Mathematics Commons^™

New Microarray Image Segmentation Using Segmentation Based Contours Method, Yuan Cheng

Doctoral Dissertations

The goal of the research developed in this dissertation is to develop a more accurate segmentation method for Affymetrix microarray images. The Affymetrix microarray biotechnologies have become increasingly important in the biomedical research field. Affymetrix microarray images are widely used in disease diagnostics and disease control. They are capable of monitoring the expression levels of thousands of genes simultaneously. Hence, scientists can get a deep understanding on genomic regulation, interaction and expression by using such tools.

We also introduce a novel Affymetrix microarray image simulation model and how the Affymetrix microarray image is simulated by using this model. This simulation …

Sasakian Finsler Manifolds, Ayşe Funda Yaliniz, Nesri̇n Çalişkan

Turkish Journal of Mathematics

In this study, almost contact Finsler structures on vector bundle are defined and the condition of normality in terms of the Nijenhuis torsion N_{\phi} of almost contact Finsler structure is obtained. It is shown that for a K-contact structure on Finsler manifold \nabla_X \xi =-\frac{1}{2} \phi X and the flag curvature for plane sections containing \xi are equal to \frac{1}{4}. By using the Sasakian Finsler structure, the curvatures of a Finsler connection \nabla on V are obtained. We prove that a locally symmetric Finsler manifold with K-contact Finsler structure has a constant curvature \frac{1}{4}. Also, the Ricci curvature on Finsler …

Products Of Conjugacy Classes And Products Of Irreducible Characters In Finite Groups, Mohammad Reza Darafsheh, Sajjad Mahmood Robati

Turkish Journal of Mathematics

Let G be a finite group. If A and B are two conjugacy classes in G, then AB is a union of conjugacy classes in G and \eta(AB) denotes the number of distinct conjugacy classes of G contained in AB. If \chi and \psi are two complex irreducible characters of G, then \chi\psi is a character of G and again we let \eta(\chi\psi) be the number of irreducible characters of G appearing as constituents of \chi\psi. In this paper our aim is to study the product of conjugacy classes in a finite group and obtain an upper bound for \eta …

Knight's Tours On 3 X N Chessboards With A Single Square Removed, Amanda M. Miller, David L. Farnsworth

Articles

The following theorem is proved: A knight’s tour exists on all 3 x n chessboards with one square removed unless: n is even, the removed square is (i, j) with i + j odd, n = 3 when any square other than the center square is removed, n = 5, n = 7 when any square other than square (2, 2) or (2, 6) is removed, n = 9 when square (1, 3), (3, 3), (1, 7), (3, 7), (2, 4), (2, 6), (2, 2), or (2, 8) is removed, or n = 11 when square (1, 3), (2, 4), …

Evaluation, Adaptation And Validation Of A Model To Predict Grass Growth In Ireland, Christina Hurtado Uria

Theses

Budgeting grass supply allows producers to minimise the quantity of purchased feed required in the diet of grazing livestock. One tool for managing grass supply could be a mathematical model that can simulate grass growth. The development of such a model would allow better management around the variability of feed supply and help identify feed surpluses and deficits, and therefore increase the accuracy of management decisions. This would be a key feature of profitable milk and meat production systems in the future which will be hugely important as global food demand increases due to population growth. It is forecasted that …

Modeling Dengue Virus Infection Patients For Each Severity Of Dengue Disease In Thailand, Montip Tiensuwan, Timothy O'Brien

Mathematics and Statistics: Faculty Publications and Other Works

Dengue is an infectious mosquito-borne viral disease. Dengue or dengue-like epidemics ranks highly among new and newly emerging infectious diseases in public health significance and may affect persons of all ages in dengue endemic area. Dengue virus infections may lead to dengue fever (DF), dengue haemorrhagic fever (DHF) and may lead to hypovolaemic shock (dengue shock syndrome, DSS) then we separate dengue data by severity of dengue disease, i.e., DF, DHF and DSS. The objective of this study is to find factors which affect the dengue virus infection patients for each severity of dengue disease in Thailand by using multiple …

Invisibility: A Mathematical Perspective, Austin G. Gomez

CMC Senior Theses

The concept of rendering an object invisible, once considered unfathomable, can now be deemed achievable using artificial metamaterials. The ability for these advanced structures to refract waves in the negative direction has sparked creativity for future applications. Manipulating electromagnetic waves of all frequencies around an object requires precise and unique parameters, which are calculated from various mathemat- ical laws and equations. We explore the possible interpretations of these parameters and how they are implemented towards the construction of a suitable metamaterial. If carried out correctly, the wave will exit the metamaterial exhibiting the same behavior as when it had entered. …

The Eichler-Selberg Trace Formula For Level-One Hecke Operators, Alex Barron

Honors Theses

This paper explains the steps involved in the proof of the Eichler-Selberg Trace Formula for Hecke operators of level one. It is based on an appendix in Serge Lang's Introduction to Modular Forms written by Don Zagier, though I also draw heavily from sections of Toshitsune Miyake's Modular Forms and Xueli Wang's and Dingyi Pei's Modular Forms with Integral and Half-Integral Weights.

Section 2 summarizes the necessary background in the theory of modular forms. The material covered here is standard, so I've left out most of the details and proofs. Most of the section is based on Chapter VII of …

Well-Covered Graphs, Unique Colorability, And Covering Range, Wanda Renea Payne

Electronic Theses and Dissertations

A graph is called well-covered if all of its maximal independent sets have the same cardinality. We give a characterization of well-covered k-trees. A graph is said to be uniquely χ-colorable if, modulo permutations of colors, it has exactly one proper χ-coloring. The k-trees with at least k+1 vertices are minimal uniquely (k +1)-colorable, i.e., they have the minimal number of edges necessary for uniquely (k+1)-colorable graphs. We introduce the k-frames, a new class of minimal uniquely (k+1)-colorable graphs that generalizes the k-trees.

The covering range of a graph is the difference between the cardinality of a largest maximal independent …

Theory And Applications Of Correspondences, Heather Olson

The Journal of Undergraduate Research

Throughout this paper, we will examine correspondences, also known as set-valued functions. A definition of correspondences and their graphs are given. Properties of correspondences including continuity, optimization, and existence of fixed points are considered. Examples are considered demonstrating these properties. Applications in the field of Economics are introduced. Specifically the optimization of consumer utility is examined through examples.

Laughing At The Looking Glass: Does Humor Style Serve As An Interpersonal Signal?, Virgil Zeigler-Hill, Avi Besser, Stephanie E. Jett

Faculty Publications

Objective: The provision of information appears to be an important feature of humor. The present studies examined whether humor serves as an interpersonal signal such that an individual's style of humor is associated with how the individual is perceived by others. Method: We examined this issue across two studies. In Study 1, undergraduate participants (257 targets) were rated more positively by their friends and family members (1194 perceivers) when they possessed more benign humor styles. In Study 2, 1190 community participants rated the romantic desirability of targets ostensibly possessing different humor styles. Results: Across both studies, our results were consistent …

Relation Lifting, With An Application To The Many-Valued Cover Modality, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jirí Velebil

Engineering Faculty Articles and Research

We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the “powerset monad” on categories, one is the preservation by T of “exactness” of certain squares. Both characterisations are generalisations of the “classical” results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks.

The results presented in this paper …

Nominal Coalgebraic Data Types With Applications To Lambda Calculus, Alexander Kurz, Daniela Petrişan, Paula Severi, Fer-Jan De Vries

Engineering Faculty Articles and Research

We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.

Nominal Computation Theory (Dagstuhl Seminar 13422), Mikołaj Bojanczyk, Bartek Klin, Alexander Kurz, Andrew M. Pitts

Engineering Faculty Articles and Research

This report documents the program and the outcomes of Dagstuhl Seminar 13422 “Nominal Computation Theory”. The underlying theme of the seminar was nominal sets (also known as sets with atoms or Fraenkel-Mostowski sets) and they role and applications in three distinct research areas: automata over infinite alphabets, program semantics using nominal sets and nominal calculi of concurrent processes.

Constructions And Enumeration Methods For Cubic Graphs And Trees, Erica R. Gilliland

Undergraduate Honors Thesis Collection

The goal of this thesis is to study two related problems that, in the broadest terms, lie in a branch of mathematics called graph theory. The first problem examines some new techniques for constructing a Hamilton graph of least possible order and having a preassigned girth, and the second concerns the enumeration of a certain type of graphs called trees.

Mathematical Self-Efficacy: Addressing The Declining Interest In Engineering Careers, Eileen Goold

Conference Papers

This paper presents the findings of a study investigating whether there is a relationship between students’ experiences with school mathematics and their choice of engineering as a career. The study was inspired by the observation that there is a lacuna in the scholarly literature concerning the nature of mathematics’ role, if any, as a significant cause of the declining number of students entering professional engineering courses. The population of interest in this study comprises professional engineers practising in Ireland. Engineers’ experiences of school mathematics, factors that contributed to their engagement with school mathematics and the impact of their feelings about …

G-Strands And Peakon Collisions On Diff(R), Darryl Holm, Rossen Ivanov

Articles

A G-strand is a map g : R x R --> G for a Lie group G that follows from Hamilton's principle for a certain class of G-invariant Lagrangians. Some G-strands on finite-dimensional groups satisfy 1+1 space-time evolutionary equations that admit soliton solutions as completely integrable Hamiltonian systems. For example, the SO(3)-strand equations may be regarded physically as integrable dynamics for solitons on a continuous spin chain. Previous work has shown that G-strands for diffeomorphisms on the real line possess solutions with singular support (e.g. peakons). This paper studies collisions of such singular solutions of G-strands when G = Diff( …

Mass Transfer From A Vertical Flat Plate Due To A Constant Upward Flow, David Mcdonnell, Brendan Redmond, Lawrence J. Crane

Articles

This paper examines the mass transfer from a vertical flat surface of a soluble material due to a constant upward flow. The mass transfer rate due to this upward flow is calculated and used to obtain the distance along the surface at which the boundary layer separates. For relatively large velocities no separation will occur and the solution approaches that of forced convection on a horizontal surface.

Spectral Multiplicity Of Selfadjoint Schrodinger Operators On Star-Graphs With Standard Interface Conditions, Sergey Simonov, Harald Woracek

Articles

We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schroedinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the interior vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of Theorem of I.S. Kac.

Extreme Wave Events In Ireland: 14 680 Bp–2012, Laura Cooke, John M. Dudley, Frédéric Dias

Articles

The island of Ireland is battered by waves from all sides, most ferociously on the west coast as the first port of call for waves travelling across the Atlantic Ocean. However, when discussing ocean events relevant to the nation of Ire- land, one must actually consider its significantly larger designated continental shelf, which is one of the largest seabed territories in Europe. With this expanded definition, it is not surprising that Ireland has been subject to many oceanic events which could be designated as “extreme”; in this paper we present what we believe to be the first catalogue of such …