Browsing UMBC Mathematics and Statistics Department by Title
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Real Time Global Illumination Solutions to the Radiosity Algorithm using Hybrid CPU/GPU Nodes
(2014)We investigate high performance solutions to the global illumination problem in computer graphics. An existing CPU serial implementation using the radiosity method is given as the performance baseline where a scene and ... 
A RieszThorin type interpolation theorem in Euclidean Jordan algebras
(20190507)In a Euclidean Jordan algebra V of rank n which carries the trace inner product, to each element a we associate the eigenvalue vector λ(a) in Rn whose components are the eigenvalues of a written in the decreasing order. ... 
Sampling Within kMeans Algorithm to Cluster Large Datasets
(2011)Due to current data collection technology, our ability to gather data has surpassed our ability to analyze it. In particular, kmeans, one of the simplest and fastest clustering algorithms, is illequipped to handle extremely ... 
Simulating the evolution of transcriptional regulatory motifs
(2012)Transcription factors are proteins that bind DNA for the purpose of regulating the expression of specific genes. The process by which transcription factors identify their binding sites is poorly understood. It is possible ... 
Simulation of a University as a Dynamical System
(2012)Dynamical systems describe how complex physical and artificial systems change over time. One such system is a university. The state of a university is described by its endowment, enrollment, research funding, graduation ... 
Simulation of the Evolution of Information Content in Transcription Factor Binding Sites Using a Parallelized Genetic Algorithm
(20110730)The analysis of transcription factor binding motifs may aid in understanding the process by which transcription factors recognize their binding sites. We wish to investigate the likelihood that transcription factors use ... 
The Simultaneous Assessment of Normality and Homoscedasticity in OneWay Random Effects Models
(Society of Statistics, Computer and Applications, 20200628)The article investigates the simultaneous assessment of normality and homoscedasticity in a oneway random effects model. Test procedures are developed assuming a smooth alternative to the normal distribution, specified ... 
Solution Uniqueness of Convex Piecewise Affine Functions Based Optimization with Applications to Constrained ℓ 1 Minimization
(20171116)In this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This ... 
Solving a TwoDimensional Elliptic Model Problem with the Conjugate Gradient Method Using MatrixFree SSOR Preconditioning in Matlab
(2009)The existing Preconditioned Conjugate Gradient method in Matlab can be optimized in terms of wall clock time and, more importantly, required storage space. The developed optimized algorithm was tested repeatedly on a two ... 
Some log and weak majorization inequalities in Euclidean Jordan algebras
(20200507)Motivated by Horn's logmajorization (singular value) inequality s(AB)≺logs(A)∗s(B) and the related weakmajorization inequality s(AB)≺ws(A)∗s(B) for square complex matrices, we consider their Hermitian analogs ... 
Sparsity and Independence: Balancing Two Objectives in Optimization for Source Separation with Application to fMRI Analysis
(Elsevier, 20170611)Because of its wide applicability in various disciplines, blind source separation (BSS), has been an active area of research. For a given dataset, BSS provides useful decompositions under minimum assumptions typically by ... 
A Spatial MultiCellular Model of the Pancreatic Islet including 𝛼, β , and 𝛿cells
(2014)Our goal is to create a computational model of an islet of Langerhans, consisting of 𝛼, β , and 𝛿cells. We will focus on varying the geometries and proportions of the cells in this islet, and study the hormonal secretion ... 
Spatiotemporal analysis of precipitation data via a sufficient dimension reduction in parallel
(American Statistical Association, 2016)Prediction of precipitation using simulations on various climate variables provided by Global Climate Models (GCM) as covariates is often required for regional hydrological assessment studies. In this paper, we use a ... 
Speedup Potential for Reconstruction Techniques for Prompt Gamma Imaging During Proton Radiotherapy
Proton beam radiation treatment was first proposed by Robert Wilson in 1946. The advantage of proton beam radiation is that the lethal dose of radiation is delivered by a sharp increase toward the end of the beam range. ... 
Spontaneous Calcium Release in Cardiac Myocytes: Store Overload and Electrical Dynamics
(Illinois State University, 2015)Heart disease is the leading cause of mortality in the United States. One cause of heart arrhythmia is calcium (Ca²⁺) mishandling in cardiac muscle cells. We adapt Izu's et al. mathematical reactiondiffusion model of ... 
State and parameter estimation from exact partial state observation in stochastic reaction networks
(20201209)We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species and provide a novel particle filter method for state and parameter estimation ... 
Statistical Analysis of a CaseControl Alzheimer's Disease: A Retropective Approach with Su cient Dimension Reduction
(2015)Alzheimer's Disease is a neurological disorder chiefly present in the elderly that affects functions of the brain such as memory and logic, eventually resulting in death. There is no known cure to Alzheimer's and evidence ... 
Stochastic Approximation Algorithm for Estimating Mixing Distribution for Dependent Observations
Estimating the mixing density of a mixture distribution remains an interesting problem in statistics literature. Using a stochastic approximation method, Newton and Zhang (1999) introduced a fast recursive algorithm for ... 
Stochastic Binary Opinion Model
(20190206)We study a stochastic binary opinion model where agents in a group are considered to hold an opinion of 0 or 1 at each moment. An agent in the group updates his/her opinion based on the group's opinion configuration and ...