Characterisation of conditional independence structures for polymatroids using vanishing sets

summary:In this paper, we characterise and classify a list of full conditional independences via the structure of the induced set of vanishing atoms. Construction of Markov random subfield and minimal characterisation of polymatroids satisfying a MRF will also be given

Mathematical models of evolution

Ankara : The Department of Industrial Engineering and Institute of Engineering and Sciences, Bilkent Univ., 1992.Thesis (Master's) -- Bilkent University, 1992.Includes bibliographical references leaves 89-93Two categories of evolutionary models are analyzed. The first category is the so-called autogenesis phenomenon. The emergence of self-organization, which has been discussed previously by Csanyi and Kampis is verified. The model is extended to an interrelated multi-level autogenesis system. Similarly, self-organization is observed in a hierarchical order for ea.ch level. The second category is the optimization model ol evolution. An ongoing process of consecutive LP runs associated with random perturbation of the parameters at each step, is designed to simulate the evolutionary mechanisms (mutations, variations and selection) and the population dynamics of a hypothetical ecological system. Two diihu'ent LP ajrproaches for Lotka-Volterra systems are compared and contrastc'd. A brief history of evolution a.nd some mathematical models that have been constructed up to date are also descrilred in the beginning chapter.Özaktaş, HakanM.S

Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory

Frames are collections of vectors in a Hilbert space which have reconstruction properties similar to orthonormal bases and applications in areas such as signal and image processing, quantum information theory, quantization, compressed sensing, and phase retrieval. Further desirable properties of frames for robustness in these applications coincide with structures that have appeared independently in other areas of mathematics, such as special matroids, Gel’Fand-Zetlin polytopes, and combinatorial designs. Within the past few years, the desire to understand these structures has led to many new fruitful interactions between frame theory and fields in pure mathematics, such as algebraic and symplectic geometry, discrete geometry, algebraic combinatorics, combinatorial design theory, and algebraic number theory. These connections have led to the solutions of several open problems and are ripe for further exploration. The central goal of our mini-workshop was to attack open problems that were amenable to an interdisciplinary approach combining certain subfields of frame theory, geometry, and combinatorics