A cyclic unary regular language is a regular language over a unary alphabet that is represented by a cyclic automaton. We propose a similarity measure for cyclic unary regular languages by modifying the Jaccard similarity coefficient and the Sorensen coefficient to measure the level of overlap between such languages. This measure computes the proportion of strings that are shared by two or more cyclic unary regular languages and is an upper bound of the Jaccard coefficient and the Sorensen coefficient. By using such similarity measure, we define a dissimilarity measure for cyclic unary regular languages that is a semimetric distance. Moreover, it can be used for the non-cyclic case.
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We extend the edit operators of substitution, deletion, and insertion of a symbol over an word by introducing two new operators (partial copy and partial elimination) inspired by biological gene duplication. We define a disruption measure for an operator over a word and prove that whereas the traditional edit operators are disruptive, partial copy and partial elimination are non-disruptive. Moreover, we show that the application of only edit operators does not generate (with low disruption) all the words over a binary alphabet, but this can indeed be done by combining partial copy and partial elimination with the substitution operator.
The vespertilionid bat Histiotus macrotus occurs in western Argentina, central regions of Chile and south of Argentina and Chile, and it may be also present in Bolivia and southern Peru. In this work, we analyzed the geographic and potential distribution of a poorly known species of South American bat. As a tool, environmental niche modeling has been used to study the distributional patterns of species and more recently, taxonomic boundaries of cryptic species. We used MaxEnt v 3.3.e, Worldclim database and a vegetation map, covering the entire area of species' occurrence. We registered 64 localities from Argentina (43), Chile (10), Peru (8) and Bolivia (5). We divided recording localities in different datasets according to several taxonomic schemes, and analyzed potential distribution models separately (i.e., all known records; Argentina-Chile; Peru) in five different models. Models including all known localities showed a disjoint distribution, with two basic core areas of high predictive values, one in NW Argentina and another in southern Chile and SW Argentina separated by the South American Arid Diagonal. A third area appeared in Atacama and Sechura deserts in the models that included Peruvian and Bolivian localities. Model including only Peruvian localities showed the opposite pattern, with high predictive values only in arid environments from southern Peru. We interpreted that localities correctly assigned to H. macrotus belong to a taxonomic complex distributed in two contrasting areas, each one inhabited by a different taxon: 1) Bolivia and NW Argentina and 2) S and central Chile and SW Argentina. Given the systematic uncertainty of Histiotus, these two forms might be sister species or may not share an immediate common ancestor within the genus. Further, we consider that the specimens from localities referred to H. macrotus from southern Peru should be revised. These alternatives await a comprehensive molecular phylogenetic analysis of Histiotus.
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