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Articles 1 - 24 of 24
Full-Text Articles in Probability
Static And Dynamic State Estimation Applications In Power Systems Protection And Control Engineering, Ibukunoluwa Olayemi Korede
Static And Dynamic State Estimation Applications In Power Systems Protection And Control Engineering, Ibukunoluwa Olayemi Korede
Doctoral Dissertations
The developed methodologies are proposed to serve as support for control centers and fault analysis engineers. These approaches provide a dependable and effective means of pinpointing and resolving faults, which ultimately enhances power grid reliability. The algorithm uses the Least Absolute Value (LAV) method to estimate the augmented states of the PCB, enabling supervisory monitoring of the system. In addition, the application of statistical analysis based on projection statistics of the system Jacobian as a virtual sensor to detect faults on transmission lines. This approach is particularly valuable for detecting anomalies in transmission line data, such as bad data or …
Large Deviations For Self Intersection Local Times Of Ornstein-Uhlenbeck Processes, Apostolos Gournaris
Large Deviations For Self Intersection Local Times Of Ornstein-Uhlenbeck Processes, Apostolos Gournaris
Doctoral Dissertations
In the area of large deviations, people concern about the asymptotic computation of small probabilities on an exponential scale. The general form of large deviations can be roughly described as: P{Yn ∈ A} ≈ exp{−bnI(A)} (n → ∞), for a random sequence {Yn}, a positive sequence bn with bn → ∞, and a coefficient I(A) ≥ 0. In applications, we often concern about the probability that the random variables take large values, that is we concern about the P{Yn ≥ λ}, where λ > 0. Here, we consider the Ornstein-Uhlenbeck process, study the properties of the local times and self intersection …
Dynamic Neuromechanical Sets For Locomotion, Aravind Sundararajan
Dynamic Neuromechanical Sets For Locomotion, Aravind Sundararajan
Doctoral Dissertations
Most biological systems employ multiple redundant actuators, which is a complicated problem of controls and analysis. Unless assumptions about how the brain and body work together, and assumptions about how the body prioritizes tasks are applied, it is not possible to find the actuator controls. The purpose of this research is to develop computational tools for the analysis of arbitrary musculoskeletal models that employ redundant actuators. Instead of relying primarily on optimization frameworks and numerical methods or task prioritization schemes used typically in biomechanics to find a singular solution for actuator controls, tools for feasible sets analysis are instead developed …
Nonparametric Bayesian Deep Learning For Scientific Data Analysis, Devanshu Agrawal
Nonparametric Bayesian Deep Learning For Scientific Data Analysis, Devanshu Agrawal
Doctoral Dissertations
Deep learning (DL) has emerged as the leading paradigm for predictive modeling in a variety of domains, especially those involving large volumes of high-dimensional spatio-temporal data such as images and text. With the rise of big data in scientific and engineering problems, there is now considerable interest in the research and development of DL for scientific applications. The scientific domain, however, poses unique challenges for DL, including special emphasis on interpretability and robustness. In particular, a priority of the Department of Energy (DOE) is the research and development of probabilistic ML methods that are robust to overfitting and offer reliable …
Characterization Of The Anomalous Ph Of Aqueous Nanoemulsions, Kieran P. Ramos
Characterization Of The Anomalous Ph Of Aqueous Nanoemulsions, Kieran P. Ramos
Doctoral Dissertations
Aqueous water-in-oil nanoemulsions have emerged as a versatile tool for use in microfluidics, drug delivery, single-molecule measurements, and other research. Nanoemulsions are often prepared with perfluorocarbons which are remarkably biocompatbile due to their stability, low surface tension, lipophobicity, and hydrophobicity. Therefore it is often assumed that droplet contents are unperturbed by the perfluorinated surface. However, in microemulsions, which are similar to nanoemulsions, it is known that either the pH of the aqueous phase or the ionization constants of encapsulated molecules are different from bulk solution. There is also recent evidence of low pH in perfluorinated aqueous nanoemulsions. The current underlying …
Function And Dissipation In Finite State Automata - From Computing To Intelligence And Back, Natesh Ganesh
Function And Dissipation In Finite State Automata - From Computing To Intelligence And Back, Natesh Ganesh
Doctoral Dissertations
Society has benefited from the technological revolution and the tremendous growth in computing powered by Moore's law. However, we are fast approaching the ultimate physical limits in terms of both device sizes and the associated energy dissipation. It is important to characterize these limits in a physically grounded and implementation-agnostic manner, in order to capture the fundamental energy dissipation costs associated with performing computing operations with classical information in nano-scale quantum systems. It is also necessary to identify and understand the effect of quantum in-distinguishability, noise, and device variability on these dissipation limits. Identifying these parameters is crucial to designing …
Allocative Poisson Factorization For Computational Social Science, Aaron Schein
Allocative Poisson Factorization For Computational Social Science, Aaron Schein
Doctoral Dissertations
Social science data often comes in the form of high-dimensional discrete data such as categorical survey responses, social interaction records, or text. These data sets exhibit high degrees of sparsity, missingness, overdispersion, and burstiness, all of which present challenges to traditional statistical modeling techniques. The framework of Poisson factorization (PF) has emerged in recent years as a natural way to model high-dimensional discrete data sets. This framework assumes that each observed count in a data set is a Poisson random variable $y ~ Pois(\mu)$ whose rate parameter $\mu$ is a function of shared model parameters. This thesis examines a specific …
Asymptotic Behavior Of The Random Logistic Model And Of Parallel Bayesian Logspline Density Estimators, Konstandinos Kotsiopoulos
Asymptotic Behavior Of The Random Logistic Model And Of Parallel Bayesian Logspline Density Estimators, Konstandinos Kotsiopoulos
Doctoral Dissertations
This dissertation is comprised of two separate projects. The first concerns a Markov chain called the Random Logistic Model. For r in (0,4] and x in [0,1] the logistic map fr(x) = rx(1 - x) defines, for positive integer t, the dynamical system xr(t + 1) = f(xr(t)) on [0,1], where xr(1) = x. The interplay between this dynamical system and the Markov chain xr,N(t) defined by perturbing the logistic map by truncated Gaussian noise scaled by N-1/2, where N -> infinity, is studied. A natural question is …
Dependence Structures In Lévy-Type Markov Processes, Eddie Brendan Tu
Dependence Structures In Lévy-Type Markov Processes, Eddie Brendan Tu
Doctoral Dissertations
In this dissertation, we examine the positive and negative dependence of infinitely divisible distributions and Lévy-type Markov processes. Examples of infinitely divisible distributions include Poissonian distributions like compound Poisson and α-stable distributions. Examples of Lévy-type Markov processes include Lévy processes and Feller processes, which include a class of jump-diffusions, certain stochastic differential equations with Lévy noise, and subordinated Markov processes. Other examples of Lévy-type Markov processes are time-inhomogeneous Feller evolution systems (FES), which include additive processes. We will provide a tour of various forms of positive dependence, which include association, positive supermodular association (PSA), positive supermodular dependence (PSD), and positive …
Inference In Networking Systems With Designed Measurements, Chang Liu
Inference In Networking Systems With Designed Measurements, Chang Liu
Doctoral Dissertations
Networking systems consist of network infrastructures and the end-hosts have been essential in supporting our daily communication, delivering huge amount of content and large number of services, and providing large scale distributed computing. To monitor and optimize the performance of such networking systems, or to provide flexible functionalities for the applications running on top of them, it is important to know the internal metrics of the networking systems such as link loss rates or path delays. The internal metrics are often not directly available due to the scale and complexity of the networking systems. This motivates the techniques of inference …
Stochastic Network Design: Models And Scalable Algorithms, Xiaojian Wu
Stochastic Network Design: Models And Scalable Algorithms, Xiaojian Wu
Doctoral Dissertations
Many natural and social phenomena occur in networks. Examples include the spread of information, ideas, and opinions through a social network, the propagation of an infectious disease among people, and the spread of species within an interconnected habitat network. The ability to modify a phenomenon towards some desired outcomes has widely recognized benefits to our society and the economy. The outcome of a phenomenon is largely determined by the topology or properties of its underlying network. A decision maker can take management actions to modify a network and, therefore, change the outcome of the phenomenon. A management action is an …
Advanced Sequential Monte Carlo Methods And Their Applications To Sparse Sensor Network For Detection And Estimation, Kai Kang
Doctoral Dissertations
The general state space models present a flexible framework for modeling dynamic systems and therefore have vast applications in many disciplines such as engineering, economics, biology, etc. However, optimal estimation problems of non-linear non-Gaussian state space models are analytically intractable in general. Sequential Monte Carlo (SMC) methods become a very popular class of simulation-based methods for the solution of optimal estimation problems. The advantages of SMC methods in comparison with classical filtering methods such as Kalman Filter and Extended Kalman Filter are that they are able to handle non-linear non-Gaussian scenarios without relying on any local linearization techniques. In this …
Numerical Solutions Of Stochastic Differential Equations, Liguo Wang
Numerical Solutions Of Stochastic Differential Equations, Liguo Wang
Doctoral Dissertations
In this dissertation, we consider the problem of simulation of stochastic differential equations driven by Brownian motions or the general Levy processes. There are two types of convergence for a numerical solution of a stochastic differential equation, the strong convergence and the weak convergence. We first introduce the strong convergence of the tamed Euler-Maruyama scheme under non-globally Lipschitz conditions, which allow the polynomial growth for the drift and diffusion coefficients. Then we prove a new weak convergence theorem given that the drift and diffusion coefficients of the stochastic differential equation are only twice continuously differentiable with bounded derivatives up to …
Wind Power Capacity Value Metrics And Variability: A Study In New England, Frederick W. Letson
Wind Power Capacity Value Metrics And Variability: A Study In New England, Frederick W. Letson
Doctoral Dissertations
Capacity value is the contribution of a power plant to the ability of the power system to meet high demand. As wind power penetration in New England, and worldwide, increases so does the importance of identifying the capacity contribution made by wind power plants. It is critical to accurately characterize the capacity value of these wind power plants and the variability of the capacity value over the long term. This is important in order to avoid the cost of keeping extra power plants operational while still being able to cover the demand for power reliably. This capacity value calculation is …
Numerical Methods For Deterministic And Stochastic Phase Field Models Of Phase Transition And Related Geometric Flows, Yukun Li
Doctoral Dissertations
This dissertation consists of three integral parts with each part focusing on numerical approximations of several partial differential equations (PDEs). The goals of each part are to design, to analyze and to implement continuous or discontinuous Galerkin finite element methods for the underlying PDE problem.
Part One studies discontinuous Galerkin (DG) approximations of two phase field models, namely, the Allen-Cahn and Cahn-Hilliard equations, and their related curvature-driven geometric problems, namely, the mean curvature flow and the Hele-Shaw flow. We derive two discrete spectrum estimates, which play an important role in proving the sharper error estimates which only depend on a …
Numerical Approximation Of Stochastic Differential Equations Driven By Levy Motion With Infinitely Many Jumps, Ernest Jum
Doctoral Dissertations
In this dissertation, we consider the problem of simulation of stochastic differential equations driven by pure jump Levy processes with infinite jump activity. Examples include, the class of stochastic differential equations driven by stable and tempered stable Levy processes, which are suited for modeling of a wide range of heavy tail phenomena. We replace the small jump part of the driving Levy process by a suitable Brownian motion, as proposed by Asmussen and Rosinski, which results in a jump-diffusion equation. We obtain Lp [the space of measurable functions with a finite p-norm], for p greater than or equal to …
Monte Carlo Methods In Finance, Je Guk Kim
Monte Carlo Methods In Finance, Je Guk Kim
Doctoral Dissertations
Monte Carlo method has received significant consideration from the context of quantitative finance mainly due to its ease of implementation for complex problems in the field. Among topics of its application to finance, we address two topics: (1) optimal importance sampling for the Laplace transform of exponential Brownian functionals and (2) analysis on the convergence of quasi-regression method for pricing American option. In the first part of this dissertation, we present an asymptotically optimal importance sampling method for Monte Carlo simulation of the Laplace transform of exponential Brownian functionals via Large deviations principle and calculus of variations the closed form …
Asymptotic Behavior Of A Class Of Spdes, Parisa Fatheddin
Asymptotic Behavior Of A Class Of Spdes, Parisa Fatheddin
Doctoral Dissertations
We establish the large and moderate deviation principles for a class of stochastic partial differential equations with a non-Lipschitz continuous coefficient. As an application we derive these principles for an important population model, Fleming-Viot Process. In addition, we establish the moderate deviation principle for another classical population model, super-Brownian motion.
Long Time Asymptotics Of Ornstein-Uhlenbeck Processes In Poisson Random Media, Fei Xing
Long Time Asymptotics Of Ornstein-Uhlenbeck Processes In Poisson Random Media, Fei Xing
Doctoral Dissertations
The Models of Random Motions in Random Media (RMRM) have been shown to have fruitful applications in various scientific areas such as polymer physics, statistical mechanics, oceanography, etc. In this dissertation, we consider a special model of RMRM: the Ornstein-Uhlenbeck process in a Poisson random medium and investigate the long time evolution of its random energy. We give complete answers to the long time asymptotics of the exponential moments of the random energy with both positive and negative coefficients, under both quenched and annealed regimes. Through these results, we find out a dramatic difference between the long time behavior of …
Automating Large-Scale Simulation Calibration To Real-World Sensor Data, Richard Everett Edwards
Automating Large-Scale Simulation Calibration To Real-World Sensor Data, Richard Everett Edwards
Doctoral Dissertations
Many key decisions and design policies are made using sophisticated computer simulations. However, these sophisticated computer simulations have several major problems. The two main issues are 1) gaps between the simulation model and the actual structure, and 2) limitations of the modeling engine's capabilities. This dissertation's goal is to address these simulation deficiencies by presenting a general automated process for tuning simulation inputs such that simulation output matches real world measured data. The automated process involves the following key components -- 1) Identify a model that accurately estimates the real world simulation calibration target from measured sensor data; 2) Identify …
Stability Of Nonlinear Filters And Branching Particle Approximations To The Filtering Problems, Zhiqiang Li
Stability Of Nonlinear Filters And Branching Particle Approximations To The Filtering Problems, Zhiqiang Li
Doctoral Dissertations
Various particle filters have been proposed and their convergence to the optimal filter are obtained for finite time intervals. However, uniform convergence results have been established only for discrete time filters. We prove the uniform convergence of a branching particle filter for continuous time setup when the optimal filter itself is exponentially stable.
The short interest rate process is modeled by an asymptotically stationary diffusion process. With the counting process observations, a filtering problem is formulated and its exponential stability is derived. Base on the stability result, the uniform convergence of a branching particle filter is proved.
Moderate Deviation Of Intersection Of Ranges Of Random Walks In The Stable Case, Justin Anthony Grieves
Moderate Deviation Of Intersection Of Ranges Of Random Walks In The Stable Case, Justin Anthony Grieves
Doctoral Dissertations
Given p independent, symmetric random walks on d-dimensional integer lattice that are the domain of attraction for a stable distribution, we calculate the moderate deviation of the intersection of ranges of the random walks in the case where the walks intersect infinitely often as time goes to infinity. That is to say, we establish a weak law convergence of intersection of ranges to intersection local time of stable processes and use this convergence as a link to establish deviation results.
Mathematical And Empirical Modeling Of Chemical Reactions In A Microreactor, Jing Hu
Mathematical And Empirical Modeling Of Chemical Reactions In A Microreactor, Jing Hu
Doctoral Dissertations
This dissertation is concerned with mathematical and empirical modeling to simulate three important chemical reactions (cyclohexene hydrogenation and dehydrogenation, preferential oxidation of carbon monoxide, and the Fischer-Tropsch (F-T) synthesis in a microreaction system.
Empirical modeling and optimization techniques based on experimental design (Central Composite Design (CCD)) and response surface methodology were applied to these three chemical reactions. Regression models were built, and the operating conditions (such as temperature, the ratio of the reactants, and total flow rate) which maximize reactant conversion and product selectivity were determined for each reaction.
A probability model for predicting the probability that a certain species …
Fuzzy Product -Limit Estimators: Soft Computing In The Presence Of Very Small And Highly Censored Data Sets, Kian Lawrence Pokorny
Fuzzy Product -Limit Estimators: Soft Computing In The Presence Of Very Small And Highly Censored Data Sets, Kian Lawrence Pokorny
Doctoral Dissertations
When very few data are available and a high proportion of the data is censored, accurate estimates of reliability are problematic. Standard statistical methods require a more complete data set, and with any fewer data, expert knowledge or heuristic methods are required. In the current research a computational system is developed that obtains a survival curve, point estimate, and confidence interval about the point estimate.
The system uses numerical methods to define fuzzy membership functions about each data point that quantify uncertainty due to censoring. The “fuzzy” data are then used to estimate a survival curve, and the mean survival …