We calculate one-loop scattering amplitudes in N=4 super Yang-Mills theory away from the origin of the moduli space and demonstrate that the results are extremely simple, in much the same way as in the conformally invariant theory. Specifically, we c
onsider the model where an SU(2) gauge group is spontaneously broken down to U(1). The complete component Lagrange density of the model is given in a form useful for perturbative calculations. We argue that the scattering amplitudes with massive external states deserve further study. Finally, our work shows that loop corrections can be readily computed in a mass-regulated N=4 theory, which may be relevant in trying to connect weak-coupling results with those at strong coupling, as discussed recently by Alday and Maldacena.
Kinematic investigations are being increasingly deployed in studies of the lowest mass stars and brown dwarfs to investigate their origins, characterize their atmospheres, and examine the evolution of their physical parameters. This article summarize
s the contributions made at the Kinematics of Very Low Mass Dwarfs Splinter Session. Results discussed include analysis of kinematic distributions of M, L and T dwarfs; theoretical tools for interpreting these distributions; identifications of very low mass halo dwarfs and wide companions to nearby stars; radial velocity variability among young and very cool brown dwarfs; and the search and identification of M dwarfs in young moving groups. A summary of discussion points at the conclusion of the Splinter is also presented.
A Dubins path is a shortest path with bounded curvature. The seminal result in non-holonomic motion planning is that (in the absence of obstacles) a Dubins path consists either from a circular arc followed by a segment followed by another arc, or fro
m three circular arcs [Dubins, 1957]. Dubins original proof uses advanced calculus; later, Dubins result was reproved using control theory techniques [Reeds and Shepp, 1990], [Sussmann and Tang, 1991], [Boissonnat, Cerezo, and Leblond, 1994]. We introduce and study a discrete analogue of curvature-constrained motion. We show that shortest bounded-curvature polygonal paths have the same structure as Dubins paths. The properties of Dubins paths follow from our results as a limiting case---this gives a new, discrete proof of Dubins result.
Simulations of core-collapse supernovae (CCSNe) result in successful explosions once the neutrino luminosity exceeds a critical curve, and recent simulations indicate that turbulence further enables explosion by reducing this critical neutrino lumino
sity. We propose a theoretical framework to derive this result and take the first steps by deriving the governing mean-field equations. Using Reynolds decomposition, we decompose flow variables into background and turbulent flows and derive self-consistent averaged equations for their evolution. As basic requirements for the CCSN problem, these equations naturally incorporate steady-state accretion, neutrino heating and cooling, non-zero entropy gradients, and turbulence terms associated with buoyant driving, redistribution, and dissipation. Furthermore, analysis of two-dimensional (2D) CCSN simulations validate these Reynolds-averaged equations, and we show that the physics of turbulence entirely accounts for the differences between 1D and 2D CCSN simulations. As a prelude to deriving the reduction in the critical luminosity, we identify the turbulent terms that most influence the conditions for explosion. Generically, turbulence equations require closure models, but these closure models depend upon the macroscopic properties of the flow. To derive a closure model that is appropriate for CCSNe, we cull the literature for relevant closure models and compare each with 2D simulations. These models employ local closure approximations and fail to reproduce the global properties of neutrino-driven turbulence. Motivated by the generic failure of these local models, we propose an original model for turbulence which incorporates global properties of the flow. This global model accurately reproduces the turbulence profiles and evolution of 2D CCSN simulations.
A bracketing metric entropy bound for the class of Laplace transforms of probability measures on [0,infty) is obtained through its connection with the small deviation probability of a smooth Gaussian process. Our results for the particular smooth Gaussian process seem to be of independent interest.
In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand that work
to include the optimal estimation of several linear parameters from a continuous time series. We show that working in the basis of the thermal driving force both simplifies the calculations and provides additional insight to why various approximate (not optimal) estimation techniques perform as they do. To illustrate this point, we compare the variance in the optimal estimator that we derive for thermal noise with those of two approximate methods which, like the optimal estimator, suppress the contribution to the variance that would come from the irrelevant, resonant motion of the oscillator. We discuss how these methods fare when the dominant noise process is either white displacement noise or noise with power spectral density that is inversely proportional to the frequency ($1/f$ noise). We also construct, in the basis of the driving force, an estimator that performs well for a mixture of white noise and thermal noise. To find the optimal multi-parameter estimators for thermal noise, we derive and illustrate a generalization of traditional matrix methods for parameter estimation that can accommodate continuous data. We discuss how this approach may help refine the design of experiments as they allow an exact, quantitative comparison of the precision of estimated parameters under various data acquisition and data analysis strategies.
Using an [OIII]5007 on-band/off-band filter technique, we identify 109 planetary nebulae (PNe) candidates in M 82, using the FOCAS instrument at the 8.2m Subaru Telescope. The use of ancillary high-resolution HST ACS H-alpha imaging aided in discrimi
nating PNe from contaminants such as supernova remnants and compact HII regions. Once identified, these PNe reveal a great deal about the host galaxy; our analysis covers kinematics, stellar distribution, and distance determination. Radial velocities were determined for 94 of these PNe using a method of slitless spectroscopy, from which we obtain a clear picture of the galaxys rotation. Overall, our results agree with those derived by CO(2-1) and HI measurements that show a falling, near-Keplerian rotation curve. However, we find a subset of our PNe that appear to lie far above the plane (~1 kpc), yet these objects appear to be rotating as fast as objects close to the plane. These objects will require further study to determine if they are members of a halo population, or if they can be interpreted as a manifestation of a thickened disk as a consequence of a past interaction with M 81. In addition, [OIII]5007 emission line photometry of the PNe allows the construction of a planetary nebula luminosity function (PNLF). Our PNLF distance determination for M 82 yields a larger distance than those derived using the TRGB, using Cepheid variable stars in nearby group member M 81, or using the PNLF of M 81. We show that this inconsistency most likely stems from our inability to completely correct for internal extinction imparted by this dusty, starburst galaxy. (Abridged)
(Abridged) We construct a catalog of radio sources detected by the GB6 (6 cm), FIRST and NVSS (20 cm), and WENSS (92 cm) radio surveys, and the SDSS optical survey. The 2.7 million entries in the publicly-available master catalog are comprised of the
closest three FIRST to NVSS matches (within 30 arcsec) and vice-versa, and unmatched sources from each survey. Entries are supplemented by data from the other radio and optical surveys, where available. We perform data analysis a ~3000 deg^2 region of sky where the surveys overlap, which contains 140,000 NVSS-FIRST sources, of which 64,000 are detected by WENSS and 12,000 by GB6. About one third of each sample is detected by SDSS. An automated classification method based on 20 cm fluxes defines three radio morphology classes: complex, resolved, and compact. Radio color-magnitude- morphology diagrams for these classes show structure suggestive of strong underlying physical correlations. Complex and resolved sources tend to have a steep spectral slope (alpha ~ -0.8) that is nearly constant from 6 to 92 cm, while the compact class contains a significant number of flat-spectrum (alpha ~ 0) sources. In the optically-detected sample, quasars dominate the flat-spectrum compact sources while steep-spectrum and resolved objects contain substantial numbers of both quasars and galaxies. Differential radio counts of quasars and galaxies are similar at bright flux levels (>100 mJy at 20 cm), while at fainter levels the quasar counts are significantly reduced below galaxy counts. The optically-undetected sample is strongly biased toward steep-spectrum sources. In samples of quasars and galaxies with SDSS spectra, we find that radio properties such as spectral slope, morphology, and radio loudness are correlated with optical color and luminosity.
In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some
forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate vs current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.
