Advances in techniques have been producing increasingly complex neural recordings, posing significant challenges for data analysis. This thesis discusses novel statistical methods for analyzing high-dimensional neural data. Part one discusses two extensions of state space models tailored to neural data analysis. First, we propose using a flexible count data distribution family in the observation model to faithfully capture over-dispersion and under-dispersion of the neural observations. Second, we incorporate nonlinear observation models into state space models to improve the flexibility of the model and get a more concise representation of the data. For both extensions, novel variational inference techniques are developed for model fitting, and simulated and real experiments show the advantages of our extensions. Part two discusses a fast region of interest (ROI) detection method for large-scale calcium imaging data based on structured matrix factorization. Part three discusses a method for sampling from a maximum entropy distribution with complicated constraints, which is useful for hypothesis testing for neural data analysis and many other applications related to maximum entropy formulation. We conclude the thesis with discussions and future works.

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Thesis (M.S.)--Ohio University, August, 1995. / Title from PDF t.p.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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This thesis is concerned with stochastic heat equation with memory and nonlinear energy supply. The main motivation to study such systems comes from Thermodynamics, see [85]. The main objective of this work is to study the existence and uniqueness of solutions to such equations and to investigate some fundamental properties of solutions like continuous dependence on initial conditions. In our approach we follow the seminal papers by Da Prato and Clement [10], where the stochastic heat equation with memory is tranformed into an integral equation in a function space and the so-called mild solutions are studied. In the aforementioned papers only linear equations with additive noise were investigated. The main contribution of this work is the extension of this approach to nonlinear equations. Our main tools are the theory of stochastic convolutions as developed in [33] and the theory of resolvent kernels for deterministic linear heat equations with memory, see[10]. Since the solution at time t depends on the whole history of the process up to time t, the resolvent kernel does not define a semigroup of operators in the state space of the process and therefore a ???standard??? theory of stochastic evolution equations as presented in the monograph [33] does not apply. A more delicate analysis of the resolvent kernles and the associated stochastic convolutions is needed. We will describe now content of this thesis in more detail. Introductory Chapters 1 and 2 collect some basic and essentially well known facts about the Wiener process, stochastic integrals, stochastic convolutions and integral kernels. However, some results in Chapter 2 dealing with stochastic convolution with respect to non-homogenous Wiener process are extensions of the existing theory. The main results of this thesis are presented in Chapters 3 and 4. In Chapter 3 we prove the existence and uniqueness of solutions to heat equations with additive noise and either Lipschitz or dissipative nonlinearities. In both cases we prove the continuous dependence of solutions on initial conditions. In Chapter 4 we prove the existence and uniqueness of solutions and continuous dependence on initial conditions for equations with multiplicative noise. The diffusion coefficients defined by unbounded operators are allowed.

A number of recently constructed bridge approach slabs using an articulation at mid span and the wide flange terminal anchorage system have experienced settlement at their expansion joints. This problem is more commonly referred to as the bump at the end of the bridge. This study investigated reasons for the bumps and recommended ways to improve the current situation. To find out possible causes of the bridge approach slab problem, literature review, questionnaire survey, and a visual inspection for 18 Houston sites were conducted. Based on the results, two bridge sites in Houston, Texas, were selected for detailed investigation. An extensive series of laboratory and field tests were performed at each site. The main causes of bump at two study sites were compression of embankment soil and natural soil, and poor compaction of embankment soil. The finite-element computer program ABAQUS was used to evaluate behavior of the current approach slab design and of a possibly more effective design. The results show that the transition zone is about 12 m with 80 percent of the maximum settlement

A number of recently constructed bridge approach slabs using an articulation at mid span and the wide flange terminal anchorage system have experienced settlement at their expansion joints. This problem is more commonly referred to as the bump at the end of the bridge. This study investigated reasons for the bumps and recommended ways to improve the current situation. To find out possible causes of the bridge approach slab problem, literature review, questionnaire survey, and a visual inspection for 18 Houston sites were conducted. Based on the results, two bridge sites in Houston, Texas, were selected for detailed investigation. An extensive series of laboratory and field tests were performed at each site. The main causes of bump at two study sites were compression of embankment soil and natural soil, and poor compaction of embankment soil. The finite-element computer program ABAQUS was used to evaluate behavior of the current approach slab design and of a possibly more effective design. The results show that the transition zone is about 12 m with 80 percent of the maximum settlement