We study the simple random walk on Uniform Infinite Half-Plane Map, which is local limit of critical Boltzmann planar maps with a large and boundary. prove that recurrent, resistance between root boundary hull radius r at least order logr. This bound expected to be sharp, better than those following from previous proofs recurrence for nonbounded-degree models. Our main tools are self-duality un...

Optical Mapping is an emerging technology for constructing ordered restriction maps of DNA molecules. The underlying computational problems for this technology have been studied and several models have been proposed in recent literature. Most of these propose combinatorial models; some of them also present statistical approaches. However, it is not a priori clear as to how these models relate t...

Given a planar point set, we wish to label the points with uniform circular labels such that each input point lies on the boundary of two labels, none of the interiors of the labels intersect, and the size of the labels is maximized. This problem is known as map-labeling with uniform circular pairs (MLUCP) and has been shown to be NP-hard. In this paper, we give an O(n logn) time, O(n) space al...

It is shown that if f is a mapping of the plane onto itself that is uniformly continuous with modulus of continuity Ω(r) which is o( √ r) as r → 0 and f is also co-uniformly continuous then f = P ◦ h where h is a homeomorphism of the plane and P is a complex polynomial. The same conclusion holds also under other assumptions on the moduli of uniform and co-uniform continuity. However, we also pr...

We test a Markov chain approximation to the segment description (Li, 2007) of chaos (and turbulence) on a tent map, the Minea system, the Hénon map, and the Lorenz system. For the tent map, we compute the probability transition matrix of the Markov chain on the segments for segment time length (iterations) T = 1, 2, 3, 100. The matrix has 1, 2, 4 tents corresponding to T = 1, 2, 3; and is almos...

Motivation. We develop a new generalized framework for fitting crystal structures into density maps. The framework includes three new scoring functions that quantify the goodness of fit between the crystal structure and density map: (A) the scattering potential score, which is based on using a more realistic representation of the input crystal structure in terms of the density map, (B) the non-...