Numerical Analysis and Computation Commons^™

Modeling Neurovascular Coupling From Clustered Parameter Sets For Multimodal Eeg-Nirs, M. Tanveer Talukdar, H. Robert Frost, Solomon G. G. Diamond

Dartmouth Scholarship

Despite significant improvements in neuroimaging technologies and analysis methods, the fundamental relationship between local changes in cerebral hemodynamics and the underlying neural activity remains largely unknown. In this study, a data driven approach is proposed for modeling this neurovascular coupling relationship from simultaneously acquired electroencephalographic (EEG) and near-infrared spectroscopic (NIRS) data. The approach uses gamma transfer functions to map EEG spectral envelopes that reflect time-varying power variations in neural rhythms to hemodynamics measured with NIRS during median nerve stimulation. The approach is evaluated first with simulated EEG-NIRS data and then by applying the method to experimental EEG-NIRS data measured from …

Almost Sure Asymptotic Stabilization Of Differential Equations With Time-Varying Delay By Lévy Noise, Dezhi Liu, Weiqun Wang, Jose Luis Menaldi

Mathematics Faculty Research Publications

This paper aims to determine that the Lévy noise can stabilize the given differential equations with time-varying delay, which has generalized the Brownian motion case. An analysis is developed and sufficient conditions on the stabilization for stochastic differential equations with time-varying delay are presented. Our stabilization criteria is in terms of linear matrix inequalities (LMIs), whence the feedback controls can be designed more easily in practice.

A Survey Of Mathematical Models Of Dengue Fever, Iurii Bakach

College of Graduate Studies: Theses & Dissertations

In this paper, we compare and contrast five models of Dengue fever. We evaluate each model using different scenarios and identify the strenghts and wecknesses of each of the model

Mathematical Modeling Of Emiliania Huxleyi And A Host-Specific Virus, Julia Middleton

Honors Theses

The world’s oceans provide the basis for life on the planet. One microscopic algae, the coccolithophores, and Emiliania huxleyi in particular, is a major source of carbon drawdown in the context of the global carbon cycle and account for a significant amount of the primary production in oceanic ecosystems. We know that the oceans are packed with marine viruses and they have an important role in the rise and fall of plankton populations but current mathematical models do not accurately account for virus-host interactions when predicting plankton blooms. Therefore I am using model optimization and comparison techniques to evaluate current …

A Class Of High-Order Runge-Kutta-Chebyshev Stability Polynomials, Stephen O'Sullivan

Articles

The analytic form of a new class of factorized Runge-Kutta-Chebyshev (FRKC) stability polynomials of arbitrary order N is presented. Roots of FRKC stability polynomials of degree L = MN are used to construct explicit schemes comprising L forward Euler stages with internal stability ensured through a sequencing algorithm which limits the internal amplification factors to ~ L². The associated stability domain scales as M² along the real axis. Marginally stable real-valued points on the interior of the stability domain are removed via a prescribed damping procedure. By construction, FRKC schemes meet all linear order conditions; for nonlinear …

Singular Value Computation And Subspace Clustering, Qiao Liang

Theses and Dissertations--Mathematics

In this dissertation we discuss two problems. In the first part, we consider the problem of computing a few extreme eigenvalues of a symmetric definite generalized eigenvalue problem or a few extreme singular values of a large and sparse matrix. The standard method of choice of computing a few extreme eigenvalues of a large symmetric matrix is the Lanczos or the implicitly restarted Lanczos method. These methods usually employ a shift-and-invert transformation to accelerate the speed of convergence, which is not practical for truly large problems. With this in mind, Golub and Ye proposes an inverse-free preconditioned Krylov subspace method, …

The Krylov Subspace Methods For The Computation Of Matrix Exponentials, Hao Wang

Theses and Dissertations--Mathematics

The problem of computing the matrix exponential e^tA arises in many theoretical and practical problems. Many methods have been developed to accurately and efficiently compute this matrix function or its product with a vector, i.e., e^tAv. In the past few decades, with the increasing need of the computation for large sparse matrices, iterative methods such as the Krylov subspace methods have proved to be a powerful class of methods in dealing with many linear algebra problems. The Krylov subspace methods have been introduced for computing matrix exponentials by Gallopoulos and Saad, and the corresponding error bounds …

One-Bit Compressive Sensing With Partial Support Information, Phillip North

CMC Senior Theses

This work develops novel algorithms for incorporating prior-support information into the field of One-Bit Compressed Sensing. Traditionally, Compressed Sensing is used for acquiring high-dimensional signals from few linear measurements. In applications, it is often the case that we have some knowledge of the structure of our signal(s) beforehand, and thus we would like to leverage it to attain more accurate and efficient recovery. Additionally, the Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization. Indeed, the field of One-Bit Compressive Sensing aims to recover a signal from measurements reduced to only their sign-bit. This …

Parameters Estimation Of Material Constitutive Models Using Optimization Algorithms, Kiswendsida Jules Kere

Williams Honors College, Honors Research Projects

Optimization Algorithms are very useful for solving engineering problems. Indeed, optimization algorithms can be used to optimize engineering designs in terms of safety and economy. Understanding the proprieties of materials in engineering designs is very important in order to make designs safe. Materials are not really perfectly homogeneous and there are heterogeneous distributions in most materials. In this paper, Self-OPTIM which is an inverse constitutive parameter identification framework will be used to identify parameters of a linear elastic material constitutive model. Data for Self-OPTIM will be obtained using ABAQUS simulation of a dog-bone uniaxial test. Optimization Algorithms will be used …

The Simulation & Evaluation Of Surge Hazard Using A Response Surface Method In The New York Bight, Michael H. Bredesen

UNF Graduate Theses and Dissertations

Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method …

Modern Approach For Designing And Solving Interval Estimated Linear Fractional Programming Models, S. Ananthalakshmi, C. Vijayalakshmi, V. Ganesan

Applications and Applied Mathematics: An International Journal (AAM)

Optimization methods have been widely applied in statistics. In mathematical programming, the coefficients of the models are always categorized as deterministic values. However uncertainty always exists in realistic problems. Therefore, interval-estimated optimization models may provide an alternative choice for considering the uncertainty into the optimization models. In this aspect, this paper concentrates, the lower and upper values of interval estimated linear fractional programming model (IELFPM) are obtained by using generalized confidence interval estimation method. An IELFPM is a LFP with interval form of the coefficients in the objective function and all requirements. The solution of the IELFPM is also analyzed.

Approximation Of The Scattering Amplitude Using Nonsymmetric Saddle Point Matrices, Amber Sumner Robertson

Master's Theses

In this thesis we look at iterative methods for solving the primal (Ax = b) and dual (A^T y = g) systems of linear equations to approximate the scattering amplitude defined by g^Tx =y^Tb. We use a conjugate gradient-like iteration for a unsymmetric saddle point matrix that is contructed so as to have a real positive spectrum. We find that this method is more consistent than known methods for computing the scattering amplitude such as GLSQR or QMR. Then, we use techniques from "matrices, moments, and quadrature" to compute the scattering amplitude …

A Two-Light Version Of The Classical Hundred Prisoners And A Light Bulb Problem: Optimizing Experimental Design Through Simulations, Alexander S. Barrett, Cyril Rakovski

e-Research: A Journal of Undergraduate Work

We propose five original strategies of successively increasing complexity and efficiency that address a novel version of a classical mathematical problem that, in essence, focuses on the determination of an optimal protocol for exchanging limited amounts of information among a group of subjects with various prerogatives. The inherent intricacy of the problem�solving protocols eliminates the possibility to attain an analytical solution. Therefore, we implemented a large-scale simulation study to exhaustively search through an extensive list of competing algorithms associated with the above-mentioned 5 generally defined protocols. Our results show that the consecutive improvements in the average amount of time necessary …

Generalized Least-Squares Regressions Iv: Theory And Classification Using Generalized Means, Nataniel Greene

Publications and Research

The theory of generalized least-squares is reformulated here using the notion of generalized means. The generalized least-squares problem seeks a line which minimizes the average generalized mean of the square deviations in x and y. The notion of a generalized mean is equivalent to the generating function concept of the previous papers but allows for a more robust understanding and has an already existing literature. Generalized means are applied to the task of constructing more examples, simplifying the theory, and further classifying generalized least-squares regressions.

Analytical Solution Of The Symmetric Circulant Tridiagonal Linear System, Sean A. Broughton, Jeffery J. Leader

Mathematical Sciences Technical Reports (MSTR)

A circulant tridiagonal system is a special type of Toeplitz system that appears in a variety of problems in scientific computation. In this paper we give a formula for the inverse of a symmetric circulant tridiagonal matrix as a product of a circulant matrix and its transpose, and discuss the utility of this approach for solving the associated system.

Mathematically Modeling Fetal Electrocardiograms, Samuel Estes, Kiersten Utsey, Erick Kalobwe

Pursuit - The Journal of Undergraduate Research at The University of Tennessee

Abstract

Some of the most common and fatal birth defects are those related to the heart. In adults, possible heart conditions are often identified through the use of an electrocardiogram (ECG). However, due to the presence of other signals and noise in the recording, fetal electrocardiography has not yet proven effective in diagnosing these defects. This paper develops a mathematical model of three-dimensional heart vector trajectories, which was used to generate synthetic maternal and fetal ECG signals. The dipole model is a useful simplification in which the electrical activity of the heart is viewed as a single time-varying vector originating …

Delay Analysis Of A Discrete-Time Non-Preemptive Priority Queue With Priority Jumps, Deepak C. Pandey, Arun K. Pal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a discrete-time non-preemptive priority queueing model with priority jumps. Two classes, real-time (high priority) and non-real time (low priority), of traffic will be considered with providing jumps from lower priority traffic to the queue of high priority traffic. We derive expressions for the joint probability generating function of the system contents of the high and the low priority traffic in the steady state and also for some performance measures such as the mean value of the system contents and the packet delay. The behavior of the priority queues with priority jumps will be illustrated by …

Stochastic Modeling Of A Concrete Mixture Plant With Preventive Maintenance, Ashish Kumar, Monika Saini, S. C. Malik

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a stochastic model for concrete mixture plant with Preventive Maintenance (PM) is analyzed in detail by using a supplementary variable technique. In a concrete mixture plant eight subsystems are arranged in a series. The system goes under PM after a maximum operation time and work as new after PM. The time to failure of each subsystem follows a negative exponential distribution while PM and repair time distributions are taken as arbitrary. A sufficient repair facility is provided to the system for conducting PM and repair of the system. Repair, maintenance and switch devices are perfect. All random …

Numerical Solution For The Systems Of Variable-Coefficient Coupled Burgers’ Equation By Two-Dimensional Legendre Wavelets Method, Hossein Aminikhah, Sakineh Moradian

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a numerical method for solving the systems of variable-coefficient coupled Burgers’ equation is proposed. The method is based on two-dimensional Legendre wavelets. Two-dimensional operational matrices of integration are introduced and then employed to find a solution to the systems of variable-coefficient coupled Burgers’ equation. Two examples are presented to illustrate the capability of the method. It is shown that the numerical results are in good agreement with the exact solutions for each problem.

A Ranking Method Based On Common Weights And Benchmark Point, Ali Payan, Abbas A. Noora, Farhad H. Lotfi

Applications and Applied Mathematics: An International Journal (AAM)

The highest efficiency score 1 (100% efficiency) is regarded as a common benchmark for Decision Making Units (DMUs). This brings about the existence of more than one DMU with the highest score. Such a case normally occurs in all Data Envelopment Analysis (DEA) models and also in all the Common Set of Weights (CSWs) methods and it may lead to the lack of thorough ranking of DMUs. And ideal DMU based on its specific structure is a unit that no unit would do better than. Therefore, it can be utilized as a benchmark for other units. We are going to …