Browsing Applied mathematics by Title
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A Complete Asymptotic Analysis of the Spectral Instabilities of SmallAmplitude Periodic Water Waves
Euler's equations govern the behavior of gravity waves on the surface of an incompressible, inviscid, and irrotational fluid (water, in this case). We consider the smallamplitude, periodic travelingwave solutions of ... 
A discovery of neural network architectures for contextdependent computations
All human and animal behavior from seeing, hearing, running, and falling in love, is the result of complex dynamics in a web of intricate networks in the brain. The human brain, in particular, contains close to 100 billion ... 
A New Method for Computing Standard Errors of Risk and Performance Estimators with Serially Correlated Returns
It is well known that small values of unsuspected returns serial correlation result in substantially inflated standard errors of sample mean estimates of mean returns, and that use of standard error estimates based on ... 
A Partial Differential Equation Approach to Three Problems in Finance: Barrier Option Pricing, Optimal Asset Liquidation and Insider Trading
We examine three problems in mathematical finance. These problems broadly fall under the subdisciplines of contract pricing and optimal execution of orders on an exchange under price impact. The first problem deals with ... 
A Stochastic RecordValue Approach to Global Simulation Optimization
Blackbox optimization is ubiquitous in machine learning, operations research and engineering simulation. Blackbox optimization algorithms typically do not assume structural information about the objective function and ... 
An adaptive multilevel method for boundary layer meteorology
(1994)This thesis presents a new adaptive multilevel numerical model for incompressible flows and applies such a model for the first time to the simulation of atmospheric boundary layers capped by shallow cumulus and stratocumulus ... 
AdjointGuided Adaptive Mesh Refinement for Hyperbolic Systems of Equations
One difficulty in developing numerical methods for timedependent partial differential equations is the fact that solutions contain timevarying regions where much higher resolution is required than elsewhere in the domain. ... 
Affine Structures and Stochastic Thermodynamics on the Space of Measures
Kolmogorov’s theory of probability emphasizes a given state space Ω and a given probabilitymeasure P, then constructs the entire calculus of measurable functions X : Ω → R. From this perspective, the properties and dynamics ... 
Analysis of an Aggregationbased Algebraic Multigrid Method and its Parallelization
The interests of this thesis are twofold. First, a twogrid convergence analysis based on the paper [ \textit{Algebraic analysis of aggregationbased multigrid } by A. Napov and Y. Notay, Numer. Lin. Alg. Appl. 18 (2011), ... 
Analysis of Exponential Filter Time Series Operators of Geometric Brownian Motion in Trading Strategies
Trading strategies based on moving average indicators have been analyzed in the academic literature numerous times using historical data to make statistical inferences about various properties such as expected returns. In ... 
Applications of Optimization and Machine Learning to Healthcare
As the field of healthcare becomes increasingly datadriven, optimization and machine learning methods provide the scientific community and practitioners with powerful tools to extract insights from the data with potential ... 
Asymptotic Behaviors and Perturbation Analysis of Stochastic Dynamics and Applications to Complex Systems
The concept of hierarchical structures prevails among scientific points of view on complex systems. From one level to another in a hierarchical structure, with proper scales in both space and time, entire new laws emerge ... 
Branching process models for cancer evolution: overview and an application to colorectal cancer initiation
We study a multitype branching process model associated with a transitional network between types. In particular, we are interested in determining the waiting time to each type in the network, employing an approximation ... 
Climate Response to Solar Variation: Cyclic and Secular
(20130225)The radiation emitted by the Sun varies both cyclically and secularly. We first study in this thesis the response of the Earth's temperature to the 11year solar cycle at the surface and in the troposphere. Then we study ... 
Closing the Loop: Optimal Stimulation of Neuronal Networks via Adaptive Control Algorithms
The Caenorhabditis elegans (C. elegans) worm is a wellstudied biological organism model. The nervous system of C. elegans is particularly appealing to study, since it is a tractable fully functional neuronal network for ... 
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 ... 
Computational methods for system identification and datadriven forecasting
This thesis develops several novel computational tools for system identification and datadriven forecasting. The material is divided into four chapters: datadriven identification of partial differential equations, neural ... 
Coordinated neural activity: Mechanistic origins and impact on stimulus coding
How does the activity of populations of neurons encode the signals they receive? Since neurons in vivo are inherently variable, each fixed input to a population will elicit not a deterministic response, but rather a ... 
Crouzeix's Conjecture and Beyond for Special Classes of Matrices
Let $A$ be an $n$ by $n$ matrix with numerical range $W(A) := \{ q^{*}Aq : q \in \mathbb{C}^n ,~\ q \_2 = 1 \}$. We are interested in functions $\hat{f}$ that maximize $\ f(A) \_2$ (the matrix norm induced by the ... 
Data assimilation problems in glaciology
Rising sea levels due to mass loss from Greenland and Antarctica threaten to inun date coastal areas the world over. For the purposes of urban planning and hazard mitigation, policy makers would like to know how much ...