Sea ice appears to form an impenetrable boundary at the ocean-atmosphere interface in polar regions, yet in fact its porous structure provides critical pathways for the exchange of heat, gases, salts, and other chemical species impacting the global...
Oligomers -- Structure -- Mathematical models. Nuclear magnetic resonance spectroscopy.
Medical Term: Nuclear Magnetic Resonance, Biomolecular.
Protein complexes play vital roles in the fundamental processes of life. In particular, homo-oligomers are involved in cell signaling, regulation, and transport. To make detailed studies of these symmetric proteins, they need to be discovered, and...
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...
This thesis investigates the embedding theory of orders in central simple algebras, placing a particular emphasis on the role that the phenomenon known as selectivity plays in the theory. Although the notion of selectivity is completely algebraic,...
Constructibility (Set theory). Trees (Graph theory).
This thesis investigates possible initial segments of the degrees of constructibility. Specifically, we completely characterize the structure of degrees in generic extensions of the constructible universe L via forcing with Souslin trees. Then we...
This thesis centers around a generalization of the classical discrete Fourier transform. We first present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite...
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...
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...
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...
One of the important challenges facing image-guided neurosurgery is the fact that the brain deforms significantly over the course of an operation during open-cranial procedures. This results in a loss of registration between the brain and the...
Let K be the function field over a finite field of odd order, and let H be a definite quaternion algebra over K. If Î‘ is an order of level M in H , we define theta series for each ideal I of Î‘ using the reduced norm on H. Using harmonic analysis...
Multisensor data fusion. Sensor networks. Plumes (Fluid dynamics). Automatic tracking. Signal processing -- Digital techniques -- Mathematics.
The work in this thesis deals with a novel approach for detecting and tracking chemical plumes in distributed sensor networks. The ultimate objective is solving the inverse location problem: given unknown sources released at unknown times, the...
We begin with a presentation of the current state of Poljak and Turzik's conjecture that a matroid is sticky if and only if it is modular as described in [5] and [1]. We show that all graphic, cographic, and regular matroids must satisfy the...
Siegel domains. Modular groups. Hecke algebras. Forms
In the 1960s Satake proved the existence of an isomorphism between the local Hecke algebra and the ring of polynomials invariant under the action of the signed permutation group W n (the Weyl group associated to Sp n over a local field)....
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n â‰¥11), Spin(n) (n = 9, n â‰¥11), SU (n) (n â‰¥7), and Sp (n) (n â‰¥5). The proof breaks into three...
Breast -- Magnetic resonance imaging. Breast -- Tomography. Near infrared spectroscopy. Optical tomography. Imaging systems -- Design and construction. Diagnostic imaging -- Mathematical models.
For a long-lived metastable system, the decay of the survival probability is typically exponential. However, deviations are known to exist at short times (the quantum Zeno effect) and at long times (algebraic tails in classical hydrodynamic...
We present new forensic tools that are capable of detecting traces of tampering in digital images without the use of watermarks or specialized hardware. These tools operate under the assumption that images contain natural properties from a variety...
Single cycle electromagnetic pulses have been difficult to experimentally generate and to theoretically analyze. With the recent development of terahertz systems based on near infrared femtosecond lasers it has become possible to perform single...