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Archive : Discrete Mathematics

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Abdullah Zafar (University of Toronto & Sports Performance Analytics Inc.)Abdullah Zafar (University of Toronto & Sports Performance Analytics Inc.)EWG 336Title:Team Passing and Movement Analysis in Professional Football: Applied Discrete Methods <br><br> Abstract: Joint work with Farzad Yousefian Ball movement is critical in football performance and match outcome as it is the primary method by which players ‘interact’ with each other. Interactions between players, over time, create specific patterns which form the collective passing behaviour of a team. Complementary to ball movement is player movement and positioning, which allows for passing opportunities to be created. To explore the modelling of both passing and movement behaviour, a total of 17 matches of a professional Portuguese football club in the Primeira Liga, 64 matches of the 2018 FIFA World Cup and 5 matches from the Canadian Women’s Team at FISU 2017 were analyzed using match video and iSCOUT software. Passing behaviour was modelled to illustrate higher-order relations between players to identify differences in play style between teams using graphs, simplicial complexes, and homology groups. Optimization of team selection and passing behaviour, based on player availability and team style, was explored using hyper-graphs and hyper simplices. Finally, algebraic braids were utilized to discretize player movement patterns within a team context as a means of integrating passing and movement analysis. 5/14/2020 6:00:00 PM5/14/2020 7:00:00 PMFalse
Xiaoye Liang, WPI and Anhui University, ChinaXiaoye Liang, WPI and Anhui University, ChinaZoom<br> Title: Irreducible T-modules of the Johnson scheme<br> Abstract: The classification of (P and Q)-polynomial scheme is the central problem in algebraic combinatorics: (P and Q)-polynomial schemes are not only interesting for their own sake but also important as underlying space for coding/design theory. This talk focuses on a typical (P and Q)-polynomial scheme — Johnson scheme. Terwilliger algebra will be introduced as it is an important tool to classify association scheme. In our work, all irreducible T-modules of the Johnson scheme are determined.5/7/2020 6:00:00 PM5/7/2020 7:00:00 PMFalse
Novi Bong from University of DelawareNovi Bong from University of DelawareEwing 336Title:Strong Dimension and Threshold strong dimension of graphs <br><br> Abstract: Let $G$ be a graph and $W$ a set of vertices of $G$. Then $W$ is said to \textbf{resolve} $G$ if for every pair $u,v$ of vertices of $G$ there is a vertex $w \in W$ such that the distance of $u$ and $v$ to $w$ are distinct, i.e. $d_G(u,w) \ne d_G(v,w)$, and $W$ \textbf{strongly resolves} $G$ if for every pair $u,v$ of vertices of $G$ there is a vertex $w \in W$ such that either a shortest $u$--$w$ path contains $v$ or a shortest $v$--$w$ path contains $u$. A smallest resolving set in a graph is called a\textbf{ basis} and its cardinality the \textbf{metric dimension} and a smallest strong resolving set is called \textbf{strong basis} and its cardinality the \textbf{strong dimension}. The metric dimension and strong dimension of a graph may decrease if edges are added to the graph. The smallest metric dimension (strong dimension) among all graphs having $G$ as spanning subgraph is called \textbf{threshold} dimension (\textbf{threshold strong dimension}) of $G$ and is denoted by $\tau(G)$ (respectively, $\tau_s(G)$). We determine bounds on the threshold strong dimension of a graphs and determine some structural properties of graphs with strong threshold dimension 2. 4/30/2020 6:00:00 PM4/30/2020 7:00:00 PMFalse
Harmony Zhan from York University, CanadaHarmony Zhan from York University, CanadaZoomTitle: Quantum Fractional Revival <br><br> Abstract: Fractional revival is a useful phenomenon in generating quantum entanglement. Given a graph with adjacency matrix $A$ and a subset $K$ of the vertices, we say $K$-fractional revival occurs if for any $a$ in $K$, the vector $\exp(itA) e_a$ is supported only on $K$. I will introduce a spectral framework to analyze fractional revival, and discuss generalizations of cospectral and strongly cospectral vertices that arise naturally. This is joint work with Ada Chan, Gabriel Coutinho, Whitney Drazen, Or Eisenberg, Chris Godsil, Gabor Lippner, Mark Kempton, and Christino Tamon. 4/23/2020 6:00:00 PM4/23/2020 7:00:00 PMFalse

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