A relevant category is a symmetric monoidal closed category with a diagonal natural transformation that satisfies some coherence conditions. Every cartesian closed category is a relevant category in this sense. The denomination relevant comes from the connection with relevant logic. It is shown that the category of sets with partial functions, which is isomorphic to the category of pointed sets...

Conventional video surveillance systems often have several shortcomings. First, target detection can’t be accurate under the light variation environment. Second, multiple target tracking becomes difficult on a crowd scene. Third, it is difficult to partition the tracked targets from a merged image blob. Finally, the tracking efficiency and precision are reduced by the inaccurate foreground dete...

Characterising graph classes by forbidding a set of graphs has been a common feature in graph theory for many years. Up to date many classes have been char-acterised with respect to the induced subgraph relation and there are a plethora of results regarding graph classes closed under the minor relation. We consider the characterisation of graph classes closed under partial orders including edge...

For each minor-closed graph class we show that a simple variant of Borůvka’s algorithm computes a MST for any input graph belonging to that class with linear costs. Among minor-closed graph classes are e.g planar graphs, graphs of bounded genus, partial k-trees for fixed k, and linkless or knotless embedable graphs. The algorithm can be implemented on a CRCW PRAM to run in logarithmic time with...

this paper deals with leader-following and leaderless consensus problems of high-order multi-input/multi-output (mimo) multi-agent systems with unknown nonlinear dynamics in the presence of uncertain external disturbances. the agents may have different dynamics and communicate together under a directed graph. a distributed adaptive method is designed for both cases. the structures of the contro...

25 The Traveling Salesman Problem (TSP) is still one of the most researched topics in computational mathematics, and we introduce a variant of it, namely the study of the closed k-walks in graphs. We 2 G. Bullington, R. Gera, L. Eroh And S.J. Winters search for a shortest closed route visiting k cities in a non complete graph without weights. This motivates the following definition. Given a set...