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Algebraic And Combinatorial Approaches For Counting Cycles Arising In Population Biology, Brian Chau
Algebraic And Combinatorial Approaches For Counting Cycles Arising In Population Biology, Brian Chau
Honors Undergraduate Theses
Within population biology, models are often analyzed for the net reproduction number or other generalized target reproduction numbers, which describe the growth or decline of the population based on specific mechanisms. This is useful in determining the strength and efficiency of control measures for inhibiting or enhancing population growth. The literature contains many algebraic and combinatorial approaches for deriving the net reproduction number and generalized target reproduction numbers from digraphs and associated matrices. Finding, categorizing, and counting the permutations of disjoint cycles, or cycles unions is a requirement of the Cycle Union approach by Lewis et al. (2019). These cycles …
Estimation And Clustering In Block Models, Majid Noroozi
Estimation And Clustering In Block Models, Majid Noroozi
Electronic Theses and Dissertations, 2020-
Networks with community structure arise in many fields such as social science, biological science, and computer science. Stochastic block models are popular tools to describe such networks. For this reason, in this dissertation which is composed of two parts we explore some stochastic block models and the relationship between them. In the first part of the dissertation, we study the Popularity Adjusted Block Model (PABM) and introduce its sparse case, the Sparse Popularity Adjusted Block Model (SPABM). The SPABM is the only existing block model which allows to set some probabilities of connections to zero. For both the PABM and …
Estimation And Clustering In Network And Indirect Data, Ramchandra Rimal
Estimation And Clustering In Network And Indirect Data, Ramchandra Rimal
Electronic Theses and Dissertations, 2020-
The first part of the dissertation studies a density deconvolution problem with small Berkson errors. In this setting, the data is not available directly but rather in the form of convolution and one needs to estimate the convolution of the unknown density with Berkson errors. While it is known that the Berkson errors improve the precision of the reconstruction, it does not necessarily happen when Berkson errors are small. Furthermore, the choice of bandwidth in density estimation has been an open problem so far. In this dissertation, we provide an in-depth study of the choice of the bandwidth which leads …
Mean Field Optimal Control And Related Problems, Wei Yan
Mean Field Optimal Control And Related Problems, Wei Yan
Electronic Theses and Dissertations, 2020-
It has been decades since the first paper that mean field problems were studied. More and more problems are considered or solved as new methods and new concepts have been developed. In this dissertation, we will present a series of results on (recursive) mean field stochastic optimal control problems. Comparing our results with those in the classical stochastic optimal control theory, there are following significant differences. First, the value function of a mean field optimal control problem is not Markovian any more, even when coefficient functions in the problem are deterministic. Second, the cost functional we considered is induced by …
Distributed Algorithms And Inverse Graph Filtering, Nazar Emirov
Distributed Algorithms And Inverse Graph Filtering, Nazar Emirov
Electronic Theses and Dissertations, 2020-
Graph signal processing provides an innovative framework to handle data residing on distributed networks, smart grids, neural networks, social networks and many other irregular domains. By leveraging applied harmonic analysis and graph spectral theory, graph signal processing has been extensively exploited, and many important concepts in classical signal processing have been extended to the graph setting such as graph Fourier transform, graph wavelets and graph filter banks. Similarly, many optimization problems in machine learning, sensor networks, power systems, control theory and signal processing can be modeled using underlying network structure. In modern applications, the size of a network is large, …
Transfunctions And Other Topics In Measure Theory, Jason Bentley
Transfunctions And Other Topics In Measure Theory, Jason Bentley
Electronic Theses and Dissertations, 2020-
Measures are versatile objects which can represent how populations or supplies are distributed within a given space by assigning sizes to subregions (or subsets) of that space. To model how populations or supplies are shifted from one configuration to another, it is natural to use functions between measures, called transfunctions. Any measurable function can be identified with its push-forward transfunction. Other transfunctions exist such as convolution operators. In this manner, transfunctions are treated as generalized functions. This dissertation serves to build the theory of transfunctions and their connections to other mathematical fields. Transfunctions that identify with continuous or measurable push-forward …
Representations Of Cuntz Algebras Associated To Random Walks, Nicholas Christoffersen
Representations Of Cuntz Algebras Associated To Random Walks, Nicholas Christoffersen
Honors Undergraduate Theses
In the present thesis, we investigate representations of Cuntz algebras coming from dilations of row co-isometries. First, we give some general results about such representations. Next, we show that by labeling a random walk, a row co-isometry appears naturally. We give an explicit form for representations that come from such random walks. Then, we give some conditions relating to the reducibility of these representations, exploring how properties of a random walk relate to the Cuntz algebra representation that comes from it