Algorithmic and enumerative aspects of the Moser-Tardos distribution

Moser & Tardos have developed a powerful algorithmic approach (henceforth "MT") to the Lovasz Local Lemma (LLL); the basic operation done in MT and its variants is a search for "bad" events in a current configuration. In the initial stage of MT, the variables are set independently. We examine the distributions on these variables which arise during intermediate stages of MT. We show that these configurations have a more or less "random" form, building further on the "MT-distribution" concept of Haeupler et al. in understanding the (intermediate and) output distribution of MT. This has a variety of algorithmic applications; the most important is that bad events can be found relatively quickly, improving upon MT across the complexity spectrum: it makes some polynomial-time algorithms sub-linear (e.g., for Latin transversals, which are of basic combinatorial interest), gives lower-degree polynomial run-times in some settings, transforms certain super-polynomial-time algorithms into polynomial-time ones, and leads to Las Vegas algorithms for some coloring problems for which only Monte Carlo algorithms were known. We show that in certain conditions when the LLL condition is violated, a variant of the MT algorithm can still produce a distribution which avoids most of the bad events. We show in some cases this MT variant can run faster than the original MT algorithm itself, and develop the first-known criterion for the case of the asymmetric LLL. This can be used to find partial Latin transversals -- improving upon earlier bounds of Stein (1975) -- among other applications. We furthermore give applications in enumeration, showing that most applications (where we aim for all or most of the bad events to be avoided) have many more solutions than known before by proving that the MT-distribution has "large" min-entropy and hence that its support-size is large

Algorithms for Constructing Overlay Networks For Live Streaming

We present a polynomial time approximation algorithm for constructing an overlay multicast network for streaming live media events over the Internet. The class of overlay networks constructed by our algorithm include networks used by Akamai Technologies to deliver live media events to a global audience with high fidelity. We construct networks consisting of three stages of nodes. The nodes in the first stage are the entry points that act as sources for the live streams. Each source forwards each of its streams to one or more nodes in the second stage that are called reflectors. A reflector can split an incoming stream into multiple identical outgoing streams, which are then sent on to nodes in the third and final stage that act as sinks and are located in edge networks near end-users. As the packets in a stream travel from one stage to the next, some of them may be lost. A sink combines the packets from multiple instances of the same stream (by reordering packets and discarding duplicates) to form a single instance of the stream with minimal loss. Our primary contribution is an algorithm that constructs an overlay network that provably satisfies capacity and reliability constraints to within a constant factor of optimal, and minimizes cost to within a logarithmic factor of optimal. Further in the common case where only the transmission costs are minimized, we show that our algorithm produces a solution that has cost within a factor of 2 of optimal. We also implement our algorithm and evaluate it on realistic traces derived from Akamai's live streaming network. Our empirical results show that our algorithm can be used to efficiently construct large-scale overlay networks in practice with near-optimal cost

Recovery of atmospheric refractivity profiles from simulated satellite-to-satellite tracking data

Techniques for recovering atmospheric refractivity profiles from simulated satellite-to-satellite tracking data are documented. Examples are given using the geometric configuration of the ATS-6/NIMBUS-6 Tracking Experiment. The underlying refractivity model for the lower atmosphere has the spherically symmetric form N = exp P(s) where P(s) is a polynomial in the normalized height s. For the simulation used, the Herglotz-Wiechert technique recovered values which were 0.4% and 40% different from the input values at the surface and at a height of 33 kilometers, respectively. Using the same input data, the model fitting technique recovered refractivity values 0.05% and 1% different from the input values at the surface and at a height of 50 kilometers, respectively. It is also shown that if ionospheric and water vapor effects can be properly modelled or effectively removed from the data, pressure and temperature distributions can be obtained

Dispersive analysis of omega --> 3pi and phi --> 3pi decays

We study the three-pion decays of the lightest isoscalar vector mesons, omega and phi, in a dispersive framework that allows for a consistent description of final-state interactions between all three pions. Our results are solely dependent on the phenomenological input for the pion-pion P-wave scattering phase shift. We predict the Dalitz plot distributions for both decays and compare our findings to recent measurements of the phi --> 3pi Dalitz plot by the KLOE and CMD-2 collaborations. Dalitz plot parameters for future precision measurements of omega --> 3pi are predicted. We also calculate the pi-pi P-wave inelasticity contribution from omega-pi intermediate states.Comment: 23 pages, 18 figures; discussion extended, Appendix D added, matches version published in EPJ

Global Wilson-Fisher fixed points

The Wilson-Fisher fixed point with $O(N)$ universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed point solutions to leading order in the derivative expansion for real or purely imaginary fields with moderate numerical effort. Universal and non-universal quantitites such as scaling exponents and mass ratios are computed, for all $N$, together with local fixed point coordinates, radii of convergence, and parameters which control the asymptotic behaviour of the effective action. We also explain when and why finite-$N$ results do not converge pointwise towards the exact infinite-$N$ limit. In the regime of purely imaginary fields, a new link between singularities of fixed point effective actions and singularities of their counterparts by Polchinski are established. Implications for other theories are indicated.Comment: 28 pages, 10 figures, v2: explanations and refs added, to appear (NPB

Lattice Study of the Extent of the Conformal Window in Two-Color Yang-Mills Theory

We perform a lattice calculation of the Schr\"odinger functional running coupling in SU(2) Yang-Mills theory with six massless Wilson fermions in the fundamental representation. The aim of this work is to determine whether the above theory has an infrared fixed point. Due to sensitivity of the $SF$ renormalized coupling to the tuning of the fermion bare mass we were unable to reliably extract the running coupling for stronger bare couplings