Magnetic Resonance Elastography (MRE) has emerged as a noninvasive, quantitative physical examination of the elastic properties of soft biological tissues including breast, liver, prostate, and brain. Implementation of constitutive relations that...
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...
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...
A metric structure on a set gives a concept of distance between any two elements of that set, and it induces a topology. In this thesis, we provide several ways to put a metric structure on the collection of CW complexes. We accomplish this by...
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...
Two localized spectroscopic imaging methods were investigated to detect and discriminate microscopic pathologies at the surface of excised breast tissues in order to improve resection completeness during breast conserving surgery. A scanning in...
Goldman and Turaev constructed a Lie bialgebra structure on the free Z-module generated by free homotopy classes of loops on an oriented surface. Turaev conjectured that the cobracket of A is zero if and only if A is a power of a simple class. Chas...
Despite the array of targeted therapeutics that currently exist to combat breast cancer, disease progression leading to metastasis, and tumor recurrence still remains a significant clinical challenge. Efforts to identify novel pathways and...
We describe a set of natural image statistics that are built upon two multi-scale image decompositions, the quadrature mirror filter pyramid decomposition and the local angular harmonic decomposition. These image statistics consist of first- and...
Coding theory. Characters of groups. Error-correcting codes (Information theory). Polynomials.
We introduce vector-valued character theory, a higher dimensional generalization of character theory. We then use vector-valued characters to extend the MacWilliams equivalence theorem for linear codes to a class of additive codes, called...
Nucleotide sequence -- Data processing. Linkage (Genetics) -- Data processing. Computer algorithms. Human population genetics. Medical Term Base Pairing -- genetics. Base Sequence -- genetics. Genome wide association studies.
This thesis investigates techniques for the discovery and use of phase information in genetic studies. ""Phase"" refers to the precise assignment of the members of a different base pairs at the same genomic locus to two possible candidate...
The theory community has worked on Secure Multiparty Computation (SMC) for more than two decades, and has produced many protocols for many settings. One common thread in these works is that the protocols cannot use a Trusted Third Party (TTP), even...
Although genome-wide association studies (GWAS) and other high-throughput initiatives have led to an information explosion in human genetics and genetic epidemiology, the mapping from genotype to phenotype remains challenging as most of the...
Gene set testing has become a critical tool for interpreting the results of high-throughput genomic experiments. Despite the development of robust statistical methods and extensive gene set collections, however, the results from gene set testing...
For ordinary knots in R 3 , there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual...
'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...
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...
Retinoids -- Mechanism of action. ; Post-translational modification. ; Tretinoin -- Therapeutic use. ; Lungs -- Cancer -- Chemoprevention.
The retinoids--natural and synthetic derivatives of vitamin A--are active in cancer therapy and chemoprevention. The signals that underlie retinoid clinical activity are triggered by induction of retinoid target genes. Therefore, a greater...
Neurofibromatosis type 1 (NF1) is a genetic disorder that predisposes affected individuals to a variety of benign and malignant nervous system tumors. NF1 is caused by a mutation in the NF1 tumor suppressor gene, which encodes neurofibromin, a...
Lung cancer is the leading cause of cancer-related mortality. There is a pressing need for improved ways to treat or prevent lung cancer. Murine lung cancer models are previously reported. Although these have explored pathways involved in lung...
Cosmic acceleration could be an effect of a ""dark energy"" fluid pervading the Universe. It could also be an indication that general relativity is not the correct theory of gravity at cosmological length scales. Unfortunately, observations of the...
Manifolds (Mathematics) Geodesics (Mathematics) Space and time.
We investigate weak and strong refocusing of light rays in a space-time and related concepts. A strongly causal space-time ( X^ n +1 , g ) is emphstrongly refocusing at x âˆˆ X if there is a point y â‰ x such that all null-geodesics through y pass...
Ataxia telangiectasia -- Molecular aspects.
DNA damage.
Cell cycle -- Regulation.
Antineoplastic agents.
Cancer cells -- Growth -- Regulation.
Medical Term Cell cycle proteins.
DNA can be damaged by many endogenous and exogenous factors. In response to DNA damage, cells activate cell cycle checkpoints to stop the cell cycle and allow time for repair of the damage. Defects in these pathways allow replication to continue...
DNA damage induces cell cycle arrest through both Chk1 and the p53 tumor suppressor protein, the latter arresting cells through induction of p21waf1 protein. Arrest permits cells to repair the damage and recover. The frequent loss of p53 in tumor...
ISGylation is a type 1 interferon-regulated process that involves conjugation of ISG15, an ubiquitin-like protein, to target proteins. This posttranslational modification is reversed by a deubiquitinase known as UBP43 or USP18. UBP43 is deregulated...
The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....
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...
ID proteins are naturally occurring dominant negative HLH-transcription factors that are highly expressed during development but generally not expressed in adult tissue except for selected cell types and some stem cells. Also, aberrant expression...
Medical imaging methods have become increasingly important in diagnosing diseases and assisting therapeutic treatment. In particular, early detection of breast cancer is considered as a critical factor in reducing the mortality rate of women....
Prostacyclin (PGI 2 ) is a major product of COX-2 catalyzed metabolism of arachidonic acid in the endothelium and has been shown to be atheroprotective. PGI 2 signals though its G-coupled protein receptor (GPCR) the human Prostacyclin receptor...
The fluxes of radiation belt electrons are highly variable, due to a competition between various acceleration, loss, and transport processes. Studies of any of the processes are equally important. My study focuses on electron-EMIC (electromagnetic...
Cell growth and division are coordinated to keep homeostasis of cell size. The components of the core machinery are conserved in a wide range of cell types. Fission yeast (S. pombe) has been an important model organism to study cell size control...
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...