Uniform Rectifiability and Harmonic Measure III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains

Let $E\subset \mathbb{R}^{n+1}$, $n\ge 2$, be a closed, Ahlfors-David regular set of dimension $n$ satisfying the "Riesz Transform bound" $$\sup_{\varepsilon>0}\int_E\left|\int_{\{y\in E:|x-y|>\varepsilon\}}\frac{x-y}{|x-y|^{n+1}} f(y) dH^n(y)\right|^2 dH^n(x) \leq C \int_E|f|^2 dH^n .$$ Assume further that $E$ is the boundary of a domain $\Omega\subset \mathbb{R}^{n+1}$ satisfying the Harnack Chain condition plus an interior (but not exterior) Corkscrew condition. Then $E$ is uniformly rectifiable

The Comparison of the Swift Gamma-Ray Bursts With and Without Measured Redshifts

Gamma-ray bursts, detected by the Swift satellite, are separated into two samples: the bursts with and without determined redshifts. These two samples are compared by the standard Student t-test and F-test. We have compared the dispersions and the mean values of the durations, peak fluxes and fluences in order to find any differences among these two samples. No essential differences were found.Comment: Published in the Proceedings of the 4th Heidelberg International Symposium on High Energy Gamma-Ray Astronomy, 200

Chance, long tails, and inference: a non-Gaussian, Bayesian theory of vocal learning in songbirds

Traditional theories of sensorimotor learning posit that animals use sensory error signals to find the optimal motor command in the face of Gaussian sensory and motor noise. However, most such theories cannot explain common behavioral observations, for example that smaller sensory errors are more readily corrected than larger errors and that large abrupt (but not gradually introduced) errors lead to weak learning. Here we propose a new theory of sensorimotor learning that explains these observations. The theory posits that the animal learns an entire probability distribution of motor commands rather than trying to arrive at a single optimal command, and that learning arises via Bayesian inference when new sensory information becomes available. We test this theory using data from a songbird, the Bengalese finch, that is adapting the pitch (fundamental frequency) of its song following perturbations of auditory feedback using miniature headphones. We observe the distribution of the sung pitches to have long, non-Gaussian tails, which, within our theory, explains the observed dynamics of learning. Further, the theory makes surprising predictions about the dynamics of the shape of the pitch distribution, which we confirm experimentally

On the Intermediate Subgroup of the Gamma-Ray Bursts in the Swift Database

A sample of 286 gamma-ray bursts, detected by Swift satellite, is studied statistically by the chi^2 test and the Student t-test, respectively. The short and long subgroups are well detected in the Swift data. But no intermediate subgroup is seen. The non-detection of this subgroup in the Swift database can be explained, once it is assumed that in the BATSE database the short and the intermediate subgroups form a common subclass.Comment: Published in 4th Heidelberg International Symposium on High Energy Gamma-Ray Astronomy, 200

The conditional process model of mindfulness and emotion regulation: An empirical test

BACKGROUND: The conditional process model (CPM) of mindfulness and emotion regulation posits that specific mediators and moderators link these constructs to mental health outcomes. The current study empirically examined the central tenets of the CPM, which posit that nonreactivity moderates the indirect effect of observation on symptoms of emotional disorders through cognitive emotion regulation strategies. METHODS: A clinical sample (n=1667) of individuals from Japan completed a battery of self-report instruments. Several path analyses were conducted to determine whether cognitive emotion regulation strategies mediate the relationship between observation and symptoms of individual emotional disorders, and to determine whether nonreactivity moderated these indirect effects. RESULTS: Results provided support the CPM. Specifically, nonreactivity moderated the indirect effect of observation on symptoms through reappraisal, but it did not moderate the indirect effect of observation on symptoms through suppression. LIMITATIONS: Causal interpretations are limited, and cultural considerations must be acknowledged given the Japanese sample CONCLUSIONS: These results underscore the potential importance of nonreactivity and emotion regulation as targets for interventions.R01 AT007257 - NCCIH NIH HHS; R34 MH099311 - NIMH NIH HH

Cavity-enhanced Raman Microscopy of Individual Carbon Nanotubes

Raman spectroscopy reveals chemically specific information and provides label-free insight into the molecular world. However, the signals are intrinsically weak and call for enhancement techniques. Here, we demonstrate Purcell enhancement of Raman scattering in a tunable high-finesse microcavity, and utilize it for molecular diagnostics by combined Raman and absorption imaging. Studying individual single-wall carbon nanotubes, we identify crucial structural parameters such as nanotube radius, electronic structure and extinction cross-section. We observe a 320-times enhanced Raman scattering spectral density and an effective Purcell factor of 6.2, together with a collection efficiency of 60%. Potential for significantly higher enhancement, quantitative signals, inherent spectral filtering and absence of intrinsic background in cavity-vacuum stimulated Raman scattering render the technique a promising tool for molecular imaging. Furthermore, cavity-enhanced Raman transitions involving localized excitons could potentially be used for gaining quantum control over nanomechanical motion and open a route for molecular cavity optomechanics