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Full-Text Articles in Physical Sciences and Mathematics
Advanced Sequential Monte Carlo Methods And Their Applications To Sparse Sensor Network For Detection And Estimation, Kai Kang
Doctoral Dissertations
The general state space models present a flexible framework for modeling dynamic systems and therefore have vast applications in many disciplines such as engineering, economics, biology, etc. However, optimal estimation problems of non-linear non-Gaussian state space models are analytically intractable in general. Sequential Monte Carlo (SMC) methods become a very popular class of simulation-based methods for the solution of optimal estimation problems. The advantages of SMC methods in comparison with classical filtering methods such as Kalman Filter and Extended Kalman Filter are that they are able to handle non-linear non-Gaussian scenarios without relying on any local linearization techniques. In this …
Big Homotopy Theory, Keith Gordon Penrod
Big Homotopy Theory, Keith Gordon Penrod
Doctoral Dissertations
Cannon and Conner developed the theory of "big fundamental groups." This is meant to expand on the notion of fundamental group and is a powerful tool that can be used for distinguishing spaces that are not distinguishable using the fundamental group. Turner proved several classical results, such as covering theory and Seifert-VanKampen for big fundamental groups. The purpose of this paper is to expand on the the theory, to refine the definitions, and to give more examples. Also, in this paper, we define big higher homotopy groups analogous to the way classical higher homotopy groups are defined.
Discrete Geometric Homotopy Theory And Critical Values Of Metric Spaces, Leonard Duane Wilkins
Discrete Geometric Homotopy Theory And Critical Values Of Metric Spaces, Leonard Duane Wilkins
Doctoral Dissertations
Building on the work of Conrad Plaut and Valera Berestovskii regarding uniform spaces and the covering spectrum of Christina Sormani and Guofang Wei developed for geodesic spaces, the author defines and develops discrete homotopy theory for metric spaces, which can be thought of as a discrete analog of classical path-homotopy and covering space theory. Given a metric space, X, this leads to the construction of a collection of covering spaces of X - and corresponding covering groups - parameterized by the positive real numbers, which we call the [epsilon]-covers and the [epsilon]-groups. These covers and groups evolve dynamically as the …