Recent Submissions

  • Exploring the Evolutionary Relationship Between Virulence and Drug Resistance 

    van den Hoogen, Josée
    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 

    Preusser, Kiraseya
    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 

    Rezaeinia, Pouya
    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 

    Diaz Torres, Mario
    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 

    McLeod, David
    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 

    Gu, Yinzheng
    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 

    Asoodeh, Shahab
    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 

    Gavanji, Parisa
    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 

    Rozins, Carly (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 

    Staal, Andrew P. (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 

    Milne, Tristan (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 

    Beheshti Vadeqan, Babak (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 

    Pohlkamp-Hartt, Joshua (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 

    Vatwani, Akshaa (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 

    Jafarpour, Saber (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 

    Molnar, Alexander (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 

    Akbari Varnousfaderani, Mohammad Jr (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 ...
  • Curves of low genus on surfaces and applications to Diophantine problems 

    Garcia, Natalia (2015-08-31)
    We describe in detail a technique due to Vojta for finding the explicit set of curves of low genus on certain algebraic surfaces of general type, and refine some of its aspects. We then provide applications of this method ...
  • Optimality of Walrand-Varaiya Type Policies and Approximation Results for Zero-Delay Coding of Markov Sources 

    Wood, Richard (2015-07-28)
    Optimal zero-delay coding of a finite state Markov source through quantization is considered. Building on previous literature, the existence and structure of optimal policies are studied using a stochastic control problem ...
  • Optimal Quantization and Approximation in Source Coding and Stochastic Control 

    Saldi, Naci (2015-06-23)
    This thesis deals with non-standard optimal quantization and approximation problems in source coding and stochastic control. The first part of the thesis considers randomized quantization. Adapted from stochastic ...

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