### Recent Submissions

• #### Evolvability and Pleiotropic Constraint ﻿

Evolvability is a population's ability to change its underlying genetic makeup through natural selection, to evolve. Most measures of short-term evolvability relate genetic change to the abundance and geometry of standing ...
• #### Modelling of Dynamic Computer Experiments with Both Qualitative and Quantitative Variables ﻿

Computer experiments are utilized as a popular tool of studying the relationship between responses and the factors that affect them. They are widely used in scientific researches and applications. Dynamic computer experiments ...
• #### Multitaper Methods for Cyclostationary Feature Detection in Time Series Data: Application to ACE Interplanetary Magnetic Field Data ﻿

In this thesis, a deeper understanding of the theory of cyclostationary processes is sought. Conventional spectrum estimation techniques assume that the data is a realization of a stationary process. If the data is ...
• #### Exploring the Evolutionary Relationship Between Virulence and Drug Resistance ﻿

One of the many possible negative outcomes of pathogen evolution is the emergence of a virulent drug resistant strain. A pathogen may exploit plasmid-mediated gene transfer to gain drug resistance and virulence genes in ...
• #### Channel Optimized Scalar Quantization over Orthogonal Multiple Access Channels with Memory ﻿

In this thesis, the joint source-channel coding method, channel optimized scalar quantization, is applied to real-valued, correlated data. The data is sent over the orthogonal multiple access channel, with non-binary noisy ...
• #### Push-sum Algorithm on Time-varying Random Graphs ﻿

In this thesis, we study the problem of achieving average consensus over a random time-varying sequence of directed graphs by extending the class of so-called push- sum algorithms to such random scenarios. Provided that ...
• #### Global Fluctuations of Random Matrices and the Second-Order Cauchy Transform ﻿

In this thesis we study the global fluctuations of random matrices (i.e., the covariance of two traces) from a second-order free probability perspective, putting a particular emphasis on block Gaussian matrices. Our main ...
• #### Disease, Sex and Evolution ﻿

This thesis focuses upon some evolutionary problems related to sexual reproduction and disease. We first consider whether we should expect a fundamental difference between the outcomes of pre- and post-copulatory sexual ...
• #### Non-commutative Independences for Pairs of Faces ﻿

In non-commutative probability theories, many different notions of independence arise in various contexts. According to the early classification work, there are only five such notions that are universal/natural in the sense ...
• #### Information and Estimation Theoretic Approaches to Data Privacy ﻿

Warner [145] in 1960s proposed a simple mechanism, now referred to as the randomized response model, as a remedy for what he termed “evasive answer bias” in survey sampling. The randomized response setting is as follows: ...
• #### Statistical Methods For Biomarker Threshold Models in Clinical Trials ﻿

In clinical trials, the main objective is to investigate the treatment effects on patients. However, many molecularly targeted drugs or treatments tend to benefit a subset of patients more, identified by a certain biomarker. ...
• #### 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 ...
• #### 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 ...
• #### 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 ...
• #### 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 ...
• #### 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 ...
• #### 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, ...
• #### Arithmetic and Intermediate Jacobians of Calabi-Yau threefolds ﻿

(2015-09-10)
This thesis is centered around particular Calabi-Yau threefolds. Borcea \cite{Borcea} and Voisin \cite{Voisin} construct Calabi-Yau threefolds using elliptic curves and K3 surfaces with non-symplectic involutions. This ...
• #### Distributed Online Optimization on time-varying networks ﻿

(2015-09-01)
This thesis introduces two classes of discrete-time distributed online optimization algorithms, with a group of agents which communicate over a network. At each time, a private convex objective function is revealed to ...