Browsing Applied mathematics by Title
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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 ... 
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. ... 
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), ... 
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 ... 
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 ... 
Datadriven discovery and model reduction of complex systems
Dynamical systems play an integral role in the continued success of scientific theories in describing and predicting the world around us. They are at the heart of countless scientific models, including electromagnetic ... 
DataDriven Sensor Placement Methods
The scalable optimization of sensor placement remains an open challenge in engineering and physical sciences. Optimal placements can only be determined in general using a bruteforce combinatorial search over the domain. ... 
Dimensionality hyperreduction 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 ... 
Dynamic, convex, and robust optimization with Bayesian learning for responseguided dosing
Medical treatment commonly involves the administration of drug doses at multiple timepoints. Intuitively, the higher the doses, the higher the likelihood of disease control as well as the risk of adverse effects and of ... 
Energy and Charge Transfer in Open Plasmonic Systems
Coherent and collective charge oscillations in metal nanoparticles (MNPs), known as localized surface plasmons, offer unprecedented control and enhancement of optical processes on the nanoscale. Since their discovery in ... 
ETGETL Portfolio Optimization
(20130225)Modern Portfolio Theory dates back to 1950s, when Markowitz proposed meanvariance portfolio optimization to construct portfolios. It provided a systematic approach to determine portfolio allocation when one is facing ... 
Exploiting Low Dimensionality in Nonlinear Optics and Other Physical Systems
(20120913)Dimensionality reduction techniques have long been used in a number of fields including nonlinear optics and fluid dynamics. Regardless of the specific technique, the underlying idea is to generate a reduced order model ... 
Finite Volume Methods for the Multilayer Shallow Water Equations with Applications to Storm Surges
(20110711)Coastal hazards related to strong storms such as hurricanes and typhoons are one of the most frequently recurring and wide spread hazards to coastal communities. Storm surges are among the most devastating effects of these ... 
Finite volume methods for Tsunamis genereated by submarine landslides
(20140430)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 ...