We present aligned hierarchies, a novel solution to the dimension reduction problem, representing high-dimensional and noisy sequential data as a low-dimensional object that encodes relevant information. In this thesis, we motivate our presentation...
We study the bijective combinatorics of reduced words. These are fundamental objects in the study of Coxeter groups. We restrict our focus to reduced words of permutations and signed permutations. Our results can all be situated within the context...
The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....
Gene set testing has become a critical tool for interpreting the results of high-throughput genomic experiments. Despite the development of robust statistical methods and extensive gene set collections, however, the results from gene set testing...
Medical imaging methods have become increasingly important in diagnosing diseases and assisting therapeutic treatment. In particular, early detection of breast cancer is considered as a critical factor in reducing the mortality rate of women....
This thesis centers around a generalization of the classical discrete Fourier transform. We first present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite...
The accelerated expansion of space in the Universe has been known for two decades. However, finding a plausible theory that describes this expansion is more difficult: Taking general relativity for granted requires us to stipulate the existence of...
'Orthogonal modular forms are algebraic modular forms arising from lattices in quadratic spaces. In this thesis, we define orthogonal modular forms, establish their basic properties, and then apply them to a case of ternary quadratic spaces to...
'The control of waves using periodic structures is crucial for modern optical, electromagnetic and acoustic devices such as diffraction gratings, filters, photonic crystals, solar cells, sensors, and absorbers. We present a high-order accurate...
We study motion planning problems, finding trajectories that connect two configurations of a system, from two different perspectives: optimality and survivability. For the problem of finding optimal trajectories, we provide a model in which the...
Electroencephalography -- Data processing. ; Epilepsy -- Diagnosis. ; Signal processing -- Mathematics. ; Time-series analysis. ; Wavelets (Mathematics).
Visual interpretation of the EEG associated with an epileptic seizure (ictal EEG) can be cumbersome and sometimes misleading, due to rapid seizure spread, limited spatial resolution and the fact that signals of interest are often obscured by...
Part I. A photoprecursor for difluorocarbene . The goal of this research was to develop a more practical and efficient photoprecursor for difluorocarbene. The first approach was concerned with the synthesis of 4,4-difluoropyrazoline-3,5-dione ( 5...
Plant genetic engineering. ; Plants -- Effect of cadmium on. ; Cadmium -- Physiological transport.
Iron plays a central role in key biological processes in both plants and animals. Lack of available iron commonly limits plant growth and nutritional value. Worldwide, dietary iron is primarily obtained from plant sources and, despite our best...
In large and complex networks such as the Internet and road networks, traffic routing is typically decentralized. Users in the network choose their routes independently to minimize their own delay, leading to complicated and nonintuitive outcomes...
Calanus finmarchicus -- Georges Bank. ; Calanus finmarchicus -- Maine Gulf of. ; Calanus finmarchicus -- North Atlantic Ocean.
Calanus finmarchicus, a kind of marine zooplankton, plays an important ecological role throughout the North Atlantic. Striking seasonal variations exist in its abundance and distribution in the Gulf of Maine/Georges Bank region. On the Bank in...
We describe a set of natural image statistics that are built upon two multi-scale image decompositions, the quadrature mirror filter pyramid decomposition and the local angular harmonic decomposition. These image statistics consist of first- and...
We consider a problem of information overload: the conflict between vast amounts of data available in electronic form and inadequate tools for finding relevant information. To alleviate this problem we look at the information organization:...
Coding theory. Characters of groups. Error-correcting codes (Information theory). Polynomials.
We introduce vector-valued character theory, a higher dimensional generalization of character theory. We then use vector-valued characters to extend the MacWilliams equivalence theorem for linear codes to a class of additive codes, called...
Free radicals (Chemistry). ; Electron donor-acceptor complexes. ; Ions.
In this study, the initial charge separation distance and its impact on free radical ion (FRI) formation are investigated in detail. Transient photocurrent techniques together with other spectroscopic methods were used with a series of donors and...