Contributed Talks III
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Quasi-Cyclic Protograph-Based Raptor-Like LDPC Codes With Girth 6 and Shortest Length  [PDF]

Multiple-edge QC-LDPC codes with a large size base matrix are considered. We propose a new method, the degree reduction method, to obtain exponent matrices of these codes which considerably reduces the complexity of the search algorithm. We also provide a necessary and sufficient condition to avoid 4-cycles from occurrence in the Tanner graph of codes obtained based on our method. Then, we apply our method to quasi-cyclic protograph-based Raptor-Like LDPC (QC-PBRL-LDPC) codes whose base matrices are multiple-edge. The numerical results show that as a consequence of this study we can obtain the minimum lifting degree of girth-6 QC-PBRL-LDPC codes.

CHRISTOPHER MARY
Geometric datatypes for geometric parsing algorithms  [PDF]

The MODOS is the computational logic for geometric datatypes, which is some common generalization of the constructive datatypes in logic and the sheaves in geometry. Correct? Complete? Questions?

https://github.com/1337777/cartier

KATHERINE MOORE, Wake Forest University
Communities in Data via Partitioned Local Depths  [PDF]

Although clustering is a crucial component of human experience, there are relatively few methods which harness the richness of a social perspective. Here, we introduce a probabilistically-interpretable measure of local depth from which the cohesion between points can be obtained, via partitioning. The PaLD approach allows one to obtain graph-type community structure (with resulting clusters) in a holistic manner which accounts for varying density and is entirely free of extraneous inputs (e.g., number of communities, neighbourhood size, optimization criteria, etc.). Some theoretical properties of cohesion are included. Joint work with Kenneth Berenhaut.

RINOVIA SIMANJUNTAK, Institut Teknologi Bandung
Multiset Dimension of Cartesian Product Graphs  [PDF]

Let $G$ be a connected graph and $W$ be a set of vertices of $G$. The representation multiset of a vertex $v$ with respect to $W$, $r_m (v|W)$, is defined as a multiset of distances between $v$ and the vertices in $W$. If $r_m (u |W) \neq r_m(v|W)$ for every pair of distinct vertices $u$ and $v$, then $W$ is called an m-resolving set of $G$. If $G$ has an m-resolving set, then the cardinality of a smallest m-resolving set is called the multiset dimension of $G$, denoted by $md(G)$; otherwise, we say that $md(G) = \infty$.

In this talk, we shall derive lower bounds for multiset dimension of Cartesian product graphs. We shall also study the conditions for the sharpness of the bounds.

MICHAEL YATAURO, Penn State - Brandywine
A Parameterized Extension of the Binding Number  [PDF]

We define an extension of the standard binding number of a graph which introduces parameters into the computation. This extension is motivated by a number of theorems that use bounds on the order of neighbor sets of vertices to determine the existence of cycles or factors within the graph. We demonstrate how this extended binding number can be integrated into such theorems. Additionally, we provide a theorem that indicates sufficient conditions on the degree sequence of a graph which guarantees a prescribed lower bound on this extended binding number. Finally, we show how these conditions can be combined with known theorems to produce sufficient conditions on the degree sequence which guarantees certain cycles or factors within the graph.