Now showing items 1-15 of 15

• #### A COMPREHENSIVE OVERVIEW OF MINIMAL-SURFACE THEORY, WITH A THOROUGH MATHEMATICAL TREATMENT OF BERNSTEIN'S THEOREM, THE WEIERSTRASS-ENNEPER REPRESENTATIONS, AND PROPERTIES OF THE GAUSS MAP ﻿

(2014-08)
Notable results in minimal-surface theory include Bernstein's Theorem, the Weierstrass-Enneper representations, and properties of the Gauss map of a minimal surface. For a solution f(x_1, x_2) of the minimal-surface ...
• #### Determining Coherent Sets in 2D Fluid Flows by Transfer Operator Methods ﻿

(2017)
Coherent sets are areas of the flow which are closed or nearly closed from the rest of the fluid (e.g. ocean garbage patches, Jupiter’s red spot). Our goal is to identify such set; this is useful for other areas of research ...
• #### Fast Illumination Normalization for Face Recognition ﻿

(2017)
Many applications of computer vision, security and surveillance require an accurate and realtime method for illumination neutralization and contrast enhancement. We present a new mathematical framework, with a real time ...

(2017)
• #### Mass spectrometry data mining for cancer detection ﻿

(2013-12)
Early detection of cancer is crucial for successful intervention strategies. Mass spectrometry-based high throughput proteomics is recognized as a major breakthrough in cancer detection. Many machine learning methods have ...
• #### Parametric Estimation of the Heston Model under the Indirect Observability Framework ﻿

(2014-08)
Estimating parameters in a given stochastic model from a discrete dataset has wide applications in various scientific studies. However, it is also common that the available data are not generated from the stochastic model ...
• #### Random Walks on a Lattice with Deterministic Local Dynamics ﻿

(2012-08)
In this thesis we prove statistical properties of dynamical systems on a lattice with randomly occurring jumps. The original model of this type, called a hybrid system, was introduced by E. Kobre and L. S. Young in 2007. ...
• #### RANK ONE DYNAMICS NEAR HETEROCLINIC CYCLES AND CONDITIONAL MEMORY LOSS FOR NONEQUILIBRIUM DYNAMICAL SYSTEMS ﻿

(2013-08)
There are two parts in this dissertation. In the first part we prove that genuine nonuniformly hyperbolic dynamics emerge when flows in $\mbb{R}^{N}$ with homoclinic loops or heteroclinic cycles are subjected to certain ...
• #### Smooth Infinitesimal Rigidity for Higher Rank Partially Hyperbolic Actions on Step-2 Nilmanifolds ﻿

(2012-05)
If Λ is finitely generated and M is compact, an action φ M → M is a C ∞ homomorphism : Λ ×from Λ to Diff(M ). There is a natural formal tangent space at the point [φ] determined by φ, which is given by the 1-cocycles ...
• #### Statistical Properties of Chaotic Dynamical Systems: Non-Stationary Central Limit Theorems and Extreme Value Theory ﻿

(2015-05)
In this thesis, some statistical properties of two interesting problems are studied. The first one is about non-stationary central limit theorems. We establish central limit theorems for a sequence of nested balls ...
• #### The Interplay of Architecture and Correlated Variability in Neuronal Networks ﻿

(2013-08)
This much is certain: neurons are coupled, and they exhibit covariations in their output. The extent of each does not have a single answer. Moreover, the strength of neuronal correlations, in particular, has been a ...
• #### Uniqueness Results of Algebraic Curves and Related Topics ﻿

(2017-05)
It is well-known that if two complex polynomials P and Q share two values without counting multiplicities, then they are the same. Such problem is called the value sharing problem. In this dissertation, we study the value ...
• #### Using Numerical Integration to Further Understand Dynamical Systems ﻿

(2017)
Some equations are impossible to solve analytically, so a numerical integrator must be used. Mainly studied the Lorenz System and the double pendulum, both of which are chaotic systems. Studied return map and symbolic ...
• #### Visual decision making in the presence of stimulus and measurement correlations ﻿

(2013-12)
Our brains process sensory information to infer the state of the world. However, the input from our senses is noisy, which may lead to errors in perceptual judgements. A number of theoretical studies have modeled perception ...
• #### Wavelet Approaches to Seismic Data Analysis ﻿

(2012-12)
There have been extensive applications of wavelets to petroleum seismic data. In this dissertation, we focus on developing and testing new wavelets approaches to seismic data compression, microseismic first arrival picking, ...