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Articles 1 - 30 of 99
Full-Text Articles in Mathematics
A Qualitative Representation Of Spatial Scenes In R2 With Regions And Lines, Joshua Lewis
A Qualitative Representation Of Spatial Scenes In R2 With Regions And Lines, Joshua Lewis
Electronic Theses and Dissertations
Regions and lines are common geographic abstractions for geographic objects. Collections of regions, lines, and other representations of spatial objects form a spatial scene, along with their relations. For instance, the states of Maine and New Hampshire can be represented by a pair of regions and related based on their topological properties. These two states are adjacent (i.e., they meet along their shared boundary), whereas Maine and Florida are not adjacent (i.e., they are disjoint).
A detailed model for qualitatively describing spatial scenes should capture the essential properties of a configuration such that a description of the represented objects …
Testing Isomorphism Of Graded Algebras, Peter A. Brooksbank, James B. Wilson, Eamonn A. O'Brien
Testing Isomorphism Of Graded Algebras, Peter A. Brooksbank, James B. Wilson, Eamonn A. O'Brien
Faculty Journal Articles
We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that often dramatically improve the performance of the algorithm and report on an implementation in Magma.
Hybrid Recommender Systems Via Spectral Learning And A Random Forest, Alyssa Williams
Hybrid Recommender Systems Via Spectral Learning And A Random Forest, Alyssa Williams
Electronic Theses and Dissertations
We demonstrate spectral learning can be combined with a random forest classifier to produce a hybrid recommender system capable of incorporating meta information. Spectral learning is supervised learning in which data is in the form of one or more networks. Responses are predicted from features obtained from the eigenvector decomposition of matrix representations of the networks. Spectral learning is based on the highest weight eigenvectors of natural Markov chain representations. A random forest is an ensemble technique for supervised learning whose internal predictive model can be interpreted as a nearest neighbor network. A hybrid recommender can be constructed by first …
Internet Searching Behaviors Of Low Literacy Breast Cancer Survivors, Francisco D. Iacobelli, Ginger L. Dragon, Giselle Mazur, Judy Guitelman
Internet Searching Behaviors Of Low Literacy Breast Cancer Survivors, Francisco D. Iacobelli, Ginger L. Dragon, Giselle Mazur, Judy Guitelman
Faculty Research and Creative Activities Symposium
Internet searching is a popular tool for patients to find health-related information. However, low literacy individuals are at a disadvantage with respect to their ability to evaluate online health information. When using common web search engines to find health information, behaviors such as misspelling, misappropriation of words and incomplete search queries can result in inadequate results and misleading information. The goal of this research is to understand the search strategies and common mistakes that low-literacy Latina breast cancer survivors exhibit when searching for information online in order to inform future information seeking interfaces. To explore search behaviors online we asked …
Nonsupereulerian Graphs With Large Size, Paul A. Catlin, Zhi-Hong Chen
Nonsupereulerian Graphs With Large Size, Paul A. Catlin, Zhi-Hong Chen
Zhi-Hong Chen
No abstract provided.
On The Edge Arboricity Of A Random Graph, P. A. Catlin, Zhi-Hong Chen, E. M. Palmer
On The Edge Arboricity Of A Random Graph, P. A. Catlin, Zhi-Hong Chen, E. M. Palmer
Zhi-Hong Chen
No abstract provided.
On Hamiltonian Line Graphs, Zhi-Hong Chen
Supereuleriaun Graphs And The Petersen Graph, Zhi-Hong Chen
Supereuleriaun Graphs And The Petersen Graph, Zhi-Hong Chen
Zhi-Hong Chen
Using a contraction method, we find some best-possible sufficient conditions for 3-edge-connected simple graphs such that either the graphs have spanning eulerian subgraphs or the graphs are contractible to the Petersen graph.
Supereulerian Graphs And The Petersen Graph, Ii, Zhi-Hong Chen, Hong-Jian Lai
Supereulerian Graphs And The Petersen Graph, Ii, Zhi-Hong Chen, Hong-Jian Lai
Zhi-Hong Chen
In this note, we verify two conjectures of Catlin in [J. Graph Theory 13 (1989) 465 - 483] for graphs with at most 11 vertices. These are used to prove the following theorem which improves prior results in [10] and [13]:
Let G be a 3-edge-connected simple graph with order n. If n is large and if for every edge 11.v E E(G), d(u) + d(v) 2 % - 2, then either G has a spanning eulerian subgraph or G can be contracted to the Petersen graph.
Fan-Type Conditions For Collapsible Graphs, Zhi-Hong Chen
Fan-Type Conditions For Collapsible Graphs, Zhi-Hong Chen
Zhi-Hong Chen
No abstract provided.
Connectivity Of Cycle Matroids And Bicircular Matroids, Zhi-Hong Chen, Kuang Ying-Qiang, Hong-Jian Lai
Connectivity Of Cycle Matroids And Bicircular Matroids, Zhi-Hong Chen, Kuang Ying-Qiang, Hong-Jian Lai
Zhi-Hong Chen
A unified approach to prove former connectivity results of Tutte, Cunningham, Inukai and Weinberg, Oxley and Wagner.
Reinforcing The Number Of Disjoint Spanning Trees, Damin Liu, Hong-Jian Lai, Zhi-Hong Chen
Reinforcing The Number Of Disjoint Spanning Trees, Damin Liu, Hong-Jian Lai, Zhi-Hong Chen
Zhi-Hong Chen
The spanning tree packing number of a connected graph G, denoted by T(G), is the maximum number of edge-disjoint spanning trees of G. In this paper, we determine the minimum number of edges that must be added to G so that the resulting graph has spanning tree packing number at least k, for a given value of k.
Even Subgraphs Of A Graph, Hong-Jian Lai, Zhi-Hong Chen
Even Subgraphs Of A Graph, Hong-Jian Lai, Zhi-Hong Chen
Zhi-Hong Chen
No abstract provided.
Why A Classification Based On Linear Approximation To Dynamical Systems Often Works Well In Nonlinear Cases, Julio Urenda, Vladik Kreinovich
Why A Classification Based On Linear Approximation To Dynamical Systems Often Works Well In Nonlinear Cases, Julio Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
It can be proven that linear dynamical systems exhibit either stable behavior, or unstable behavior, or oscillatory behavior, or transitional behavior. Interesting, the same classification often applies to nonlinear dynamical systems as well. In this paper, we provide a possible explanation for this phenomenon, i.e., we explain why a classification based on linear approximation to dynamical systems often works well in nonlinear cases.
Exercises Integrating High School Mathematics With Robot Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal
Exercises Integrating High School Mathematics With Robot Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal
Computer Science: Faculty Publications and Other Works
This paper presents progress in developing exercises for high school students incorporating level-appropriate mathematics into robotics activities. We assume mathematical foundations ranging from algebra to precalculus, whereas most prior work on integrating mathematics into robotics uses only very elementary mathematical reasoning or, at the other extreme, is comprised of technical papers or books using calculus and other advanced mathematics. The exercises suggested are relevant to any differerential-drive robot, which is an appropriate model for many different varieties of educational robots. They guide students towards comparing a variety of natural navigational strategies making use of typical movement primitives. The exercises align …
Spanning Eulerian Subgraphs And Catlin’S Reduced Graphs, Wei-Guo Chen, Zhi-Hong Chen
Spanning Eulerian Subgraphs And Catlin’S Reduced Graphs, Wei-Guo Chen, Zhi-Hong Chen
Zhi-Hong Chen
A graph G is collapsible if for every even subset R ⊆ V (G), there is a spanning connected subgraph HR of G whose set of odd degree vertices is R. A graph is reduced if it has no nontrivial collapsible subgraphs. Catlin [4] showed that the existence of spanning Eulerian subgraphs in a graph G can be determined by the reduced graph obtained from G by contracting all the collapsible subgraphs of G. In this paper, we present a result on 3-edge-connected reduced graphs of small orders. Then, we prove that a 3-edge-connected graph G of order n …
Properties Of Catlin’S Reduced Graphs And Supereulerian Graphs, Wei-Guo Chen, Zhi-Hong Chen, Mei Lu
Properties Of Catlin’S Reduced Graphs And Supereulerian Graphs, Wei-Guo Chen, Zhi-Hong Chen, Mei Lu
Zhi-Hong Chen
A graph G is called collapsible if for every even subset R ⊆ V (G), there is a spanning connected subgraph H of G such that R is the set of vertices of odd degree in H. A graph is the reduction of G if it is obtained from G by contracting all the nontrivial collapsible subgraphs. A graph is reduced if it has no nontrivial collapsible subgraphs. In this paper, we first prove a few results on the properties of reduced graphs. As an application, for 3-edge-connected graphs G of order n with d(u) + d(v) ≥ 2(n/p − …
Lai’S Conditions For Spanning And Dominating Closed Trails, Wei-Guo Chen, Zhi-Hong Chen, Mei Lu
Lai’S Conditions For Spanning And Dominating Closed Trails, Wei-Guo Chen, Zhi-Hong Chen, Mei Lu
Zhi-Hong Chen
No abstract provided.
9th Annual Postdoctoral Science Symposium, University Of Texas Md Anderson Cancer Center Postdoctoral Association
9th Annual Postdoctoral Science Symposium, University Of Texas Md Anderson Cancer Center Postdoctoral Association
Annual Postdoctoral Science Symposium Abstracts
The mission of the Annual Postdoctoral Science Symposium (APSS) is to provide a platform for talented postdoctoral fellows throughout the Texas Medical Center to present their work to a wider audience. The MD Anderson Postdoctoral Association convened its inaugural Annual Postdoctoral Science Symposium (APSS) on August 4, 2011.
The APSS provides a professional venue for postdoctoral scientists to develop, clarify, and refine their research as a result of formal reviews and critiques of faculty and other postdoctoral scientists. Additionally, attendees discuss current research on a broad range of subjects while promoting academic interactions and enrichment and developing new collaborations.
Degree And Neighborhood Conditions For Hamiltonicity Of Claw-Free Graphs, Zhi-Hong Chen
Degree And Neighborhood Conditions For Hamiltonicity Of Claw-Free Graphs, Zhi-Hong Chen
Zhi-Hong Chen
For a graph H , let σ t ( H ) = min { Σ i = 1 t d H ( v i ) | { v 1 , v 2 , … , v t } is an independent set in H } and let U t ( H ) = min { | ⋃ i = 1 t N H ( v i ) | | { v 1 , v 2 , ⋯ , v t } is an independent set in H } . We show that for a given number ϵ and given integers …
Circumferences Of 3-Connected Claw-Free Graphs, Ii, Zhi-Hong Chen
Circumferences Of 3-Connected Claw-Free Graphs, Ii, Zhi-Hong Chen
Zhi-Hong Chen
For a graph H , the circumference of H , denoted by c ( H ) , is the length of a longest cycle in H . It is proved in Chen (2016) that if H is a 3-connected claw-free graph of order n with δ ≥ 8 , then c ( H ) ≥ min { 9 δ − 3 , n } . In Li (2006), Li conjectured that every 3-connected k -regular claw-free graph H of order n has c ( H ) ≥ min { 10 k − 4 , n } . Later, Li posed …
Effective Statistical Energy Function Based Protein Un/Structure Prediction, Avdesh Mishra
Effective Statistical Energy Function Based Protein Un/Structure Prediction, Avdesh Mishra
University of New Orleans Theses and Dissertations
Proteins are an important component of living organisms, composed of one or more polypeptide chains, each containing hundreds or even thousands of amino acids of 20 standard types. The structure of a protein from the sequence determines crucial functions of proteins such as initiating metabolic reactions, DNA replication, cell signaling, and transporting molecules. In the past, proteins were considered to always have a well-defined stable shape (structured proteins), however, it has recently been shown that there exist intrinsically disordered proteins (IDPs), which lack a fixed or ordered 3D structure, have dynamic characteristics and therefore, exist in multiple states. Based on …
Krylov Subspace Spectral Methods With Non-Homogenous Boundary Conditions, Abbie Hendley
Krylov Subspace Spectral Methods With Non-Homogenous Boundary Conditions, Abbie Hendley
Master's Theses
For this thesis, Krylov Subspace Spectral (KSS) methods, developed by Dr. James Lambers, will be used to solve a one-dimensional, heat equation with non-homogenous boundary conditions. While current methods such as Finite Difference are able to carry out these computations efficiently, their accuracy and scalability can be improved. We will solve the heat equation in one-dimension with two cases to observe the behaviors of the errors using KSS methods. The first case will implement KSS methods with trigonometric initial conditions, then another case where the initial conditions are polynomial functions. We will also look at both the time-independent and time-dependent …
Some Theoretical Links Between Shortest Path Filters And Minimum Spanning Tree Filters, Sravan Danda, Aditya Challa, B. S.Daya Sagar, Laurent Najman
Some Theoretical Links Between Shortest Path Filters And Minimum Spanning Tree Filters, Sravan Danda, Aditya Challa, B. S.Daya Sagar, Laurent Najman
Journal Articles
Edge-aware filtering is an important pre-processing step in many computer vision applications. In the literature, there exist several versions of collaborative edge-aware filters based on spanning trees and shortest path heuristics which work well in practice. For instance, tree filter (TF) which is recently proposed based on a minimum spanning tree (MST) heuristic yields promising results in many filtering applications. However, links between the tree-based filters and shortest path-based filters are faintly explored. In this article, we introduce an edge-aware generalization of the TF termed as UMST filter based on a subgraph generated by edges of all MSTs. The major …
Mathematics And Programming Exercises For Educational Robot Navigation, Ronald I. Greenberg
Mathematics And Programming Exercises For Educational Robot Navigation, Ronald I. Greenberg
Computer Science: Faculty Publications and Other Works
This paper points students towards ideas they can use towards developing a convenient library for robot navigation, with examples based on Botball primitives, and points educators towards mathematics and programming exercises they can suggest to students, especially advanced high school students.
From Optimization To Equilibration: Understanding An Emerging Paradigm In Artificial Intelligence And Machine Learning, Ian Gemp
Doctoral Dissertations
Many existing machine learning (ML) algorithms cannot be viewed as gradient descent on some single objective. The solution trajectories taken by these algorithms naturally exhibit rotation, sometimes forming cycles, a behavior that is not expected with (full-batch) gradient descent. However, these algorithms can be viewed more generally as solving for the equilibrium of a game with possibly multiple competing objectives. Moreover, some recent ML models, specifically generative adversarial networks (GANs) and its variants, are now explicitly formulated as equilibrium problems. Equilibrium problems present challenges beyond those encountered in optimization such as limit-cycles and chaotic attractors and are able to abstract …
On Continuous Images Of Ultra-Arcs, Paul Bankston
On Continuous Images Of Ultra-Arcs, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
Any space homeomorphic to one of the standard subcontinua of the Stone-Čech remainder of the real half-line is called an ultra-arc. Alternatively, an ultra-arc may be viewed as an ultracopower of the real unit interval via a free ultrafilter on a countable set. It is known that any continuum of weight is a continuous image of any ultra-arc; in this paper we address the problem of which continua are continuous images under special maps. Here are some of the results we present.
A New Study Of Applying Complexity Theoretical Tools In Algorithm Design, Shuai Xu
A New Study Of Applying Complexity Theoretical Tools In Algorithm Design, Shuai Xu
FIU Electronic Theses and Dissertations
Given n vectors with dimension m in Boolean domain, how to find two vectors whose pairwise Hamming distance is minimum? This problem is known as the Closest Pair Problem. If these vectors are generated uniformly at random except two of them are correlated with Pearson-correlation coefficient, then the problem is called the Light Bulb Problem. In this work, we propose a novel coding-based scheme for the Closest Pair Problem. We design both randomized and deterministic algorithms, which achieve the best-known running time when the length of input vectors m is small and the minimum distance is very small compared to …
Closing Banquet Eulogies, Russell Howell, C. Ray Rosentrater
Closing Banquet Eulogies, Russell Howell, C. Ray Rosentrater
ACMS Conference Proceedings 2019
A tribute to David Lay; A tribute to John Roe
A Tribute To Robert U. Ayres For A Lifetime Of Work In Technological Forecasting And Related Areas, Steven M. Miller
A Tribute To Robert U. Ayres For A Lifetime Of Work In Technological Forecasting And Related Areas, Steven M. Miller
Research Collection School Of Computing and Information Systems
Bob Ayres was born in the UnitedStates in 1932. For his university studies at the bachelors, masters and PhD levels, he concentrated in physics and mathematics. When we think of Bob today, we think of his pioneering work across the areas of technological forecasting, industrial metabolism and industrial ecology, and the role of energy and thermodynamics in economic growth. How did a person with a strong fundamental education as a physicist end up as a pioneering thinker and thought leader at the intersection of energy, environment and economics?