Low energy expansion of the four-particle genus-one amplitude in type II superstring theory

A diagrammatic expansion of coefficients in the low-momentum expansion of the genus-one four-particle amplitude in type II superstring theory is developed. This is applied to determine coefficients up to order s^6R^4 (where s is a Mandelstam invariant and R^4 the linearized super-curvature), and partial results are obtained beyond that order. This involves integrating powers of the scalar propagator on a toroidal world-sheet, as well as integrating over the modulus of the torus. At any given order in s the coefficients of these terms are given by rational numbers multiplying multiple zeta values (or Euler--Zagier sums) that, up to the order studied here, reduce to products of Riemann zeta values. We are careful to disentangle the analytic pieces from logarithmic threshold terms, which involves a discussion of the conditions imposed by unitarity. We further consider the compactification of the amplitude on a circle of radius r, which results in a plethora of terms that are power-behaved in r. These coefficients provide boundary `data' that must be matched by any non-perturbative expression for the low-energy expansion of the four-graviton amplitude. The paper includes an appendix by Don Zagier.Comment: JHEP style. 6 eps figures. 50 page

Supernova neutrinos and antineutrinos: ternary luminosity diagram and spectral split patterns

In core-collapse supernovae, the nu_e and anti-nu_e species may experience collective flavor swaps to non-electron species nu_x, within energy intervals limited by relatively sharp boundaries ("splits"). These phenomena appear to depend sensitively upon the initial energy spectra and luminosities. We investigate the effect of generic variations of the fractional luminosities (l_e, l_{anti-e}, l_x) with respect to the usual "energy equipartition" case (1/6, 1/6, 1/6), within an early-time supernova scenario with fixed thermal spectra and total luminosity. We represent the constraint l_e+l_{anti-e}+4l_x=1 in a ternary diagram, which is explored via numerical experiments (in single-angle approximation) over an evenly-spaced grid of points. In inverted hierarchy, single splits arise in most cases, but an abrupt transition to double splits is observed for a few points surrounding the equipartition one. In normal hierarchy, collective effects turn out to be unobservable at all grid points but one, where single splits occur. Admissible deviations from equipartition may thus induce dramatic changes in the shape of supernova (anti)neutrino spectra. The observed patterns are interpreted in terms of initial flavor polarization vectors (defining boundaries for the single/double split transitions), lepton number conservation, and minimization of potential energy.Comment: 24 pages, including 14 figures (1 section with 2 figures added). Accepted for publication in JCA

Approximate conditional distributions of distances between nodes in a two-dimensional sensor network

When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph, defined to be the number of edges on a shortest path between them. In this paper, we consider a network of sensors placed uniformly at random in a two-dimensional region and study two conditional distributions related to these distances. The first is the probability distribution of distances in the graph, conditioned on Euclidean distances; the other is the probability density function associated with Euclidean distances, conditioned on distances in the graph. We study these distributions both analytically (when feasible) and by means of simulations. To the best of our knowledge, our results constitute the first of their kind and open up the possibility of discovering improved solutions to certain sensor-network problems, as for example sensor localization

Closed-Form transformation between geodetic and ellipsoidal coordinates

We present formulas for direct closed-form transformation between geodetic coordinates(Φ, λ, h) and ellipsoidal coordinates (β, λ, u) for any oblate ellipsoid of revolution.These will be useful for those dealing with ellipsoidal representations of the Earth's gravityfield or other oblate ellipsoidal figures. The numerical stability of the transformations for nearpolarand near-equatorial regions is also considered

HMM model selection issues for soccer video

There has been a concerted effort from the Video Retrieval community to develop tools that automate the annotation process of Sports video. In this paper, we provide an in-depth investigation into three Hidden Markov Model (HMM) selection approaches. Where HMM, a popular indexing framework, is often applied in a ad hoc manner. We investigate what effect, if any, poor HMM selection can have on future indexing performance when classifying specific audio content. Audio is a rich source of information that can provide an effective alternative to high dimensional visual or motion based features. As a case study, we also illustrate how a superior HMM framework optimised using a Bayesian HMM selection strategy, can both segment and then classify Soccer video, yielding promising results