High energy heavy ion collisions create quark gluon plasmas that behave like almost perfect fluids. Very similar features to those led this insight have also been observed in experimental data from of small systems, involving protons or other light nuclei. We describe recent developments aimed at understanding whether, and if so how, systems produce relatively few particles (orders magnitude le...

In a seminal paper, Charikar et al. derive upper and lower bounds on the approximation ratios for several grammar-based compressors, but in all cases there is gap between bound. Here gaps LZ78 BISECTION are closed by showing that ratio of ?((n/log n) 2/3 ), whereas ?(?(n/log n)). addition, bound...

The minimum rank of a directed graph Γ is defined to be the smallest possible rank over all real matrices whose ijth entry is nonzero whenever (i, j) is an arc in Γ and is zero otherwise. The symmetric minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i = j) is nonzero whenever {i, j} is an edge in G and is zero o...

In this paper we introduce the graph layout parameter neighbourhood-width as a variation of the well-known cut-width. The cut-width of a graph G = (V ,E) is the smallest integer k, such that there is a linear layout : V → {1, . . . , |V |}, such that for every 1 i < |V | there are at most k edges {u, v} with (u) i and (v)> i. The neighbourhood-width of a graph is the smallest integer k, such th...

Characterizing tissue by measuring its physical properties has potential for improving the diagnostic capabilities of medical ultrasound. One parameter that is estimated using the power spectrum of backscattered ultrasound echoes is the characteristic size or correlation length of the tissue microstructure responsible for the scattering. Unfortunately, the characteristic size measurement has tr...

In this paper, we present a fast and optimal method for the lossy encoding of object boundaries which are given as 8-connect chain codes. We approximate the boundary by a polygon and consider the problem of nding the polygon which can be encoded with the smallest number of bits for a given maximum distortion. To this end, we derive a fast and optimal scheme which is based on a shortest path alg...

In this paper, we present fast and efficient methods for the lossy encoding of object boundaries that are given as eight-connect chain codes. We approximate the boundary by a polygon, and consider the problem of finding the polygon which leads to the smallest distortion for a given number of bits. We also address the dual problem of finding the polygon which leads to the smallest bit rate for a...

The computation of solution paths for continuation problems requires the solution of a sequence of nonlinear systems of equations. Each nonlinear system can be solved by computing the solution of a succession of linear systems of equations determined by Jacobian matrices associated with the nonlinear system of equations. Points on the solution path where the Jacobian matrix is singular are refe...