Related papers: Matching strings in encoded sequences

In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…

We study the recurrence to mistake dynamical balls, that is, dynamical balls that admit some errors and whose proportion of errors decrease tends to zero with the length of the dynamical ball. We prove, under mild assumptions, that the…

We analyze the dynamical generation of entanglement in systems of two interacting spins initially prepared in a product of spin coherent states. For arbitrary time-independent Hamiltonians, we derive a semiclassical expression for the…

The problem of finding a center string that is `close' to every given string arises and has many applications in computational biology and coding theory. This problem has two versions: the Closest String problem and the Closest Substring…

The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being…

We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been…

We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…

This paper studies the problem of encoding messages into sequences which can be uniquely recovered from some noisy observations about their substrings. The observed reads comprise consecutive substrings with some given minimum overlap. This…

The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages,…

Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…

The relation between force and stretch in the worm-like chain model of entropic elasticity is examined. Although no closed-form expression is valid for all values of forcing, solutions in the form of asymptotic series can be obtained under…

This paper considers an information bottleneck problem with the objective of obtaining a most informative representation of a hidden feature subject to a R\'enyi entropy complexity constraint. The optimal bottleneck trade-off between…

In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting…

Let $S$ be a string of length $n$. In this paper we introduce the notion of \emph{string attractor}: a subset of the string's positions $[1,n]$ such that every distinct substring of $S$ has an occurrence crossing one of the attractor's…

We define entanglement entropy in string perturbation theory using the orbifold method -- a stringy analog of the replica method in field theory. To this end, we use the Newton series to analytically continue in $N$ the partition functions…

We discuss further our proposed modification of the Susskind-Horowitz-Polchinski scenario in which black hole entropy goes over to string entropy as one scales the string length scale up and the string coupling constant down, keeping…

We characterize non-perturbatively the R\'enyi entropies of degree n=2,3,4, and 5 of three-dimensional, strongly coupled many-fermion systems in the scale-invariant regime of short interaction range and large scattering length, i.e. in the…

Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…

Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a key problem in computational biology, such as identifying related mutations across multiple genetic sequences. We…

We study the R\'enyi entanglement entropy and the Shannon mutual information for a class of spin-1/2 quantum critical XXZ chains with random coupling constants which are partially correlated. In the XX case, distinctly from the usual…