are at a distance at most k from x or from any of its rotations. In this article, we present a new algorithm for approximate circular string matching under the edit distance model with optimal average-case search time O(n(k + log m)/m). Optimal average-case search time can also be achieved by the algorithms for multiple approximate string matching (Fredriksson and Navarro, 2004) using x and its rotations as the set of multiple patterns. Here we reduce the preprocessing time and space requirements compared to that approach

Dictionary matching in a stream

We consider the problem of dictionary matching in a stream. Given a set of strings, known as a dictionary, and a stream of characters arriving one at a time, the task is to report each time some string in our dictionary occurs in the stream. We present a randomised algorithm which takes O(log log(k + m)) time per arriving character and uses O(k log m) words of space, where k is the number of strings in the dictionary and m is the length of the longest string in the dictionary

The streaming kk-mismatch problem

We consider the streaming complexity of a fundamental task in approximate pattern matching: the $k$-mismatch problem. It asks to compute Hamming distances between a pattern of length $n$ and all length-$n$ substrings of a text for which the Hamming distance does not exceed a given threshold $k$. In our problem formulation, we report not only the Hamming distance but also, on demand, the full \emph{mismatch information}, that is the list of mismatched pairs of symbols and their indices. The twin challenges of streaming pattern matching derive from the need both to achieve small working space and also to guarantee that every arriving input symbol is processed quickly. We present a streaming algorithm for the $k$-mismatch problem which uses $O(k\log{n}\log\frac{n}{k})$ bits of space and spends \ourcomplexity time on each symbol of the input stream, which consists of the pattern followed by the text. The running time almost matches the classic offline solution and the space usage is within a logarithmic factor of optimal. Our new algorithm therefore effectively resolves and also extends an open problem first posed in FOCS'09. En route to this solution, we also give a deterministic $O( k (\log \frac{n}{k} + \log |\Sigma|) )$-bit encoding of all the alignments with Hamming distance at most $k$ of a length-$n$ pattern within a text of length $O(n)$. This secondary result provides an optimal solution to a natural communication complexity problem which may be of independent interest.Comment: 27 page

Ligand-based virtual screening using binary kernel discrimination

This paper discusses the use of a machine-learning technique called binary kernel discrimination (BKD) for virtual screening in drug- and pesticide-discovery programmes. BKD is compared with several other ligand-based tools for virtual screening in databases of 2D structures represented by fragment bit-strings, and is shown to provide an effective, and reasonably efficient, way of prioritising compounds for biological screening

The problem of fingerprints selection for topological localization

Visual navigation is extensively used in contemporary robotics. In particular, we can mention different systems of visual landmarks. In this paper, we consider one-dimensional color panoramas. Panoramas can be used for creating fingerprints. Fingerprints give us unique identifiers for visually distinct locations by recovering statistically significant features. Also, it can be used as visual landmarks for mobile robot navigation. In this paper, we consider a method for automatic generation of fingerprints. Since a fingerprint is a circular string, different string-matching algorithms can be used for selection of fingerprints. In particular, we consider the problem of finding the consensus of circular strings under the Hamming distance metric. We propose an approach to solve the problem. In particular, we consider the center string problem, the center circular string problem, and the center circular string with fixed letters problem. We obtain an explicit reduction from the center circular string problem to the satisfiability problem. We propose a genetic algorithm for solution of the center circular string problem. Also, we propose a genetic algorithm for the prediction the effectiveness of the use of special algorithm for four circular strings

Super spin chain coherent state actions and AdS5×S5AdS_5 \times S^5 superstring

We consider a generalization of the leading-order matching of coherent state actions for semiclassical states on the super Yang-Mills and the superstring sides of the AdS/CFT duality to sectors with fermions. In particular, we discuss the $SU(1|1)$ and $SU(2|3)$ sectors containing states with angular momentum $J$ in $S^5$ and spin in $AdS_5$. On the SYM side, we start with the dilatation operator in the $SU(2|3)$ sector having super spin chain Hamiltonian interpretation and derive the corresponding coherent state action which is quartic in fermions. This action has essentially the same ``Landau-Lifshitz'' form as the action in the bosonic SU(3) sector with the target space $CP^2$ replaced by the projective superspace $CP^{2|2}$. We then attempt to relate it to the corresponding truncation of the full $AdS_5 \times S^5$ superstring action written in a light-cone gauge where it has simple quartic fermionic structure. In particular, we find that part of the superstring action describing $SU(1|1)$ sector reduces to an action of a massive two-dimensional relativistic fermion, with the expansion in the effective coupling $\lambda/J^2$ being equivalent to a non-relativistic expansion