A distance-based method to reconstruct a phylogenetic tree with n leaves takes a distance matrix, n × n symmetric matrix with 0s in the diagonal, as its input and reconstructs a tree with n leaves using tools in combinatorics. A safety radius is a radius from a tree metric (a distance matrix realizing a true tree) within which the input distance matrices must all lie in order to satisfy a preci...

Recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology [14]. More precisely, the asymptotic dimension for a metric space is the smallest integer n such that for any r > 0, there exists a uniformly bounded cover C = {Ui}i∈I of the metric space for which the rmultiplicity of C is at most n + 1, i.e. no ball of radius r in the metric space interse...

We present a simple physical mechanism that can account for the observed stellar mass spectrum for masses M∗>∼ 0.5M⊙. The model depends solely on the competitive accretion that occurs in stellar clusters where each star’s accretion rate depends on the local gas density and the square of the accretion radius. In a stellar cluster, there are two different regimes depending on whether the gas or t...

We have presented a derivation of the asymptotic equations for transverse magnetic multiple scattering coefficients of an infinite grating of penetrable circular cylinders for obliquely incident plane electromagnetic waves. We have first deducted an “Ansatz” delineating the asymptotic behavior of the transverse magnetic multiple scattering coefficients associated with the most generalized condi...

Context. To constrain Randall-Sundrum type braneworld gravity models and the expected rapid evaporation of astrophysical black holes due to the emission of gravitational modes in the extra dimension. Aims. It is argued that the black-hole X-ray binary XTE J1118+480 is suitable for a constraint on the asymptotic curvature radius of the extra dimension in such braneworld models. An upper limit on...

We determine a lower bound for the spectral radius of a graph in terms of the number of vertices and the diameter of the graph. For the specific case of graphs with diameter three we give a slightly better bound. We also construct families of graphs with small spectral radius, thus obtaining asymptotic results showing that the bound is of the right order. We also relate these results to the ext...

We show that locally repairable codes (LRCs) can be list decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error correction capabilities. The new decoding radius is derived and the asymptotic behavior is analyzed. We give a general list decoding algorithm for LRCs that achieves this radius along with an explicit realization for a class of LRCs ...

The manner in which the extreme modes of droplet evaporation (namely, the constant contact radius and the constant contact angle modes) become indistinguishable on strongly hydrophobic substrates is described. Simple asymptotic expressions are obtained which provide good approximations to the evolutions of the contact radius, the contact angle, and the volume of droplets evaporating in the extr...