Browsing by Author "Fallat, Shaun"

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Browsing by Author "Fallat, Shaun"

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  • Mitchell, Lon; Fallat, Shaun (International Linear Algebra Society, 2013-01)
    The Colin de Verdi`ere parameters mu and nu are defined to be the maximum nullity of certain real symmetric matrices associated with a given graph. In this work, both of these parameters are calculated for all chordal ...
  • Agasthian, Vijayaparvathy (Faculty of Graduate Studies and Research, University of Regina, 2015-03)
    The convergence of iterative methods for numerically solving the linear systems of equations associated with different types of splittings has been well studied in the literature. In this dissertation, we define new types ...
  • Doucette, Jennifer Lee (Faculty of Graduate Studies and Research, University of Regina, 2012-04)
    The ability of predator populations to expand their ranges and adapt to new environments is often attributed to having a generalist dietary strategy, which is thought to be represented both at the population and individual ...
  • Butler, Steve; Catral, Minnie; Fallat, Shaun; Hall, Tracy; Hogben, Leslie; van den Driessche, Pauline; Young, michael (Elsevier, 2015)
    The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric n ×n matrix is a sequence from A,S, or N according as all, some, or none of its principal minors of order k are nonzero. Such sequences give ...
  • Purdy, Alison May (Faculty of Graduate Studies and Research, University of Regina, 2010)
    The Erdős-Ko-Rado Theorem is a fundamental result in extremal set theory. It describes the size and structure of the largest collection of subsets of size k from a set of size n having the property that any two subsets ...
  • Ahmadi, Bahman (Faculty of Graduate Studies and Research, University of Regina, 2013-07)
    In extremal set theory, the Erd}os-Ko-Rado (EKR) theorem gives an upper bound on the size of intersecting k-subsets of the set {1; : : : ;n}. Furthemore, it classi es the maximum-sized families of intersecting k-subsets. ...
  • Barrett, Wayne; Butler, Steve; Catral, Minnie; Hall, Tracy; Fallat, Shaun; Hogben, Leslie; Young, Michael (International Linear Algebra Society, 2014-06)
    Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all ...
  • Abedini, Ali (Faculty of Graduate Studies and Research, University of Regina, 2014-07)
    Carbon dioxide (CO2) injection processes are among the most promising enhanced oil recovery techniques based on their great potential to improve oil production while utilizing geological storage of carbon dioxide to ...
  • Ahmadi, Bahman; Alinaghipour, Fatemeh; Cavers, Michael; Fallat, Shaun; Meagher, Karen; Nasserasr, Shahla (International Linear Algebra Society, 2013-09)
    The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven and then applied to ...
  • Barrett, Wayne; Fallat, Shaun; Hall, Tracy; Hogben, Leslie (Public Knowledge Network, 2013)
    We establish the bounds 4 on the Nordhaus- Gaddum sum upper bound multipliers for all graphs G, in connections with certain Colin de Verdi ere type graph parameters. The Nordhaus-Gaddum sum lower bound is conjectured ...
  • Tessier, Ryan Brett (Faculty of Graduate Studies and Research, University of Regina, 2013-08)
    A sample compression scheme of size k for a concept class C is a pair of functions (f; g) called the compression function and the reconstruction function. The functions have the property that for any sample S consistent ...
  • Meagher, Karen; Fallat, Shaun; Yang, Boting (Elsevier, 2015)
    The positive semidefinite zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring and is related to a more conventional version of zero forcing. We establish a relation ...
  • Fallat, Shaun; Nasserasr, Shahla (The Charles Babbage Research Centre, 2013-02)
    In this work, we study the structure of the null spaces of matrices associated with graphs. Our primary tool is utilizing Schur complements based on certain collections of independent vertices. This idea is applied in ...
  • Alinaghipour, Fatemeh; Fallat, Shaun; Meagher, Karen (2014)
    The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced ...
  • Barioli, Francesco; Barrett, Wayne; Fallat, Shaun; Hall, Tracy; Hogben, Leslie; Shader, Bryan; van den Driessche, Pauline; van der Holst, Hein (Wiley Periodicals, Inc., 2013)
    Tree-width, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number is used to study the ...
  • Barrett, Wayne; Butler, Steve; Catral, Minnie; Fallat, Shaun; Hall, Tracy; Hogben, Leslie; van den Driessche, Pauline; Young, Michael (Elsevier, 2014)
    Given an n-by-n matrix, its principal rank characteristic sequence is a sequence of length n + 1 of 0s and 1s where, for k = 0; 1,..., n, a 1 in the kth position indicates the existence of a principal submatrix of rank ...
  • Malik, Obaid Ullah (Faculty of Graduate Studies and Research, University of Regina, 2014-06)
    A regular, discrete time series is an ordered sequence of coarse-grained observations taken at fixed time intervals. Here we consider regular, discrete, retail price time series datasets acquired through crowdsourcing. ...
  • Purdy, Alison May (Faculty of Graduate Studies and Research, University of Regina, 2014-09)
    The Erdös-Ko-Rado theorem, a theorem which gives the size and structure of the largest pairwise intersecting collection of k-subsets from a base set of size n, has inspired many variations on the theme of the maximum ...
  • Alinaghipour Taklimi, Fatemeh (Faculty of Graduate Studies and Research, University of Regina, 2013-08)
    For any simple graph G on n vertices, the (positive semi-de nite) minimum rank of G is de ned to be the smallest possible rank among all (positive semi-de nite) real symmetric n × n matrices whose entry in position (i; ...