The Connection Between Thermal and Non-Thermal Emission in Gamma-ray Bursts: General Considerations and GRB090902B as a Case Study

Photospheric (thermal) emission is inherent to the gamma-ray burst (GRB) "fireball" model. We show here, that inclusion of this component in the analysis of the GRB prompt emission phase naturally explains some of the prompt GRB spectra seen by the Fermi satellite over its entire energy band. The sub-MeV peak is explained as multi-color black body emission, and the high energy tail, extending up to the GeV band, results from roughly similar contributions of synchrotron emission, synchrotron self Compton(SSC) and Comptonization of the thermal photons by energetic electrons originating after dissipation of the kinetic energy above the photosphere. We show how this analysis method results in a complete, self consistent picture of the physical conditions at both emission sites of the thermal and non-thermal radiation. We study the connection between the thermal and non-thermal parts of the spectrum, and show how the values of the free model parameters are deduced from the data. We demonstrate our analysis method on GRB090902B: We deduce a Lorentz factor in the range 920 <= \eta <= 1070, photospheric radius r_{ph} ~ 7.2 - 8.4 * 10^{11} cm and dissipation radius r_\gamma >= 3.5 - 4.1 * 10^{15} cm. By comparison to afterglow data, we deduce that a large fraction, epsilon_d ~85% - 95% of the kinetic energy is dissipated, and that large fraction, ~equipartition of this energy is carried by the electrons and the magnetic field. This high value of epsilon_d questions the "internal shock" scenario as the main energy dissipation mechanism for this GRB.Comment: 15 pages, 5 figures; minor revisions, typos corrected. Accepted for publication in MNRA

Control of Four-Level Quantum Coherence via Discrete Spectral Shaping of an Optical Frequency Comb

We present an experiment demonstrating high-resolution coherent control of a four-level atomic system in a closed (diamond) type configuration. A femtosecond frequency comb is used to establish phase coherence between a pair of two-photon transitions in cold Rb atoms. By controlling the spectral phase of the frequency comb we demonstrate the optical phase sensitive response of the diamond system. The high-resolution state selectivity of the comb is used to demonstrate the importance of the signs of dipole moment matrix elements in this type of closed-loop excitation. Finally, the pulse shape is optimized resulting in a 256% increase in the two-photon transition rate by forcing constructive interference between the mode pairs detuned from an intermediate resonance.Comment: 5 pages, 4 figures Submitted to Physical Review Letter

Bias Characterization in Probabilistic Genotype Data and Improved Signal Detection with Multiple Imputation

Missing data are an unavoidable component of modern statistical genetics. Different array or sequencing technologies cover different single nucleotide polymorphisms (SNPs), leading to a complicated mosaic pattern of missingness where both individual genotypes and entire SNPs are sporadically absent. Such missing data patterns cannot be ignored without introducing bias, yet cannot be inferred exclusively from nonmissing data. In genome-wide association studies, the accepted solution to missingness is to impute missing data using external reference haplotypes. The resulting probabilistic genotypes may be analyzed in the place of genotype calls. A general-purpose paradigm, called Multiple Imputation (MI), is known to model uncertainty in many contexts, yet it is not widely used in association studies. Here, we undertake a systematic evaluation of existing imputed data analysis methods and MI. We characterize biases related to uncertainty in association studies, and find that bias is introduced both at the imputation level, when imputation algorithms generate inconsistent genotype probabilities, and at the association level, when analysis methods inadequately model genotype uncertainty. We find that MI performs at least as well as existing methods or in some cases much better, and provides a straightforward paradigm for adapting existing genotype association methods to uncertain data

The variance of identity-by-descent sharing in the Wright-Fisher model

Widespread sharing of long, identical-by-descent (IBD) genetic segments is a hallmark of populations that have experienced recent genetic drift. Detection of these IBD segments has recently become feasible, enabling a wide range of applications from phasing and imputation to demographic inference. Here, we study the distribution of IBD sharing in the Wright-Fisher model. Specifically, using coalescent theory, we calculate the variance of the total sharing between random pairs of individuals. We then investigate the cohort-averaged sharing: the average total sharing between one individual and the rest of the cohort. We find that for large cohorts, the cohort-averaged sharing is distributed approximately normally. Surprisingly, the variance of this distribution does not vanish even for large cohorts, implying the existence of "hyper-sharing" individuals. The presence of such individuals has consequences for the design of sequencing studies, since, if they are selected for whole-genome sequencing, a larger fraction of the cohort can be subsequently imputed. We calculate the expected gain in power of imputation by IBD, and subsequently, in power to detect an association, when individuals are either randomly selected or specifically chosen to be the hyper-sharing individuals. Using our framework, we also compute the variance of an estimator of the population size that is based on the mean IBD sharing and the variance in the sharing between inbred siblings. Finally, we study IBD sharing in an admixture pulse model, and show that in the Ashkenazi Jewish population the admixture fraction is correlated with the cohort-averaged sharing.Comment: Includes Supplementary Materia

Consensus and meta-analysis regulatory networks for combining multiple microarray gene expression datasets

Microarray data is a key source of experimental data for modelling gene regulatory interactions from expression levels. With the rapid increase of publicly available microarray data comes the opportunity to produce regulatory network models based on multiple datasets. Such models are potentially more robust with greater confidence, and place less reliance on a single dataset. However, combining datasets directly can be difficult as experiments are often conducted on different microarray platforms, and in different laboratories leading to inherent biases in the data that are not always removed through pre-processing such as normalisation. In this paper we compare two frameworks for combining microarray datasets to model regulatory networks: pre- and post-learning aggregation. In pre-learning approaches, such as using simple scale-normalisation prior to the concatenation of datasets, a model is learnt from a combined dataset, whilst in post-learning aggregation individual models are learnt from each dataset and the models are combined. We present two novel approaches for post-learning aggregation, each based on aggregating high-level features of Bayesian network models that have been generated from different microarray expression datasets. Meta-analysis Bayesian networks are based on combining statistical confidences attached to network edges whilst Consensus Bayesian networks identify consistent network features across all datasets. We apply both approaches to multiple datasets from synthetic and real (Escherichia coli and yeast) networks and demonstrate that both methods can improve on networks learnt from a single dataset or an aggregated dataset formed using a standard scale-normalisation

Nonlinear interactions with an ultrahigh flux of broadband entangled photons

We experimentally demonstrate sum-frequency generation (SFG) with entangled photon-pairs, generating as many as 40,000 SFG photons per second, visible even to the naked eye. The nonclassical nature of the interaction is exhibited by a linear intensity-dependence of the nonlinear process. The key element in our scheme is the generation of an ultrahigh flux of entangled photons while maintaining their nonclassical properties. This is made possible by generating the down-converted photons as broadband as possible, orders of magnitude wider than the pump. This approach is readily applicable for other nonlinear interactions, and may be applicable for various quantum-measurement tasks.Comment: 4 pages, 2 figures, Accepted to Phys. Rev. Let

Piecewise adiabatic population transfer in a molecule via a wave packet

We propose a class of schemes for robust population transfer between quantum states that utilize trains of coherent pulses and represent a generalized adiabatic passage via a wave packet. We study piecewise Stimulated Raman Adiabatic Passage with pulse-to-pulse amplitude variation, and piecewise chirped Raman passage with pulse-to-pulse phase variation, implemented with an optical frequency comb. In the context of production of ultracold ground-state molecules, we show that with almost no knowledge of the excited potential, robust high-efficiency transfer is possibleComment: 4 pages, 5 figures. Submitted to Phys. Rev. Let

Spectral components in the bright, long GRB 061007: properties of the photosphere and the nature of the outflow

We present a time-resolved spectral analysis of the bright, long GRB 061007 (z=1.261) using Swift BAT and Suzaku WAM data. We find that the prompt emission of GRB 061007 can be equally well explained by a photospheric component together with a power law as by a Band function, and we explore the implications of the former model. The photospheric component, which we model with a multicolour blackbody, dominates the emission and has a very stable shape throughout the burst. This component provides a natural explanation for the hardness-intensity correlation seen within the burst and also allows us to estimate the bulk Lorentz factor and the radius of the photosphere. The power-law component dominates the fit at high energies and has a nearly constant slope of -1.5. We discuss the possibility that this component is of the same origin as the high-energy power laws recently observed in some Fermi LAT bursts.Comment: Accepted for publication in MNRA

On the Gamma Ray Burst Origin of Extremely Energetic Cosmic Rays

Air shower experiments have detected cosmic ray events of energies upto 300 EeV. Most likely these cosmic rays have originated from compact objects. Their exact sources are yet to be identified. It has been suggested before that gamma ray bursts are possible sources of ultra-high energy cosmic rays. The two models of gamma ray burst emissions most often discussed are the internal and external shock models. We have calculated the proton spectrum above 60EeV from all gamma ray bursts distributed upto a redshift of 0.02 in the internal shock model assuming redshift and luminosity distributions consistent with observations, log normal distributions for their values of Lorentz factors, variability times and duration of bursts. Within the external shock model we have calculated the proton flux above 60EeV from all nearby gamma ray bursts assuming log normal distributions in their values of total energies, Lorentz factors at the deceleration epoch and compared with the observed data. We find that gamma ray bursts can produce cosmic ray proton flux comparable to the flux observed by the Pierre Auger experiment both within the internal and external shock models. We have also studied the dependence of the maximum proton energies and the cooling breaks in the proton spectrum on the various parameters like Lorentz factor, energy of the GRB fireball, variability time (in case of internal shocks), ambient particle density (in case of external shocks). Our results are important to understand how the various observable parameters determine which mechanism e.g. $p\gamma$ interactions, synchrotron cooling of protons will dominate over one another inside these sources.Comment: 16pages,8figures. version accepted in Astroparticle Physic

The observable effects of a photospheric component on GRB's and XRF's prompt emission spectrum

A thermal radiative component is likely to accompany the first stages of the prompt emission of Gamma-ray bursts (GRB's) and X-ray flashes (XRF's). We analyze the effect of such a component on the observable spectrum, assuming that the observable effects are due to a dissipation process occurring below or near the thermal photosphere. We consider both the internal shock model and a 'slow heating' model as possible dissipation mechanisms. For comparable energy densities in the thermal and the leptonic component, the dominant emission mechanism is Compton scattering. This leads to a nearly flat energy spectrum (\nu F_\nu \propto \nu^0) above the thermal peak at ~10-100 keV and below 10-100 MeV, for a wide range of optical depths 0.03 <~ \tau_{\gamma e} <~ 100, regardless of the details of the dissipation mechanism or the strength of the magnetic field. At lower energies steep slopes are expected, while above 100 MeV the spectrum depends on the details of the dissipation process. For higher values of the optical depth, a Wien peak is formed at 100 keV - 1 MeV, and no higher energy component exists. For any value of \tau_{\gamma e}, the number of pairs produced does not exceed the baryon related electrons by a factor larger than a few. We conclude that dissipation near the thermal photosphere can naturally explain both the steep slopes observed at low energies and a flat spectrum above 10 keV, thus providing an alternative scenario to the optically thin synchrotron - SSC model.Comment: Discussion added on the results of Baring & Braby (2004); Accepted for publication in Ap.