We start by introducing avoidance coupling of Markov chains, with an overview of existing results. We then introduce and motivate a new notion, uniform coupling. We show that the only Markovian avoidance coupling on a cycle is of this type, and...
In the past decade, the use of ordinal patterns in the analysis of time series and dynamical systems has become an important tool. Ordinal patterns (otherwise known as a permutation patterns) are found in time series by taking n data points at...
This thesis contains some results concerning groupoid dynamical systems and crossed products. We introduce the notion of a proper groupoid dynamical system and of its generalized fixed point algebra. We show that our notion of proper groupoid...
Predictive control. Adaptive control systems -- Design. Airplanes -- Control systems.
A direct method to design data-based model predictive controllers is presented. The design method uses system identification techniques to identify model predictive controller gains directly from a set of excitation input and disturbance corrupted...
We examine variations of cops and robbers games on graphs. Our goals are to introduce some randomness into their study, and to estimate (expected) capture time. We show that a cop chasing a random walker can capture him in expected time n + o(n)....
The proliferation of mobile devices and other consumer products has greatly expanded the market for CMOS image sensors. This in turn has promoted a trend of continued improvement in image sensor performance, as companies seek to gain an advantage...
Continual improvements to clinical breast imaging technologies have led to ever earlier detections and increasingly accurate localizations of female breast cancers. While these advancements have certainly improved the prognoses of many patients,...
We present new forensic tools that are capable of detecting traces of tampering in digital images without the use of watermarks or specialized hardware. These tools operate under the assumption that images contain natural properties from a variety...
After decades of searching we have yet to find the progenitor systems for type Ia supernovae. In fact most of what we know about this homogeneous class of supernovae is from spectral features associated with the incinerated remains of the C+O white...
Recent years have witnessed a new class of monitoring applications that need to continuously collect information from remote data sources. Those data sources, such as web click-streams, stock quotes, and sensor data, are often characterized as...
Information retrieval -- Mathematical models. ; Electronic information resource searching. ; Computer algorithms. ; Decision making -- Data processing. ; Mathematical optimization.
This thesis presents a unified method for simultaneous solution of three problems in Information Retrieval--metasearch (the fusion of ranked lists returned by retrieval systems to elicit improved performance), efficient system evaluation (the...
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥5). The proof breaks into three...
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
In this thesis we develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating...
Breast -- Magnetic resonance imaging. Breast -- Tomography. Near infrared spectroscopy. Optical tomography. Imaging systems -- Design and construction. Diagnostic imaging -- Mathematical models.
For a local field K, we study the affine buildings Ξ n and Δ n naturally associated to SL n ( K ) and Sp n ( K ), respectively. Since Sp n ( K ) is a subgroup of SL 2 n ( K ), we investigate properties of a natural embedding of Δ n in Ξ 2 n ....
Casimir effect. Zero-point field. Electric conductivity. Quantum electrodynamics.
The Casimir force arises from an alteration of boundary condition in vacuum and is often regarded as a manifestation of quantum zero point energy. Considerable progress has been made in the last decade with an impressive achievement of experimental...
Proteins are ubiquitous in cells and are essential to a wide range of biological processes. Since existing proteins occupy only a small portion of the space of possible amino acid composition, understanding their sequence-structure-function...