On the origin of >10 GeV photons in gamma-ray burst afterglows

Fermi/LAT has detected long-lasting high-energy photons (>100 MeV) from gamma-ray bursts (GRBs), with the highest energy photons reaching about 100 GeV. One proposed scenario is that they are produced by high-energy electrons accelerated in GRB forward shocks via synchrotron radiation. We study the maximum synchrotron photon energy in this scenario, considering the properties of the microturbluence magnetic fields behind the shock, as revealed by recent Particle-in-Cell simulations and theoretical analyses of relativistic collisionless shocks. Due to the small-scale nature of the micro-turbulent magnetic field, the Bohm acceleration approximation breaks down at such high energies. This effect leads to a typical maximum synchrotron photon of a few GeV at 100 s after the burst and this maximum synchrotron photon energy decreases quickly with time. We show that the fast decrease of the maximum synchrotron photon energy leads to a fast decay of the synchrotron flux. The 10-100 GeV photons detected after the prompt phase can not be produced by the synchrotron mechanism. They could originate from the synchrotron self-Compton emission of the early afterglow if the circum-burst density is sufficiently large, or from the external inverse-Compton process in the presence of central X-ray emission, such as X-ray flares and prompt high-latitude X-ray emission.Comment: 13 pages, 3 figures, accepted by ApJ Letter

The geometry of kernelized spectral clustering

Clustering of data sets is a standard problem in many areas of science and engineering. The method of spectral clustering is based on embedding the data set using a kernel function, and using the top eigenvectors of the normalized Laplacian to recover the connected components. We study the performance of spectral clustering in recovering the latent labels of i.i.d. samples from a finite mixture of nonparametric distributions. The difficulty of this label recovery problem depends on the overlap between mixture components and how easily a mixture component is divided into two nonoverlapping components. When the overlap is small compared to the indivisibility of the mixture components, the principal eigenspace of the population-level normalized Laplacian operator is approximately spanned by the square-root kernelized component densities. In the finite sample setting, and under the same assumption, embedded samples from different components are approximately orthogonal with high probability when the sample size is large. As a corollary we control the fraction of samples mislabeled by spectral clustering under finite mixtures with nonparametric components.Comment: Published at http://dx.doi.org/10.1214/14-AOS1283 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Anomalous Higgs couplings in angular asymmetries of H --> Zl+l- and e+e- --> HZ

We study in detail the impact of anomalous Higgs couplings in angular asymmetries of the crossing-symmetric processes H --> Zl+l- and e+e- --> HZ. Beyond Standard Model physics is parametrized in terms of the SU(3)xSU(2)_LxU(1)_Y dimension-six effective Lagrangian. In the light of present bounds on d = 6 interactions we study how angular asymmetries can reveal non-standard CP-even and CP-odd couplings. We provide approximate expressions to all observables of interest making transparent their dominant dependence on anomalous couplings. We show that some asymmetries may reveal BSM effects that are hidden in other observables. In particular, CP-even and CP-odd d = 6 HZgamma couplings as well as (to a lesser extent) HZll contact interactions can generate asymmetries at the several percent level, while having small or no effects on the di-lepton invariant mass spectrum of H --> Zl+l-. Finally, the higher di-lepton invariant mass probed in e+e- --> HZ leads to interesting differences in the asymmetries with respect to those of H --> Zl+l- that may lead to complementary anomalous coupling searches at the LHC and e+e- colliders.Comment: 34 pages, 14 figures. Minor changes, one additional figure (Fig. 5), one reference added (Ref. [34]). Matches published versio

Statistical guarantees for the EM algorithm: From population to sample-based analysis

We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in the limit of infinite data), followed by results that apply to updates based on a finite set of samples. First, we characterize the domain of attraction of any global maximizer of the population likelihood. This characterization is based on a novel view of the EM updates as a perturbed form of likelihood ascent, or in parallel, of the gradient EM updates as a perturbed form of standard gradient ascent. Leveraging this characterization, we then provide non-asymptotic guarantees on the EM and gradient EM algorithms when applied to a finite set of samples. We develop consequences of our general theory for three canonical examples of incomplete-data problems: mixture of Gaussians, mixture of regressions, and linear regression with covariates missing completely at random. In each case, our theory guarantees that with a suitable initialization, a relatively small number of EM (or gradient EM) steps will yield (with high probability) an estimate that is within statistical error of the MLE. We provide simulations to confirm this theoretically predicted behavior