Browsing Applied mathematics by Title
Now showing items 71-90 of 117
-
On computing shape: a study of the neural processes concerning naturalistic boundary conformation within the ventral visual pathway
The perception of shape is a remarkable computation, solved rapidly by the brain to extract boundary features within natural scenes while being robust against many visual obstacles. Interestingly, while observers typically ... -
On driven neural assemblies: synchrony, chaos and entropy.
(2014-02-24)In this dissertation, I address mathematical problems arising from the field of theo- retical neuroscience that share a common theme: temporally driven neural networks treated as perturbed, coupled nonlinear dynamical ... -
On neural encoding: its estimation, application, and development
The spiking activity of neurons encodes information about sensory stimuli and about planned or executed motor outputs. An important problem in computational neuroscience is the development of predictive models that describe ... -
On the asymptotic behavior of internal layer solutions of advection-diffusion-reaction equations
(2001)We study the behavior of solutions of certain parabolic partial differential equations of the form ut = epsilon2 uxx + epsilong(u) ux + h(u) in the limit epsilon → 0+. Solutions of advection-diffusion and reaction-diffusion ... -
On the instability of water waves with surface tension.
We analyze the stability of solutions to Euler's equations in the presence of surface tension. First we compute stationary solutions to periodic Euler's equations in a travelling frame of reference and then we analyze their ... -
On the Riemann-Hilbert approach to the numerical solution of boundary-value problems for evolution partial differential equations
Integrable systems play an important role in many research areas in Mathematics and Physics. For such systems, the Inverse Scattering Transform provides an alternate way to solve the initial-value problem in terms of ... -
Optimization Formulations and Algorithms for Cancer Therapy
Underlying all cancer therapy protocols are the competing objectives of maximizing tumor control and minimizing normal-tissue complications. As such, we can formulate many aspects of the cancer treatment planning workflow ... -
Optimization methods for parameter identifications in settings with only partial knowledge
This work summarizes two projects focused on incorporating prior knowledge into machine learning models. In the first project, a universal feature selection method for linear mixed-effect models is developed. Namely, Sparse ... -
Optimization of Infectious-Disease Mitigation Strategies with Economic or Equity Perspectives
Infectious-disease outbreaks in human, livestock, and plant populations continue to be a problem that can affect our day-to-day lives and have broader societal implications. There- fore, the need to prevent the spread of ... -
Optimization-based analysis of rigid mechanical systems with unilateral contact and kinetic friction
(2008)A widely-accepted technique for the analysis of rigid mechanical systems with unilateral contact and Coulomb friction is to formulate the contact forces (or impulses) as the unknowns of a linear complementarily problem ... -
Polynomial-Based Methods for Time-Integration
This thesis is divided into two parts: The first introduces a new time integration framework that is based on interpolating polynomials, and the second extends exponential integration to the spectral deferred correction ... -
Reduced Order Model for Global Atmospheric Chemistry Data
Global atmospheric chemistry is an exceptionally high-dimensional problem as it involves hundreds of chemical species that are coupled with each other via a set of ordinary differential equations. Models of atmospheric ... -
Representations in Biological and Artificial Neural Networks
Remarkably, artificial neural networks (ANNs) have shown astounding success in almost all aspects of artificial intelligence. Meanwhile, large scale experiments have gathered an unprecedented amount of data about the ... -
Reproducing color images with custom inks
(1998)This dissertation investigates the general problem of reproducing color images on an off-set printing press using custom inks in any combination and number. Many mathematical and algorithmic challenges arise when printing ... -
Revealing structure in trained neural networks through dimensionality-based methods
Neural networks trained by machine learning optimization methods are currently being analyzed to shed light on brain function. While exciting progress is being made, the complicated nature of the network models typically ... -
Riemann-Hilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions
(2013-11-14)The computation of special functions has important implications throughout engineering and the physical sciences. Nonlinear special functions include the solutions of integrable partial differential equations and the ... -
Robust Approaches for Unsupervised Learning
Today, data science and machine learning are a cornerstone in the engineering, physical, social, and biological sciences. Often, the data available in these fields is large and unlabeled, motivating the development of ... -
Robust dynamic optimization: theory and applications
Many applications in decision-making use a dynamic optimization framework to model a system evolving uncertainly in discrete time, and an agent who chooses actions/controls from a set of available choices in order to ... -
Robust Modeling and Algorithm Design for Science and Engineering
Efficiently extracting information from data sets is at the core of modern scientific com- puting and data-driven discovery. Modeling and algorithm design thus become crucial for research in many scientific and engineering ... -
Robust Real-Time Image Processing Through Dynamic Mode Decomposition
(2013-11-14)In many areas of research, robust and efficient data-mining, and data-driven modeling, have become essential to progressing our understanding of increasingly complex and nonlinear relations often embedded in cluttered ...