It is easy to deduce from Ramsey's Theorem that, given positive integers a1, a2, . . . , am and a finite colouring of the set N of positive integers, there exists an injectiv...
A matrix A is said to be partition regular (PR) over a subset S of the positive integers if whenever S is finitely coloured, there exists a vector x, with all elements in the sam...
A linear equation L is called k-regular if every k-coloring of the positive integers contains a monochromatic solution to L. Richard Rado conjectured that for every positive intege...
We study thresholds for Ramsey properties of random discrete structures. In particular, we determine the threshold for Rado’s theorem for solutions of partition regular systems o...
We present a variational approach to motion estimation of instationary fluid flows. Our approach extends prior work along two directions: (i) The full incompressible Navier-Stokes ...