Mathematics and Statistics Faculty Publications
Copyright (c) 2016 Utah State University All rights reserved.
http://digitalcommons.usu.edu/mathsci_facpub
Recent documents in Mathematics and Statistics Faculty Publications
enus
Wed, 06 Jan 2016 04:45:56 PST
3600

IndividualBased Modeling: Mountain Pine Beetle Seasonal Biology in Response to Climate
http://digitalcommons.usu.edu/mathsci_facpub/199
http://digitalcommons.usu.edu/mathsci_facpub/199
Mon, 14 Dec 2015 09:40:39 PST
Over the past decades, as significant advances were made in the availability and accessibility of computing power, individualbased models (IBM) have become increasingly appealing to ecologists (Grimm 1999). The individualbased modeling approachprovides a convenient framework to incorporate detailed knowledge of individuals and of their interactions within populations (Lomnicki 1999). Variability among individuals is essential to the success of populations that are exposed to changing environments, and because natural selection acts on this variability, it is an essential component of population performance. © Springer International Publishing Switzerland 2015.
]]>
Jacques Regniere et al.

Linear Operators That Preserve Graphical Properties of Matrices: Isolation Numbers
http://digitalcommons.usu.edu/mathsci_facpub/198
http://digitalcommons.usu.edu/mathsci_facpub/198
Mon, 02 Feb 2015 12:51:02 PST
Let A be a Boolean {0, 1} matrix. The isolation number of A is the maximum number of ones in A such that no two are in any row or any column (that is they are independent), and no two are in a 2 × 2 submatrix of all ones. The isolation number of A is a lower bound on the Boolean rank of A. A linear operator on the set of m × n Boolean matrices is a mapping which is additive and maps the zero matrix, O, to itself. A mapping strongly preserves a set, S, if it maps the set S into the set S and the complement of the set S into the complement of the set S. We investigate linear operators that preserve the isolation number of Boolean matrices. Specifically, we show that T is a Boolean linear operator that strongly preserves isolation number k for any 1 ⩽ k ⩽ min{m, n} if and only if there are fixed permutation matrices P and Q such that for X∈m,n(𝔹)T(X)=PXQ or, m = n and T (X) = PX t Q where X t is the transpose of X.
]]>
LeRoy B. Beasley et al.

Stability of travelingwave solutions for a Schrodinger system with powertype nonlinearities
http://digitalcommons.usu.edu/mathsci_facpub/197
http://digitalcommons.usu.edu/mathsci_facpub/197
Tue, 25 Nov 2014 14:44:29 PST
In this article, we consider the Schrodinger system with powertype nonlinearities,(Formula presented) where j = 1,...,m, uj are complexvalued functions of (x, t) 2 RN+1, a, b are real numbers. It is shown that when b > 0, and a + (m  1)b > 0, for a certain range of p, travelingwave solutions of this system exist, and are orbitally stable.
]]>
Nghiem Nguyen et al.

SelfAssessment: Aiding Awareness of Achievement
http://digitalcommons.usu.edu/mathsci_facpub/195
http://digitalcommons.usu.edu/mathsci_facpub/195
Mon, 18 Mar 2013 15:03:22 PDT
David E. Brown

The Development and Evaluation of a Program for Improving and
Assessing the Teaching of Mathematics and Statistics
http://digitalcommons.usu.edu/mathsci_facpub/196
http://digitalcommons.usu.edu/mathsci_facpub/196
Mon, 18 Mar 2013 15:03:22 PDT
David E. Brown et al.

Assessing Proofs with Rubrics: The RVF Method
http://digitalcommons.usu.edu/mathsci_facpub/194
http://digitalcommons.usu.edu/mathsci_facpub/194
Mon, 18 Mar 2013 15:03:21 PDT
David E. Brown

Probe Interval Orders
http://digitalcommons.usu.edu/mathsci_facpub/193
http://digitalcommons.usu.edu/mathsci_facpub/193
Mon, 18 Mar 2013 15:03:20 PDT
David E. Brown et al.

Variations on Interval Graphs
http://digitalcommons.usu.edu/mathsci_facpub/192
http://digitalcommons.usu.edu/mathsci_facpub/192
Mon, 18 Mar 2013 15:03:19 PDT
David E. Brown et al.

Characterizations of Interval Bigraphs and Unit Interval
Bigraphs
http://digitalcommons.usu.edu/mathsci_facpub/191
http://digitalcommons.usu.edu/mathsci_facpub/191
Mon, 18 Mar 2013 15:03:18 PDT
David E. Brown et al.

Interval kgraphs
http://digitalcommons.usu.edu/mathsci_facpub/190
http://digitalcommons.usu.edu/mathsci_facpub/190
Mon, 18 Mar 2013 15:03:17 PDT
David E. Brown et al.

Relationships Among Classes of Interval Bigraphs, (0,1)matrices, and
Circular Arc Graphs
http://digitalcommons.usu.edu/mathsci_facpub/189
http://digitalcommons.usu.edu/mathsci_facpub/189
Mon, 18 Mar 2013 15:03:16 PDT
David E. Brown et al.

On Cycle and Bicycle Extendability in Chordal and Chordal Bipartite Graphs
http://digitalcommons.usu.edu/mathsci_facpub/188
http://digitalcommons.usu.edu/mathsci_facpub/188
Mon, 18 Mar 2013 15:03:14 PDT
LeRoy B. Beasley et al.

Bipartite Probe Interval Graphs, Interval Point Bigraphs, and Circular ArcGraphs
http://digitalcommons.usu.edu/mathsci_facpub/187
http://digitalcommons.usu.edu/mathsci_facpub/187
Mon, 18 Mar 2013 15:03:13 PDT
David E. Brown et al.

A Characterization of Cyclefree Unit Probe Interval Graphs
http://digitalcommons.usu.edu/mathsci_facpub/185
http://digitalcommons.usu.edu/mathsci_facpub/185
Mon, 18 Mar 2013 15:03:12 PDT
A graph is a probe interval graph (PIG) if its vertices can be partitioned into probes and nonprobes with an interval assigned to each vertex so that vertices are adjacent if and only if their corresponding intervals overlap and at least one of them is a probe. PIGs are a generalization of interval graphs introduced by Zhang for an application concerning the physical mapping of DNA in the human genome project. PIGs have been characterized in the cyclefree case by Sheng, and other miscellaneous results are given by McMorris, Wang, and Zhang. Johnson and Spinrad give a polynomial time recognition algorithm for when the partition of vertices into probes and nonprobes is given. The complexity for the general recognition problem is not known. Here, we restrict attention to the case where all intervals have the same length, that is, we study the unit probe interval graphs and characterize the cyclefree graphs that are unit probe interval graphs via a list of forbidden induced subgraphs.
]]>
David E. Brown et al.

Interval Tournaments
http://digitalcommons.usu.edu/mathsci_facpub/186
http://digitalcommons.usu.edu/mathsci_facpub/186
Mon, 18 Mar 2013 15:03:12 PDT
A tournament is an orientation of a complete graph. A directed graph is an interval digraph if for each vertex v there corresponds an ordered pair of intervals (Sv, Tv) such that u → v if and only if Su ∩ Tv ≠ ∅. A bipartite graph is an interval bigraph if to each vertex there corresponds an interval such that vertices are adjacent if and only if their corresponding intervals intersect and each vertex belongs to a different partite set. We use the equivalence of the models for interval digraphs and interval bigraphs to characterize tournaments that are interval digraphs via forbidden subtournaments and prove that a tournament on n vertices is an interval digraph if and only if it has a transitive (n − 1)subtournament. We also characterize the obstructions to the existence of a transitive subtournament of order n − 1 in a tournament of order n.
]]>
David E. Brown et al.

Extending Partial Tournanents
http://digitalcommons.usu.edu/mathsci_facpub/184
http://digitalcommons.usu.edu/mathsci_facpub/184
Mon, 18 Mar 2013 15:03:11 PDT
Let A be a (0,1,∗)matrix with main diagonal all 0’s and such that if ai,j=1 or ∗ then aj,i=∗ or 0. Under what conditions on the row sums, and or column sums, of A is it possible to change the ∗’s to 0’s or 1’s and obtain a tournament matrix (the adjacency matrix of a tournament) with a specified score sequence? We answer this question in the case of regular and nearly regular tournaments. The result we give is best possible in the sense that no relaxation of any condition will always yield a matrix that can be so extended.
]]>
LeRoy B. Beasley et al.

Preserving Regular Tournaments and Term Rank1
http://digitalcommons.usu.edu/mathsci_facpub/183
http://digitalcommons.usu.edu/mathsci_facpub/183
Mon, 18 Mar 2013 15:03:10 PDT
We investigate linear operators which map certain types of tournaments to themselves. To this end we also characterize term rank1 preservers on the set of matrices whose associated digraphs are simple loopless directed graphs, and find that this set of operators is more diverse than might be expected.
]]>
LeRoy B. Beasley et al.

Embedding Tournaments
http://digitalcommons.usu.edu/mathsci_facpub/182
http://digitalcommons.usu.edu/mathsci_facpub/182
Mon, 18 Mar 2013 15:03:09 PDT
LeRoy B. Beasley et al.

Cycle Extendability in Graphs and Digraphs
http://digitalcommons.usu.edu/mathsci_facpub/181
http://digitalcommons.usu.edu/mathsci_facpub/181
Mon, 18 Mar 2013 15:03:08 PDT
In 1990, Hendry conjectured that all chordal Hamiltonian graphs are cycle extendable, that is, the vertices of each nonHamiltonian cycle are contained in a cycle of length one greater. Let A be a symmetric (0,1)matrix with zero main diagonal such that A is the adjacency matrix of a chordal Hamiltonian graph. Hendry’s conjecture in this case is that every k×k principle submatrix of A that dominates a full cycle permutation k×k matrix is a principle submatrix of a (k+1)×(k+1) principle submatrix of A that dominates a (k+1)×(k+1) full cycle permutation matrix. This article generalizes the concept of cycleextendability to Sextendable; that is, with S⊆{1,2,…,n} and G a graph on n vertices, G is Sextendable if the vertices of every nonHamiltonian cycle are contained in a cycle length i greater, where i∈S. We investigate this concept in directed graphs and in particular tournaments, i.e., antisymmetric matrices with zero main diagonal.
]]>
LeRoy B. Beasley et al.

Linear Time Recognition Algorithms and Structure Theorems for Bipartite Tolerance and Bipartite Probe Interval Graphs
http://digitalcommons.usu.edu/mathsci_facpub/180
http://digitalcommons.usu.edu/mathsci_facpub/180
Mon, 18 Mar 2013 15:03:07 PDT
A graph is a probe interval graph if its vertices can be partitioned into probes and nonprobes with an interval associated to each vertex so that vertices are adjacent if and only if their corresponding intervals intersect and at least one of them is a probe. A graph G = (V,E) is a tolerance graph if each vertex v ∈V can be associated to an interval Iv of the real line and a positive real number tv such that uv ∈E if and only if Iu ∩Iv ≥ min (tu,tv). In this paper we present O(V + E) recognition algorithms for both bipartite probe interval graphs and bipartite tolerance graphs. We also give a new structural characterization for each class which follows from the algorithms.
]]>
David E. Brown et al.