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Full-Text Articles in Physical Sciences and Mathematics
Lattice-Gas Cellular Automata In Modeling Biological Pattern Formation, Gizem Yuce
Lattice-Gas Cellular Automata In Modeling Biological Pattern Formation, Gizem Yuce
Theses and Dissertations
There are several phenomena present in the physical world which can be defined or predicted by specific models. Cellular automata are basic mathematical models for characterization of natural systems by generating simple components and their local interactions. These models are specified on simple updating rules yet demonstrate complex behavior of physical phenomena. Besides this, lattice-gas cellular automata models go one step further and differ from cellular automata by having split updating rule into two parts as collision and propagation. In this study, the goal is to analyze hexagonal lattice-gas cellular automata with single cell type by using agent-based modeling and …
Clustering Biological Data With Self-Adjusting High-Dimensional Sieve, Josselyn Gonzalez
Clustering Biological Data With Self-Adjusting High-Dimensional Sieve, Josselyn Gonzalez
Theses and Dissertations
Data classification as a preprocessing technique is a crucial step in the analysis and understanding of numerical data. Cluster analysis, in particular, provides insight into the inherent patterns found in data which makes the interpretation of any follow-up analyses more meaningful. A clustering algorithm groups together data points according to a predefined similarity criterion. This allows the data set to be broken up into segments which, in turn, gives way for a more targeted statistical analysis. Cluster analysis has applications in numerous fields of study and, as a result, countless algorithms have been developed. However, the quantity of options makes …
Mathieu-Zhao Subspaces Of Vertex Algebras, Matthew Speck
Mathieu-Zhao Subspaces Of Vertex Algebras, Matthew Speck
Theses and Dissertations
A Mathieu-Zhao subspace is a generalization of an ideal of an associative ring-algebra, A, first formalized in 2010. A vertex algebra is an algebraic structure first developed in conjunction with string theory in the 1960s and later axiomatized by mathematicians in the 1990s. We formally introduce the definition of a Mathieu-Zhao subspace, M, of a vertex algebra, V. Building on natural connections to associative algebras, we classify an infinite set of non-trivial, non-ideal Mathieu-Zhao subspaces for simple and general vertex algebras by group action eigenspace decomposition. Finally, we state the locally nilpotent epsilon-derivation (LNED) conjecture for vertex algebras.