We conservatively extend classical elementary differential calculus to the Cartesian closed category of convergence spaces. By specializing results about the convergence space representation of directed graphs, we use Cayley graphs to obtain a differential calculus on groups, from which we then extract a Boolean differential calculus, in which both linearity and the product rule, also called th...

Re-identification, that is recognizing that an object appearing in a scene is a reoccurrence of an object seen previously by the system (by the same camera or possibly by a different one) is a challenging problem in video surveillance. In this paper, the problem is addressed using a structural, graph-based representation of the objects of interest. A recently proposed graph kernel is adopted fo...

This work contributes to detection and tracking of walking or running humans in surveillance video sequences. We propose a 2D model-based approach to the whole body tracking in a video sequence captured from a single camera view. An extended six-link biped human model is employed. We assume that a static camera observes the scene horizontally or obliquely. Persons can be seen from a continuum o...

A closed 2-cell embedding of a graph embedded in some surface is an embedding such that each face is bounded by a cycle in the graph. The strong embedding conjecture says that every 2-connected graph has a closed 2-cell embedding in some surface. In this paper, we prove that any 2-connected graph without V8 (the M obius 4-ladder) as a minor has a closed 2-cell embedding in some surface. As a c...

‎let $x=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the hankel matrix of size $2times n$ and let $g$ be a closed graph on the vertex set $[n].$ we study the binomial ideal $i_gsubset k[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $x$ which correspond to the edges of $g.$ we show that...

Baker [1] devised a powerful technique to obtain approximation schemes for various problems restricted to planar graphs. Her technique can be directly extended to various other graph classes, among the most general ones the graphs avoiding a fixed apex graph as a minor. Further generalizations (e.g., to all proper minor closed graph classes) are known, but they use a combination of techniques a...

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...