Implications of long tails in the distribution of mutant effects

Long-tailed distributions possess an in nite variance, yet a nite sample that is drawn from such a distribution has a nite variance. In this work we consider a model of a population subject to mutation, selection and drift. We investigate the implications of a long-tailed distribution of mutant allelic e¤ects on the distribution of genotypic e¤ects in a model with a continuum of allelic e¤ects. While the analysis is confined to asexual populations, it does also have implications for sexual populations. We obtain analytical results for a selectively neutral population as well as one subject to selection. We supplement these analytical results with numerical simulations, to take into account genetic drift. We nd that a long-tailed distribution of mutant e¤ects may a¤ect both the equilibrium and the evolutionary adaptive behaviour of a population

Near-periodic substitution and the genetic variance induced by environmental change

We investigate a model that describes the evolution of a diploid sexual population in a changing environment. Individuals have discrete generations and are subject to selection on the phenotypic value of a quantitative trait, which is controlled by a finite number of bialleic loci. Environmental change is taken to lead to a uniformly changing optimal phenotypic value. The population continually adapts to the changing environment, by allelic substitution, at the loci controlling the trait. We investigate the detailed interrelation between the process of allelic substitution and the adaptation and variation of the population, via infinite population calculations and finite population simulations. We find a simple relation between the substitution rate and the rate of change of the optimal phenotypic value

Neutral beam model for the anomalous gamma-ray emission component in GRB 941017

Gonz\'alez et al. (2003) have reported the discovery of an anomalous radiation component from ~ 1 -- 200 MeV in GRB 941017. This component varies independently of and contains > 3 times the energy found in the prompt ~ 50 keV -- 1 MeV radiation component that is well described by the relativistic synchrotron-shock model. Acceleration of hadrons to very high energies can give rise to two additional emission components, one produced inside the GRB blast wave and one associated with an escaping beam of ultra-high energy (UHE; > 10^{14} eV) neutrons, gamma rays, and neutrinos. The first component extending to ~ 100 MeV is from a pair-photon cascade induced by photomeson processes with the internal synchrotron photons coincident with the prompt radiation. The outflowing UHE neutral beam can undergo further interactions with external photons from the backscattered photon field to produce a beam of hyper-relativistic electrons that lose most of their energy during a fraction of a gyroperiod in the assumed Gauss-strength magnetic fields of the circumburst medium. The synchrotron radiation of these electrons has a spectrum with vF_v index equal to +1 that can explain the anomalous component in GRB 941017. This interpretation of the spectrum of GRB 941017 requires a high baryon load of the accelerated particles in GRB blast waves. It implies that most of the radiation associated with the anomalous component is released at > 500 MeV, suitable for observations with GLAST, and with a comparable energy fluence in ~100 TeV neutrinos that could be detected with a km-scale neutrino telescope like IceCube.Comment: 4 pages, 1 figure, minor corrections, Astronomy and Astrophysics Letters, in pres

Improving the Convergence of an Iterative Algorithm Proposed By Waxman

In the iterative algorithm recently proposed by Waxman for solving eigenvalue problems, we point out that the convergence rate may be improved. For many non-singular symmetric potentials which vanish asymptotically, a simple analytical relationship between the coupling constant of the potential and the ground state eigenvalue is obtained which can be used to make the algorithm more efficient

Efficiency and spectrum of internal gamma-ray burst shocks

We present an analysis of the Internal Shock Model of GRBs, where gamma-rays are produced by internal shocks within a relativistic wind. We show that observed GRB characteristics impose stringent constraints on wind and source parameters. We find that a significant fraction, of order 20 %, of the wind kinetic energy can be converted to radiation, provided the distribution of Lorentz factors within the wind has a large variance and provided the minimum Lorentz factor is higher than 10^(2.5)L_(52)^(2/9), where L=10^(52)L_(52)erg/s is the wind luminosity. For a high, >10 %, efficiency wind, spectral energy breaks in the 0.1 to 1 MeV range are obtained for sources with dynamical time R/c < 1 ms, suggesting a possible explanation for the observed clustering of spectral break energies in this range. The lower limit to wind Lorenz factor and the upper limit, around (R/10^7 cm)^(-5/6) MeV to observed break energies are set by Thomson optical depth due to electron positron pairs produced by synchrotron photons. Natural consequences of the model are absence of bursts with peak emission energy significantly exceeding 1 MeV, and existence of low luminosity bursts with low, 1 keV to 10 keV, break energies.Comment: 10 pages, 5 ps-figures. Expanded discussion of magnetic field and electron energy fraction. Accepted for publication in Astrophysical Journa

Towards a Model for the Progenitors of Gamma-Ray Bursts

We consider models for gamma-ray bursts in which a collimated jet expands either into a homogeneous medium or into a stellar wind environment, and calculate the expected afterglow temporal behavior. We show that (i) following a break and a faster decay, afterglows should exhibit a flattening, which may be detectable in both the radio and optical bands; (ii) Only observations at times much shorter than a day can clearly distinguish between a fireball interacting with a homogeneous medium and one interacting with a stellar wind. Using our results we demonstrate that constraints can be placed on progenitor models. In particular, existing data imply that while some long duration bursts may be produced by collapses of massive stars, it is almost certain that not all long duration bursts are produced by such progenitors.Comment: 13 pages; Submitted to Ap

Rex E. Lee Conference on the Office of the Solicitor General of the United States: Clinton II Panel

I will say a few words about Dickerson, both because Michael has made it impossible not to and also because in some ways it represents the very best about how all of the wonderful, tried-and-true processes of the SG\u27s Office ought to work. Dickerson was very much like the other case that Michael talked about (which is one of, I think, two significant privilege controversies which the Independent Counsel laid on our doorstep). These cases may have appeared to the outside world as paradigmatically cases in which we would be hearing from the White House, or talking to the White House, or thinking about things other than the long-term institutional interests of the United States. But absolutely nothing of the sort ever happened, nor was any effort made by any political person to intrude in our decision-making policy

Neutrino flux predictions for known Galactic microquasars

It has been proposed recently that Galactic microquasars may be prodigious emitters of TeV neutrinos that can be detected by upcoming km^2 neutrino telescopes. In this paper we consider a sample of identified microquasars and microquasar candiates, for which available data enables rough determination of the jet parameters. By employing the parameters inferred from radio observations of various jet ejection events, we determine the neutrino fluxes that should have been produced during these events by photopion production in the jet. Despite the large uncertainties in our analysis, we demonstrate that in several of the sources considered, the neutrino flux at Earth, produced in events similar to those observed, would exceed the detection threshold of a km^2 neutrino detector. The class of microquasars may contain also sources with bulk Lorentz factors larger than those characteristic of the sample considered here, directed along our line of sight. Such sources, which may be very difficult to resolve at radio wavelengths and hence may be difficult to identify as microqusar candidates, may emit neutrinos with fluxes significantly larger than typically obtained in the present analysis. These sources may eventually be identified through their neutrino and gamma-ray emission.Comment: 17 pages. Submitted to Ap