Applied Mathematics Commons^™

Multiclass Classification Using Support Vector Machines, Duleep Prasanna W. Rathgamage Don

College of Graduate Studies: Theses & Dissertations

In this thesis, we discuss different SVM methods for multiclass classification and introduce the Divide and Conquer Support Vector Machine (DCSVM) algorithm which relies on data sparsity in high dimensional space and performs a smart partitioning of the whole training data set into disjoint subsets that are easily separable. A single prediction performed between two partitions eliminates one or more classes in a single partition, leaving only a reduced number of candidate classes for subsequent steps. The algorithm continues recursively, reducing the number of classes at each step until a final binary decision is made between the last two classes …

Investigation Of Toppling Ball Flight In American Football With A Mechanical Field-Goal Kicker, Chase M Pfeifer, Timothy J. Gay, Jeff A. Hawks, Shane Farritor, Judith M. Burnfield

Department of Mechanical and Materials Engineering: Faculty Publications

A mechanical field-goal kicking machine was used to investigate toppling ball flight in American football place-kicking, eliminating a number of uncontrollable impact variables present with a human kicker. Ball flight trajectories were recorded using a triangulation-based projectile tracking system to account for the football’s 3-dimensional position during flight as well as initial launch conditions. The football flights were described using kinematic equations relating to projectile motion including stagnant air drag and were compared to measured trajectories as well as projectile motion equations that exclude stagnant air drag. Measured football flight range deviations from the non-drag equations of projectile motion corresponded …

Existing And Regularity Of Minimizers For Nonlocal Energy Functionals, Mikil D. Foss, Petronela Radu, Cory Wright

Department of Mathematics: Faculty Publications

In this paper, we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics [19] or nonlocal diffusion models [1]. We derive nonlocal versions of the Euler-Lagrange equations under two sets of growth assumptions for the integrand. Existence of minimizers is shown for integrands with joint convexity (in the function and nonlocal gradient components). By using the convolution structure, we show regularity of solutions for certain Euler-Lagrange equations. No growth assumptions are needed for the existence and regularity of minimizers results, in contrast with the classical theory.

Wavelet Anova Bisection Method For Identifying Simulation Model Bias, Andrew D. Atkinson, Raymond R. Hill, Joseph J. Pignatiello Jr., G. Geoffrey Vining, Edward D. White, Eric Chicken

Faculty Publications

High-resolution computer models can simulate complex systems and processes in order to evaluate a solution quickly and inexpensively. Many simulation models produce dynamic functional output, such as a set of time-series data generated during a process. These computer models require verification and validation (V&V) to assess the correctness of these simulations. In particular, the model validation effort evaluates if the model is an appropriate representation of the real-world system that it is meant to simulate. However, when assessing a model capable of generating functional output, it is useful to learn more than simply whether the model is valid or invalid. …

Generating Species Assemblages For Restoration And Experimentation: A New Method That Can Simultaneously Converge On Average Trait Values And Maximize Functional Diversity, David C. Laughlin, Loïc Chalmandrier, Chaitanya Joshi, Michael Renton, John M. Dwyer, Jennifer L. Funk

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

1.Restoring resilient ecosystems in an era of rapid environmental change requires a flexible framework for selecting assemblages of species based on functional traits. However, current trait‐based models have been limited to algorithms that select species assemblages that only converge on specified average trait values, and could not accommodate the common desire among restoration ecologists to generate functionally diverse assemblages.

2.We have solved this problem by applying a nonlinear optimization algorithm to solve for the species relative abundances that maximize Rao's quadratic entropy (Q) subject to other linear constraints. Rao's Q is a closed‐form algebraic expression of functional diversity …

The Mechanics And Thermodynamics Of Amyloid Beta Protein Aggregation In Competing Pathways, Edward Steen

Theses, Dissertations and Culminating Projects

The primary purpose of this paper is to investigate the mechanics of Aβ protein aggregation within the brain through mathematical modeling and simulation. Aggregation of Aβ is the cause of plaques within the brain of Alzheimer’s Disease sufferers. Because the pathways of aggregation from monomer to oligomer to polymer are numerous and complex, we have had to simplify our model to a limited number of species. Of great concern, too, is the process by which Aβ can form as “off-pathway” species, which is when Aβ reacts with fatty acid micelles. It is this species of Aβ, which due to its …

Effect Of Neuromodulation Of Short-Term Plasticity On Information Processing In Hippocampal Interneuron Synapses, Elham Bayat Mokhtari

Graduate Student Theses, Dissertations, & Professional Papers

Neurons convey information about the complex dynamic environment in the form of signals. Computational neuroscience provides a theoretical foundation toward enhancing our understanding of nervous system. The aim of this dissertation is to present techniques to study the brain and how it processes information in particular neurons in hippocampus.

We begin with a brief review of the history of neuroscience and biological background of basic neurons. To appreciate the importance of information theory, familiarity with the information theoretic basics is required, these basics are presented in Chapter 2. In Chapter 3, we use information theory to estimate the amount of …

Special Issue : Neutrosophic Multi-Criteria Decision Making, Florentin Smarandache, Jun Ye, Yan Hui Guo

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of a neutrosophic quadruple BCK/BCI-number is considered in the first article (“Neutrosophic Quadruple BCK/BCI-Algebras”, by Young Bae Jun, Seok-Zun Song, Florentin Smarandache, and Hashem Bordbar), and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied. Given subsets A and B of a BCK/BCI-algebra, the set NQ(A,B), which consists of neutrosophic quadruple BCK/BCInumbers with a condition, is established. Conditions for the set NQ(A,B) to be a (positive implicative) ideal of a …

Spanning Tree Problem With Neutrosophic Edge Weights, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Arindam Dey, Le Hoang Son

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set and neutrosophic logic theory are renowned theories to deal with complex, not clearly explained and uncertain real life problems, in which classical fuzzy sets/models may fail to model properly. This paper introduces an algorithm for finding minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph (abbr. UNWCG) where the arc/edge lengths are represented by a single valued neutrosophic numbers. To build the MST of UNWCG, a new algorithm based on matrix approach has been introduced. The proposed algorithm is compared to other existing methods and finally a numerical example is provided.

Operadores Con Conjunto Neutrosóficos De Valor Único Oversets, Undersets Y Offset, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Over-/Under-/Off-Set and Logic were defined for the first time in 1995 and published in 2007. During 1995-2016 was presented them to various national and international conferences and seminars. These new notions are totally different from other sets/logics/probabilities. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, to Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0}. This is no surprise since our realworld has numerous examples and applications of over-/under-/off-neutrosophic components. Palabras clave. desbordado neutrosophic, underset neutrosophic, neutrosophic offset, neutrosophic sobre la lógica, neutrosophic bajo la lógica, neutrosophic off lógica, neutrosophic sobre la probabilidad, neutrosophic bajo probabilidad, neutrosophic de probabilidad, más de miembros (grado de pertenencia> 1), bajo de miembros (grado de pertenencia <0) , (grado de pertenencia fuera del intervalo [0, 1]) offmembership.

Neutrosophic Computing With Sympy (Computación Neutrosófica Mediante Sympy ), Maykel Leyva-Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this article the concept of neutrosophic number is presented. Jupyter through Google Colaboratory is introduced for calculations. The Sympy library is used to perform the process of neutrosophic computation. Systems of linear neutrosóficas equations are solved by means of the symbolic computation in python. A case study was developed for the determination of vehicular traffic with indeterminacy. As future works are the development of new applications in different areas of engineering and science.

Fundamentals Of Neutrosophic Logic And Sets And Their Role In Artificial Intelligence (Fundamentos De La Lógica Y Los Conjuntos Neutrosóficos Y Su Papel En La Inteligencia Artificial ), Florentin Smarandache, Maykel Leyva-Vazquez

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophy is a new branch of philosophy which studies the origin, nature and scope of neutralities. This has formed the basis for a series of mathematical theories that generalize the classical and fuzzy theories such as the neutrosophic sets and the neutrosophic logic. In the paper, the fundamental concepts related to neutrosophy and its antecedents are presented. Additionally, fundamental concepts of artificial intelligence will be defined and how neutrosophy has come to strengthen this discipline.

N-Valued Refined Neutrosophic Logic And Its Applications To Physics (Lógica Neutrosófica Refinada N-Valuada Y Sus Aplicaciones A La Física), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general nsymbol or numerical valued refined neutrosophic logic. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively.

Modelo De Recomendación Basado En Conocimiento Y Números Svn, Maykel Leyva-Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Recommendation models are useful in the decision-making process that allow the user a set of options that are expected to meet their expectations. Recommendation models are useful in the decision-making process that offer the user a set of options that are expected to meet their SVN expectations to express linguistic terms.

Neutrosophic Operational Research - Vol. 3., Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …

Special Subset Vertex Subgraphs For Social Networks, Florentin Smarandache, W. B. Vasantha Kandasamy, Ilanthenral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the new notion of special subset vertex subgraph of subset vertex graphs introduced recently in [46]. These subset vertex graphs takes the vertex set values from the power set P(X) of any set X. The main speciality of these subset vertex graphs is that once a set of subsets from P(X) is given, the edges of the graph are fixed in a unique way, so for a given collection of subset vertices the graph is always unique [46]. The special subset vertex subgraphs of G are the ones, which have the …

New Trends In Neutrosophic Theory And Applications Volume Ii, Florentin Smarandache, Surapati Pramanik

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, …

Fuzzy And Neutrosophic Sets In Semigroups, Florentin Smarandache, Young Bae Jun, Madad Khan

Branch Mathematics and Statistics Faculty and Staff Publications

The first chapter, Characterizations of regular and duo semigroups based on int-soft set theory, investigates the relations among int-soft semigroup, int-soft (generalized) bi-ideal, int-soft quasi-ideal and int-soft interior ideal. Using int-soft left (right) ideal, an int-soft quasi-ideal is constructed. We show that every int-soft quasi-ideal can be represented as the soft intersection of an int-soft left ideal and an int-soft right ideal. Using int-soft quasiideal, an int-soft bi-ideal is established. Conditions for a semigroup to be regular are displayed.

An Investigation Of The Influence Of The 2007-2009 Recession On The Day Of The Week Effect For The S&P 500 And Its Sectors, Marcel Alwin Trick

Masters Theses

"Several studies have shown that the mean returns and the volatility structure of stock markets change seasonally or by day of the week. For instance, some authors found out that Monday returns are lower compared to Friday returns or that volatility on Wednesdays are lower compared to the rest of the week. Other researchers showed that these effects have changed after certain periods of economic stress. This led to the question, whether the day of the week effects in returns and volatility are in the US stock market and if patterns have changed from pre-recession through the 2007-2009 recession into …

Pseudo-Companion Matrices For Polynomial Systems, Melinda Kleczynski

Dissertations, Master's Theses and Master's Reports

Roots of a scalar polynomial in one variable are frequently found by computing the eigenvalues of the standard companion matrix. In this exploratory work, we introduce the pseudo-companion matrix for finding roots of multivariable polynomial systems. In some cases, a perturbation of the polynomial system is used for the matrix construction, yielding approximate roots of the original polynomial system. The coordinates of the roots, or their approximations, are obtained from the eigenvectors of this matrix. In this thesis, we describe the process of constructing the pseudo-companion matrix and computing the polynomial roots using illustrative examples.