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- W2602411525 abstract "In this thesis we look at results concerning two separate topics.The first topic belongs to the general problem of reconstruction of interaction networks using only per-site information. In chapter 2 a method for exact reconstruction of leaky integrate-and-fire networks from spike time data is presented. This method is capable of reconstructing networks of several hundred neurons in a relatively short time; it is not only a significant advance on the current state of the art with respect to model neuron networks, it stands as a proof in principle that the problem of exact reconstruction of pulse-coupled networks is not inherently intractable due to discrete interactions.The second topic is the relation between Potts / Ising models from statistical physics and the chromatic polynomial from graph theory. Chapter 3 presents a new method for computing the chromatic polynomial of a given graph based on algebraic operators that can be implemented with simple match-and-replace rules in any symbolic math system. On strip lattices the running time of the new method is competitive with previous specialized lattice-based methods from statistical physics; however, it is also capable of working on arbitrary graphs without modification, so vastly expands the structural range of graphs that can be accessed. Among the results presented here is the chromatic polynomial of the $4 times 4 times 4$ simple cubic lattice (free boundary conditions), the first time this has ever been successfully computed; previous research had been restricted to relatively unphysical 2-dimensional systems by feasibility issues. In chapter 4 the greater flexibility of the new method is exploited to do extensive calculations of chromatic polynomials on random graphs with between 12 and 30 vertices across the entire range of edge-densities. Our finding is that the complex root sets of the chromatic polynomials of random graphs fall into stereotypical locations depending on size and density; in particular, when the average degree is fixed the point at which the complex root set will meet the real line is very predictable, and independent of the total number of vertices." @default.
- W2602411525 created "2017-04-07" @default.
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- W2602411525 date "2011-04-05" @default.
- W2602411525 modified "2023-09-27" @default.
- W2602411525 title "Topological Optimization in Network Dynamical Systems" @default.
- W2602411525 hasPublicationYear "2011" @default.
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