Structuring the elementary components of graphs having a perfect internal matching

AbstractGraphs with perfect internal matchings are decomposed into elementary components, and these components are given a structure reflecting the order in which they can be reached by external alternating paths. It is shown that the set of elementary components can be grouped into pairwise disjoint families determined by the “two-way accessible” relationship among them. A family tree is established by which every family member, except the root, has a unique father and mother identified as another elementary component and one of its canonical classes, from which the given member is two-way accessible. It is proved that every member of the family is only accessible through a distinguished canonical class of the root by external alternating paths. The families themselves are arranged in a partial order according to the order they can be covered by external alternating paths, and a complete characterization of the graph's forbidden and impervious edges is elaborated

Splitters and barriers in open graphs having a perfect internal matching

A counterpart of Tutte's Theorem and Berge's formula is proved for open graphs with perfect (maximum) internal matchings. Properties of barriers and factor-critical graphs are studied in the new context, and an efficient algorithm is given to find maximal barriers of graphs having a perfect internal matching

Turing Automata and Graph Machines

Indexed monoidal algebras are introduced as an equivalent structure for self-dual compact closed categories, and a coherence theorem is proved for the category of such algebras. Turing automata and Turing graph machines are defined by generalizing the classical Turing machine concept, so that the collection of such machines becomes an indexed monoidal algebra. On the analogy of the von Neumann data-flow computer architecture, Turing graph machines are proposed as potentially reversible low-level universal computational devices, and a truly reversible molecular size hardware model is presented as an example

Elementary decomposition of soliton automata

Soliton automata are the mathematical models of certain possible molecular switching devices. In this paper we work out a decomposition of soliton automata through the structure of their underlying graphs. These results lead to the original aim, to give a characterization of soliton automata in general case

Grounding semantics in robots for Visual Question Answering

In this thesis I describe an operational implementation of an object detection and description system that incorporates in an end-to-end Visual Question Answering system and evaluated it on two visual question answering datasets for compositional language and elementary visual reasoning

Competencies, Technological Change and Network Dynamics. The case of the bio-pharmaceutical industry

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Mathematical Methods for the Quantification of Actin-Filaments in Microscopic Images

In cell biology confocal laser scanning microscopic images of the actin filament of human osteoblasts are produced to assess the cell development. This thesis aims at an advanced approach for accurate quantitative measurements about the morphology of the bright-ridge set of these microscopic images and thus about the actin filament. Therefore automatic preprocessing, tagging and quantification interplay to approximate the capabilities of the human observer to intuitively recognize the filaments correctly. Numerical experiments with random models confirm the accuracy of this approach