Numerical Analysis and Computation Commons^™

Markov Chain Profit Modelling And Evaluation Between Two Dissimilar Systems Under Two Types Of Failures, Saminu I. Bala, Ibrahim Yusuf

Applications and Applied Mathematics: An International Journal (AAM)

No abstract provided.

Generalized Least-Powers Regressions I: Bivariate Regressions, Nataniel Greene

Publications and Research

The bivariate theory of generalized least-squares is extended here to least-powers. The bivariate generalized least-powers problem of order p seeks a line which minimizes the average generalized mean of the absolute pth power deviations between the data and the line. Least-squares regressions utilize second order moments of the data to construct the regression line whereas least-powers regressions use moments of order p to construct the line. The focus is on even values of p, since this case admits analytic solution methods for the regression coefficients. A numerical example shows generalized least-powers methods performing comparably to generalized least-squares methods, …

Design Optimization Of A Stochastic Multi-Objective Problem: Gaussian Process Regressions For Objective Surrogates, Juan Sebastian Martinez, Piyush Pandita, Rohit K. Tripathy, Ilias Bilionis

The Summer Undergraduate Research Fellowship (SURF) Symposium

Multi-objective optimization (MOO) problems arise frequently in science and engineering situations. In an optimization problem, we want to find the set of input parameters that generate the set of optimal outputs, mathematically known as the Pareto frontier (PF). Solving the MOO problem is a challenge since expensive experiments can be performed only a constrained number of times and there is a limited set of data to work with, e.g. a roll-to-roll microwave plasma chemical vapor deposition (MPCVD) reactor for manufacturing high quality graphene. State-of-the-art techniques, e.g. evolutionary algorithms; particle swarm optimization, require a large amount of observations and do not …

Optimizing The Mix Of Games And Their Locations On The Casino Floor, Jason D. Fiege, Anastasia D. Baran

International Conference on Gambling & Risk Taking

We present a mathematical framework and computational approach that aims to optimize the mix and locations of slot machine types and denominations, plus other games to maximize the overall performance of the gaming floor. This problem belongs to a larger class of spatial resource optimization problems, concerned with optimizing the allocation and spatial distribution of finite resources, subject to various constraints. We introduce a powerful multi-objective evolutionary optimization and data-modelling platform, developed by the presenter since 2002, and show how this software can be used for casino floor optimization. We begin by extending a linear formulation of the casino floor …

Stationary And Time-Dependent Optimization Of The Casino Floor Slot Machine Mix, Anastasia D. Baran, Jason D. Fiege

International Conference on Gambling & Risk Taking

Modeling and optimizing the performance of a mix of slot machines on a gaming floor can be addressed at various levels of coarseness, and may or may not consider time-dependent trends. For example, a model might consider only time-averaged, aggregate data for all machines of a given type; time-dependent aggregate data; time-averaged data for individual machines; or fully time dependent data for individual machines. Fine-grained, time-dependent data for individual machines offers the most potential for detailed analysis and improvements to the casino floor performance, but also suffers the greatest amount of statistical noise. We present a theoretical analysis of single …

Priority Queueing System With A Single Server Serving Two Queues M[X1],M[X2]/G1,G2/1 With Balking And Optional Server Vacation, G. Ayyappan, P. Thamizhselvi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we study a vacation queueing system with a single server simultaneously dealing with an M^{[x₁] _/}G₁/1 and an M^{[x₂] /}G₂/1 queues. Two classes of units, priority and non-priority, arrive at the system in two independent compound Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority and non-priority units. We further assume that the server may take a vacation of random length just after serving the last customer in the priority unit present in the system. If the server …

Flesch-Kincaid Reading Grade Level Re-Examined: Creating A Uniform Method For Calculating Readability On A Certification Exam, Emily Neuhoff, Kristiana M. Feeser, Kayla Sutherland, Thomas Hovatter

Online Journal for Workforce Education and Development

Abstract

Objective: This study attempted to establish a consistent measurement technique of the readability of a state-wide Certified Nursing Assistant’s (CNA) certification exam. Background: Monitoring the readability level of an exam helps ensure all test versions do not exceed the maximum reading level of the exam, and that knowledge of the subject matter, rather than reading ability, is being assessed. Method: A two part approach was used to specify and evaluate readability. First, two methods (Microsoft Word^® (MSW) software and published readability formulae) were used to calculate Flesch Reading Ease (FRE) and Flesch-Kincaid Reading Grade Level (FKRGL) for multiple …

Hpcnmf: A High-Performance Toolbox For Non-Negative Matrix Factorization, Karthik Devarajan, Guoli Wang

COBRA Preprint Series

Non-negative matrix factorization (NMF) is a widely used machine learning algorithm for dimension reduction of large-scale data. It has found successful applications in a variety of fields such as computational biology, neuroscience, natural language processing, information retrieval, image processing and speech recognition. In bioinformatics, for example, it has been used to extract patterns and profiles from genomic and text-mining data as well as in protein sequence and structure analysis. While the scientific performance of NMF is very promising in dealing with high dimensional data sets and complex data structures, its computational cost is high and sometimes could be critical for …

Simulation Of Nuclear Fusion Using A One Dimensional Particle In Cell Method, Steven T. Margell

Cal Poly Humboldt theses and projects

In this thesis several novel techniques are developed to simulate fusion events in an isotropic, electrostatic three-dimensional Deuterium-Tritium plasma. These techniques allow us to accurately predict three-dimensional collision events with a one-dimensional model while simultaneously reducing compute time via a nearest neighbor algorithm. Furthermore, a fusion model based on first principles is developed that yields an average fusion reactivity which correlates well with empirical results.

Stability Condition Of A Retrial Queueing System With Abandoned And Feedback Customers, Amina A. Bouchentouf, Abbes Rabhi, Lahcene Yahiaoui

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the stability of a retrial queueing system with two orbits, abandoned and feedback customers. Two independent Poisson streams of customers arrive to the system, and flow into a single-server service system. An arriving one of type i; i = 1; 2, is handled by the server if it is free; otherwise, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. The customer in the orbit either attempts service again after a random time or gives up receiving service and leaves the system …

Analysis Of Repairable M[X]/(G1,G2)/1 - Feedback Retrial G-Queue With Balking And Starting Failures Under At Most J Vacations, P. Rajadurai, M. C. Saravanarajan, V. M. Chandrasekaran

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of service and negative customers. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. The negative customer, arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters into the orbit or leaves the system. If the orbit is empty at the service completion of each type …

Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker

Electronic Theses and Dissertations

Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a …

Generating Random Vectors Using Transformation With Multiple Roots And Its Applications, Qidi Peng, Henry Schellhorn, Lu Zhu

Applications and Applied Mathematics: An International Journal (AAM)

An approach is proposed to generate random vectors using transformation with multiple roots. This approach generalizes the one-dimensional inverse transformation with multiple roots method to higher dimensions, i.e., to random vectors with or without densities. In this approach, multiple roots of the transformation and probabilities of selecting each of the roots are derived. The strategies for constructing such a transformation are discussed and several examples are presented to motivate this simulation approach.

A Note On An M/M/S Queueing System With Two Reconnect And Two Redial Orbits, Amina A. Bouchentouf, Hanane Sakhi

Applications and Applied Mathematics: An International Journal (AAM)

A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new …

Analysis Of Repairable M[X]/(G1,G2)/1 - Feedback Retrial G-Queue With Balking And Starting Failures Under At Most J Vacations, P. Rajadurai, M. C. Saravanarajan, V. M. Chandrasekaran

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of services and negative customers. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them get into the orbit. The negative customer, is arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters the orbit or leaves the system. If the orbit is empty at the service completion of each type …

Modeling Traffic At An Intersection, Kaleigh L. Mulkey, Saniita K. Fasenntao

Symposium of Student Scholars

The main purpose of this project is to build a mathematical model for traffic at a busy intersection. We use elements of Queueing Theory to build our model: the vehicles driving into the intersection are the “arrival process” and the stop light in the intersection is the “server.”

We collected traffic data on the number of vehicles arriving to the intersection, the duration of green and red lights, and the number of vehicles going through the intersection during a green light. We built a SAS macro code to simulate traffic based on parameters derived from the data.

In our program …

Generalized Least-Squares Regressions V: Multiple Variables, Nataniel Greene

Publications and Research

The multivariate theory of generalized least-squares is formulated here using the notion of generalized means. The multivariate generalized least-squares problem seeks an m dimensional hyperplane which minimizes the average generalized mean of the square deviations between the data and the hyperplane in m + 1 variables. The numerical examples presented suggest that a multivariate generalized least-squares method can be preferable to ordinary least-squares especially in situations where the data are ill- conditioned.

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 …

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 …

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.

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 …

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 …

Generalized Least-Squares Regressions Iii: Further Theory And Classification, Nataniel Greene

Publications and Research

This paper continues the work of this series with two results. The first is an exponential equivalence theorem which states that every generalized least-squares regression line can be generated by an equivalent exponential regression. It follows that every generalized least-squares line has an effective normalized exponential parameter between 0 and 1 which classifies the line on the spectrum between ordinary least-squares and the extremal line for a given set of data. The second result is the presentation of fundamental formulas for the generalized least-squares slope and y-intercept.

Building A Predictive Model For Baseball Games, Jordan Robertson Tait

All Graduate Theses, Dissertations, and Other Capstone Projects

In this paper, we will discuss a method of building a predictive model for Major League Baseball Games. We detail the reasoning for pursuing the proposed predictive model in terms of social popularity and the complexity of analyzing individual variables. We apply a coarse-grain outlook inspired by Simon Dedeos' work on Human Social Systems, in particular the open source website Wikipedia [2] by attempting to quantify the influence of winning and losing streaks instead of analyzing individual performance variables. We will discuss initial findings of data collected from the LA Dodgers and Colorado Rockies and apply further statistical analysis to …

Using Fuzzy Linear Regression To Estimate Relationship Between Forest Fires And Meteorological Conditions, Hande G. Akdemir, Fatma Tiryaki

Applications and Applied Mathematics: An International Journal (AAM)

Each year, millions of hectares of forest land are destroyed by fires causing great financial loss and ecological damage. In this paper, our aim is to study the effect of the variation of meteorological conditions on the total burned area in hectares, by using fuzzy linear regression analysis based on Tanaka’s approaches. The total burned area is considered a dependent variable. Air temperature (in ºC), relative humidity (in %), wind speed (in km/h) and rainfall (in mm/m² ) are considered to be independent variables. The relationship between input and output data is estimated using data provided in data mining …

Random Search Models Of Foraging Behavior: Theory, Simulation, And Observation, Ben C. Nolting

Department of Mathematics: Dissertations, Theses, and Student Research

Many organisms, from bacteria to primates, use stochastic movement patterns to find food. These movement patterns, known as search strategies, have recently be- come a focus of ecologists interested in identifying universal properties of optimal foraging behavior. In this dissertation, I describe three contributions to this field. First, I propose a way to extend Charnov's Marginal Value Theorem to the spatially explicit framework of stochastic search strategies. Next, I describe simulations that compare the efficiencies of sensory and memory-based composite search strategies, which involve switching between different behavioral modes. Finally, I explain a new behavioral analysis protocol for identifying the …

Stochastic Dea With A Perfect Object And Its Application To Analysis Of Environmental Efficiency, Alexander Vaninsky

Publications and Research

The paper introduces stochastic DEA with a Perfect Object (SDEA PO). The Perfect Object (PO) is a virtual Decision Making Unit (DMU) that has the smallest inputs and greatest outputs. Including the PO in a collection of actual objects yields an explicit formula of the efficiency index. Given the distributions of DEA inputs and outputs, this formula allows us to derive the probability distribution of the efficiency score, to find its mathematical expectation, and to deliver common (group–related) and partial (object-related) efficiency components. We apply this approach to a prospective analysis of environmental efficiency of the major national and regional …

Singular Ergodic Control For Multidimensional Gaussian-Poisson Processes, J. L. Menaldi, M. Robin

Mathematics Faculty Research Publications

Singular control for multidimensional Gaussian-Poisson processes with a long-run (or ergodic) and a discounted criteria are discussed. The dynamic programming yields the corresponding Hamilton-Jacobi-Bellman equations, which are discussed. Full details on the proofs and further extensions are left for coming works.

Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene

Publications and Research

In the first paper of this series, a variety of known and new symmetric and weighted least-squares regression methods were presented with efficient derivations. This paper continues and generalizes the previous work with a theory for deriving, analyzing, and classifying all symmetric and weighted least-squares regression methods.

Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene

Publications and Research

Ordinary least-squares regression suffers from a fundamental lack of symmetry: the regression line of y given x and the regression line of x given y are not inverses of each other. Alternative symmetric regression methods have been developed to address this concern, notably: orthogonal regression and geometric mean regression. This paper presents in detail a variety of least squares regression methods which may not have been known or fully explicated. The derivation of each method is made efficient through the use of Ehrenberg's formula for the ordinary least-squares error and through the extraction of a weight function g(b) which characterizes …