Population Diversity in Ant-inspired Optimization Algorithms

Finding a balance between exploration and exploitation is very important in the case of metaheuristics optimization, especially in the systems leveraging population of individuals expressing (as in Evolutionary Algorithms, etc.) or constructing (as in Ant Colony Optimization) solutions. Premature convergence is a real problem and finding means of its automatic detection and counteracting are of great importance. Measuring diversity in Evolutionary Algorithms working in real-value search space is often computationally complex, but feasible while measuring diversity in combinatorial domain is practically impossible (cf. Closest String Problem). Nevertheless, we propose several practical and feasible diversity measurement techniques dedicated to Ant Colony Optimization algorithms, leveraging the fact that even though analysis of the search space is at least an NP problem, we can focus on the pheromone table, where the direct outcomes of the search are expressed and can be analyzed. Besides proposing the measurement techniques, we apply them to assess the diversity of several variants of ACO, and closely analyze their features for the classic ACO. The discussion of the results is the first step towards applying the proposed measurement techniques in auto-adaptation of the parameters affecting directly the exploitation and exploration features in ACO in the future.

Using the longest run subsequence problem within homology-based scaffolding

Genome assembly is one of the most important problems in computational genomics. Here, we suggest addressing an issue that arises in homology-based scaffolding, that is, when linking and ordering contigs to obtain larger pseudo-chromosomes by means of a second incomplete assembly of a related species. The idea is to use alignments of binned regions in one contig to find the most homologous contig in the other assembly. We show that ordering the contigs of the other assembly can be expressed by a new string problem, the longest run subsequence problem (LRS). We show that LRS is NP-hard and present reduction rules and two algorithmic approaches that, together, are able to solve large instances of LRS to provable optimality. All data used in the experiments as well as our source code are freely available. We demonstrate its usefulness within an existing larger scaffolding approach by solving realistic instances resulting from partial Arabidopsis thaliana assemblies in short computation time.

Qualitative analysis for a new generalized 2-component Camassa-Holm system

<p style='text-indent:20px;'>This paper considers the Cauchy problem for a 2-component Camassa-Holm system</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} m_t = ( u m)_x+ u _xm- v m, \ \ n_t = ( u n)_x+ u _xn+ v n, \end{equation*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ n+m = \frac{1}{2}( u _{xx}-4 u ) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ n-m = v _x $\end{document}</tex-math></inline-formula>, this model was proposed in [<xref ref-type="bibr" rid="b2">2</xref>] from a novel method to the Euler-Bernoulli Beam on the basis of an inhomogeneous matrix string problem. The local well-posedness in Sobolev spaces <inline-formula><tex-math id="M3">\begin{document}$ H^s(\mathbb{R})\times H^{s-1}(\mathbb{R}) $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M4">\begin{document}$ s&gt;\frac{5}{2} $\end{document}</tex-math></inline-formula> of this system was investigated through the Kato's theory, then the blow-up criterion for this system was described by the technique on energy methods. Finally, we established the analyticity in both time and space variables of the solutions for this system with a given analytic initial data.</p>

Efficient Identification of k-Closed Strings

A closed string contains a proper factor occurring as both a prefix and a suffix but not elsewhere in the string. Closed strings were introduced by Fici (WORDS 2011) as objects of combinatorial interest. This paper addresses a new problem by extending the closed string problem to the [Formula: see text]-closed string problem, for which a level of approximation is permitted up to a number of Hamming distance errors, set by the parameter [Formula: see text]. We address the problem of deciding whether or not a given string of length [Formula: see text] over an integer alphabet is [Formula: see text]-closed and additionally specifying the border resulting in the string being [Formula: see text]-closed. Specifically, we present an [Formula: see text]-time and [Formula: see text]-space algorithm to achieve this along with the pseudocode of an implementation and proof-of-concept experimental results.