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Now showing items 1-10 of 10

#### Multitaper Methods for Time-Frequency Spectrum Estimation and Unaliasing of Harmonic Frequencies

(2009-02-05)

This thesis is concerned with various aspects of stationary and nonstationary time series analysis. In the nonstationary case, we study estimation of the Wold-Cram'er evolutionary spectrum, which is a time-dependent ...

#### Pairwise Optimization of Modulation Constellations for Non-Uniform Sources

(2009-10-07)

The design of two-dimensional signal constellations for the transmission of binary non-uniform memoryless sources over additive white Gaussian noise channels is investigated. The main application of this problem is the ...

#### Invariants of Modular Two-Row Groups

(2009-10-06)

It is known that the ring of invariants of any two-row group is Cohen-Macaulay.
This result inspired the conjecture that the ring of invariants of any two-row group is a complete intersection. In this thesis, we study ...

#### Some Advances in the Multitaper Method of Spectrum Estimation

(2009-02-09)

Four contributions to the multitaper method of applied spectrum estimation
are presented. These are a generalization of the multitaper
method of spectrum estimation to time-series possessing irregularly
spaced ...

#### Error-Resilient Tile Sets for DNA Self-Assembly

(2009-08-25)

Experiments have demonstrated that DNA molecules can compute like a machine to
solve mathematical problems, which is significant because of their parallel computation ability. However, due to the nature of biochemical ...

#### A Geometric Approach to Energy Shaping

(2009-09-02)

In this thesis is initiated a more systematic geometric exploration of energy shaping. Most of the previous results have been dealt wih particular cases and
neither the existence nor the space of solutions has been discussed ...

#### Minimal Presentations of Sofic Shifts and Properties of Periodic-Finite-Type Shifts

(2009-08-12)

Constrained codes have been used in data storage systems, such as magnetic tapes,
CD’s and DVD’s, in order to reduce the likelihood of errors by predictable noise.
The study of constrained codes is based on the study of ...

#### Topics in Combinatorics and Random Matrix Theory

(2009-09-27)

Motivated by the longest increasing subsequence problem, we examine sundry
topics at the interface of enumerative/algebraic combinatorics and random matrix theory.
We begin with an expository account of the increasing ...

#### Transcendence of Various Infinite Series and Applications of Baker's Theorem

(2009-11-13)

We consider various infinite series and examine their arithmetic nature. Series of interest are of the form $$\sum_{n =0}^{\infty} \frac{f(n)A(n)}{B(n)}, \;\;\;\; \sum_{n \in \mathbb{Z}}\frac{f(n)A(n)}{B(n)}, \;\;\;\; ...

#### The circular law: Proof of the replacement principle

(2009-07-13)

It was conjectured in the early 1950¡¯s that the empirical
spectral distribution (ESD) of an $n \times n$ matrix whose entries
are independent and identically distributed with mean zero and
variance one, normalized by ...