We study the bijective combinatorics of reduced words. These are fundamental objects in the study of Coxeter groups. We restrict our focus to reduced words of permutations and signed permutations. Our results can all be situated within the context...
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...
Liver disease of different etiologies confers significant morbidity and mortality and hence it constitutes a major health concern worldwide. Stemming from a range of causes, such as viral, drug-induced, alcoholic, or autoimmune, the rate of...
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...
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...
The Euler '-function and Carmichael -function are extremely important in modern number theory, and much work has been devoted to studying the distribution and arithmetic properties of the values of each function. One interesting unresolved question...
Vibrio cholerae is the etiologic agent of the severe diarrheal disease cholera. Colonization of the host environment by V. cholerae requires the type IV toxin co-regulated pilus (TCP). Adequate colonization by V. cholerae is essential for cholera...
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...
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...
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...
Systemic sclerosis (SSc) is a rare and often-fatal systemic autoimmune disease characterized by vasculature dysfunction, immune activation, and extracellular matrix deposition in skin and internal organs. The etiology of SSc is unknown, but it is...
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...
Robots -- Control systems. ; Robots -- Motion. ; Computer algorithms. ; Electronic data processing -- Distributed processing.
Self-reconfiguring robots are robots composed of many physically connected modules which can change their structural configuration to support multiple functionalities. We claim that self-reconfiguring robots are more versatile, extensible, and...
CD antigens. T cells -- Receptors. Receptor-ligand complexes. Transplantation immunology. Immunological tolerance -- Molecular aspects. Antigens
Voltage-dependent sodium channels (Na v ) are critical determinants of the ability of a neuron to generate and propagate action potentials. While a large family of Na v isoforms has been identified, the impact of specific isoforms on the electrical...
The study of twin primes gives rise to several famously difficult problems in number theory--in fact, we still cannot definitively say whether there are infinitely many twin primes. In this work, we consider a related problem, namely: What is the...
Spatial heterogeneity inherent in ecological systems impacts both diversity and community structure. However, little is known about the influence of habitat heterogeneity on temporal variability in communities. I performed several studies to...
Electronic mail systems -- Security measures. Electronic mail systems -- Social aspects. Trust.
A secure system that cannot be used by real users to secure real-world processes is not really secure at all. While many believe that usability and security are diametrically opposed, a growing body of research from the field of Human-Computer...
We present designs, theory and the results of fabrication and testing for a novel parallel microrobotic assembly scheme using stress-engineered MEMS microrobots. The robots are 240-280 Î¼m Ã— 60 Î¼m Ã— 7-20 Î¼m in size, each robot consist of a...
Gene regulation is a principle tool that all organisms utilize to control development, growth, and responses to environmental conditions. Understanding how organisms orchestrate the spatiotemporal regulation of gene expression remains a fundamental...
Automated trust negotiation is a new approach to access control and authentication for the open systems such as the Internet, where sensitive interactions sometimes occur among entities with no prior knowledge of each other. Trust negotiation...
Robot hands -- Design and construction. Robots -- Motion -- Mathematical models. Manipulators (Mechanism) -- Design and construction. Textile fabrics. Knots and splices. String.
Flexible objects are a challenge to manipulate. Their motions are hard to predict, and the high number of degrees of freedom makes sensing, control, and planning difficult. Additionally, they have more complex friction and contact issues than rigid...
Proteins -- Structure -- Mathematical models. Recombinant proteins -- Mathematical models. Mathematical optimization -- Data processing. Dynamic programming. Protein engineering.
Site-directed protein recombination produces improved and novel protein variants by recombining sequence fragments from parent proteins. The resulting hybrids accumulate multiple mutations that have been evolutionarily accepted together. Subsequent...
Biofilm formation is a complex process culminating in a multicellular microbial structure encased in an extracellular matrix. In order for planktonic cells to initiate and proceed through biofilm formation, they must appropriately regulate a number...
Exogenous enzymes, signaling peptides, and other classes of non-human proteins represent a potentially massive but largely untapped pool of biotherapeutic agents. From a practical perspective, however, the use of foreign proteins as novel...
Cellulolytic microorganisms hold promise for industrially applied microbial cellulose utilization in the generation biofuels from renewable resources. Consolidated bioprocessing (CBP), a one-step process combining cellulase production, cellulose...