Weighted Finite Automata over Strong Bimonoids

We investigate weighted finite automata over strings and strong bimonoids. Such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold. We define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid satisfies local finiteness conditions. Moreover, we show that in this case the given weighted automata can be determinized

The Cognitum: A Perception-Dependent Concept Needed in Baraminology

The taxonomic concept of cognitum (pl., cognita) is introduced to study design among baramins and to relieve other taxonomic concepts (e.g. holobaramin, baramin, basic type) concepts from considerations that may hinder their development. The cognitum is defined as a group of organisms recognized through the human cognitive senses as belonging together and sharing an underlying, unifying gestalt. This concept recognizes the importance of human neuro-cognitive processes in classification. It also implies that, at creation, organisms were endued with characteristics that elicit a unique, divinely-created psychological response in humans and that, after the Flood, the descendant species of the surviving representatives of the baramins retained these specially created characteristics. The cognitum affords research into the relative contribution by objective biosystematic techniques and neuro-cognitive phenomena to the study of biological design and classification. It also promises to clarify current problems in singly nested hierarchies, conflicting characters (homoplasy), fuzzy boundaries of groups, and unplaced taxa. Through its use in the study of biological phenomena, criteria that have been or might be proposed for baramins can be evaluated independently

Subshifts as Models for MSO Logic

We study the Monadic Second Order (MSO) Hierarchy over colourings of the discrete plane, and draw links between classes of formula and classes of subshifts. We give a characterization of existential MSO in terms of projections of tilings, and of universal sentences in terms of combinations of "pattern counting" subshifts. Conversely, we characterise logic fragments corresponding to various classes of subshifts (subshifts of finite type, sofic subshifts, all subshifts). Finally, we show by a separation result how the situation here is different from the case of tiling pictures studied earlier by Giammarresi et al.Comment: arXiv admin note: substantial text overlap with arXiv:0904.245

Weighted tree-walking automata

We define weighted tree-walking automata. We show that the class of tree series recognizable by weighted tree-walking automata over a commutative semiring K is a subclass of the class of regular tree series over K. If K is not a ring, then the inclusion is strict

Independently Evolving Species in Asexual Bdelloid Rotifers

Asexuals are an important test case for theories of why species exist. If asexual clades displayed the same pattern of discrete variation as sexual clades, this would challenge the traditional view that sex is necessary for diversification into species. However, critical evidence has been lacking: all putative examples have involved organisms with recent or ongoing histories of recombination and have relied on visual interpretation of patterns of genetic and phenotypic variation rather than on formal tests of alternative evolutionary scenarios. Here we show that a classic asexual clade, the bdelloid rotifers, has diversified into distinct evolutionary species. Intensive sampling of the genus Rotaria reveals the presence of well-separated genetic clusters indicative of independent evolution. Moreover, combined genetic and morphological analyses reveal divergent selection in feeding morphology, indicative of niche divergence. Some of the morphologically coherent groups experiencing divergent selection contain several genetic clusters, in common with findings of cryptic species in sexual organisms. Our results show that the main causes of speciation in sexual organisms, population isolation and divergent selection, have the same qualitative effects in an asexual clade. The study also demonstrates how combined molecular and morphological analyses can shed new light on the evolutionary nature of species

Definable transductions and weighted logics for texts

AbstractA text is a word together with an additional linear order on it. We study quantitative models for texts, i.e. text series which assign to texts elements of a semiring. We introduce an algebraic notion of recognizability following Reutenauer and Bozapalidis as well as weighted automata for texts combining an automaton model of Lodaya and Weil with a model of Ésik and Németh. After that we show that both formalisms describe the text series definable in a certain fragment of weighted logics as introduced by Droste and Gastin. In order to do so, we study certain definable transductions and show that they are compatible with weighted logics