Commensurated subgroups of arithmetic groups, totally disconnected groups and adelic rigidity

Investigations into and around a 30-year old conjecture of Gregory Margulis and Robert Zimmer on the commensurated subgroups of S-arithmetic groups.Comment: 50 page

Randomized Algorithms for the Loop Cutset Problem

We show how to find a minimum weight loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in the method of conditioning for inference. Our randomized algorithm for finding a loop cutset outputs a minimum loop cutset after O(c 6^k kn) steps with probability at least 1 - (1 - 1/(6^k))^c6^k, where c > 1 is a constant specified by the user, k is the minimal size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm often finds a loop cutset that is closer to the minimum weight loop cutset than the ones found by the best deterministic algorithms known

Flat-Cored Dark Matter in Cuspy Clusters of Galaxies

Sand, Treu, & Ellis (2002) have measured the central density profile of cluster MS2137-23 with gravitational lensing and velocity dispersion and removed the stellar contribution with a reasonable M/L. The resulting dark matter distribution within r<50 kpc was fitted by a density cusp of r^{-beta} with beta=0.35. This stands in an apparent contradiction to the CDM prediction of beta~1, and the disagreement worsens if adiabatic compression of the dark matter by the infalling baryons is considered. Following El-Zant, Shlosman & Hoffman (2001), we argue that dynamical friction acting on galaxies moving within the dark matter background counters the effect of adiabatic compression by transfering the orbital energy of galaxies to the dark matter, thus heating up and softening the central density cusp. Using N-body simulations of massive solid clumps moving in clusters we show that indeed the inner dark matter distribution flattens (with beta approx 0.35 for a cluster like MS2137-23) when the galaxies spiral inward. We find as a robust result that while the dark matter distribution becomes core-like, the overall mass distribution preserves its cuspy nature, in agreement with X-ray and lensing observations of clusters.Comment: 7 pages, 3 figures, to be published in Astrophysical Journal Letter

Hitting Diamonds and Growing Cacti

We consider the following NP-hard problem: in a weighted graph, find a minimum cost set of vertices whose removal leaves a graph in which no two cycles share an edge. We obtain a constant-factor approximation algorithm, based on the primal-dual method. Moreover, we show that the integrality gap of the natural LP relaxation of the problem is \Theta(\log n), where n denotes the number of vertices in the graph.Comment: v2: several minor changes

Lower Bounds for Structuring Unreliable Radio Networks

In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks---a generalization of the standard graph-based model that now includes unreliable links controlled by an adversary. We begin by proving that a natural geographic constraint on the network topology is required to solve these problems efficiently (i.e., in time polylogarthmic in the network size). We then prove the importance of the assumption that nodes are provided advance knowledge of their reliable neighbors (i.e, neighbors connected by reliable links). Combined, these results answer an open question by proving that the efficient MIS and CDS algorithms from [Censor-Hillel, PODC 2011] are optimal with respect to their dual graph model assumptions. They also provide insight into what properties of an unreliable network enable efficient local computation.Comment: An extended abstract of this work appears in the 2014 proceedings of the International Symposium on Distributed Computing (DISC

Emergence of hyperons in failed supernovae: trigger of the black hole formation

We investigate the emergence of strange baryons in the dynamical collapse of a non-rotating massive star to a black hole by the neutrino-radiation hydrodynamical simulations in general relativity. By following the dynamical formation and collapse of nascent proto-neutron star from the gravitational collapse of a 40Msun star adopting a new hyperonic EOS table, we show that the hyperons do not appear at the core bounce but populate quickly at ~0.5-0.7 s after the bounce to trigger the re-collapse to a black hole. They start to show up off center owing to high temperatures and later prevail at center when the central density becomes high enough. The neutrino emission from the accreting proto-neutron star with the hyperonic EOS stops much earlier than the corresponding case with a nucleonic EOS while the average energies and luminosities are quite similar between them. These features of neutrino signal are a potential probe of the emergence of new degrees of freedom inside the black hole forming collapse.Comment: 11 pages, 3 figures, accepted for publication in ApJ

Classical stochastic diffusion theory for thermal desorption from solid surfaces

As a first step in the microscopic study of dynamic processes on surfaces and at interfaces, we have considered the thermal desorption of adsorbed species on solid surfaces. We review recent developments based on a classical stochastic diffusion formulation. Using this theory, we obtained a simple rate expression, R=(Omega0/2pi) f(T)exp(–De/kT), where Omega0 is the surface-adsorbate vibrational frequency and De the dissociation energy. For atoms f(T)=1, whereas for molecules f(T) depends on the parameters for the frustrated rotations at the surface. The effect of coverage on the rate of desorption and the process of desorption into a fluid are also examined. Finally, we discuss the relationship between our theory and the expressions obtained from activated complex (transition-state) theory