Multiclass Total Variation Clustering,
2013
University of San Francisco
Multiclass Total Variation Clustering, X Bresson, T Laurent, David Uminsky, J Von Brecht
Mathematics
Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a general framework for multiclass total variation clustering that does not rely on recursion. The results greatly outperform previous total variation algorithms and compare well with state-of-the-art NMF approaches.
Modeling, Analysis, And Applications Of Complex Systems,
2013
Missouri University of Science and Technology
Modeling, Analysis, And Applications Of Complex Systems, Chuandong Li, Xiaodi Li, Shukai Duan, Yanzhi Zhang
Mathematics and Statistics Faculty Research & Creative Works
Recent advances in theory and applications of complex dynamical systems have contributed much to the successful handling of certain problems in biology, physics, economics, engineering, and so forth that until recently were thought too difficult to be analyzed. These complex systems may be characterized by systems with uncertainty, impulse, time delay, stochastic perturbation, hybrid dynamics, distributed dynamics, and chaotic dynamics. The overall aim of this special issue is to bring together the latest or innovative knowledge and advances in mathematics for handling complex systems, which may depend largely on methods from mathematical analysis, artificial intelligence, statistics, and engineering, including nonlinear …
A Bound On The Vertical Transport Of Heat In The 'Ultimate' State Of Slippery Convection At Large Prandtl Numbers,
2013
Missouri University of Science and Technology
A Bound On The Vertical Transport Of Heat In The 'Ultimate' State Of Slippery Convection At Large Prandtl Numbers, Xiaoming Wang, Jared P. Whitehead
Mathematics and Statistics Faculty Research & Creative Works
An upper bound on the rate of vertical heat transport is established in three dimensions for stress-free velocity boundary conditions on horizontally periodic plates. a variation of the background method is implemented that allows negative values of the quadratic form to yield 'small' (O.1=Pr/) corrections to the subsequent bound. for large (but finite) Prandtl numbers this bound is an improvement over the 'ultimate' Ra1=2 scaling and, in the limit of infinite Pr, agrees with the bound of Ra5=12 recently derived in that limit for stress-free boundaries. © 2013 Cambridge University Press.
Well-Posedness Of The Hele-Shaw-Cahn-Hilliard System,
2013
Missouri University of Science and Technology
Well-Posedness Of The Hele-Shaw-Cahn-Hilliard System, Xiaoming Wang, Zhifei Zhang
Mathematics and Statistics Faculty Research & Creative Works
We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. for initial data in Hs, s>d2+1, the existence and uniqueness of solution in C([0,T];Hs) ∪L2(0,T;Hs+2) that is global in time in the two-dimensional case (d=2) and local in time in the three-dimensional case (d=3) are established. Several blow-up criterions in the three-dimensional case are provided as well. One of the tools that we utilized is the Littlewood-Paley theory in order to establish certain key commutator estimates. © 2012 Elsevier Masson SAS.
Remarks On Quadratic Bundles Related To Hermitian Symmetric Spaces,
2013
Technological University Dublin
Remarks On Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev
Conference papers
We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)\times U(n)). We discuss the spectral properties of scattering operator, develop the direct scattering problem associated with it and stress on the effect of reduction on these. By applying a modification of Zakharov-Shabat's dressing procedure we demonstrate how one can obtain reflectionless potentials. That way one is able to generate soliton solutions to the nonlinear evolution equations belonging to the integrable hierarchy associated with quadratic bundles under study.
The Balm Copula,
2013
Kettering University
The Balm Copula, Boyan N. Dimitrov, Nikolai Kolev
Mathematics Publications
The class of probability distributions possessing the almost-lack-of-memory property appeared about 20 years ago. It reasonably took place in research and modeling, due to its suitability to represent uncertainty in periodic random environment. Multivariate version of the almost-lack-of-memory property is less known, but it is not less interesting. In this paper we give the copula of the bivariate almost-lack-of-memory (BALM) distributions and discuss some of its properties and applications. An example shows how the Marshal-Olkin distribution can be turned into BALM and what is its copula.
Ehrhart's Polynomial For Equilateral Triangles In Z3,
2013
Columbus State University
Ehrhart's Polynomial For Equilateral Triangles In Z3, Eugen J. Ionascu
Faculty Bibliography
In this paper we calculate the Ehrhart’s polynomial associated with a 2-dimensional regular polytope (i.e. equilateral triangles) in Z3. The polynomial takes a relatively simple form in terms of the coordinates of the vertices of the triangle. We give some equivalent formula in terms of a parametrization of these objects which allows one to construct equilateral triangles with given properties. In particular, we show that given a prime number p which is equal to 1 or −5 (mod 8), there exists an equilateral triangle with integer coordinates whose Ehrhart polynomial is L(t) = (pt + 2)(t + 1)/2, t ∈ …
On The Matrix Equation Xa + Ax_T = 0, Ii,
2013
Pomona College
On The Matrix Equation Xa + Ax_T = 0, Ii, Alice Zhuo-Yu Chan '14, Luis Alberto Garcia '14, Stephan Ramon Garcia, Amy L. Shoemaker '14
Pomona Faculty Publications and Research
The matrix equation $XA + AX^T = 0$ was recently introduced by De Ter\'an and Dopico to study the dimension of congruence orbits. They reduced the study of this equation to a number of special cases, several of which have not been explicitly solved. In this note we obtain an explicit, closed-form solution in the difficult Type 0-I interaction case.
Concavity Of Solutions Of A 2n-Th Order Problem With Symmetry,
2013
University of Dayton
Concavity Of Solutions Of A 2n-Th Order Problem With Symmetry, Abdulmalik Altwaty, Paul W. Eloe
Mathematics Faculty Publications
In this article we apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a 2n-th order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach space. Inequalities that extend the notion of concavity to 2n-th order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.
The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions,
2013
FBAS, IIU, Islamabad
The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, Muhammad Usman
Mathematics Faculty Publications
The present paper investigates the peristaltic motion of an incompressible non-Newtonian fluid with variable viscosity through a porous medium in an inclined symmetric channel under the effect of the slip condition. A long wavelength approximation is used in mathematical modeling. The system of the governing nonlinear partial differential equation has been solved by using the regular perturbation method and the analytical solutions for velocity and pressure rise have been obtained in the form of stream function. In the obtained solution expressions, the long wavelength and low Reynolds number assumptions are utilized. The salient features of pumping and trapping phenomena are …
Prospective Teachers’ Interactive Visualization And Affect In Mathematical Problem-Solving,
2013
University of Montana
Prospective Teachers’ Interactive Visualization And Affect In Mathematical Problem-Solving, Inés Mª Gómez-Chacón
The Mathematics Enthusiast
Research on technology-assisted teaching and learning has identified several families of factors that contribute to the effective integration of such tools. Focusing on one such family, affective factors, this article reports on a qualitative study of 30 prospective secondary school mathematics teachers designed to acquire insight into the affect associated with the visualization of geometric loci using GeoGebra. Affect as a representational system was the approach adopted to gain insight into how the use of dynamic geometry applications impacted students’ affective pathways. The data suggests that affect is related to motivation through goals and self-concept. Basic instrumental knowledge and the …
Editorial: (Why) Yet Another Issue On Problem Solving?,
2013
University of Montana
Editorial: (Why) Yet Another Issue On Problem Solving?, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
Cognition And Affect In Mathematics Problem Solving With Prospective Teachers,
2013
University of Montana
Cognition And Affect In Mathematics Problem Solving With Prospective Teachers, Lorenzo J. Blanco, Eloisa Guerrero Barona, Ann Caballero Carrasco
The Mathematics Enthusiast
Recent studies relating the affective domain with the teaching and learning of mathematics, and more specifically with mathematics problem solving, have focused on teacher education. The authors of these studies have been ever more insistently pointing to the need to design educational programs that take an integrated cognitive and affective approach to mathematics education. Given this context, we have designed and implemented a program of intervention on mathematics problem solving for prospective primary teachers. We here describe some results of that program.
The Beverton–Holt Q-Difference Equation,
2013
Missouri University of Science and Technology
The Beverton–Holt Q-Difference Equation, Martin Bohner, Rotchana Chieochan
Mathematics and Statistics Faculty Research & Creative Works
The Beverton–Holt model is a classical population model which has been considered in the literature for the discrete-time case. Its continuous-time analogue is the well-known logistic model. In this paper, we consider a quantum calculus analogue of the Beverton–Holt equation. We use a recently introduced concept of periodic functions in quantum calculus in order to study the existence of periodic solutions of the Beverton–Holt q-difference equation. Moreover, we present proofs of quantum calculus versions of two so-called Cushing–Henson conjectures. © 2013 The Author(s). Published by Taylor & Francis.
Supercharacters, Exponential Sums, And The Uncertainty Principle,
2013
Pomona College
Supercharacters, Exponential Sums, And The Uncertainty Principle, J.L. Brumbaugh '13, Madeleine Bulkow '14, Patrick S. Fleming, Luis Alberto Garcia '14, Stephan Ramon Garcia, Gizem Karaali, Matt Michal '15, Andrew P. Turner '14
Pomona Faculty Publications and Research
The theory of supercharacters, which generalizes classical character theory, was recently introduced by P. Diaconis and I.M. Isaacs, building upon earlier work of C. Andre. We study supercharacter theories on $(Z/nZ)^d$ induced by the actions of certain matrix groups, demonstrating that a variety of exponential sums of interest in number theory (e.g., Gauss, Ramanujan, and Kloosterman sums) arise in this manner. We develop a generalization of the discrete Fourier transform, in which supercharacters play the role of the Fourier exponential basis. We provide a corresponding uncertainty principle and compute the associated constants in several cases.
Fourteenth Kenneth C. Schraut Memorial Lecture (Poster),
2013
University of Dayton
Fourteenth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics
Kenneth C. Schraut Memorial Lectures
No abstract provided.
Generalized Gauss Maps And Integrals For Three-Component Links: Toward Higher Helicities For Magnetic Fields And Fluid Flows,
2013
Bryn Mawr College
Generalized Gauss Maps And Integrals For Three-Component Links: Toward Higher Helicities For Magnetic Fields And Fluid Flows, Dennis Deturck, Herman Gluck, Rafal Komendarczyk, Paul Melvin, Clayton Shonkwiler, David Shea Vela-Vick
Mathematics Faculty Research and Scholarship
To each three-component link in the 3-sphere we associate a generalized Gauss map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin invariants that classify its generalized Gauss map up to homotopy. We view this as a natural extension of the familiar situation for two-component links in 3-space, where the linking number is the degree of the classical Gauss map from the 2-torus to the 2-sphere. The generalized Gauss map, like its prototype, is geometrically natural in the sense …
Extender Sets And Multidimensional Subshifts,
2013
Department of Mathematics, University of Denver
Extender Sets And Multidimensional Subshifts, Nic Ormes, Ronnie Pavlov
Mathematics Preprint Series
In this paper, we consider a Z d extension of the well-known fact that subshifts with only finitely many follower sets are sofic. As in [4], we adopt a natural Z d analogue of a follower set called an extender set. The extender set of a finite word w in a Z d subshift X is the set of all configurations of symbols on the rest of Z d which form a point of X when concatenated with w. As our main result, we show that for any d ≥ 1 and any Z d subshift X, if there exists …
Symmetric Random Walks On Homeo+(R),
2013
Eastern Illinois University
Symmetric Random Walks On Homeo+(R), B. Deroin, V. Klepstyn, A. Navas, Kamlesh Parwani
Faculty Research and Creative Activity
We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence. Except for a few special cases, which can be treated separately, we prove a property of "global stability at a finite distance": roughly speaking, there exists a compact interval such that any two trajectories get closer and closer whenever one of them returns to the compact interval. The probabilistic techniques employed here lead to interesting results for the study of group actions on the …
Functions Defined By Improper Integrals,
2013
Trinity University
Functions Defined By Improper Integrals, William Trench
Mathematics Faculty Research
This is a supplement to the author's Introduction to Real Analysis. It has been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Textbook Initiative. It may be copied, modified, redistributed, translated, and built upon subject to the Creative Commons license Attribution-NonCommercial-ShareAlike 3.0 Unported License. A complete instructor's solution manual is available by email to [email protected] subject to verification of the requestor's faculty status.
