Euglena and its Relatives

Life and Its Close Relatives

When driven by an external thermodynamic gradient, nonbiological physical systems can exhibit a wide range of behaviours usually associated with living systems. Consequently, Artificial Life researchers should be open to the possibility that there is no hard-and-fast distinction between the biological and the physical. This suggests a novel field of research: the application of biologists’ meth...

Geometric Range Searching and Its Relatives Geometric Range Searching and Its Relatives

Colourful Linear Programming and its Relatives

We consider the following Colourful generalization of Linear Programming: given sets of points S, ... , Sk C Rd, referred to as colours, and a point b E Rd, decide whether there is a colourful T = {s ..., Sk such that b E conv(T), and if there is one, find it. Linear Programming is obtained by taking k = d + 1 and S = = Sd,+. + If k = d + 1 and b E nf I+ conv(S) then a solution always exists: w...

The Van Kampen Obstruction and Its Relatives

We review a cochain-free treatment of the classical van Kampen obstruction θ to embeddability of an n-polyhedron into R2n and consider several analogues and generalizations of θ, including an extraordinary lift of θ which in the manifold case has been studied by J.-P. Dax. The following results are obtained. • The mod2 reduction of θ is incomplete, which answers a question of Sarkaria. • An odd...

The curve complex and its relatives

As we have seen in the previous lecture, Teichmüller space T (S) for a surface of finite type S = Sg,n (genus g and n punctures or boundary components) is a parameter space for various types of structures that can be imposed on the same topological surface S. I’ll adopt the view that T (S) is the space of metrics on S, marked with a set of generators for the fundamental group, up to (measurable...