Browsing Applied mathematics by Issue Date
Now showing items 21-40 of 114
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Single-column and mixed-layer model analysis of subtropical stratocumulus response mechanisms relevant to climate change
(2013-11-14)Subtropical stratocumulus clouds are important part of the Earth's energy budget. The response of low clouds to Earth's changing climate is one of the dominant uncertainties in global warming projections, due primarily ... -
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 ... -
Towards Patient-Specific Mathematical Radiation Oncology
(2013-11-14)The war against cancer continues to take its toll on society, even after many decades of focused, intensive research into its origins and cures. Increasingly, efforts are being made to incorporate physical sciences and ... -
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 ... -
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 ... -
Value function approximation methods for Linearly-solvable Markov Decision Process
(2014-02-24)Optimal control provides an appealing machinery to complete complicated control tasks with limited prior knowledge. Both global methods and online trajectory optimization methods are powerful techniques for solving optimal ... -
Finite volume methods for Tsunamis generated by submarine landslides
(2014-04-30)Submarine landslides can generate tsunamis, and the generated waves can be catastrophic when a large volume of landslide material is involved. Moreover, large earthquakes are often accompanied by submarine landslides that ... -
Variability in Modified Estimators of VaR and ES
Modified Value-at-Risk (mVaR) and Modified Expected Shortfall (mES) are risk estimators that can be calculated without modelling the distribution of asset returns. These modifided estimators use skewness and kurtosis ... -
Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing
Medical treatment commonly involves the administration of drug doses at multiple time-points. Intuitively, the higher the doses, the higher the likelihood of disease control as well as the risk of adverse effects and of ... -
Dimensionality hyper-reduction and machine learning for dynamical systems with varying parameters
This work demonstrates methods for hyper reduction and efficient computation of solutions of dynamical systems using optimization and machine learning techniques. We consider nonlinear partial differential equations that ... -
Stochastic Modeling of Reversible Biochemical Reaction-Diffusion Systems and High-Resolution Shock-Capturing Methods for Fluid Interfaces
My thesis contains two parts, both of which are motivated by biological problems. One is on stochastic reaction-diffusion for biochemical systems and the other on shock-capturing methods for fluid interfaces. In both parts, ... -
Machine learning and data decompositions for complex networked dynamical systems
Machine learning has become part of our daily lives. Its applications include personalized advertisements, stock price predictions, and self-driving cars. The goal of this thesis is to study ways to apply machine learning ... -
Lagrangian coherent structures and the dynamics of inertial particles
Dynamics of inertial particles in two-dimensional planar flow have been investigated by evaluating finite-time Lyapunov exponents (FTLE). The first part of our work deals with inertial particle dynamics. The Maxey-Riley ... -
Collective Activity in Neural Networks: the Mathematical Structure of Connection Graphs and Population Codes
Correlated, or synchronized, spiking activity among pairs of neurons is widely observed across the nervous system. How do these correlations arise from the dynamics of neural networks? The interconnectivity of neurons is ... -
This Brain Is a Mess: Inference, Random Graphs, and Biophysics to Disentangle Neuronal Networks
At first glance, the neuronal network seems like a tangled web in many areas throughout the nervous system. Often, our best guess is that such “messy” connections are close to random, while obeying certain statistical ... -
Multi-scale modeling of paracrine PDGF-driven glioma growth and invasion
The most common primary brain tumor in adults, glioma claims thousands of lives each year. Despite efforts to improve survival rates, the standard of care has remain unchanged for more than a decade. Recent research has ... -
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 ... -
Irreversibility in Stochastic Dynamic Models and Efficient Bayesian Inference
This thesis is the summary of an excursion around the topic of reversibility. We start the journal from a classical mechanical view of the “time reversal symmetry”: we look into the details to track the movements of all ... -
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 ... -
High order shock capturing methods with compact stencils for use with adaptive mesh refinement and mapped grids
This thesis focuses on several developments toward creating a high order shock capturing method that can be used on mapped grids with block-structured adaptive mesh refinement (AMR). The discontinuous Galerkin (DG) method ...