Topology Control for Maintaining Network Connectivity and Maximizing Network Capacity Under the Physical Model

In this paper we study the issue of topology control under the physical Signal-to-Interference-Noise-Ratio (SINR) model, with the objective of maximizing network capacity. We show that existing graph-model-based topology control captures interference inadequately under the physical SINR model, and as a result, the interference in the topology thus induced is high and the network capacity attained is low. Towards bridging this gap, we propose a centralized approach, called Spatial Reuse Maximizer (MaxSR), that combines a power control algorithm T4P with a topology control algorithm P4T. T4P optimizes the assignment of transmit power given a fixed topology, where by optimality we mean that the transmit power is so assigned that it minimizes the average interference degree (defined as the number of interferencing nodes that may interfere with the on-going transmission on a link) in the topology. P4T, on the other hand, constructs, based on the power assignment made in T4P, a new topology by deriving a spanning tree that gives the minimal interference degree. By alternately invoking the two algorithms, the power assignment quickly converges to an operational point that maximizes the network capacity. We formally prove the convergence of MaxSR. We also show via simulation that the topology induced by MaxSR outperforms that derived from existing topology control algorithms by 50%-110% in terms of maximizing the network capacity

The SIC Question: History and State of Play

Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott's code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research.Comment: 16 pages, 1 figure, many references; v3: updating bibliography, dimension eight hundred forty fou

Ultrasoft NLL Running of the Nonrelativistic O(v) QCD Quark Potential

Using the nonrelativistic effective field theory vNRQCD, we determine the contribution to the next-to-leading logarithmic (NLL) running of the effective quark-antiquark potential at order v (1/mk) from diagrams with one potential and two ultrasoft loops, v being the velocity of the quarks in the c.m. frame. The results are numerically important and complete the description of ultrasoft next-to-next-to-leading logarithmic (NNLL) order effects in heavy quark pair production and annihilation close to threshold.Comment: 25 pages, 7 figures, 3 tables; minor modifications, typos corrected, references added, footnote adde

Homogenization for advection-diffusion in a perforated domain

The volume of a Wiener sausage constructed from a diffusion process with periodic, mean-zero, divergence-free velocity field, in dimension 3 or more, is shown to have a non-random and positive asymptotic rate of growth. This is used to establish the existence of a homogenized limit for such a diffusion when subject to Dirichlet conditions on the boundaries of a sparse and independent array of obstacles. There is a constant effective long-time loss rate at the obstacles. The dependence of this rate on the form and intensity of the obstacles and on the velocity field is investigated. A Monte Carlo algorithm for the computation of the volume growth rate of the sausage is introduced and some numerical results are presented for the Taylor–Green velocity field

Implementing invariant mass cuts and finite lifetime effects in top-antitop production at threshold

The effects of the finite top quark width in the top pair production cross section close to the threshold are discussed in this talk. We introduce a $t\bar{t}$ cross section with a cut on the invariant masses of the top and antitop that can be calculated theoretically with effective field theory (EFT) methods. The matching procedure to implement the physical phase-space boundaries in the NRQCD framework (``phase-space matching'') is briefly outlined.Comment: 4 pages, 4 figures. Talk given at the 14th International QCD Conference (Montpellier 7-12th July 2008

Three-Loop Anomalous Dimension of the Heavy Quark Pair Production Current in Non-Relativistic QCD

The three-loop non-mixing contributions to the anomalous dimension of the leading order quark pair production current in non-relativistic QCD are computed. It is demonstrated that the renormalization procedure can only be carried out consistently if the dynamics of both soft and the ultrasoft degrees of freedom is present for all scales below the heavy quark mass, and if the soft and ultrasoft renormalization scales are always correlated.Comment: 19 pages, revtex, 5 postscript figures include

Retrieval of interatomic separations of molecules from laser-induced high-order harmonic spectra

We illustrate an iterative method for retrieving the internuclear separations of N$_2$, O$_2$ and CO$_2$ molecules using the high-order harmonics generated from these molecules by intense infrared laser pulses. We show that accurate results can be retrieved with a small set of harmonics and with one or few alignment angles of the molecules. For linear molecules the internuclear separations can also be retrieved from harmonics generated using isotropically distributed molecules. By extracting the transition dipole moment from the high-order harmonic spectra, we further demonstrated that it is preferable to retrieve the interatomic separation iteratively by fitting the extracted dipole moment. Our results show that time-resolved chemical imaging of molecules using infrared laser pulses with femtosecond temporal resolutions is possible.Comment: 14 pages, 9 figure