A Bayesian Approach to Comparing Cosmic Ray Energy Spectra

A common problem in ultra-high energy cosmic ray physics is the comparison of energy spectra. The question is whether the spectra from two experiments or two regions of the sky agree within their statistical and systematic uncertainties. We develop a method to directly compare energy spectra for ultra-high energy cosmic rays from two different regions of the sky in the same experiment without reliance on agreement with a theoretical model of the energy spectra. The consistency between the two spectra is expressed in terms of a Bayes factor, defined here as the ratio of the likelihood of the two-parent source hypothesis to the likelihood of the one-parent source hypothesis. Unlike other methods, for example chi^2 tests, the Bayes factor allows for the calculation of the posterior odds ratio and correctly accounts for non-Gaussian uncertainties. The latter is particularly important at the highest energies, where the number of events is very small.Comment: 22 pages, 10 figures, accepted for publication in Ap

Experimental assessment of presumed filtered density function models

Measured filtered density functions (FDFs) as well as assumed beta distribution model of mixture fraction and “subgrid” scale (SGS) scalar variance, used typically in large eddy simulations, were studied by analysing experimental data, obtained from two-dimensional planar, laser induced fluorescence measurements in isothermal swirling turbulent flows at a constant Reynolds number of 29 000 for different swirl numbers (0.3, 0.58, and 1.07)

Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation

It has been shown in our previous publication (Blawzdziewicz,Cristini,Loewenberg,2003) that high-viscosity drops in two dimensional linear creeping flows with a nonzero vorticity component may have two stable stationary states. One state corresponds to a nearly spherical, compact drop stabilized primarily by rotation, and the other to an elongated drop stabilized primarily by capillary forces. Here we explore consequences of the drop bistability for the dynamics of highly viscous drops. Using both boundary-integral simulations and small-deformation theory we show that a quasi-static change of the flow vorticity gives rise to a hysteretic response of the drop shape, with rapid changes between the compact and elongated solutions at critical values of the vorticity. In flows with sinusoidal temporal variation of the vorticity we find chaotic drop dynamics in response to the periodic forcing. A cascade of period-doubling bifurcations is found to be directly responsible for the transition to chaos. In random flows we obtain a bimodal drop-length distribution. Some analogies with the dynamics of macromolecules and vesicles are pointed out.Comment: 22 pages, 13 figures. submitted to Journal of Fluid Mechanic

Image Storage in Hot Vapors

We theoretically investigate image propagation and storage in hot atomic vapor. A $4f$ system is adopted for imaging and an atomic vapor cell is placed over the transform plane. The Fraunhofer diffraction pattern of an object in the object plane can thus be transformed into atomic Raman coherence according to the idea of ``light storage''. We investigate how the stored diffraction pattern evolves under diffusion. Our result indicates, under appropriate conditions, that an image can be reconstructed with high fidelity. The main reason for this procedure to work is the fact that diffusion of opposite-phase components of the diffraction pattern interfere destructively.Comment: 11 pages, 3 figure

Exponential families of mixed Poisson distributions

If I=(I1,…,Id) is a random variable on [0,∞)d with distribution μ(dλ1,…,dλd), the mixed Poisson distribution MP(μ) on View the MathML source is the distribution of (N1(I1),…,Nd(Id)) where N1,…,Nd are ordinary independent Poisson processes which are also independent of I. The paper proves that if F is a natural exponential family on [0,∞)d then MP(F) is also a natural exponential family if and only if a generating probability of F is the distribution of v0+v1Y1+cdots, three dots, centered+vqYq for some qless-than-or-equals, slantd, for some vectors v0,…,vq of [0,∞)d with disjoint supports and for independent standard real gamma random variables Y1,…,Yq

A New Model-Independent Method for Extracting Spin-Dependent Cross Section Limits from Dark Matter Searches

A new method is proposed for extracting limits on spin-dependent WIMP-nucleon interaction cross sections from direct detection dark matter experiments. The new method has the advantage that the limits on individual WIMP-proton and WIMP-neutron cross sections for a given WIMP mass can be combined in a simple way to give a model-independent limit on the properties of WIMPs scattering from both protons and neutrons in the target nucleus. Extension of the technique to the case of a target material consisting of several different species of nuclei is discussed.Comment: 15 pages, 6 Encapsulated Postscript figure

MEASURING SPIRAL ARM TORQUES: RESULTS FOR M100

Spiral arms, if they are massive, exert gravitational torques that transport angular momentum radially within galactic disks. These torques depend not on the pattern speed or permanence of the arms but only on the nonaxisymmetric mass distribution. Hence the torques can be measured from photometry. We demonstrate this using $gri$ CCD data for M100 (NGC 4321). Since we find consistency among the three bands, we believe that dust and young stars in the arms do not seriously bias our results. If the present epoch is representative, the timescale for redistribution of angular momentum in M100 is $5-10$ Gyr, the main uncertainty being the mass-to-light ratio of the disk.Comment: Uuencoded compressed PostScript (300k) - 26 pages, figs. 3-9; submitted to AJ. Full PostScript version (with all figures) is available through anonymous ftp at ftp://astro.princeton.edu/ognedin/Torque/paper.ps or ftp://astro.princeton.edu/library/preprints/pop613.ps.Z or through WWW http://www.astro.princeton.edu/~library/prep.htm

The association of statin use after cancer diagnosis with survival in pancreatic cancer patients: a SEER-medicare analysis.

BackgroundPancreatic cancer has poor prognosis and existing interventions provide a modest benefit. Statin has anti-cancer properties that might enhance survival in pancreatic cancer patients. We sought to determine whether statin treatment after cancer diagnosis is associated with longer survival in those with pancreatic ductal adenocarcinoma (PDAC).MethodsWe analyzed data on 7813 elderly patients with PDAC using the linked Surveillance, Epidemiology, and End Results (SEER) - Medicare claims files. Information on the type, intensity and duration of statin use after cancer diagnosis was extracted from Medicare Part D. We treated statin as a time-dependent variable in a Cox regression model to determine the association with overall survival adjusting for follow-up, age, sex, race, neighborhood income, stage, grade, tumor size, pancreatectomy, chemotherapy, radiation, obesity, dyslipidemia, diabetes, chronic pancreatitis and chronic obstructive pulmonary disease (COPD).ResultsOverall, statin use after cancer diagnosis was not significantly associated with survival when all PDAC patients were considered (HR = 0.94, 95%CI 0.89, 1.01). However, statin use after cancer diagnosis was associated with a 21% reduced hazard of death (Hazard ratio = 0.79, 95% confidence interval (CI) 0.67, 0.93) in those with grade I or II PDAC and to a similar extent in those who had undergone a pancreatectomy, in those with chronic pancreatitis and in those who had not been treated with statin prior to cancer diagnosis.ConclusionsWe found that statin treatment after cancer diagnosis is associated with enhanced survival in patients with low-grade, resectable PDAC