Mathematics Commons^™

Fundamentals Of Protein Structure Alignment, Allen Holder, Mark Brandt, Yosi Shibberu

Mathematical Sciences Technical Reports (MSTR)

The central dogma of molecular biology asserts a one way transfer of information from a cell’s genetic code to the expression of proteins. Proteins are the functional workhorses of a cell, and studying these molecules is at the foundation of much of computational biology. Our goal here is to present a succinct introduction to the biological, mathematical, and computational aspects of making pairwise comparisons between protein structures. The presentation is intended to be useful for those who are entering this research area. The chapter begins with a brief introduction to the biology of protein comparison, which is followed by a …

Computable Linear Orders And Turing Reductions, Whitney P. Turner

Master's Theses

This thesis explores computable linear orders through Turing Reductions and codes zero jump and zero double jump into linear orders using discrete, dense, and block linear relations.

Liar's Domination In Grid Graphs, Christopher Kent Sterling

Electronic Theses and Dissertations

As introduced by Slater in 2008, liar's domination provides a way of modeling protection devices where one may be faulty. Assume each vertex of a graph G is the possible location for an intruder such as a thief. A protection device at a vertex v is assumed to be able to detect the intruder at any vertex in its closed neighborhood N[v] and identify at which vertex in N[v] the intruder is located. A dominating set is required to identify any intruder's location in the graph G, and if any one device can fail to …

Preferential Arrangement Containment In Strict Superpatterns, Martha Louise Liendo

Electronic Theses and Dissertations

Most results on pattern containment deal more directly with pattern avoidance, or the enumeration and characterization of strings which avoid a given set of patterns. Little research has been conducted regarding the word size required for a word to contain all patterns of a given set of patterns. The set of patterns for which containment is sought in this thesis is the set of preferential arrangements of a given length. The term preferential arrangement denotes strings of characters in which repeated characters are allowed, but not necessary. Cardinalities for sets of all preferential arrangements of given lengths and alphabet sizes …

Source Unfoldings Of Convex Polyhedra Via Certain Closed Curves, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu

Computer Science: Faculty Publications

Abstract. We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygonal curve Q in a particular class rather than based on a point. The class requires that Q “lives on a cone” to both sides; it includes simple, closed quasigeodesics. Cutting a particular subset of the cut locus of Q (in P) leads to a non-overlapping unfolding of the polyhedron. This gives a new general method to unfold the surface of any convex polyhedron to a simple, planar polygon

On Algorithmic Fractional Packings Of Hypergraphs, Jill Dizona

USF Tampa Graduate Theses and Dissertations

Let F₀ be a fixed k-uniform hypergraph, and let H be a given k-uniform hypergraph on n vertices. An F₀-packing of H is a family F of edge-disjoint copies of F₀ which are subhypergraphs in H. Let n_F0(H) denote the maximum size |F| of an F₀-packing F of H. It is well-known that computing n_F0(H) is NP-hard for nearly any choice of F₀.

In this thesis, we consider the special case when F₀ is a linear hypergraph, that is, when no two edges …

Wronskian, Grammian And Pfaffian Solutions To Nonlinear Partial Differential Equations, Alrazi Abdeljabbar

USF Tampa Graduate Theses and Dissertations

It is significantly important to search for exact soliton solutions to nonlinear partial differential equations (PDEs) of mathematical physics. Transforming nonlinear PDEs into bilinear forms using the Hirota differential operators enables us to apply the Wronskian and Pfaffian techniques to search for exact solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation with not only constant coefficients but also variable coefficients under a certain constraint

(u_t + α ₁(t)u_xxy + 3α ₂(t)u_xu_y)_x +α ₃ (t)u_ty -α ₄(t)u_zz + α ₅(t)(u_x + α ₃(t)u_y) = …

A Study Of Women Working In The Actuarial Field, Jillian Emberg

Honors Projects in Mathematics

The goal of this project is to examine how women fit into the actuarial career path and how cultural expectations, biological factors, and personal aspirations affect their experiences in the field. Dramatic changes in the profession have occurred since its emergence in the nineteenth century to become more welcoming to women who choose to enter the profession. However, despite the equalizing demographic shifts of the field, it is still a male-dominated profession. This paper attempts to analyze why some of the changes in the demographics of the field have occurred as well as explain what factors contribute to women’s underrepresentation …

Estimating Correlation Under Interval And Fuzzy Uncertainty: Case Of Hierarchical Estimation, Ali Jalal-Kamali

Departmental Technical Reports (CS)

In many situations, we are interested in finding the correlation ρ between different quantities x and y based on the values x_i and y_i of these quantities measured in different situations i. The correlation is easy to compute when we know the exact sample values x_i and y_i. In practice, the sample values come from measurements or from expert estimates; in both cases, the values are not exact. Sometimes, we know the probabilities of different values of measurement errors, but in many cases, we only know the upper bounds Δ_xi and Δ_yi on …

Semi-Heuristic Target-Based Fuzzy Decision Procedures: Towards A New Interval Justification, Christian Servin, Van-Nam Huynh, Yoshiteru Nakamori

Departmental Technical Reports (CS)

To more adequately describe human decision making, V.-N. Nuynh, Y. Nakamori, and others proposed a special semi-heuristic target-based fuzzy decision procedure. A usual justification for this procedure is based on the selection of the simplest possible membership functions and "and"- and "or"-operations; if we use more complex membership functions and "and"- and "or"-operations, we get different results. Interestingly, in practical applications, the procedure based on the simplest choices most adequately describes human preferences. It is therefore desirable to come up with a justification that explains this empirical fact. Such a justification is proposed in this paper

Function Estimation Of Irregularly Spaced Data With Long Memory Dependence, Rosalie Michelle Wheeler

Dissertations

We examine the problem of estimating an underlying function from collected data. The methods considered include parametric regression, density estimation, kernel estimation, wavelet regression, and specific results from when our underlying function f\left(x\right) is a member of the Besov or the Triebel spaces. Then we consider the problem of long memory error in several settings, including data which is equally spaced, data which is unequally spaced, and data which is a member of the Holder class and several other spaces. Ultimately we focus on three different problems. The first involves using linear interpolation or local averaging to account for the …

When Is A Trigonometric Polynomial Not A Trigonometric Polynomial?, Joseph E. Borzellino, Morgan Sherman

Mathematics

No abstract provided.

Resonant Solutions And Turning Points In An Elliptic Problem With Oscillatory Boundary Conditions, Alfonso Castro, Rosa Pardo

All HMC Faculty Publications and Research

We consider the elliptic equation -Δu + u = 0 with nonlinear boundary conditions ∂u/∂n = λu + g(λ,x,u), where the nonlinear term g is oscillatory and satisfies g(λ,x,s)/s→0 as |s|→0. We provide sufficient conditions on g for the existence of sequences of resonant solutions and turning points accumulating to zero.

Continued Radicals And Cantor Sets, Thomas Tyler Clark

Masters Theses & Specialist Projects

We examine the formation of sets homeomorphic to the ternary Cantor set by continued radicals. We determine properties of bridges and gaps and calculate the thickness of the Cantor set. From this we apply information from continued fractions to continued radicals to obtain new results. We also consider the measure of several Cantor sets.

Scientific Notebook At Pace University: Technology For 21st Century Mathematics And Science, Brian Evans, Demos Athanasopoulos

Cornerstone 3 Reports : Interdisciplinary Informatics

No abstract provided.

How To Define Average Class Size (And Deviations From The Average Class Size) In A Way Which Is Most Adequate For Teaching Effectiveness, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When students select a university, one of the important parameters is the average class size. This average is usually estimated as an arithmetic average of all the class sizes. However, it has been recently shown that to more adequately describe students' perception of a class size, it makes more sense to average not over classes, but over all students -- which leads to a different characteristics of the average class size. In this paper, we analyze which characteristic is most adequate from the viewpoint of efficient learning. Somewhat surprisingly, it turns out that the arithmetic average is the most adequate …

Behavioral Economics And Physician Behavior, Allyssa S. Ward

Honors Theses

This study seeks to answer whether the availability heuristic leads physicians to utilize more medical care than is economically efficient. Do rare, salient events alter physicians' perceptions about the probability of patient harm? Do these events lead physicians to overutilize certain medical procedures? This study uses Pennsylvania inpatient hospital admissions data from 2009 aggregated at the physician level to investigate these questions. The data come from the 2009 Pennsylvania Health Care Cost Containment Council (PHC4).

The study is divided into two parts. In Part I, we examine whether bad outcomes during childbirth (defined as maternal mortality, an obstetric fistula or …

Modeling Spatial Uncertainties In Geospatial Data Fusion And Mining, Boris Kovalerchuk, Leonid Perlovsky, Michael Kovalerchuk

All Faculty Scholarship for the College of the Sciences

Geospatial data analysis relies on Spatial Data Fusion and Mining (SDFM), which heavily depend on topology and geometry of spatial objects. Capturing and representing geometric characteristics such as orientation, shape, proximity, similarity, and their measurement are of the highest interest in SDFM. Representation of uncertain and dynamically changing topological structure of spatial objects including social and communication networks, roads and waterways under the influence of noise, obstacles, temporary loss of communication, and other factors. is another challenge. Spatial distribution of the dynamic network is a complex and dynamic mixture of its topology and geometry. Historically, separation of topology and geometry …

The Effects Of Goal Setting In A Developmental Algebra Course, Richard Leo Hunt

Masters Theses & Specialist Projects

The purpose of this study was to study the effects of goal setting on students in a developmental algebra course. This study examined the effects on test scores for students that were prescribed a test score goal, students that created their own test score goal, and then compared to a control group. Three classes of developmental algebra were chosen with a total of 25 participants with reported results. Results showed that students with a goal on a test did not score significantly better than students without a goal, but did score significantly better on a test after the goal than …

Translation Representations And Scattering By Two Intervals, Palle Jorgensen, Steen Pedersen, Feng Tian

Mathematics and Statistics Faculty Publications

Studying unitary one-parameter groups in Hilbert space (U(t), H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L²-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U(t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator and scattering matrix. We illustrate our results in the Lax-Phillips model where (U(t), H) represents an acoustic wave equation …