We study the following one-person game against a random graph: the Player’s goal is to 2-colour a random sequence of edges e1, e2, . . . of a complete graph on n vertices, avoiding a monochromatic triangle for as long as possible. The game is over when a monochromatic triangle is created. The online version of the game requires that the Player should colour each edge when it comes, before looki...

Motivation The handshake problem Compute a set of disjoint edges : a matching, in constant time (a round). Motivation The handshake problem Compute a set of disjoint edges : a matching, in constant time (a round).

One of the most conventional toppling instabilities is the block-flexural toppling failure that occurs in civil and mining engineering projects. In this kind of failure, some rock columns are broken due to tensile bending stresses, and the others are overturned due to their weights, and finally, all of the blocks topple together. A specific feature of spheroidal weathering is the rounding of th...

The immunologists of my generation were brought up on Sir Macfarlane Burnet's clonal selection theory.' Anticipating Margaret Thatcher's view of society, we believed that all that matters in the immune system is the sum of the decisions taken by individual lympho-cytes. Engagement of its receptor by antigen suffices to drive a lymphocyte to respond. For T cells the only exception is the thymus,...

We consider the problem of implementing distributed protocols, despite adversarial channel errors, on synchronous-messaging networks with arbitrary topology. In our first result we show that any n-party T -round protocol on an undirected communication network G can be compiled into a robust simulation protocol on a sparse (O(n) edges) subnetwork so that the simulation tolerates an adversarial e...

In the Oriented-cycle game, the two players, called OMaker and OBreaker, alternately direct edges of the complete graph on n vertices. OMaker directs exactly one edge, whereas OBreaker is allowed to direct between one andb edges in each round. OMaker wins if the final tournament contains a directed cycle, otherwise OBreaker wins. It is not that difficult to see that OMaker has a winning strateg...

A systematic framework is given that accommodates existing max-min filter methods and suggests new ones. Putting the upper and lower envelopes UPP = MIN(MAX) and LOW = MAX(MIN) in the roles that MAX, MIN or original play in existing filters we can distinguish edges in ramp edges and texture (or noise) edges; all methods presented come in three versions: for edges, ramp edges and non-ramp ("text...

We consider the problem of learning a general graph G = (V,E) using edge-detecting queries, where the number of vertices |V | = n is given to the learner. The information theoretic lower bound gives m log n for the number of queries, where m = |E| is the number of edges. In case the number of edges m is also given to the learner, Angluin-Chen’s Las Vegas algorithm Angluin and Chen (2008) runs i...