Graph Partitioning Using Matrix Values For Preconditioning Symmetric Positive Definite Systems,
2014
Old Dominion University
Graph Partitioning Using Matrix Values For Preconditioning Symmetric Positive Definite Systems, Eugenr Vecharynski, Yousef Saad, Masha Sosonkina
Computational Modeling & Simulation Engineering Faculty Publications
Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel matrix-vector multiplication, and typically disregard the information on the coefficients of the matrix. This information, however, may have a significant impact on the quality of the preconditioning procedure used within the chosen iterative scheme. In the present paper, we suggest a spectral partitioning algorithm, which takes into account the information on the matrix coefficients and constructs partitions with respect to the objective of enhancing the quality …
On Commutator Socle-Regular Abelian P-Groups,
2014
Technological University Dublin
On Commutator Socle-Regular Abelian P-Groups, Brendan Goldsmith, Peter Danchev
Articles
We define the notion of a commutator socle-regular Abelian p-group. After establishing some crucial properties of commutator socle-regularity, we investigate its relationship with socle-regularity, strong socle-regularity and projection socle-regularity.
02. Animal Science,
2014
Southwestern Oklahoma State University
02. Animal Science, University Of Central Oklahoma
Oklahoma Research Day Abstracts
No abstract provided.
07. Criminal Justice,
2014
Southwestern Oklahoma State University
07. Criminal Justice, University Of Central Oklahoma
Oklahoma Research Day Abstracts
No abstract provided.
11. Genetics,
2014
Southwestern Oklahoma State University
11. Genetics, University Of Central Oklahoma
Oklahoma Research Day Abstracts
No abstract provided.
18. Statistics,
2014
Southwestern Oklahoma State University
18. Statistics, University Of Central Oklahoma
Oklahoma Research Day Abstracts
No abstract provided.
Partitioning The Blocks Of A Steiner Triple System Into Partial Parallel Classes,
2014
Michigan Technological University
Partitioning The Blocks Of A Steiner Triple System Into Partial Parallel Classes, Jezerca Hodaj
Dissertations, Master's Theses and Master's Reports - Open
Does there exist a Steiner Triple System on v points, whose blocks can be partitioned into partial parallel classes of size m, where m ≤ [v⁄3], m | b and b is the number of blocks of the STS(v)? We give the answer for 9 ≤ v ≤ 43. We also show that whenever 2|b, v ≡ 3 (mod 6) we can find an STS(v) whose blocks can be partitioned into partial parallel classes of size 2, and whenever 4|b , v ≡ 3 (mod 6), there exists an STS(v) whose blocks …
Math Department Newsletter, 2013-2014,
2014
Sacred Heart University
Math Department Newsletter, 2013-2014, Mathematics Department
Mathematics Newsletter
No abstract provided.
Ordinary Modular Forms And Companion Points On The Eigencurve,
2014
Bryn Mawr College
Ordinary Modular Forms And Companion Points On The Eigencurve, John Bergdall
Mathematics Faculty Research and Scholarship
We give a new proof of a result due to Breuil and Emerton which relates the splitting behavior at p of the p-adic Galois representation attached to a p-ordinary modular form to the existence of an overconvergent p-adic companion form for f.
A Testing Based Extraction Algorithm For Identifying Significant Communities In Networks,
2014
University of San Francisco
A Testing Based Extraction Algorithm For Identifying Significant Communities In Networks, James D. Wilson, Simi Wang, Peter J. Mucha, Shankar Bhamidi, Andrew B. Nobel
Mathematics
A common and important problem arising in the study of networks is how to divide the vertices of a given network into one or more groups, called communities, in such a way that vertices of the same community are more interconnected than vertices belonging to different ones. We propose and investigate a testing based community detection procedure called Extraction of Statistically Significant Communities (ESSC). The ESSC procedure is based on p-values for the strength of connection between a single vertex and a set of vertices under a reference distribution derived from a conditional configuration network model. The procedure automatically selects …
On Switching Diffusions: The Feynman-Kac Formula And Near-Optimal Controls,
2014
Wayne State University
On Switching Diffusions: The Feynman-Kac Formula And Near-Optimal Controls, Nicholas Baran
Wayne State University Dissertations
We consider diffusions in two different contexts. First, we consider the so-called Feynman-Kac formula(s) for switching diffusions. These formulas provide stochastic representations for solutions of certain weakly coupled elliptical systems of partial differential equations. The formulas are verified for the boundary value problem, the initial value problem, and the initial boundary value problem. Second, we show the existence of near-optimal controls for a system driven by wideband noise in the presence of regime-switching. Using a relaxed control formulation, together with weak convergence methods, we show that given a stochastic optimal control problem, one may find a control that is near-optimal. …
Fast Algorithms For Analyzing Partially Ranked Data,
2014
Harvey Mudd College
Fast Algorithms For Analyzing Partially Ranked Data, Matthew Mcdermott
HMC Senior Theses
Imagine your local creamery administers a survey asking their patrons to choose their five favorite ice cream flavors. Any data collected by this survey would be an example of partially ranked data, as the set of all possible flavors is only ranked into subsets of the chosen flavors and the non-chosen flavors. If the creamery asks you to help analyze this data, what approaches could you take? One approach is to use the natural symmetries of the underlying data space to decompose any data set into smaller parts that can be more easily understood. In this work, I describe …
A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance,
2014
Harvey Mudd College
A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance, Sorathan Chaturapruek
HMC Senior Theses
The obstacle avoidance navigation problem for Unmanned Aerial Vehicles (UAVs) is a very challenging problem. It lies at the intersection of many fields such as probability, differential geometry, optimal control, and robotics. We build a mathematical framework to solve this problem for quadrotors using both a theoretical approach through a Hamiltonian system and a machine learning approach that learns from human sub-experts' multiple demonstrations in obstacle avoidance. Prior research on the machine learning approach uses an algorithm that does not incorporate geometry. We have developed tools to solve and test the obstacle avoidance problem through mathematics.
Who Wants To Play Sadisticube?,
2014
Bridgewater State University
Who Wants To Play Sadisticube?, Danica Baker
Undergraduate Review
Logic puzzles and games are popular amongst many people for the purpose of entertainment. They also provide intriguing questions for mathematical research. One popular game that has inspired interesting research is Rubik’s Cube. Researchers at MIT have investigated the Rubik’s Cube to find the maximum number of moves, from any starting position, needed to win the game [6]. Another logic puzzle that has recently become very popular is Sudoku. Sudoku is a Japanese number game where a 9x9 grid is set up with a few numbers scattered on the grid. Mathematicians have been investigating Sudoku, exploring questions such as the …
A Frobenius Question Related To Actions On Curves In Characteristic P,
2014
Gettysburg College
A Frobenius Question Related To Actions On Curves In Characteristic P, Darren B. Glass
Math Faculty Publications
We consider which integers g can occur as the genus and of a curve defined over a field of characteristic p which admits an automorphism of degree pq, where p and q are distinct primes. This investigation leads us to consider a certain family of three-dimensional Frobenius problems and prove explicit formulas giving their solution in many cases.
Integrability, Recursion Operators And Soliton Interactions,
2014
Bulgarian Academy of Sciences
Integrability, Recursion Operators And Soliton Interactions, Boyka Aneva, Georgi Grahovski, Rossen Ivanov, Dimitar Mladenov
Book chapter/book
This volume contains selected papers based on the talks,presentedat the Conference Integrability, Recursion Operators and Soliton Interactions, held in Sofia, Bulgaria (29-31 August 2012) at the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences. Included are also invited papers presenting new research developments in the thematic area. The Conference was dedicated to the 65-th birthday of our esteemed colleague and friend Vladimir Gerdjikov. The event brought together more than 30 scientists, from 6 European countries to celebrate Vladimir's scientific achievements. All participants enjoyed a variety of excellent talks in a friendly and stimulating atmosphere. …
Some Dynamic Hardy-Type Inequalities With General Kernel,
2014
Missouri University of Science and Technology
Some Dynamic Hardy-Type Inequalities With General Kernel, Martin Bohner, Ammara Nosheen, Josip Pečarić, Awais Younus
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we extend some Hardy-type inequalities with certain kernels to arbitrary time scales. Certain classical and some new integral and discrete inequalities are deduced in seek of applications. © Zagreb Paper JMI-08-12.
On The Maximum Leaf Number Of A Family Of Circulant Graphs,
2014
Ateneo de Manila University
On The Maximum Leaf Number Of A Family Of Circulant Graphs, Felix P. Muga Ii
Mathematics Faculty Publications
This paper determines the maximum leaf number and the connected domination number of some undirected and connected circulant networks which are optimal among all the maximum leaf numbers and connected domination numbers of circulant networks of the same order n and the same degree 2k. We shall tackle this problem by working on the largest possible number of vertices between two consecutive jump sizes.
A New Subgroup Chain For The Finite Affine Group,
2014
Harvey Mudd College
A New Subgroup Chain For The Finite Affine Group, David Alan Lingenbrink Jr.
HMC Senior Theses
The finite affine group is a matrix group whose entries come from a finite field. A natural subgroup consists of those matrices whose entries all come from a subfield instead. In this paper, I will introduce intermediate sub- groups with entries from both the field and a subfield. I will also examine the representations of these intermediate subgroups as well as the branch- ing diagram for the resulting subgroup chain. This will allow us to create a fast Fourier transform for the group that uses asymptotically fewer opera- tions than the brute force algorithm.
Cycle Lengths Of Θ-Biased Random Permutations,
2014
Harvey Mudd College
Cycle Lengths Of Θ-Biased Random Permutations, Tongjia Shi
HMC Senior Theses
Consider a probability distribution on the permutations of n elements. If the probability of each permutation is proportional to θK, where K is the number of cycles in the permutation, then we say that the distribution generates a θ-biased random permutation. A random permutation is a special θ-biased random permutation with θ = 1. The mth moment of the rth longest cycle of a random permutation is Θ(nm), regardless of r and θ. The joint moments are derived, and it is shown that the longest cycles of a permutation can either be positively or …
