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Full-Text Articles in Physical Sciences and Mathematics
Using Feed-Forward Networks To Infer The Activity Of Feedback Neuronal Networks, Xinxian Huang
Using Feed-Forward Networks To Infer The Activity Of Feedback Neuronal Networks, Xinxian Huang
Dissertations
The nervous system is one of the most important organ systems in a multicellular body. Animals, including human beings perceive, learn, think and deliver motion instructions through their nervous system. The basic structural units of the nervous system are individual neurons which constitute different neuronal networks with distinct functions. In each network, constituent neurons are coupled with different connection patterns, for example, some neurons send feed-forward information to the coupling neurons while others are mutually coupled. Because it is often difficult to analyze large interconnected feedback neuronal networks, it is important to derive techniques to reduce the complexity of the …
A Duality Theory For The Algebraic Invariants Of Substitution Tiling Spaces, Jeffrey Myers Ford
A Duality Theory For The Algebraic Invariants Of Substitution Tiling Spaces, Jeffrey Myers Ford
All Graduate Theses, Dissertations, and Other Capstone Projects
We present here a method for computing the homology of a substitution tiling space. There is a well established cohomology theory that uses simple matrix computations to determine if two tiling spaces are dierent. We will show how to compute Putnam's homology groups for these spaces using simple linear algebra. We construct a Markov Partition based on the substitution rules, and exploit the properties of this partition as a shift of finite type to construct algebraic invariants for the tiling space. These invariants form a chain complex, of which we can compute the homology. In our examples we will demonstrate …