Physical Sciences and Mathematics Commons^™

Integrating Path-Dependent Functionals On Yeh-Wiener Space, Ian Pierce, David Skough

Department of Mathematics: Faculty Publications

Denote by Ca,b(Q) the generalized two-parameter Yeh-Wiener space with associated Gaussian measure. We investigate several scenarios in which integrals of functionals on this space can be reduced to integrals of related functionals over an appropriate single-parameter generalized Wiener space Cˆa,ˆb[0, T ]. This extends some interesting results of R. H. Cameron and D. A. Storvick.

Among Several Successful Algorithms, Simpler Ones Usually Work Better: A Possible Explanation Of An Empirical Observation, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Often, several different algorithms can solve a certain practical problem. Sometimes, algorithms which are successful in solving one problem can solve other problems as well. How can we decide which of the original algorithms is the most promising -- i.e., which is more probable to be able to solve other problem? In many cases, the simplest algorithms turns out to be the most successful. In this paper, we provide a possible explanation for this empirical observation.

Enumeration Of Tilings Of Quartered Aztec Rectangles, Tri Lai

Department of Mathematics: Faculty Publications

We generalize a theorem of W. Jockusch and J. Propp on quartered Aztec diamonds by enumerating the tilings of quartered Aztec rectangles. We use subgraph replacement method to transform the dual graph of a quartered Aztec rectangle to the dual graph of a quartered lozenge hexagon, and then use Lindstr¨om-Gessel- Viennot methodology to find the number of tilings of a quartered lozenge hexagon.

Von Neumann Algebras And Extensions Of Inverse Semigroups, Allan P. Donsig, Adam H. Fuller, David R. Pitts

Department of Mathematics: Faculty Publications

In the 1970s, Feldman and Moore classified separably acting von Neumann algebras containing Cartan MASAs using measured equivalence re- lations and 2-cocycles on such equivalence relations. In this paper, we give a new classification in terms of extensions of inverse semigroups. Our approach is more algebraic in character and less point-based than that of Feldman-Moore. As an application, we give a restatement of the spectral theorem for bimodules in terms of subsets of inverse semigroups. We also show how our viewpoint leads naturally to a description of maximal subdiagonal algebras.

Nonsmooth Algorithms And Nesterov's Smoothing Technique For Generalized Fermat-Torricelli Problems, Nguyen Mau Nam, Nguyen Thai An, R. Blake Rector, Jie Sun

Mathematics and Statistics Faculty Publications and Presentations

We present algorithms for solving a number of new models of facility location which generalize the classical Fermat--Torricelli problem. Our first approach involves using Nesterov's smoothing technique and the minimization majorization principle to build smooth approximations that are convenient for applying smooth optimization schemes. Another approach uses subgradient-type algorithms to cope directly with the nondifferentiability of the cost functions. Convergence results of the algorithms are proved and numerical tests are presented to show the effectiveness of the proposed algorithms.

A Mentoring Program For Inquiry-Based Teaching In A College Geometry Class, Nathaniel Miller, Nathan Wakefield

Department of Mathematics: Faculty Publications

This paper describes a mentoring program designed to prepare novice instructors to teach a college geometry class using inquiry-based methods. The mentoring program was used in a medium-sized public university with approximately 12,000 undergraduate students and 1,500 graduate students. The authors worked together to implement a mentoring program for the first time. One author was an associate professor and experienced using inquiry-based learning. The other author was a graduate student in mathematics education. During the course of the year the graduate student first observed and then taught a college level inquiry-based geometry course for pre-service teachers. This article describes the …

Examining The Consistence Of Futures Margin Levels Using Bivariate Extreme Value Copulas, X. Gong, Hung T. Nguyen, Vladik Kreinovich, Songsak Sriboonchitta

Departmental Technical Reports (CS)

This study examines the consistence of the futures margin levels of different commodities and combinations in the CME group by Extreme Value Copula (EVC). We find that if we ignore the co-movements of the commodities, the margins become consistent with each other, and the margin violation rates hover around 0.5%. However, if we consider the co-movement of the related commodities using EVC, the margin levels are found to be not consistent anymore, especially in the combinations of strongly related commodities which are in the same category. Therefore, we suggest that the CME group should try to harmonize the margins policy …

Granularity Explains Empirical Factor-Of-Three Relation Between Probabilities Of Pulmonary Embolism In Different Patient Categories, Beverly Rivera, Francisco Zapata, Vladik Kreinovich

Departmental Technical Reports (CS)

Pulmonary embolism is a very dangerous difficult-to-detect medical condition. To diagnose pulmonary embolism, medical practitioners combine indirect signs of this condition into a single score, and then classify patients into low-probability, intermediate-probability, and high-probability categories. Empirical analysis shows that, when we move from each category to the next one, the probability of pulmonary embolism increases by a factor of three. In this paper, we provide a theoretical explanation for this empirical relation between probabilities.

How To Gauge Unknown Unknowns: A Possible Theoretical Explanation Of The Usual Safety Factor Of 2, Joe Lorkowski, Vladik Kreinovich

Departmental Technical Reports (CS)

To gauge the accuracy of a measuring instrument, engineers analyze possible factors contributing to the instrument's inaccuracy. In addition to known factors, however, there are usually unknown factors which also contribute to the instrument's inaccuracy. To properly gauge the instrument's accuracy -- and thus, to make sure that we do not compromise our safety by underestimating the inaccuracy -- we need to also take these "unknown unknowns" into account. In practice, this is usually done by multiplying the original estimate for inaccuracy by a "safety" factor of 2. In this paper, we provide a possible theoretical explanation for this empirical …

Shifted One-Parameter Supersymmetric Family Of Quartic Asymmetric Double-Well Potentials, Haret C. Rosu, S.C. Mancas, Pisin Chen

Publications

Extending our previous work (Rosu, Mancas, Chen, Ann.Phys. 343 (2014) 87-102), we define supersymmetric partner potentials through a particular Riccati solution of the form F (x) = (x - c)^2 - 1, where c is a real shift parameter, and work out the quartic double-well family of one-parameter isospectral potentials obtained by using the corresponding general Riccati solution. For these parametric double well potentials, we study how the localization properties of the two wells depend on the parameter of the potentials for various values of the shifting parameter.

Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped harmonic oscillators in R with completely decentralized nearest neighbor interaction. We then use the theory to establish that in a certain range of the parameters transients grow linearly in the number of agents (and faster outside that range). Finally, in the regime where this linear growth occurs we give the constant of proportionality as a function of the signal velocities …

Numerical Modeling Of The Effects Of Hydrologic Conditions And Sediment Transport On Geomorphic Patterns In Wetlands, Mehrnoosh Mahmoudi

FIU Electronic Theses and Dissertations

This dissertation focused on developing a numerical model of spatial and temporal changes in bed morphology of ridge and slough features in wetlands with respect to hydrology and sediment transport when a sudden change in hydrologic condition occurs. The specific objectives of this research were: (1) developing a two-dimensional hydrology model to simulate the spatial distribution of flow depth and velocity over time when a pulsed flow condition is applied, (2) developing a process-based numerical model of sediment transport coupled with flow depth and velocity in wetland ecosystems, and (3) use the developed model to explore how sediment transport may …

Formalizing The Informal, Precisiating The Imprecise: How Fuzzy Logic Can Help Mathematicians And Physicists By Formalizing Their Intuitive Ideas, Olga Kosheleva, Renata Reiser, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy methodology transforms expert ideas -- formulated in terms of words from natural language -- into precise rules and formulas. In this paper, we show that by applying this methodology to intuitive physical and mathematical ideas, we can get known fundamental physical equations and known mathematical techniques for solving these equations. This fact makes us confident that in the future, fuzzy techniques will help physicists and mathematicians to transform their imprecise ideas into new physical equations and new techniques for solving these equations.

Dressing Method And Quadratic Bundles Related To Symmetric Spaces: Vanishing Boundary Conditions, Tihomir Valchev

Articles

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m) x U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schroedinger equation which serves as a motivational example for our general considerations. We extensively discuss how one can apply Zakharov-Shabat's dressing procedure to derive reflectionless potentials obeying zero boundary conditions. Those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy. One can distinguish between generic soliton type solutions and rational solutions.

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.

On Quasilinear Parabolic Evolution Equations In Weighted Lp-Spaces Ii, Jeremy Lecrone, Mathias Wilke, Jan Prüss

Department of Math & Statistics Faculty Publications

Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in 2010, is extended in this paper to include singular lower order terms, while keeping low initial regularity. The results are applied to reaction-diffusion problems, including Maxwell-Stefan diffusion, and to geometric evolution equations like the surface-diffusion flow or the Willmore flow. The method presented here will be applicable to other parabolic systems, including free boundary problems.

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.

Development Of A Methodology That Couples Satellite Remote Sensing Measurements To Spatial-Temporal Distribution Of Soil Moisture In The Vadose Zone Of The Everglades National Park, Luis G. Perez

FIU Electronic Theses and Dissertations

Spatial-temporal distribution of soil moisture in the vadose zone is an important aspect of the hydrological cycle that plays a fundamental role in water resources management, including modeling of water flow and mass transport. The vadose zone is a critical transfer and storage compartment, which controls the partitioning of energy and mass linked to surface runoff, evapotranspiration and infiltration. This dissertation focuses on integrating hydraulic characterization methods with remote sensing technologies to estimate the soil moisture distribution by modeling the spatial coverage of soil moisture in the horizontal and vertical dimensions with high temporal resolution.

The methodology consists of using …

Kekule's Benzene Structure: A Case Study Of Teaching Usefulness Of Symmetry, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Benzene is one of the basic building blocks of organic molecules. One of the reasons for benzene's ubiquity is its unusual ring structure first discovered by Kekule in 1865. In this paper, we show that a simple symmetry-based analysis can narrow down possible benzene structures to three ring ones, including the Kekule's ring. Thus, Kekule's benzene structure provides a good pedagogical example on which one can explain usefulness of symmetries.

Light Pollution Research Through Citizen Science, John Kanemoto

STAR Program Research Presentations

Light pollution (LP) can disrupt and/or degrade the health of all living things, as well as, their environments. The goal of my research at the NOAO was to check the accuracy of the citizen science LP reporting systems entitled: Globe at Night (GaN), Dark Sky Meter (DSM), and Loss of the Night (LoN). On the GaN webpage, the darkness of the night sky (DotNS) is reported by selecting a magnitude chart. Each magnitude chart has a different density/number of stars around a specific constellation. The greater number of stars implies a darker night sky. Within the DSM iPhone application, a …

A Soft Condensed Matter Approach Towards Mathematical Modelling Of Mass Transport And Swelling In Food Grains, Michael Chapwanya, N. Misra

Articles

Soft condensed matter (SCM) physics has recently gained importance for a large class of engineering materials. The treatment of food materials from a soft matter perspective, however, is only at the surface and is gaining importance for understanding the complex phenomena and structure of foods. In this work, we present a theoretical treatment of navy beans from a SCM perspective to describe the hydration kinetics. We solve the transport equations within a porous matrix and employ the Flory–Huggin’s equation for polymer–solvent mixture to balance the osmotic pressure. The swelling of the legume seed is modelled as a moving boundary with …

One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov

Articles

In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.

The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, Nora Youngs

Department of Mathematics: Dissertations, Theses, and Student Research

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can - in principle - be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, algebraic objects …

Boundary Value Problems Of Nabla Fractional Difference Equations, Abigail M. Brackins

Department of Mathematics: Dissertations, Theses, and Student Research

In this dissertation we develop the theory of the nabla fractional self-adjoint difference equation,

∇_a^ν(p∇y)(t)+q(t)y(ρ(t)) = f(t),

where 0 < ν < 1.We begin with an introduction to the nabla fractional calculus. In the second chapter, we show existence and uniqueness of the solution to a fractional self-adjoint initial value problem. We find a variation of constants formula for this fractional initial value problem, and use the variation of constants formula to derive the Green's function for a related boundary value problem. We study the Green's function and its properties in several settings. For a simplified boundary value problem, we show that the Green's function is nonnegative and we find its maximum and the maximum of its integral. For a boundary value problem with generalized boundary conditions, we find the Green's function and show that it is a generalization of the first Green's function. In the third chapter, we use the Contraction Mapping Theorem to prove existence and uniqueness of a positive solution to a forced self-adjoint fractional difference equation with a finite limit. We explore modifications to the forcing term and modifications to the space of functions in which the solution exists, and we provide examples to demonstrate the use of these theorems.

Advisers: Lynn Erbe and Allan Peterson

A Coupled Pde Model For The Morphological Instability Of A Multi-Component Thin Film During Surface Electromigration, Mahdi Bandegi

Masters Theses & Specialist Projects

In this thesis a model involving two coupled nonlinear PDEs is developed to study instability of a two-component metal film due to horizontal electric field and in a high-temperature environment similar to operational conditions of integrated circuits. The proposed model assumes the anisotropies of the diffusional mobilities for two atomic species, and negligible stresses in the film. The purpose of the modeling is to describe and understand the time-evolution of the shape of the film surface. Toward this end, the linear stability analysis (LSA) of the initially planar film surface with respect to small shape perturbations is performed. Such characteristics …

A Women In Mathematics, Computer Science, And Physics Course, Jim Crumley, Kristen Nairn, Lynn Ziegler, Pamela L. Bacon, Yu Zhang

MapCores Faculty Publications

Increasing women's participation is a concern in disciplines beyond
physics. As part of our Mathematics, Physics, Computer Science
Research Scholars (MapCores) program, we teach a women in science
class covering these three areas. Our course is a special version of
our college's first year seminar, which is a course designed to
prepare our students to read, write, and speak at a college-level. We
structure our FYS to promote academic confidence and interest in our
disciplines for the women in MapCores. It covers not only contributions
that women have made and barriers that women face in these
disciplines, but also research …

Variable Viscosity Condition In The Modeling Of A Slider Bearing, Kedar Nath Uprety, S.C. Mancas

Publications

To reduce tear and wear of machinery lubrication is essential. Lubricants form a layer between two surfaces preventing direct contact and reduce friction between moving parts and hence reduce wear. In this short letter the lubrication of two slider bearings with parallel and nonparallel is studied. First, we show that bearings with parallel plates cannot support any load. For bearings with nonparallel plates we are interested on how constant and temperature dependent viscosity affects the properties of the bearings. Also, a critical temperature for which the bearings would fail due to excess in temperature is found for both latter cases. …

A Comparison Of Five Malaria Transmission Models: Benchmark Tests And Implications For Disease Control, Dorothy I. Wallace, Ben S. Southworth, Xun Shi, Jonathan W. Chipman, Andrew K. Githeko

Dartmouth Scholarship

Background: Models for malaria transmission are usually compared based on the quantities tracked, the form taken by each term in the equations, and the qualitative properties of the systems at equilibrium. Here five models are compared in detail in order to develop a set of performance measures that further illuminate the differences among models.

Methods: Five models of malaria transmission are compared. Parameters are adjusted to correspond to similar biological quantities across models. Nine choices of parameter sets/initial conditions are tested for all five models. The relationship between malaria incidence in humans and (1) malaria incidence in vectors, (2) man-biting …

Using Second-Order Probabilities To Make Maximum Entropy Approach To Copulas More Reasonable, Hung T. Nguyen, Vladik Kreinovich, Berlin Wu

Departmental Technical Reports (CS)

Copulas are a general way of describing dependence between two or more random variables. When we only have partial information about the dependence, i.e., when several different copulas are consistent with our knowledge, it is often necessary to select one of these copulas. A frequently used method of selecting this copula is the maximum entropy approach, when we select a copula with the largest entropy. However, in some cases, the maximum entropy approach leads to an unreasonable selection -- e.g., even if we know that the two random variables are positively correlated, the maximum entropy approach completely ignores this information. …

New Distance And Similarity Measures Of Interval Neutrosophic Sets, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we proposed a new distance and several similarity measures between interval neutrosophic sets.