A chain rule for the expected suprema of Gaussian processes

The expected supremum of a Gaussian process indexed by the image of an index set under a function class is bounded in terms of separate properties of the index set and the function class. The bound is relevant to the estimation of nonlinear transformations or the analysis of learning algorithms whenever hypotheses are chosen from composite classes, as is the case for multi-layer models

The Evolution of Multi-component Visual Signals in Darters (genus Etheostoma)

As complex traits evolve, each component of the trait may be under different selection pressures and could respond independently to distinct evolutionary forces. We used comparative methods to examine patterns of evolution in multiple components of a complex courtship signal in darters, specifically addressing the question of how nuptial coloration evolves across different areas of the body. Using spectral reflectance, we defined 4 broad color classes present on the body and fins of 17 species of freshwater fishes (genus Etheostoma) and quantified differences in hue within each color class. Ancestral state reconstruction suggests that most color traits were expressed in the most recent common ancestor of sampled species and that differences among species are mostly due to losses in coloration. The evolutionary lability of coloration varied across body regions; we found significant phylogenetic signal for orange color on the body but not for most colors on fins. Finally, patterns of color evolution and hue of the colors were correlated among the two dorsal fins and between the anterior dorsal and anal fins, but not between any of the fins and the body. The observed patterns support the hypothesis that different components of complex signals may be subject to distinct evolutionary pressures, and suggests that the combination of behavioral displays and morphology in communication may have a strong influence on patterns of signal evolution [Current Zoology 57 (2): 125–139, 2011]

Convex recovery of a structured signal from independent random linear measurements

This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with recent results for standard Gaussian measurements, but the argument applies to a much wider class of measurement ensembles. To demonstrate the power of this approach, the paper presents a short analysis of phase retrieval by trace-norm minimization. The key technical tool is a framework, due to Mendelson and coauthors, for bounding a nonnegative empirical process.Comment: 18 pages, 1 figure. To appear in "Sampling Theory, a Renaissance." v2: minor corrections. v3: updated citations and increased emphasis on Mendelson's contribution

Radio Spectral Index Analysis and Classes of Ejection in LS I +61 303

LS I +61303 is a gamma-ray binary with periodic radio outbursts coincident with the orbital period of P=26.5 d. The origin of the radio emission is unclear,it could be due either to a jet, as in microquasars, or to the shock boundary between the Be star and a possible pulsar wind. We here analyze the radio spectral index over 6.7 yr from Green Bank Interferometer data at 2.2 GHz and 8.3 GHz. We find two new characteristics in the radio emission. The first characteristic is that the periodic outbursts indeed consist of two consecutive outbursts; the first outburst is optically thick, whereas the second outburst is optically thin. The spectrum of LS I +61 303 is well reproduced by the shock-in-jet model commonly used in the context of microquasars and AGNs: the optically thin spectrum is due to shocks caused by relativistic plasma ("transient jet") traveling through a pre-existing much slower steady flow ("steady jet"). This steady flow is responsible for the preceding optically thick spectrum. The second characteristic we find is that the observed spectral evolution, from optically thick to optically thin emission, occurs twice during the orbital period. We observed this occurrence at the orbital phase of the main 26.5 d outburst and also at an earlier phase, shifted by $\Delta \Phi \sim$ 0.3 (i.e almost 8 days before). We show that this result qualitatively and quantitatively agrees with the two-peak accretion/ejection model proposed in the past for LS I +61303. We conclude that the radio emission in LS I +61303 originates from a jet and suggest that the variable TeV emission comes from the usual Compton losses expected as an important by-product in the shock-in-jet theory.Comment: 27 pages, 7 figures, accepted for publication in Ap

Velocity Anisotropy Of Two Deep Crystalline Samples

Using ultrasonic velocity measurements taken over a multiplicity of directions we show that samples exhibit weak to moderate anisotropy of seismic velocities. We further define the anisotropic geometry with high resolution scanning electron microscopy. Our data indicate that one sample, a granite, is transversely anisotropic, and that the presence of fine to moderately fine microcracks is the most important factor effecting the velocities. We model the angular velocity dependence using 5 elastic constants and show that all 9 observed velocities fit these predictions to within 0.1 km/s. We are unable to obtain similar fits to a second sample, a mica-schist, in the same fashion. SEM observations indicate this rock displays orthorhombic symmetry. We made additional velocity measurements in order to calculate 9 elastic constants, and found that the predicted angular velocity dependence agreed much better with our velocity observations.Massachusetts Institute of Technology. Full Waveform Acoustic Logging ConsortiumEnte nazionale per l'energia elettric