This thesis investigates a notion of Turing reducibility introduced by Winkler [8] that is total on all computably enumerable oracles. Groszek and Weber show in [7] that this is a new notion of reducibility and it is not transitive. They give su...
Proteins are ubiquitous in cells and are essential to a wide range of biological processes. Since existing proteins occupy only a small portion of the space of possible amino acid composition, understanding their sequence-structure-function...
In this thesis, we characterize and enumerate the permutations which are realized by the orbits of signed shifts, a family of discrete dynamical systems on words. The permutations, which are called patterns of the signed shifts, are given by the...
During our fieldwork with real-world organizations---including those in Public Key Infrastructure (PKI), network configuration management, and the electrical power grid---we repeatedly noticed that security policies and related security artifacts...
Access control is a core component of any information-security strategy. Researchers have spent tremendous energy over the past forty years defining abstract access-control models and proving various properties about them. However, surprisingly...
This thesis contains material relating to two separate subjects. The first section determines when the C*-algebra affiliated to a directed graph has continuous trace. We use groupoid methods and the focus is on producing conditions on a graph that...
Opinion dynamics is a complex procedure that entails a cognitive process when it deals with how a person integrates influential opinions to form revised opinion. Early research on opinion formation and social influence can be traced back to the...
In utero exposure to maternal malnutrition is associated with increase offspring susceptibility to cardiometabolic and neuropsychiatric disease. Epigenetic mechanisms mediate, at least in part, fetal adaptations to adverse in utero environments...
The Mixed Lineage Leukemia (MLL1) gene was first cloned as a hot spot of chromosomal translocations in acute leukemia. More than 70 fusion proteins of MLL1 have been described in both lymphoid and myeloid leukemia and many are highly associated...
In Chapter 2 we look at the distribution of permutation statistics in the context of pattern-avoiding permutations. The first part of this chapter deals with a recursively defined bijection of Robertson [37] between 123- and 132-avoiding...
Robustness to genetic perturbations is a fundamental property of all living things. The genetic code is degenerate, RNA secondary structure is robust to sequence changes, and protein structure is robust to amino acid substitutions. Complex systems...
Eukaryotic cells are compartmentalized into membrane-enclosed organelles. Genetic screens and reconstituted biochemical assays have revealed that intracellular protein trafficking is mediated by a conserved mechanism of vesicle budding, transport,...
Vibrio cholerae is the etiologic agent of cholera in humans. Intestinal colonization occurs via ingestion of contaminated food and water and results in symptoms that include the production of the characteristic rice water stool, vomiting, and...
The problem of moving rigid bodies efficiently is of particular interest in robotics because the simplest model of a mobile robot or of a manipulated object is often a rigid body. Path planning, controller design and robot design may all benefit...
In order to most effectively investigate protein structure and improve protein function, it is necessary to carefully plan appropriate experiments. The combinatorial number of possible experiment plans demands effective criteria and efficient...
Wireless communication systems. Computer networks. Routers (Computer networks).
A mesh network is a network of wireless routers that employ multi-hop routing and can be used to provide network access for mobile clients. Mobile mesh networks can be deployed rapidly to provide an alternate communication infrastructure for...
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
In this dissertation, I present an examination of the role of two biotic interactions in the population dynamics of Vibrio cholerae. Traits with a genetic basis such as size, physiological processes, stress tolerance, and even behavior, are key...
Novel biotherapeutics have reshaped drug discovery and promise a continued revolution in disease therapy, yet therapeutic proteins present unique design challenges. One distinguishing risk factor is the prospect of eliciting an adaptive immune...
Toxoplasma gondii is an obligate intracellular pathogen that is able to survive in a range of hosts due to its repertoire of secreted effector proteins. Utilizing the type I and type II Δku80 strains we engineered a collection of targeted knockout...
We provide a theoretical model for a design involving a dc voltage biased Josephson junction (JJ) that strongly drives a high quality factor microwave cavity via the ac Josephson effect. We explore the rich classical dynamics of the resultant...
The advent of hypervisors revolutionized the computing industry in terms of malware prevention and detection, secure virtual machine managers, and cloud resilience. However, this has resulted in a disjointed response to handling known threats...
The performance of machine learning algorithms largely depends on data representation. As a critical step in machine learning, representation learning (feature learning) learns a transformation of training data to give a new representation that can...
'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 recognition of foreign peptides by MHC (Major Histocompatibility Complex) proteins is a critical step in the immune response mounted by higher vertebrates against pathogens. MHC proteins have many allelic variants, each recognizing different...
Partially ordered sets and permutations are combinatorial structures having vast applications in theoretical computer science. In this thesis, we study various computational and algorithmic problems related to these structures. The first chapter of...
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...
The Border Gateway Protocol (BGP) that manages inter-domain routing on the Internet lacks security. Protective measures using public key cryptography introduce complexities and costs. To support authentication and other security functionality in...
An interval order is an ordered set whose elements are in correspondence with a collection of intervals in a linearly ordered set, with disjoint intervals ordered by their relative position. The order complex of an ordered set is the simplicial...
RUNX1 is a transcription factor regulating hematopoietic development. Study of the RUNX1 structure revealed two functional domains. The runt domain binds DNA and mediates interaction with CBFß. Sequences C terminal to the runt domain form the...