A polynomial time algorithm for determining zero Euler–Petrie genus of an Eulerian graph

AbstractA dual-Eulerian graph is a plane graph which has an ordering defined on its edge set which forms simultaneously an Euler circuit in the graph and an Euler circuit in the dual graph. Dual-Eulerian graphs were defined and studied in the context of silicon optimization of cmos layouts. They are necessarily of low connectivity, hence may have many planar embeddings. We give a polynomial time algorithm to answer the question whether or not a planar multigraph admits an embedding which is dual-Eulerian and construct such an embedding, if it exists

Straight-ahead walks in Eulerian graphs

AbstractA straight-ahead walk in an embedded Eulerian graph G always passes from an edge to the opposite edge in the rotation at the same vertex. A straight-ahead walk is called Eulerian if all the edges of the embedded graph G are traversed in this way starting from an arbitrary edge. An embedding that contains an Eulerian straight-ahead walk is called an Eulerian embedding. In this article, we characterize some properties of Eulerian embeddings of graphs and of embeddings of graphs such that the corresponding medial graph is Eulerian embedded. We prove that in the case of 4-valent planar graphs, the number of straight-ahead walks does not depend on the actual embedding in the plane. Finally, we show that the minimal genus over Eulerian embeddings of a graph can be quite close to the minimal genus over all embeddings

On the interplay between embedded graphs and delta-matroids

The mutually enriching relationship between graphs and matroids has motivated discoveries in both fields. In this paper, we exploit the similar relationship between embedded graphs and delta-matroids. There are well-known connections between geometric duals of plane graphs and duals of matroids. We obtain analogous connections for various types of duality in the literature for graphs in surfaces of higher genus and delta-matroids. Using this interplay, we establish a rough structure theorem for delta-matroids that are twists of matroids, we translate Petrie duality on ribbon graphs to loop complementation on delta-matroids, and we prove that ribbon graph polynomials, such as the Penrose polynomial, the characteristic polynomial, and the transition polynomial, are in fact delta-matroidal. We also express the Penrose polynomial as a sum of characteristic polynomials

Latitude, longitude, and beyond:mining mobile objects' behavior

Rapid advancements in Micro-Electro-Mechanical Systems (MEMS), and wireless communications, have resulted in a surge in data generation. Mobility data is one of the various forms of data, which are ubiquitously collected by different location sensing devices. Extensive knowledge about the behavior of humans and wildlife is buried in raw mobility data. This knowledge can be used for realizing numerous viable applications ranging from wildlife movement analysis, to various location-based recommendation systems, urban planning, and disaster relief. With respect to what mentioned above, in this thesis, we mainly focus on providing data analytics for understanding the behavior and interaction of mobile entities (humans and animals). To this end, the main research question to be addressed is: How can behaviors and interactions of mobile entities be determined from mobility data acquired by (mobile) wireless sensor nodes in an accurate and efficient manner? To answer the above-mentioned question, both application requirements and technological constraints are considered in this thesis. On the one hand, applications requirements call for accurate data analytics to uncover hidden information about individual behavior and social interaction of mobile entities, and to deal with the uncertainties in mobility data. Technological constraints, on the other hand, require these data analytics to be efficient in terms of their energy consumption and to have low memory footprint, and processing complexity

Assumption University of Windsor General Calendar 1960-1961

https://scholar.uwindsor.ca/universitywindsorgeneralcalendars/1004/thumbnail.jp

The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts

The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe