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Now showing items 1-8 of 8

#### On the Equivalence Between Maximum Likelihood and Minimum Distance Decoding for Binary Contagion and Queue-Based Channels with Memory

(2016-02-17)

We study the optimal maximum likelihood (ML) block decoding of general binary codes sent over two classes of binary additive noise channels with memory. Specifically, we consider the infinite and finite memory Polya contagion ...

#### An impulsive differential equation model for Marek's disease

(2016-09-22)

Many dynamical processes are subject to abrupt changes in state. Often these perturbations can be periodic and of short duration relative to the evolving process. These types of phenomena are described well by what are ...

#### On the role of regularity in mathematical control theory

(2016-04-08)

In this thesis, we develop a coherent framework for
studying time-varying vector fields of different regularity classes and their flows. This setting has the benefit of unifying all classes of regularity. In particular, ...

#### Computationally Intensive Methods for Spectrum Estimation

(2016-04-27)

Spectrum estimation is an essential technique for analyzing time series data. A leading method in the field of spectrum estimation is the multitaper method. The multitaper method has been applied to many scientific fields ...

#### Irreducibility of Random Hilbert Schemes

(2016-09-13)

We prove that a random Hilbert scheme that parametrizes the closed
subschemes with a fixed Hilbert polynomial in some projective space is
irreducible and nonsingular with probability greater than $0.5$. To
consider the ...

#### Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

(2016-08-23)

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an ...

#### Higher rank sieves and applications

(2016-04-25)

This thesis focuses on some of the key sieve theoretic ideas behind recent progress on bounded gaps between the primes. One such idea is the notion of higher rank sieve weights, first proposed by Atle Selberg and applied ...

#### Geometry of Dirac Operators

(2016-07-05)

Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$.
Then
\[
\textsc{Atiyah Singer: } \quad
\text{Ind } \mathsf{D}= \int_M ...