Mathematics Commons^™

Information Hiding With Data Diffusion Using Convolutional Encoding For Super-Encryption, Jonathan Blackledge, Paul Tobin, J. Myeza, C.M. Adolfo

Articles

The unification of data encryption with information hiding methods continues to receive significant attention because of the importance of protecting encrypted information by making it covert. This is because one of the principal limitations in any cryptographic system is that encrypted data flags the potential importance of the data (i.e. the plaintext information that has been encrypted) possibly leading to the launch of an attack which may or may not be successful. Information hiding overcomes this limitation by making the data (which may be the plaintext or the encrypted plaintext) imperceptible, the security of the hidden information being compromised if …

A Continuous Time Model Of Centrally Controlled Motion With Random Switching Terms, J. C. Dallon, L C. Despain, E J. Evans, C P. Grant, Willaim V. Smith

Faculty Publications

This paper considers differential problems with random switching, with specific applications to the motion of cells and centrally coordinated motion. Starting with a differential-equation model of cell motion that was proposed previously, we set the relaxation time to zero and consider the simpler model that results. We prove that this model is well-posed, in the sense that it corresponds to a pure jump-type continuous time Markov process (without explosion). We then describe the model's long-time behavior, first by specifying an attracting steady-state distribution for a projection of the model, then by examining the expected location of the cell center when …

An Introduction To Ricci Flow For Two-Dimensional Manifolds, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The study of diferentiable manifolds is a deep an extensive area of mathematics. A technique such as the study of the Ricci flow turns out to be a very useful tool in this regard. This flow is an evolution of a Riemannian metric driven by a parabolic type of partial differential equation. It has attracted great interest recently due to its important achievements in geometry such as Perelman's proof of the geometrization conjecture and Brendle-Schoen's proof of the differentiable sphere theorem. It is the purpose here to give a comprehensive introduction to the Ricci flow on manifolds of dimension two …

Normal Subgroups Of Wreath Product 3-Groups, Ryan Gopp

Williams Honors College, Honors Research Projects

Consider the regular wreath product group P of Z₉ with (Z₃ x Z₃). The problem of determining all normal subgroups of P that are contained in its base subgroup is equivalent to determining the subgroups of a certain matrix group M that are invariant under two particular endomorphisms of M. This thesis is a partial solution to the latter. We use concepts from linear algebra and group theory to find and count so-called doubly-invariant subgroups of M.

Orthogonal Polynomials On An Arc Of The Unit Circle With Respect To A Generalized Jacobi Weight: A Riemann-Hilbert Method Approach, Lynsey Cargile Naugle

Electronic Theses and Dissertations

We investigate the asymptotic behavior of polynomials orthogonal over a symmetric arc of the unit circle with respect to a generalized Jacobi-type weight. Full asymptotic expansions for the orthogonal polynomials are obtained at every point of the complex plane. Our method of proof is based on a characterization of the orthogonal polynomials as solutions of a 2X2 matrix Riemann-Hilbert problem, which extends to the unit circle the original Riemann-Hilbert characterization for orthogonal polynomials on the real line, first discovered by Fokas, Its, and Kitaev. In order to extricate the behavior of the polynomials from its Riemann-Hilbert matrix representation, we follow …

On A Time Domain Boundary Integral Equation Formulation For Acoustic Scattering By Rigid Bodies In Uniform Mean Flow, Fang Q. Hu, Michelle E. Pizzo, Douglas M. Nark

Mathematics & Statistics Faculty Publications

It has been well-known that under the assumption of a uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation. However, the constant mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the assumed uniform flow. A customary boundary condition for rigid surfaces is that the normal acoustic velocity be zero. In this paper, a careful study of the acoustic energy conservation equation is presented that shows such a boundary condition would in fact lead to source …

Construction Of Weavings In The Plane, Eden Delight Miro, Aliw-Iw Zambrano, Agnes Garciano

Mathematics Faculty Publications

This work develops, in graph-theoretic terms, a methodology for systematically constructing weavings of overlapping nets derived from 2-colorings of the plane. From a 2-coloring, two disjoint simple, connected graphs called nets are constructed. The union of these nets forms an overlapping net, and a weaving map is defined on the intersection points of the overlapping net to form a weaving. Furthermore, a procedure is given for the construction of mixed overlapping nets and for deriving weavings from them.

Discovering New Tessellations Using Dynamic Geometry Software, Ma. Louise Antonette N. De Las Peñas, Eduard C. Taganap

Mathematics Faculty Publications

In this paper we use dynamic geometry software to investigate a class of tilings called k-uniform tilings or tessellations. A tiling consisting of regular polygons whose vertices belong to k-transitivity classes under the action of its symmetry group (vertex-k-transitive) is said to be k-uniform. We also present constructions of tilings consisting of irregular polygons that are vertex-k-transitive.

On Homology Of Associative Shelves, Alissa Crans

Mathematics, Statistics and Data Science Faculty Works

Homology theories for associative algebraic structures are well established and have been studied for a long time. More recently, homology theories for selfdistributive algebraic structures motivated by knot theory, such as quandles and their relatives, have been developed and investigated. In this paper, we study associative self-distributive algebraic structures and their one-term and two-term (rack) homology groups.

Optimization And Control Of Agent-Based Models In Biology: A Perspective, G. An, B. G. Fitzpatrick, S. Christley, P. Federico, A. Kanarek, R. Miller Neilan, M. Oremland, R. Salinas, R. Laubeanbacher, S. Lenhart

Mathematics, Statistics and Data Science Faculty Works

Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might …

Interaction Graphs Derived From Activation Functions And Their Application To Gene Regulation, Simon Joyce

Graduate Dissertations and Theses

Interaction graphs are graphic representations of complex networks of mutually interacting components. Their main application is in the field of gene regulatory networks, where they are used to visualize how the expression levels of genes activate or inhibit the expression levels of other genes.

First we develop a natural transformation of activation functions and their derived interaction graphs, called conjugation, that is related to a natural transformation of signed digraphs called switching isomorphism. This is a useful tool for the analysis of interaction graphs used throughout the rest of the dissertation.

We then discuss the question of what restrictions, if …

On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao

Senior Independent Study Theses

Suppose G is a finite linearly reductive group. The degree bound for the syzygy ideal of the invariant ring of G is given in [2]. We develop the theory of commutative algebra and give the proof from [2] that the ideal of relations of the minimal set of generators of invariant ring of a finite linearly reductive group G is generated in degree at most 2|G|.

Covering Subsets Of The Integers And A Result On Digits Of Fibonacci Numbers, Wilson Andrew Harvey

Theses and Dissertations

A covering system of the integers is a finite system of congruences where each integer satisfies at least one of the congruences. Two questions in covering systems have been of particular interest in the mathematical literature. First is the minimum modulus problem, whether the minimum modulus of a covering system of the integers with distinct moduli can be arbitrarily large, and the second is the odd covering problem, whether a covering system of the integers with distinct moduli can be constructed with all moduli odd. We consider these and similar questions for subsets of the integers, such as the set …

Deep Learning: An Exposition, Ryan Kingery

Theses and Dissertations

In this paper we describe and survey the field of deep learning, a type of machine learning that has seen tremendous growth and popularity over the past decade for its ability to substantially outperform other learning methods at important tasks. We focus on the problem of supervised learning with feedforward neural networks. After describing what these are we give an overview of the essential algorithms of deep learning, backpropagation and stochastic gradient descent. We then survey some of the issues that occur when applying deep learning in practice. Last, we conclude with an important application of deep learning to the …

Nonequispaced Fast Fourier Transform, David Hughey

Theses and Dissertations

Two algorithms for fast and accurate evaluation of high degree trigonometric polynomials at many scattered points are presented. Both methods rely on highly localized kernels and the Fast Fourier Transform. The first algorithm uses the function values at uniformly distributed grid points and kernels that reproduce trigonometric polynomials, while the second method uses kernels that approximate well the function on the frequency side. Both algorithm are termed Nonequispaced Fast Fourier Transform. The first algorithm is coded in MATLAB and shown to approximate well the function to be evaluated.

Subdivision Of Measures Of Squares, Dylan Bates

Theses and Dissertations

The primary goal of our work is to establish a method to relate simple measures to a given set of moments. We calculate the moments of squares via linear polynomial weight measures and straight line cuts and use this to calculate the centre of mass of the square. The one-to-one correspondence that is found is needed to represent surfaces with gaps, which can estimate arbitrary measures on squares. From this, a subdivision scheme is developed, which successively quadrisects squares and uses the relation to estimate the new measures in order to provide a good representation of the original surface. One …

Multiple Solutions With Constant Sign Of A Dirichlet Problem For A Class Of Elliptic Systems With Variable Exponent Growth, Li Yin, Jinghua Yao, Qihu Zhang, Chunshan Zhao

Mathematical Sciences: Faculty Publications

We present here, in the system setting, a new set of growth conditions under which we manage to use a novel method to verify the Cerami compactness condition. By localization argument, decomposition technique and variational methods, we are able to show the existence of multiple solutions with constant sign for the problem without the well-known Ambrosetti--Rabinowitz type growth condition. More precisely, we manage to show that the problem admits four, six and infinitely many solutions respectively.

Gorenstein Injective Envelopes And Covers Over Two Sided Noetherian Rings, Alina Iacob

Mathematical Sciences: Faculty Publications

We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat. In the second part of the paper we consider the connection between the Gorenstein injective modules and the strongly cotorsion modules. We prove that when the ring R is commutative noetherian of finite Krull dimension, the class of Gorenstein injective modules coincides with that of strongly cotorsion modules if and only if the ring R is in fact Gorenstein.

A Zariski-Local Notion Of F-Total Acyclicity For Complexes Of Sheaves, Lars Winther Christensen, Sergio Estrada, Alina Iacob

Mathematical Sciences: Faculty Publications

We study a notion of total acyclicity for complexes of flat sheaves over a scheme. It is Zariski-local—i.e. it can be verified on any open affine covering of the scheme—and for sheaves over a quasi-compact semi-separated scheme it agrees with the categorical notion. In particular, it agrees, in their setting, with the notion studied by Murfet and Salarian for sheaves over a noetherian semi-separated scheme. As part of the study we recover, and in several cases extend the validity of, recent results on existence of covers and precovers in categories of sheaves. One consequence is the existence of an adjoint …

Gorenstein Flat And Projective (Pre)Covers, Sergio Estrada, Alina Iacob, Sinem Odabasi

Mathematical Sciences: Faculty Publications

We consider a right coherent ring R. We prove that the class of Gorenstein flat complexes is covering in the category of complexes of left R-modules Ch(R). When R is also left n-perfect, we prove that the class of Gorenstein projective complexes is special precovering in Ch(R).

Teachers' Theories Of Teaching And Learning And The Use Of Math Interventions, Nicole P. Jones

Walden Dissertations and Doctoral Studies

Despite the academic gap between students with learning disabilities (LD) and their nondisabled peers, schools continue to educate students with LD in regular education classrooms. In secondary math classes, such as Algebra 1, students with LD have high percentages of failure. The purpose of this cross-sectional study was to examine the relationship between teachers' personal theories of teaching and learning and their use of math interventions. Fox's (1983) theoretical framework of teaching and learning was used as a conceptual lens. Surveys were administered to 20 high school math teachers in an urban Northeastern U.S. school district. An ordinal logistic regression …

Group Divisible Designs With Two Groups And Three Associate Classes, Ladamas Saiphet

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Explicit Formula For Conditional Expectations Of Product Of Polynomial And Exponential Function Of Affine Transform Of Extended Cox-Ingersoll-Ross Process, Phiraphat Sutthimat

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis an explicit formula for conditional expectations of the product of polynomial and exponential function of an affine transform is derived under the extended function of an transform is derived under the extended Cox-Ingersoll-Ross (ECIR) process. By applying the Feynman-Kac theorem, the explicit formula is revealed from the solution of the corresponding partial differential equation. To support the validity of the obtained results, we, herein, conduct Monte Carlo simulations to investigate the accuracy of the explicit formula.

Cuckoo Search And Enhanced Artificial Bee Colony Heuristic Methods For Vehicle Routing Problem With Backhaul And Time Window Constraints, Tanawat Worawattawechai

Chulalongkorn University Theses and Dissertations (Chula ETD)

The vehicle routing problem with backhauls and time windows (VRPBTW) aims to find a feasible vehicle route that minimizes the total traveling distance while imposing capacity, backhaul, and time-window constraints. In this dissertation, a mathematical model of VRPBTW is introduced to obtain an optimal solution. The heuristics, namely the nearest urgent candidate (NUC), which applies the urgency priority and candidate techniques, and the nearest neighbor with roulette wheel selection (NNRW) which is a combination of a roulette wheel selection method and the improved nearest neighbor heuristic, are also presented to solve this problem. Moreover, two metaheuristic methods are presented to …

การวิเคราะห์การคำนวณเมคสแปนสำหรับปัญหาการจัดตารางการผลิตแบบตามสั่ง, วันเฉลิม โฮชิน

Chulalongkorn University Theses and Dissertations (Chula ETD)

เมคสแปนในปัญหาการจัดตารางการผลิตแบบตามสั่งเป็นค่าที่สำคัญในการหาค่าผลเฉลยใกล้เคียงของการค้นหาแบบทาบู อย่างไรก็ตามขั้นตอนการหาค่าผลเฉลยใกล้เคียงเป็นส่วนที่ใช้เวลาประมวลผลนานที่สุด วิทยานิพนธ์เล่มนี้ทำการปรับปรุงเทคนิคการหาค่าผลเฉลยใกล้เคียงด้วยค่าเมคสแปนที่ถูกเสนอโดย Nowicki และ Smutnicki (2005) และเปรียบเทียบความซับซ้อนของเวลาของวิธีการหาค่าผลเฉลยใกล้เคียง ระหว่างวิธีการของ Nowicki และ Smutnicki และวิธีการที่ได้ปรับปรุงขึ้น ความแตกต่างที่สำคัญของทั้งสองวิธีการคือการหาตำแหน่งสำคัญบางตำแหน่งบนลำดับโทโพโลยีของผลเฉลยเมล็ดพันธุ์ ทั้งสองวิธีการใช้ปัญหามาตรฐานที่มีจำนวนโอเปอเรชันไม่เกิน 400 โอเปอเรชัน ในการทดสอบ ผลการทดลองพบว่า ขั้นตอนวิธีการค้นหาแบบทาบูที่ใช้ขั้นตอนการหาค่าผลเฉลยใกล้เคียงด้วยวิธีการที่ได้ปรับปรุงขึ้น ใช้เวลาประมวลผลน้อยกว่าวิธีการค้นหาแบบทาบูที่ใช้ขั้นตอนการหาค่าผลเฉลยใกล้เคียงด้วยวิธีการของ Nowicki และ Smutnicki

Boundedness Of Green Operators For Nonlocal Equations On Weighted Lebesgue Spaces, Itthinat Nuntajittanond

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this research. we establish the local existence and uniqueness of solutions for the Cauchy problem of the nonlocal equation of the form ∂ₜU(x.t) = ∫R n J(x.Y)U(Y,t)dY – U (x.t) + (In(e + I x I2)) U p (x,t) where p > 1 and ∂ > 0 are constants. In this research, the kernel / of the nonlocal term may not radially symmetric. We investigate the Cauchy problem on weighted Lebesgue spaces with a logarithmic weight. One of the most important results in this thesis is the boundedness of the corresponding Green operator on the weight Lebesgue spaces. We also establish …

Anomalous Assemblage Detection Using Nearest Neighbor Distance, Kayyasit Singkarn

Chulalongkorn University Theses and Dissertations (Chula ETD)

The outlierness of an instance in this thesis is defined based on the distance between two instances. For some datasets, outliers may not be isolated and formed small clusters. C-anomalous assemblage is a group of associated outliers having the number of instances less than or equal to C percent of the total instances. This thesis presents the anomalous assemblage detection algorithm called CND using a nearest neighbor distance for an anomalous score. The algorithm computes the index k equal to floor function of C percent times the total number of instances and uses the k-nearest neighbor distance for representing an …

Selection Problems In O-Minimal Structures, Saronsad Sokantika

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this dissertation, we improve the Definable Michael's Selection Theorem in o-minimal expansions of real closed fields. Then applications of this theorem are established; for instance, we prove the following statement: Let be an o-minimal expansion of and T be a definable set-valued map where n = 1 or m=1. If T has a continuous selection, then T has a definable continuous selection. Moreover, we prove the statement: Let be an o-minimal expansion of a real closed field and be a closed subset of Rn. If T: E --> Rm is a definable continuous set-valued map and T is bounded …

Measurement For Disordered Proteins Affecting Scale-Free Network, Satanat Kitsiranuwat

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Clifford Algebra-Valued Segal-Bargmann Transform, Sorawit Eaknipitsari

Chulalongkorn University Theses and Dissertations (Chula ETD)

A classical Segal-Bargmann transform maps square-integrable functions on R to holomorphic square-integrable functions on C with respect to some Gaussian measure. In this work, we extend the classical Segal-Bargmann transform to functions taking values in a Clifford algebra. We establish that in this setting, the generalized Segal-Bargmann transform is a unitary isomorphism mapping Clifford algebra-valued square-integrable functions on Rⁿ with respect to some Gaussian measure to monogenic square-integrable functions on Rⁿ⁺¹ with respect to another Gaussian measure. We also discuss about the differential and multiplication operators in the monogenic functions space as well as certain properties of their domains.