Mathematics and Statistics Faculty Presentations
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http://digitalcommons.usu.edu/mathsci_presentations
Recent documents in Mathematics and Statistics Faculty Presentations
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Fri, 18 Nov 2016 02:04:50 PST
3600

Population density, not host competence, drives patterns of disease in an invaded community
http://digitalcommons.usu.edu/mathsci_presentations/56
http://digitalcommons.usu.edu/mathsci_presentations/56
Wed, 16 Nov 2016 12:57:10 PST
Generalist parasites can strongly influence interactions between native and invasive species. Host competence can be used to predict how an invasive species will affect community disease dynamics; the addition of a highly competent, invasive host is predicted to increase disease. However, densities of invasive and native species can also influence the impacts of invasive species on community disease dynamics. We examined whether information on host competence alone could be used to accurately predict the effects of an invasive host on disease in native hosts. We first characterized the relative competence of an invasive species and a native host species to a native parasite. Next, we manipulated species composition in mesocosms and found that host competence results did not accurately predict community dynamics. While the invasive host was more competent than the native, the presence of the native (lower competence) host increased disease in the invasive (higher competence) host. To identify potential mechanisms driving these patterns, we analyzed a twohost, oneparasite model parameterized for our system. Our results demonstrate that patterns of disease were primarily driven by relative population densities, mediated by asymmetry in intra and interspecific competition. Thus, information on host competence alone may not accurately predict how an invasive species will influence disease in native species. Â© 2016 by The University of Chicago.
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C. L. Searle

An Introduction to Differential Geometry Through Computation
http://digitalcommons.usu.edu/mathsci_presentations/55
http://digitalcommons.usu.edu/mathsci_presentations/55
Fri, 11 Nov 2016 10:55:50 PST
Mark Eric Fels

Characterizations of Interval Bigraphs and Unit Interval Bigraphs
http://digitalcommons.usu.edu/mathsci_presentations/53
http://digitalcommons.usu.edu/mathsci_presentations/53
Mon, 18 Mar 2013 16:00:55 PDT
David E. Brown

Variations on Interval Graphs
http://digitalcommons.usu.edu/mathsci_presentations/54
http://digitalcommons.usu.edu/mathsci_presentations/54
Mon, 18 Mar 2013 16:00:55 PDT
David E. Brown

Several Characterizations for Unit Interval Bigraphs
http://digitalcommons.usu.edu/mathsci_presentations/51
http://digitalcommons.usu.edu/mathsci_presentations/51
Mon, 18 Mar 2013 16:00:54 PDT
David E. Brown

Varieties of Interval Graphs, Probe Interval Graphs, and (0, 1)Matrices
http://digitalcommons.usu.edu/mathsci_presentations/52
http://digitalcommons.usu.edu/mathsci_presentations/52
Mon, 18 Mar 2013 16:00:54 PDT
David E. Brown

Probe Interval Graphs, Circular Arc Graphs and Interval
Point Bigraphs
http://digitalcommons.usu.edu/mathsci_presentations/50
http://digitalcommons.usu.edu/mathsci_presentations/50
Mon, 18 Mar 2013 16:00:53 PDT
David E. Brown

The Hierarchy of Probe Interval, Tolerance, and Interval kGraphs
http://digitalcommons.usu.edu/mathsci_presentations/49
http://digitalcommons.usu.edu/mathsci_presentations/49
Mon, 18 Mar 2013 16:00:52 PDT
We introduce a series of generalizations of probe interval graphs called tprobe interval graphs, (a probe interval graph is a 1probe interval graph) and show, via a method similar to graph homomorphism, that each class, including the class of probe interval graphs, is contained in the class of interval kgraphs. Any probe interval graph is clearly a tolerance graph, but for some t>1 this relationship fails. We wish to determine this t. Also, the interval kgraphs whose complement describes a poset are believed to have a nice characterication via forbidden subgraphs, and we give the conjecture here, and a new description of these interval kgraphs that is similar to the salient property of function graphs.
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David E. Brown et al.

Interval Tournaments
http://digitalcommons.usu.edu/mathsci_presentations/48
http://digitalcommons.usu.edu/mathsci_presentations/48
Mon, 18 Mar 2013 16:00:51 PDT
David E. Brown

A Journey Through Interval Intersection Graph Country
http://digitalcommons.usu.edu/mathsci_presentations/46
http://digitalcommons.usu.edu/mathsci_presentations/46
Mon, 18 Mar 2013 16:00:50 PDT
David E. Brown

Developing Mathematical Maturity via Combinatorial Proofs
http://digitalcommons.usu.edu/mathsci_presentations/47
http://digitalcommons.usu.edu/mathsci_presentations/47
Mon, 18 Mar 2013 16:00:50 PDT
David E. Brown

Development of a Program for the Assessment and Improvement of Teaching
http://digitalcommons.usu.edu/mathsci_presentations/44
http://digitalcommons.usu.edu/mathsci_presentations/44
Mon, 18 Mar 2013 16:00:49 PDT
David E. Brown

Assessing and Improving Teaching
http://digitalcommons.usu.edu/mathsci_presentations/45
http://digitalcommons.usu.edu/mathsci_presentations/45
Mon, 18 Mar 2013 16:00:49 PDT
David E. Brown

Assessing and Improving Teaching Performance
http://digitalcommons.usu.edu/mathsci_presentations/42
http://digitalcommons.usu.edu/mathsci_presentations/42
Mon, 18 Mar 2013 16:00:48 PDT
David E. Brown

Linear Time Recognition Algorithms and Structural Characterizations for Bipartite Tolerance
and Probe Interval Graphs
http://digitalcommons.usu.edu/mathsci_presentations/43
http://digitalcommons.usu.edu/mathsci_presentations/43
Mon, 18 Mar 2013 16:00:48 PDT
A graph G is a tolerance graph if and only if each vertex v ∈ V (G) can be associated with an interval Iv of the real numbers and a positive real number tv with uv ∈ E(G) if and only if Iv ∩ Iu  ≥ min{tv , tu }. Graph G is a probe interval graph if there is a partition of V (G) into sets P and N with each vertex associated to an interval of the real number line such that uv ∈ E if and only if Iu ∩ Iv ̸= Ø and {u, v} ∩ P ̸= Ø. We give a recognition algorithm for bipartite tolerance graphs that yields a structural characterization in terms of 2connected blocks. With a few modifications, the same recognition algorithm works for bipartite probe interval graphs and yields a structural characterization for them in terms of 2edgeconnected blocks. The recognition algorithm is O(V  + E) for both classes of graphs.
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David E. Brown et al.

Lexicographic BreadthFirst Search and Recognition Algorithms for Unit Interval Graphs
http://digitalcommons.usu.edu/mathsci_presentations/41
http://digitalcommons.usu.edu/mathsci_presentations/41
Mon, 18 Mar 2013 16:00:47 PDT
David E. Brown

Assessing Proofs with Rubrics: The RVF Method
http://digitalcommons.usu.edu/mathsci_presentations/39
http://digitalcommons.usu.edu/mathsci_presentations/39
Mon, 18 Mar 2013 16:00:46 PDT
We present an easytoimplement 3axis rubric for the formative and summative assessment of openended solutions and proofs. The rubric was constructed for the use on the written work of students in a Discrete Mathematics class at a researchoriented university, with the following in mind: (1) To aid in the efficiency and consistency of assessment of proofs and openended solutions, with the possibility of being comfortably implemented by an undergraduate assistant; (2) To provide the simultaneous formative and summative assessment of the students’ written work. Thus, the questions we address are: How can we foster good technical writing skills in a way that improvement can be measured? How can large amounts of written work be processed and assessed so that summative and formative judgments are passed but without much time used by the instructor/professor/TA? The axes we use are labeled validity, readability, and fluency, corresponding to (respectively) correctness of calculations and deductions, the ease with which the solution or proof can be read, and the extent to which a student is able to use and communicate via the technical notions relevant to the problem or proof — for example appropriateness and correctness of notation. The rubric format is communicated to the students and discussed in class before any written work is assessed. The rubric has been implemented by professors and teaching assistants only after being trained in its use.
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David E. Brown et al.

Assessing and Improving Teaching Performance
http://digitalcommons.usu.edu/mathsci_presentations/40
http://digitalcommons.usu.edu/mathsci_presentations/40
Mon, 18 Mar 2013 16:00:46 PDT
David E. Brown

Orders: Interval, IntervalProbe, and Intervalk
http://digitalcommons.usu.edu/mathsci_presentations/38
http://digitalcommons.usu.edu/mathsci_presentations/38
Mon, 18 Mar 2013 16:00:45 PDT
If an interval graph is such that its complement can be oriented transitively, that orientation yields an interval order. A graph G is an intervalprobe graph if its vertices can be partitioned into P (probes) and N (nonprobes) and each vertex v can correspond to an interval Iv so that vertices u and v are adjacent if and only if Iu ∩Iv ̸= Ø and {u,v}∩P ̸= Ø. A graph G is an interval kgraph if its vertices can be properly colored and each vertex v can correspond to an interval Iv so that vertices u and v are adjacent if and only if Iu ∩Iv ̸= Ø and u and v are colored differently. Interval probe graphs generalize interval graphs and interval kgraphs generalize intervalprobe graphs. This talk will contain recent characterizations of interval probe orders (order obtained from a transitive orientation of an intervalprobe graph) of interval korders (order obtained from a transitive orientation of an interval kgraph).
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David E. Brown

Cycle Extendability in Graphs, Bigraphs and Digraphs
http://digitalcommons.usu.edu/mathsci_presentations/36
http://digitalcommons.usu.edu/mathsci_presentations/36
Mon, 18 Mar 2013 16:00:44 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. In this talk, we discuss some preliminary results on a generalization of the concept of cycle extendability 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 present some results on tournaments, i.e., complete directed graphs, and some observations about cycleextendability and Sextendability for nondirected graphs.
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LeRoy B. Beasley et al.