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Articles 61 - 90 of 550
Full-Text Articles in Mathematics
Dynamical Role Of Pivotal Brain Regions In Parkinson Symptomatology Uncovered With Deep Learning, Alex A. Nguyen, Pedro D. Maia, Xiao Gao, Pablo F. Damasceno, Ashish Raj
Dynamical Role Of Pivotal Brain Regions In Parkinson Symptomatology Uncovered With Deep Learning, Alex A. Nguyen, Pedro D. Maia, Xiao Gao, Pablo F. Damasceno, Ashish Raj
Mathematics Faculty Publications - Archive
The release of a broad, longitudinal anatomical dataset by the Parkinson’s Progression Markers Initiative promoted a surge of machine-learning studies aimed at predicting disease onset and progression. However, the excessive number of features used in these models often conceals their relationship to the Parkinsonian symptomatology. Objectives: The aim of this study is two-fold: (i) to predict future motor and cognitive impairments up to four years from brain features acquired at baseline; and (ii) to interpret the role of pivotal brain regions responsible for different symptoms from a neurological viewpoint. Methods: We test several deep-learning neural network configurations, and report our …
Some Quadratic Regular Algebras On Four Generators Wtih A 1-Dimensional Nonreduced Line Scheme, Anthony Iv Mastriania
Some Quadratic Regular Algebras On Four Generators Wtih A 1-Dimensional Nonreduced Line Scheme, Anthony Iv Mastriania
Mathematics Dissertations - Archive
In the 1980s, M. Artin, J. Tate, and M. Van den Bergh applied geometric techniques to noncommutative algebras. Their work introduced algebraic concepts called point modules and line modules and an associated geometric concept, which was later called the point scheme. In 2002, Shelton and Vancliff defined the concept of line scheme and developed a method for computing the line scheme of any quadratic algebra that satisfies certain conditions. Artin, Tate, and Van den Bergh were able to classify so-called quantum P²s by their point scheme; quantum P³s however are much more challenging and involve computing the line scheme. In …
Liutex Analysis By Pod And Dmd For Vortex Formations In Boundary Layer Transition, Sita Charkrit
Liutex Analysis By Pod And Dmd For Vortex Formations In Boundary Layer Transition, Sita Charkrit
Mathematics Dissertations - Archive
Vortices are considered as the building blocks of turbulent flows. To study how one type of vortex becomes another type especially in flow transition is one way to get better understanding about turbulence. In this dissertation, two types of vortex formations, i.e., the hairpin vortex formation and the formation of vortex structure from symmetry to asymmetry, are studied by the direct numerical simulation. According to Liu et al. (2019), Liutex has been proposed as a new physical quantity with scalar, vector and tensor forms. A Liutex vector is defined as a rotation part of fluid motion without shear contamination. The …
Mathematical Modeling Of A Network Of Neurons Regarding Glucose Transport Deficiency Induced Epileptic Seizures, Ariel N. Leslie
Mathematical Modeling Of A Network Of Neurons Regarding Glucose Transport Deficiency Induced Epileptic Seizures, Ariel N. Leslie
Mathematics Dissertations - Archive
Epilepsy is a complex phenomena of a system of neurons simultaneously firing that are highly intensive and synchronized. Seizures are a common and well known physical feature for all types of epileptic disorders [8]. Epilepsy is known to be traced back to spatial and temporal patterns working in sequence. The rhythms, patterns, and oscillatory dynamics explain the mechanistic nature of neurons especially in absence seizures [37]. An electroencephalogram device (EEG) monitors the electrical activity within the brain using small electrodes, which measures voltage fluctuations on the scalp. Previous models such as Wilson-Cowan (1972) [34], introduced a model showing the dynamics …
Forecasting Dengue Fever In Brazil: An Assessment Of Climate Conditions, Lucas M. Stolerman, Pedro D. Maia, Nathan Kutz
Forecasting Dengue Fever In Brazil: An Assessment Of Climate Conditions, Lucas M. Stolerman, Pedro D. Maia, Nathan Kutz
Mathematics Faculty Publications - Archive
Local climate conditions play a major role in the biology of the Aedes aegypti mosquito, the main vector responsible for transmitting dengue, zika, chikungunya and yellow fever in urban centers. For this reason, a detailed assessment of periods in which changes in climate conditions affect the number of human cases may improve the timing of vector-control efforts. In this work, we develop new machine-learning algorithms to analyze climate time series and their connection to the occurrence of dengue epidemic years for seven Brazilian state capitals. Our method explores the impact of two key variables—frequency of precipitation and average temperature—during a …
Prediction Of Remaining Lifetime Distribution From Functional Trajectories Based On Censored Observations, Izzet Sozucok
Prediction Of Remaining Lifetime Distribution From Functional Trajectories Based On Censored Observations, Izzet Sozucok
Mathematics Dissertations - Archive
The goal in functional data studies on failure time or on death time of the objects is to find a relationship between age-at-death (failure time) and current values of a functional predictors. In this study, a novel technique is applied to predict the failure time of devices (such as bearings in a mechanical system) and to try to predict the “age-at-death” distributions under censoring data. We concern ourselves with circumstances where all co-variate trajectories are observed until a current time t. The predictors observed up to current time can be shown by time-varying principal component scores which is continuously updated …
Image Analysis Based On Differential Operators With Applications To Brain Mris, Zicong Zhou
Image Analysis Based On Differential Operators With Applications To Brain Mris, Zicong Zhou
Mathematics Dissertations - Archive
In differential geometry, computational diffeomorphism (smooth and invertible mapping) has become a fast-growing field in developing the theoretical frameworks and computational toolboxes for the tasks such as computer vision, movie production, gaming industry, medical imaging, etc. Mesh generation is one of components in computational diffeomorphism. In this dissertation, the deformation and variational methods (developed by Dr. Guojun Liao and his co-workers) for mesh generation are discussed, modified and generalized to 3D scenario. The former is based on the control of Jacobian determinant and the latter is based on the controls of both Jacobian determinant and curl vector of a diffeomorphism. …
Modeling An M/M/1 Queue With Unreliable Service And A Working Vacation, Joshua Kent Patterson
Modeling An M/M/1 Queue With Unreliable Service And A Working Vacation, Joshua Kent Patterson
Mathematics Dissertations - Archive
We define the new term ’unreliable service’ where the service itself is unreliable (i.e. may fail). We discuss how this differs from the current literature, and give examples showing just how common this phenomena is in many real-world scenarios. We first consider the classic M/M/1 queue with unreliable service and find some striking similarities with the well studied M/M/1 derivation. Next, we consider the M/M/1 queue with unreliable service and a working vacation. In each of these cases, surprising explicit results are found including positive recurrence conditions, the stationary queue length distribution, and a decomposition of both the queue length …
On Optimizing The Sum Of Rayleigh Quotients On The Unit Sphere, Aohud Abdulrahman Binbuhaer
On Optimizing The Sum Of Rayleigh Quotients On The Unit Sphere, Aohud Abdulrahman Binbuhaer
Mathematics Dissertations - Archive
Given symmetric matrices and positive definite matrices, we are concerned with the solution of the maximization of the function that is mentioned in the dissertation. We establish necessary optimality conditions for local maximizers. Moreover, a self-consistent-field (SCF) iterative method for solving this maximization problem is introduced and analyzed. We use the Trust-Region SCF iteration to improve the convergence of the SCF method.
Mathematical Modeling Of Zika Virus Transmission And Multiple Pathogen Interactions, Omomayowa Olawoyin
Mathematical Modeling Of Zika Virus Transmission And Multiple Pathogen Interactions, Omomayowa Olawoyin
Mathematics Dissertations - Archive
The purpose of this dissertation is twofold: to deepen our understanding of the complex transmission routes of the Zika virus (ZIKV), and to study multiple pathogen interactions (specifically cocirculation of Zika and dengue and discrete-time coinfection models) through the lens of invasion reproductive numbers (IRNs) which measure the ability of a disease to invade a population endemic with another disease(s). In addition to being transmitted to humans through the bite of infected female Aedes aegypti mosquitoes, studies show that the ZIKV can also be sexually and vertically transmitted within both populations. We develop a new mathematical model of the ZIKV …
Modeling The Effects Of The Immune System On Bone Fracture Healing, Imelda Trejo Lorenzo
Modeling The Effects Of The Immune System On Bone Fracture Healing, Imelda Trejo Lorenzo
Mathematics Dissertations - Archive
Bone fracture healing is a complex biological process that results in a full reconstruction of the bone. However, it is not always an easy and successful process. Indeed, in some unfavorable conditions, the bone fracture healing fails with approximately 10% of fractures resulting in nonunion. Furthermore, the risk of nonunion healing increases with age, severe trauma, and immune deficiency. In addition, clinical consequences of fractures include surgical management, prolonged hospitalization, and rehabilitation resulting in high socioeconomic costs. A better understanding of bone healing would enable to find optimal conditions for successful outcomes and to develop strategies for fracture treatments under …
Optimal Control Methods For Chagas Disease, Francis Mastrome
Optimal Control Methods For Chagas Disease, Francis Mastrome
Mathematics Theses - Archive
Chagas disease is the world's most neglected tropical disease. Having a lack of cure makes the primary focus on the disease preventing it and controlling it. This study takes into account three different control measures: bed nets, low-volume insecticide spraying, and improving housing conditions, analyzes their cost effectiveness compared to each other, and determines which combination of the three control measures prevents the most T. cruzi infections in a rural Latin American village over a decade. It was shown that there is a a hierarchical importance in the control measures when preventing the spread of Chagas disease. In order of …
Optimizing Krylov Subspace Methods For Linear Systems And Least Squares Problems, Mei Yang
Optimizing Krylov Subspace Methods For Linear Systems And Least Squares Problems, Mei Yang
Mathematics Dissertations - Archive
The linear system and the linear least squares problem are two fundamental numerical linear algebra problems. Krylov subspace methods are the most practical and common techniques to build solvers. In this thesis, we focus on optimizing Krylov subspace methods for nonsymmetric linear systems and least squares problems. For nonsymmetric linear systems Ax=b one of Krylov subspace methods is GMRES, which seeks approximate solutions over the Krylov subspace K_k (A,b) (with the initial guess x_0=0). Constructing different search spaces and applying restart strategy are two techniques used to deal with possible slow convergence and to reduce computational cost in GMRES and …
Modeling Plant Virus Propagation And An Optimal Control, Mark Jackson
Modeling Plant Virus Propagation And An Optimal Control, Mark Jackson
Mathematics Dissertations - Archive
Plants are a food source for man and many species. They also are sources of medicines, fibers for clothes, and are essential for a healthy environment. But plants are subject to diseases many of which are caused by viruses. These viruses often kill the plant. As a result, billions of dollars are lost every year because of virus related crop loss. Most of the time, virus propagation is done by a vector, usually insects that bite infected plants, get themselves infected and then bite susceptible plants. To combat the vectors, and ultimately the viruses, pesticides are often used as a …
Mathematical Modeling Of The Bone Remodeling Process, Iris Lizeth Alvarado
Mathematical Modeling Of The Bone Remodeling Process, Iris Lizeth Alvarado
Mathematics Dissertations - Archive
The skeleton is a very important organ that needs to be continuously remodeled due to microdamage, changes in mechanical loading, or mineral homeostasis. The bone remodeling process is responsible for maintaining the structure and function of the skeletal system. Accumulation of microdamage that goes unrepaired within the bone matrix can lead to bone fragility and loss of mechanical properties. Evidence suggests that when microdamage is present in the bone structure, osteocyte apoptosis plays an important role in the initiation of the bone remodeling process. Osteocytes are known to release RANKL a promoter of osteoclastogenesis (bone-resorbing cells) and scelorstion an inhibitor …
Posterior Normal Approximation Of Real-Time Degradation Modeling Using Laplace Approximation, Mahmoud Ali Jawad
Posterior Normal Approximation Of Real-Time Degradation Modeling Using Laplace Approximation, Mahmoud Ali Jawad
Mathematics Dissertations - Archive
Preventing failure that can cause delays or catastrophe, has been the focus and motivation for engineers, and other establishments that deals with heavy and light machinery, equipment, and devices. One of the biggest challenges, is accuracy and heavy computations of remaining useful life distribution. In this thesis we will use Laplace Approximations (LA) to avoid relying on complicated numerical computations, in calculating the remaining useful life distribution (RLD). LA is useful method to approximate the posterior distribution of Bayesian formula that incorporates linear degradation model and prior distribution. This proposed approach is applicable to various degradation models composed of univariate …
Projective Geometry Associated To Some Quadratic, Regular Algebras Of Global Dimension Four, Derek C. Tomlin
Projective Geometry Associated To Some Quadratic, Regular Algebras Of Global Dimension Four, Derek C. Tomlin
Mathematics Dissertations - Archive
The attempted classification of regular algebras of global dimension four, so-called quantum P³s, has been a driving force for modern research in noncommutative algebra. Inspired by the work of Artin, Tate, and Van den Bergh, geometric methods via schemes of d-linear modules have been developed by various researchers to further their classification. In this thesis, we compute and analyze the line scheme of two families of algebras -- for both families, almost every algebra can be considered a candidate for a generic quadratic quantum P³. For the first family of algebras, we find that, viewed as a closed subscheme of …
A Study On The Rotational B-Family Of Equations, Emel Bolat
A Study On The Rotational B-Family Of Equations, Emel Bolat
Mathematics Dissertations - Archive
In this thesis, we study a mathematical model of long-crested water waves propagating in one direction with the effect of Earth's rotation near the equator by following the formal asymptotic procedures. Firstly, we derive a new model equation called the rotational b-family of equations by using the Camassa-Holm approximation of the two-dimensional incompressible and irrotational Euler equations. Secondly,we establish that the local well-posedness of the Cauchy problem for the rotational b-family of equations on the Sobolev space H⁸, for s > 3=2. In addition, we study the effects of the Coriolis force and nonlocal higher nonlinearities on blow-up criteria and wave-breaking …
Asymptotic Properties Of The Deconvolution Kernel Density Estimate Based On 2-Dependent Error Structure With Applications To Remaining Useful Life Problems In Reliability Theory, Geoffrey H. Schuette
Asymptotic Properties Of The Deconvolution Kernel Density Estimate Based On 2-Dependent Error Structure With Applications To Remaining Useful Life Problems In Reliability Theory, Geoffrey H. Schuette
Mathematics Dissertations - Archive
This thesis is motivated from an engineering question, which led us to the deconvolution problem with a dependent error structure. We establish a deconvolution kernel density estimator by adapting the methods of kernel density estimates and Fourier Transforms. In this approach, the contaminated data with additive random errors are assumed dependent and satisfying smooth or super smooth conditions. Under both smooth and supper smooth conditions, we derived: 1. optimal rates of convergence in terms of mean integrated squared error for deconvolution kernel density estimator; 2. the limiting distribution of the estimator.
Scattering And Inverse Scattering On The Line For A First-Order System With Energy-Dependent Potentials, Ramazan Ercan
Scattering And Inverse Scattering On The Line For A First-Order System With Energy-Dependent Potentials, Ramazan Ercan
Mathematics Dissertations - Archive
A first-order system of two linear ordinary differential equations is analyzed. The linear system contains a spectral parameter, and it has two coefficients that are functions of the spatial variable ��. Those two functions act as potentials in the linear system and they also linearly contain the spectral parameter λ, and hence they are referred to as energy-dependent potentials. Such a linear system arises in the solution to a pair of integrable nonlinear partial differential equations (known as the derivative nonlinear Schrödinger equations) via the so-called inverse scattering transform method. The direct and inverse problems for the corresponding first-order linear …
Discrete Time Risk Models With Random Premiums, Llewellyn Hillyer Smith
Discrete Time Risk Models With Random Premiums, Llewellyn Hillyer Smith
Mathematics Dissertations - Archive
Over the past century insurance companies relied to a large extent on the continuous time Mathematical Risk Model proposed by Lundberg, known for its ability to estimate the probability of ruin(capital reserve falling below zero), given the initial capital, linear premium rate and cumulative random size claims occurring at random times. In this Dissertation we introduce a discrete time risk model that allows random premiums, and derive the estimates of the ruin probabilities on both finite and infinite time horizons. Tools applied are drawn from modern probability and include,Martingales, Invariance Principle for Brownian motions, and Large Deviation Principle for the …
A Method For Inferring Regional Origins Of Neurodegeneration, Justin Torok, Pedro D. Maia, Fon Powell, Sneha Pandya, Ashish Raj
A Method For Inferring Regional Origins Of Neurodegeneration, Justin Torok, Pedro D. Maia, Fon Powell, Sneha Pandya, Ashish Raj
Mathematics Faculty Publications - Archive
Alzheimer’s disease, the most common form of dementia, is characterized by the emergence and spread of senile plaques and neurofibrillary tangles, causing widespread neurodegeneration. Though the progression of Alzheimer’s disease is considered to be stereotyped, the significant variability within clinical populations obscures this interpretation on the individual level. Of particular clinical importance is understanding where exactly pathology, e.g. tau, emerges in each patient and how the incipient atrophy pattern relates to future spread of disease. Here we demonstrate a newly developed graph theoretical method of inferring prior disease states in patients with Alzheimer’s disease and mild cognitive impairment using an …
Numerical Solution Of Saddle Point Problems By Projection, Gul Karaduman
Numerical Solution Of Saddle Point Problems By Projection, Gul Karaduman
Mathematics Dissertations - Archive
In this thesis, we work on iterative solutions of large linear systems of saddle point problems of the form A B1 T B2 0 x y = f 0 , where A ∈ R n×n , B1, B2 ∈ R m×n , f ∈ R n , and n ≥ m. Many applications in computational sciences and engineering give rise to saddle point problems such as finite element approximations to Stokes problems, image reconstruction, tomography, genetics, statistics and model order reduction for …
Statistical Estimation In Multivariate Normal Distribution With A Block Of Missing Observations, Yi Liu
Statistical Estimation In Multivariate Normal Distribution With A Block Of Missing Observations, Yi Liu
Mathematics Dissertations - Archive
Missing observations occur quite often in data analysis. We study a random sample from a multivariate normal distribution with a block of missing observations, here the observations missing is not at random. We use maximum likelihood method to obtain the estimators from such a sample. The properties of the estimators are derived. The prediction problem is considered when the response variable has missing values. The variances of the mean estimators of the response variable under with and without extra information are compared. We prove that the variance of the mean estimator of the response variable using all data is smaller …
Estimating Memory Deterioration Rates Following Neurodegeneration And Traumatic Brain Injuries In A Hopfield Network Model, Melanie Weber, Pedro D. Maia, J. Nathan Kutz
Estimating Memory Deterioration Rates Following Neurodegeneration And Traumatic Brain Injuries In A Hopfield Network Model, Melanie Weber, Pedro D. Maia, J. Nathan Kutz
Mathematics Faculty Publications - Archive
Neurodegenerative diseases and traumatic brain injuries (TBI) are among the main causes of cognitive dysfunction in humans. At a neuronal network level, they both extensively exhibit focal axonal swellings (FAS), which in turn, compromise the information encoded in spike trains and lead to potentially severe functional deficits. There are currently no satisfactory quantitative predictors of decline in memory-encoding neuronal networks based on the impact and statistics of FAS. Some of the challenges of this translational approach include our inability to access small scale injuries with non-invasive methods, the overall complexity of neuronal pathologies, and our limited knowledge of how networks …
Preventing Neurodegenerative Memory Loss In Hopfield Neuronal Networks Using Cerebral Organoids Or External Microelectronics, M. Morrison, P. D. Maia, J. N. Kutz
Preventing Neurodegenerative Memory Loss In Hopfield Neuronal Networks Using Cerebral Organoids Or External Microelectronics, M. Morrison, P. D. Maia, J. N. Kutz
Mathematics Faculty Publications - Archive
Developing technologies have made significant progress towards linking the brain with brain-machine interfaces (BMIs) which have the potential to aid damaged brains to perform their original motor and cognitive functions. We consider the viability of such devices for mitigating the deleterious effects of memory loss that is induced by neurodegenerative diseases and/or traumatic brain injury (TBI). Our computational study considers the widely used Hopfield network, an autoassociative memory model in which neurons converge to a stable state pattern after receiving an input resembling the given memory. In this study, we connect an auxiliary network of neurons, which models the BMI …
A Study On Traveling Wave Solutions In The Shallow-Water-Type System, Ting Luo
A Study On Traveling Wave Solutions In The Shallow-Water-Type System, Ting Luo
Mathematics Dissertations - Archive
The study of water waves reveals the physical principles of many phenomena of scientific and engineering interest. In this dissertation I consider three models: two-component Camassa-Holm system(2CH), generalized two-component Camassa-Holm equation(g2CH) and rotation-Camassa-Holm equation(R-CH). In the first part, we consider the stability of the Camassa-Holm peakons and antipeakons in the dynamics of the two-component Camassa-Holm system. The second part shows that the train of $N$-smooth traveling waves of this system is dynamically stable to perturbations in energy space with a range of parameters. In the third part, we formally derive the simplified phenomenological models with the Coriolis effect due to …
Stability Study On Shear Flow And Vortices In Late Boundary Layer Transition, Jie Tang
Stability Study On Shear Flow And Vortices In Late Boundary Layer Transition, Jie Tang
Mathematics Dissertations - Archive
Turbulence is still an unsolved scientific problem, it has been regarded as “the most important unsolved problem of classical physics”. Dr. Liu proposed a new mechanism about turbulence generation and sustenance after decades of research on turbulence and transition. His new idea challenged the classical theorem in many aspects. One of them is the flow stability of transition. Dr. Liu believes that inside the flow field, shear (dominant in laminar) is very unstable while rotation (dominant in turbulence) is relative stable. This inherent property of flow creates the trend that non-vertical vorticity must transfer to vertical vorticity, and causes the …
Image Reconstruction From Incomplete Radon Data And Generalized Principal Component Analysis, Sl Ghi Choi
Image Reconstruction From Incomplete Radon Data And Generalized Principal Component Analysis, Sl Ghi Choi
Mathematics Dissertations - Archive
Image reconstruction in various types of tomography requires inversion of the Radon transform and its generalizations. While there are many stable and robust algorithms for such inversions from reasonably well sampled data, most of these algorithms fail when applied to limited view data. In the dissertation we develop a new method of stable reconstruction from limited view data for functions, whose support is a union of finitely many circles. Such images, among other things, are good approximations of tomograms of certain types of tumors in lungs. Our method is based on a modified version of GPCA (General Principle Component Analysis) …
Evoked And Spontaneous Neurotransmitter Releases For Independent Synaptic Currents: Mathematical Modeling And Analysis, Sat Byul Seo
Evoked And Spontaneous Neurotransmitter Releases For Independent Synaptic Currents: Mathematical Modeling And Analysis, Sat Byul Seo
Mathematics Dissertations - Archive
Synapses play a major role in neuron communications in the brain. The synapses act through a chemical process called synaptic fusion between pre-synaptic and post-synaptic terminals. Presynaptic terminals release neurotransmitters either in response to action potential or spontaneously independent of presynaptic activity. In the case of glutamate, released neurotransmitters acivate N-methyl-D-asparate (NMDA) receptors within a single postsynaptic site and give rise to miniature postsynaptic currents. In this dissertation, we develop a mathematical model in 3-D to emulate spontaneous and evoked neurotransmissions resulted from glutamate release within a single synapse. We propose numerical methods for solving piecewise continuous heat diffusion equation, …