Death and prudential deprivation

Dying is (sometimes) bad for the dier because it prevents her from being the subject of wellbeing she otherwise would (the deprivation account). I argue for this from a (plausible) principle about which futures are bad for a prudential subject (the future-comparison principle). A strengthening of this principle yields that death is not always bad, and that the badness of death does not consist in that it destroys the dier

Bayesian analysis of resolved stellar spectra: application to MMT/Hectochelle Observations of the Draco dwarf spheroidal

We introduce a Bayesian method for fitting faint, resolved stellar spectra in order to obtain simultaneous estimates of redshift and stellar-atmospheric parameters. We apply the method to thousands of spectra---covering 5160-5280 Angs. at resolution R~20,000---that we have acquired with the MMT/Hectochelle fibre spectrograph for red-giant and horizontal branch candidates along the line of sight to the Milky Way's dwarf spheroidal satellite in Draco. The observed stars subtend an area of ~4 deg^2, extending ~3 times beyond Draco's nominal `tidal' radius. For each spectrum we tabulate the first four moments---central value, variance, skewness and kurtosis---of posterior probability distribution functions representing estimates of the following physical parameters: line-of-sight velocity v_los, effective temperature (T_eff), surface gravity (logg) and metallicity ([Fe/H]). After rejecting low-quality measurements, we retain a new sample consisting of 2813 independent observations of 1565 unique stars, including 1879 observations for 631 stars with (as many as 13) repeat observations. Parameter estimates have median random errors of sigma_{v_los}=0.88 km/s, sigma_{T_eff}=162 K, sigma_logg=0.37 dex and sigma_[Fe/H]=0.20 dex. Our estimates of physical parameters distinguish ~470 likely Draco members from interlopers in the Galactic foreground.Comment: published in Monthly Notices of the Royal Astronomical Society, all data are publicly available at the following address: http://www.andrew.cmu.edu/user/mgwalker/hectochelle

Critical Behavior in the Gravitational Collapse of a Scalar Field with Angular Momentum in Spherical Symmetry

We study the critical collapse of a massless scalar field with angular momentum in spherical symmetry. In order to mimic the effects of angular momentum we perform a sum of the stress-energy tensors for all the scalar fields with the same eigenvalue, l, of the angular momentum operator and calculate the equations of motion for the radial part of these scalar fields. We have found that the critical solutions for different values of l are discretely self-similar (as in the original l=0 case). The value of the discrete, self-similar period, Delta_l, decreases as l increases in such a way that the critical solution appears to become periodic in the limit. The mass scaling exponent, gamma_l, also decreases with l.Comment: 10 pages, 8 figure

A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. In this manuscript, we present a data driven method for approximating the leading eigenvalues, eigenfunctions, and modes of the Koopman operator. The method requires a data set of snapshot pairs and a dictionary of scalar observables, but does not require explicit governing equations or interaction with a "black box" integrator. We will show that this approach is, in effect, an extension of Dynamic Mode Decomposition (DMD), which has been used to approximate the Koopman eigenvalues and modes. Furthermore, if the data provided to the method are generated by a Markov process instead of a deterministic dynamical system, the algorithm approximates the eigenfunctions of the Kolmogorov backward equation, which could be considered as the "stochastic Koopman operator" [1]. Finally, four illustrative examples are presented: two that highlight the quantitative performance of the method when presented with either deterministic or stochastic data, and two that show potential applications of the Koopman eigenfunctions

The Algebra of Strand Splitting. II. A Presentation for the Braid Group on One Strand

Presentations are computed for a braided version BV of Thompson's group V and for V itself showing that there is an Artin group/Coxeter group relation between them. The presentation for V is obtained from that for BV by declaring all that all generators are involutions.Comment: 15 page

Blazar Gamma-Rays, Shock Acceleration, and the Extragalactic Background Light

The observed spectra of blazars, their intrinsic emission, and the underlying populations of radiating particles are intimately related. The use of these sources as probes of the extragalactic infrared background, a prospect propelled by recent advances in TeV-band telescopes, soon to be augmented by observations by NASA's upcoming Gamma-Ray Large Area Space Telescope (GLAST), has been a topic of great recent interest. Here, it is demonstrated that if particles in blazar jets are accelerated at relativistic shocks, then gamma-ray spectra with indices less than 1.5 can be produced. This, in turn, loosens the upper limits on the near infrared extragalactic background radiation previously proposed. We also show evidence hinting that TeV blazars with flatter spectra have higher intrinsic TeV gamma-ray luminosities and we indicate that there may be a correlation of flatness and luminosity with redshift.Comment: Version to appear in ApJ Letters, Vol. 667, 20 Sept. 200

Astrophysical gyrokinetics: Turbulence in pressure-anisotropic plasmas at ion scales and beyond

We present a theoretical framework for describing electromagnetic kinetic turbulence in a multi-species, magnetized, pressure-anisotropic plasma. Turbulent fluctuations are assumed to be small compared to the mean field, to be spatially anisotropic with respect to it, and to have frequencies small compared to the ion cyclotron frequency. At scales above the ion Larmor radius, the theory reduces to the pressure-anisotropic generalization of kinetic reduced magnetohydrodynamics (KRMHD) formulated by Kunz et al. (2015). At scales at and below the ion Larmor radius, three main objectives are achieved. First, we analyse the linear response of the pressure-anisotropic gyrokinetic system, and show it to be a generalisation of previously explored limits. The effects of pressure anisotropy on the stability and collisionless damping of Alfvenic and compressive fluctuations are highlighted, with attention paid to the spectral location and width of the frequency jump that occurs as Alfven waves transition into kinetic Alfven waves. Secondly, we derive and discuss a general free-energy conservation law, which captures both the KRMHD free-energy conservation at long wavelengths and dual cascades of kinetic Alfven waves and ion entropy at sub-ion-Larmor scales. We show that non-Maxwellian features in the distribution function change the amount of phase mixing and the efficiency of magnetic stresses, and thus influence the partitioning of free energy amongst the cascade channels. Thirdly, a simple model is used to show that pressure anisotropy can cause large variations in the ion-to-electron heating ratio due to the dissipation of Alfvenic turbulence. Our theory provides a foundation for determining how pressure anisotropy affects the turbulent fluctuation spectra, the differential heating of particle species, and the ratio of parallel and perpendicular phase mixing in space and astrophysical plasmas.Comment: 59 pages, 6 figures, accepted for publication in Journal of Plasma Physics (original 28 Nov 2017); abstract abridge

The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V

We construct a braided version of Thompson's group V.Comment: 27 page