Mathematics Commons^™

Construction Of The Paths Of Brownian Motions On Star Graphs I, Vadim Kostrykin, Jürgen Potthoff, Robert Schrader

Communications on Stochastic Analysis

No abstract provided.

Limiting Distributions Of Galton-Watson Branching Processes With Immigration, Yoshinori Uchimura, Kimiaki Saitô

Communications on Stochastic Analysis

No abstract provided.

Wick Product And Clark-Ocone Formula In Abstract Wiener Space, Fariborz Asadian

Communications on Stochastic Analysis

No abstract provided.

Generalised Clark-Ocone Formulae For Differential Forms, Y Yang

Communications on Stochastic Analysis

No abstract provided.

Functional Itô'S Calculus And Dynamic Convex Risk Measures For Derivative Securities, Tak Kuen Siu

Communications on Stochastic Analysis

No abstract provided.

Chaos Representations For Marked Point Processes, Samuel N Cohen

Communications on Stochastic Analysis

No abstract provided.

Construction Of The Paths Of Brownian Motions On Star Graphs Ii, Vadim Kostrykin, Jürgen Potthoff, Robert Schrader

Communications on Stochastic Analysis

No abstract provided.

Asymptotic Spectral Analysis Of A Distance K-Graph Of N-Fold Direct Product Of A Graph, Jun Kurihara

Communications on Stochastic Analysis

No abstract provided.

Involvement Of Microrna Families In Cancer, Stefan Wuchty, Dolores Arjona, Serdar Bozdag, Peter O. Bauer

Mathematics, Statistics and Computer Science Faculty Research and Publications

Collecting representative sets of cancer microRNAs (miRs) from the literature we show that their corresponding families are enriched in sets of highly interacting miR families. Targeting cancer genes on a statistically significant level, such cancer miR families strongly intervene with signaling pathways that harbor numerous cancer genes. Clustering miR family-specific profiles of pathway intervention, we found that different miR families share similar interaction patterns. Resembling corresponding patterns of cancer miRs families, such interaction patterns may indicate a miR family’s potential role in cancer. As we find that the number of targeted cancer genes is a naı¨ve proxy for a cancer …

Rank-Based Estimation And Prediction For Mixed Effects Models In Nested Designs, Yusuf K. Bilgic

Dissertations

Hierarchical designs frequently occur in many research areas. The experimental design of interest is expressed in terms of fixed effects but, for these designs, nested factors are a natural part of the experiment. These nested effects are generally considered random and must be taken into account in the statistical analysis. Traditional analyses are quite sensitive to outliers and lose considerable power to detect the fixed effects of interest.

This work proposes three rank-based fitting methods for handling random, fixed and scale effects in k-level nested designs for estimation and inference. An algorithm, which iteratively obtains robust prediction for both scale …

On Lattice Structure Of The Probability Functions On L*, Mashaallah Mashinchi, Ghader Khaledi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the set of all probability functions on L* is studied, where L* is the lattice of bothvalued fuzzy sets or intuitionistic fuzzy sets. It is shown that the set of all probability functions on L* endowed with two appropriate operations has a monoid structure which is also a distributive complete lattice. Also the lattice structure of the set of all probability functions on L* induced by an appropriate function on [0, 1] to itself is studied. Some lattice (dual) isomorphisms are discussed that suggests probabilities on L* could be considered in the framework of theories modeling imprecision.

Exact Solutions Of The Generalized Benjamin Equation And (3 + 1)- Dimensional Gkp Equation By The Extended Tanh Method, N. Taghizadeh, M. Mirzazadeh, S. R. Moosavi Noori

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the extended tanh method is used to construct exact solutions of the generalized Benjamin and (3 + 1)-dimensional gKP equation. This method is shown to be an efficient method for obtaining exact solutions of nonlinear partial differential equations. It can be applied to nonintegrable equations as well as to integrable ones.

The Intersection Between Science And Computer Science Is Almost Empty, Dick Hamlet

Systems Science Friday Noon Seminar Series

Traditionally, a science such as physics overlaps with mathematics and engineering in a way that has been astonishingly productive. The math provides precise expression for the science, which in turn supplies the engineering with the information it needs to exploit physical phenomena. Computer science naturally wishes to put itself in the center of the traditional picture as a science. Unfortunately, it won't wash. The `science' of programming is pure and simple mathematics, not science. The distinction is more than linguistic, since science and mathematics have quite distinct goals and methods. By making the wrong choice, computer science research has been …

A Simple Bijection Between Standard 3×N Tableaux And Irreducible Webs For ����3, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

Combinatorial spiders are a model for the invariant space of the tensor product of representations. The basic objects, webs, are certain directed planar graphs with boundary; algebraic operations on representations correspond to graph-theoretic operations on webs. Kuperberg developed spiders for rank 2 Lie algebras and ����₂. Building on a result of Kuperberg’s, Khovanov-Kuperberg found a recursive algorithm giving a bijection between standard Young tableaux of shape 3 × n and irreducible webs for ����₃whose boundary vertices are all sources. In this paper, we give a simple and explicit map from standard Young tableaux of shape 3 …

Mathematical And Computational Modelling For Biosensors: A Modular Approach, Yupeng Liu

Doctoral

Biosensors are analytic devices which detect biochemical and physiological changes and represent an emerging technology for low-cost, rapid and simple-to-operate biomedical diagnostic tools. Biosensor design and functionality are based on well understood physical and chemical processes which can be easily translated into mathematical models involving ordinary and partial di erential equations. Using mathematical and computational modelling techniques to characterize the biosensor response as a function of its input parameters in a wide range of physical contexts can guide the experimental work, thus reducing development time and costs.
This thesis is based on a close collaboration with Biochemistry researchers at the …

Mathematics And Religion: Our Languages Of Sign And Symbol (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Mathematics and Religion: Our Languages of Sign and Symbol by Javier Leach. West Conshohocken, PA: Templeton Press, 2010, 188 pages. ISBN 9781599471495.

2d Novel Structures Along An Opitcal Fiber, Charles-Julien Vandamme, S.C. Mancas

Publications

By using spectral methods, we present seven classes of stable and unstable structures that occur in a dissipative media. By varying parameters and initial conditions we find ranges of existence of stable structures (spinning elliptic, pulsating, stationary, organized exploding), and unstable structures (filament, disorganized exploding, creeping). By varying initial conditions, vorticity, and parameters of the equation, we find a reacher behavior of solutions in the form of creeping-vortex (propellers), spinning rings and spinning “bean-shape” solitons. Each class differentiates from the other by distinctive features of their shape and energy evolution, as well as domain of existence.

Balance With Unbounded Complexes, Edgar E. Enochs, Sergio Estrada, Alina Iacob

Mathematical Sciences: Faculty Publications

Given a double complex X there are spectral sequences with the E₂ terms being either H_I (H_II(X)) or H_II(H_I(X)). But if H_I(X)=H_II(X)=0, then both spectral sequences have all their terms 0. This can happen even though there is nonzero (co)homology of interest associated with X. This is frequently the case when dealing with Tate (co)homology. So, in this situation the spectral sequences may not give any information about the (co)homology of interest. In this article, we …

Energy Methods For Reaction-Diffusion Problems, Xing Zhong

Dissertations

Nonlinear reaction-diffusion equations arise in many areas of applied sciences such as combustion modeling, population dynamics, chemical kinetics, etc. A fundamental problem in the studies of these equations is to understand the long time behavior of solutions of the associated Cauchy problem. These kinds of questions were originally studied in the context of combustion modeling.

For suitable nonlinearity and a monotone increasing one-parameter family of initial data starting with zero data, small values of the parameter lead to extinction, whereas large values of the parameter may lead to spreading, i.e., the solution converging locally uniformly to a positive spatially independent …

Instabilities In Newtonian Films And Nematic Liquid Crystal Droplets, Te-Sheng Lin

Dissertations

The instabilities of Newtonian films and nematic liquid crystal droplets within the framework of the long wave (lubrication) approximation are studied. For Newtonian films, it is found that, under destabilizing gravitational force, a contact line, modeled by a commonly used precursor film model, leads to free surface instabilities without any additional natural or imposed perturbations. In addition, there is a coupling between the surface instabilities and the transverse (fingering) instabilities which leads to complex behavior. All the observed phenomena are characterized by a single parameter D = (3Ca)^1/3 cot α where Ca is the capillary number and …

Mathematical Models Of Combustion At High Pressure, Daniel Fong

Dissertations

In this dissertation, we develop new mathematical theories of flame propagation that are valid at elevated, or extreme, pressures. Of particular interest is the regime of burning in which the pressure exceeds the critical pressure of the species undergoing chemical reaction. Fluids and flames are known to behave differently under these extreme conditions as opposed to atmospheric pressure. The focus of this dissertation is to investigate these differences by deriving reduced models that contain the unique features.

In the first part of this dissertation, we analyze the structure of laminar diffusion flames at high pressure in the limit of large …

Communal Partitions Of Integers, Darren B. Glass

Math Faculty Publications

There is a well-known formula due to Andrews that counts the number of incongruent triangles with integer sides and a fixed perimeter. In this note, we consider the analagous question counting the number of k-tuples of nonnegative integers none of which is more than 1/(k−1) of the sum of all the integers. We give an explicit function for the generating function which counts these k-tuples in the case where they are ordered, unordered, or partially ordered. Finally, we discuss the application to algebraic geometry which motivated this question.

Simplified Models Of Vector Control Impact Upon Malaria Transmission By Zoophagic Mosquitoes, Samson S. Kiware, Nakul Chitnis, Sarah J. Moore, Gregor J. Devine, Silas Majambere, Stephen Merrill, Gerry F. Killeen

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

High coverage of personal protection measures that kill mosquitoes dramatically reduce malaria transmission where vector populations depend upon human blood. However, most primary malaria vectors outside of sub-Saharan Africa can be classified as “very zoophagic,” meaning they feed occasionally (

Methods and Findings

We extended a published malaria transmission model to examine the relationship between transmission, control, and the baseline proportion of bloodmeals obtained from humans (human blood index). The lower limit of the human blood index enables derivation of simplified models for zoophagic vectors that (1) Rely on only three field-measurable parameters. (2) Predict immediate and delayed (with …

Remainders And Connectedness Of Ordered Compactifications, Sinem Ayse Karatas

Masters Theses & Specialist Projects

The aim of this thesis is to establish the principal properties for the theory of ordered compactifications relating to connectedness and to provide particular examples. The initial idea of this subject is based on the notion of the Stone-Cech compactification.
The ordered Stone-Cech compactification oX of an ordered topological space X is constructed analogously to the Stone-Cech compactification X of a topological space X, and has similar properties. This technique requires a conceptual understanding of the Stone-Cech compactification and how its product applies to the construction of ordered topological spaces with continuous increasing functions. Chapter 1 introduces background information.

Chapter …

Second-Order Convex Splitting Schemes For Gradient Flows With Ehrlich-Schwoebel Type Energy: Application To Thin Film Epitaxy, Jie Shen, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

We construct unconditionally stable, unconditionally uniquely solvable, and second order accurate (in time) schemes for gradient flows with energy of the form {equation presented} dx. the construction of the schemes involves the appropriate combination and extension of two classical ideas: (i) appropriate convex-concave decomposition of the energy functional and (ii) the secant method. as an application, we derive schemes for epitaxial growth models with slope selection (F(y) = 1/4 (|y| 2 - 1) 2) or without slope selection (F(y) = -1/2 ln(1 + |y| 2)). Two types of unconditionally stable uniquely solvable second-order schemes are presented. the first type inherits …

Long Time Stability Of A Classical Efficient Scheme For Two-Dimensional Navier-Stokes Equations, S. Gottlieb, F. Tone, C. Wang, X. Wang, D. Wirosoetisno

Mathematics and Statistics Faculty Research & Creative Works

This paper considers the long-time stability property of a popular semi-implicit scheme for the two-dimensional incompressible Navier-Stokes equations in a periodic box that treats the viscous term implicitly and the nonlinear advection term explicitly. We consider both the semi discrete (discrete in time but continuous in space) and fully discrete schemes with either Fourier Galerkin spectral or Fourier pseudo spectral (collocation) methods. We prove that in all cases, the scheme is long time stable provided that the timestep is sufficiently small. the long-time stability in the L 2 and H 1 norms further leads to the convergence of the global …

Interactive Concept To Aid In Understanding Dimensional Analysis, Alicia Hicks

Symposium 2012

Many students struggle with learning how to utilize dimensional analysis. This confusion is due to not understanding the concept of dose per volume, leading to difficulty when starting the sequencing. This could be one of the contributing causes to medication errors in clinical practice. Does using models, such as Play-doh and pebbles, help students learn the concept of milligrams per milliliters when calculating dosages using dimensional analysis method? A series of pre- and post-tests are used to measure learning growth in each of the treatment groups. Three treatment groups were utilized: Control: one group had no intervention between the pre …

Development Of Nabla Fractional Calculus And A New Approach To Data Fitting In Time Dependent Cancer Therapeutic Study, Nihan Acar

Masters Theses & Specialist Projects

The aim of this thesis is to develop discrete fractional models of tumor growth for a given data and to estimate parameters of these models in order to have better data tting. We use discrete nabla fractional calculus because we believe the discrete counterpart of this mathematical theory will give us a better and more accurate outcome.

This thesis consists of ve chapters. In the rst chapter, we give the history of the fractional calculus, and we present some basic de nitions and properties that are used in this theory. We de ne nabla fractional exponential and then nabla fractional …

Quantitative Patterns Of Stylistic Influence In The Evolution Of Literature, James M. Hughes, Nicholas J. Foti, David C. Krakauer, Daniel N. Rockmore

Dartmouth Scholarship

Literature is a form of expression whose temporal structure, both in content and style, provides a historical record of the evolution of culture. In this work we take on a quantitative analysis of literary style and conduct the first large-scale temporal stylometric study of literature by using the vast holdings in the Project Gutenberg Digital Library corpus. We find temporal stylistic localization among authors through the analysis of the similarity structure in feature vectors derived from content-free word usage, nonhomogeneous decay rates of stylistic influence, and an accelerating rate of decay of influence among modern authors. Within a given time …

On A Problem Of Burnside, Matthew Mizuhara

Honors Theses

Burnside posed the question as to whether or not there exist groups having an external automorphism that behaves in a certain, specific way like an inner automorphism: we shall define such automorphisms to be nearly-inner.

NI-groups are fairly rare. With the aid of the computer algebra system Magma - in particular with the aid of its small group database - we set out to test this hypothesis.