Given a graph, does there exist an orientation of the edges such that the resulting directed graph is strongly connected? Robbins’ theorem [Robbins, Am. Math. Monthly, 1939] states that such an orientation exists if and only if the graph is 2-edge connected. A natural extension of this problem is the following: Suppose that the edges of the graph is partitioned into trails. Can we orient the tr...

In the last decades, orientation estimation has often been investigated for instance in the domain of still image analysis for feature extraction [5] or in the context of video stream processing for motion analysis [10] [20] [27]. Applications of orientation estimation vary, for example, from the enhancement of ancient engravings to the analysis of fingerprint images or seismic data [8]. Orient...

The cyclic and dihedral groups can be made to act on the set Acyc(Y ) of acyclic orientations of an undirected graph Y , and this gives rise to the equivalence relations ∼κ and ∼δ, respectively. These two actions and their corresponding equivalence classes are closely related to combinatorial problems arising in the context of Coxeter groups, sequential dynamical systems, the chip-firing game, ...

Given an undirected graph, one can assign directions to each of the edges of the graph, thus orienting the graph. To be as egalitarian as possible, one may wish to find an orientation such that no vertex is unfairly hit with too many arcs directed into it. We discuss how this objective arises in problems resulting from telecommunications. We give optimal, polynomial-time algorithms for: finding...

A tree-composition is a tree-like family that serves to describe the obstacles to k-edge-connected orientability of mixed graphs. Here we derive a structural result on tree-compositions that gives rise to a simple algorithm for computing an obstacle when the orientation does not exist. As another application, we show a min–max theorem on the minimal in-degree of a given node set in a k-edge-con...

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I discuss the physics prospects at future high–energy ee linear colliders. After summarizing some aspects of these future machines, I will review a few topics in the Standard Model which can be studied at these colliders: top quark, W/Z vector bosons and Higgs particles physics. A brief discussion on the exploration of extensions of the Standard Model such as Supersymmetry and Grand Unified The...