The Right Mutation Strength for Multi-Valued Decision Variables

The most common representation in evolutionary computation are bit strings. This is ideal to model binary decision variables, but less useful for variables taking more values. With very little theoretical work existing on how to use evolutionary algorithms for such optimization problems, we study the run time of simple evolutionary algorithms on some OneMax-like functions defined over $\Omega = \{0, 1, \dots, r-1\}^n$. More precisely, we regard a variety of problem classes requesting the component-wise minimization of the distance to an unknown target vector $z \in \Omega$. For such problems we see a crucial difference in how we extend the standard-bit mutation operator to these multi-valued domains. While it is natural to select each position of the solution vector to be changed independently with probability $1/n$, there are various ways to then change such a position. If we change each selected position to a random value different from the original one, we obtain an expected run time of $\Theta(nr \log n)$. If we change each selected position by either $+1$ or $-1$ (random choice), the optimization time reduces to $\Theta(nr + n\log n)$. If we use a random mutation strength $i \in \{0,1,\ldots,r-1\}^n$ with probability inversely proportional to $i$ and change the selected position by either $+i$ or $-i$ (random choice), then the optimization time becomes $\Theta(n \log(r)(\log(n)+\log(r)))$, bringing down the dependence on $r$ from linear to polylogarithmic. One of our results depends on a new variant of the lower bounding multiplicative drift theorem.Comment: an extended abstract of this work is to appear at GECCO 201

Dynamical Behavior of a stochastic SIRS epidemic model

In this paper we study the Kernack - MacKendrick model under telegraph noise. The telegraph noise switches at random between two SIRS models. We give out conditions for the persistence of the disease and the stability of a disease free equilibrium. We show that the asymptotic behavior highly depends on the value of a threshold $\lambda$ which is calculated from the intensities of switching between environmental states, the total size of the population as well as the parameters of both SIRS systems. According to the value of $\lambda$, the system can globally tend towards an endemic case or a disease free case. The aim of this work is also to describe completely the omega-limit set of all positive solutions to the model. Moreover, the attraction of the omega-limit set and the stationary distribution of solutions will be pointed out.Comment: 16 page

Lens Galaxy Properties of SBS1520+530: Insights from Keck Spectroscopy and AO Imaging

We report on an investigation of the SBS 1520+530 gravitational lens system and its environment using archival HST imaging, Keck spectroscopic data, and Keck adaptive-optics imaging. The AO imaging has allowed us to fix the lens galaxy properties with a high degree of precision when performing the lens modeling, and the data indicate that the lens has an elliptical morphology and perhaps a disk. The new spectroscopic data suggest that previous determinations of the lens redshift may be incorrect, and we report an updated, though inconclusive, value z_lens = 0.761. We have also spectroscopically confirmed the existence of several galaxy groups at approximately the redshift of the lens system. We create new models of the lens system that explicitly account for the environment of the lens, and we also include improved constraints on the lensing galaxy from our adaptive-optics imaging. Lens models created with these new data can be well-fit with a steeper than isothermal mass slope (alpha = 2.29, with the density proportional to r^-alpha) if H_0 is fixed at 72 km/s/Mpc; isothermal models require H_0 ~ 50 km/s/Mpc. The steepened profile may indicate that the lens is in a transient perturbed state caused by interactions with a nearby galaxy.Comment: 12 pages, 10 figures, submitted to Ap

Results of a self-triggered prototype system for radio-detection of extensive air showers at the Pierre Auger Observatory

We describe the experimental setup and the results of RAuger, a small radio-antenna array, consisting of three fully autonomous and self-triggered radio-detection stations, installed close to the center of the Surface Detector (SD) of the Pierre Auger Observatory in Argentina. The setup has been designed for the detection of the electric field strength of air showers initiated by ultra-high energy cosmic rays, without using an auxiliary trigger from another detection system. Installed in December 2006, RAuger was terminated in May 2010 after 65 registered coincidences with the SD. The sky map in local angular coordinates (i.e., zenith and azimuth angles) of these events reveals a strong azimuthal asymmetry which is in agreement with a mechanism dominated by a geomagnetic emission process. The correlation between the electric field and the energy of the primary cosmic ray is presented for the first time, in an energy range covering two orders of magnitude between 0.1 EeV and 10 EeV. It is demonstrated that this setup is relatively more sensitive to inclined showers, with respect to the SD. In addition to these results, which underline the potential of the radio-detection technique, important information about the general behavior of self-triggering radio-detection systems has been obtained. In particular, we will discuss radio self-triggering under varying local electric-field conditions.Comment: accepted for publication in JINS

A system for online beam emittance measurements and proton beam characterization

A system for online measurement of the transverse beam emittance was developed. It is named $^{4}$PrOB$\varepsilon$aM (4-Profiler Online Beam Emittance Measurement) and was conceived to measure the emittance in a fast and efficient way using the multiple beam profiler method. The core of the system is constituted by four consecutive UniBEaM profilers, which are based on silica fibers passing across the beam. The $^{4}$PrOB$\varepsilon$aM system was deployed for characterization studies of the 18~MeV proton beam produced by the IBA Cyclone 18 MeV cyclotron at Bern University Hospital (Inselspital). The machine serves daily radioisotope production and multi-disciplinary research, which is carried out with a specifically conceived Beam Transport Line (BTL). The transverse RMS beam emittance of the cyclotron was measured as a function of several machine parameters, such as the magnetic field, RF peak voltage, and azimuthal angle of the stripper. The beam emittance was also measured using the method based on the quadrupole strength variation. The results obtained with both techniques were compared and a good agreement was found. In order to characterize the longitudinal dynamics, the proton energy distribution was measured. For this purpose, a method was developed based on aluminum absorbers of different thicknesses, a UniBEaM detector, and a Faraday cup. The results were an input for a simulation of the BTL developed in the MAD-X software. This tool allows machine parameters to be tuned online and the beam characteristics to be optimized for specific applications.Comment: published in Journal of Instrumentatio

Luminous Satellites II: Spatial Distribution, Luminosity Function and Cosmic Evolution

We infer the normalization and the radial and angular distributions of the number density of satellites of massive galaxies ($\log_{10}[M_{h}^*/M\odot]>10.5$) between redshifts 0.1 and 0.8 as a function of host stellar mass, redshift, morphology and satellite luminosity. Exploiting the depth and resolution of the COSMOS HST images, we detect satellites up to eight magnitudes fainter than the host galaxies and as close as 0.3 (1.4) arcseconds (kpc). Describing the number density profile of satellite galaxies to be a projected power law such that P(R)\propto R^{\rpower}, we find \rpower=-1.1\pm 0.3. We find no dependency of \rpower on host stellar mass, redshift, morphology or satellite luminosity. Satellites of early-type hosts have angular distributions that are more flattened than the host light profile and are aligned with its major axis. No significant average alignment is detected for satellites of late-type hosts. The number of satellites within a fixed magnitude contrast from a host galaxy is dependent on its stellar mass, with more massive galaxies hosting significantly more satellites. Furthermore, high-mass late-type hosts have significantly fewer satellites than early-type galaxies of the same stellar mass, likely a result of environmental differences. No significant evolution in the number of satellites per host is detected. The cumulative luminosity function of satellites is qualitatively in good agreement with that predicted using subhalo abundance matching techniques. However, there are significant residual discrepancies in the absolute normalization, suggesting that properties other than the host galaxy luminosity or stellar mass determine the number of satellites.Comment: 23 pages, 12 figures, Accepted for publication in the Astrophysical Journa

Light Nuclei solving Auger puzzles. The Cen-A imprint

Ultra High Energy Cosmic Rays (UHECR) map at 60 EeV have been found recently by AUGER group spreading anisotropy signatures in the sky. The result have been interpreted as a manifestation of AGN sources ejecting protons at GZK edges mostly from Super-galactic Plane. The result is surprising due to the absence of much nearer Virgo cluster. Moreover, early GZK cut off in the spectra may be better reconcile with light nuclei (than with protons). In addition a large group (nearly a dozen) of events cluster suspiciously along Cen-A. Finally, proton UHECR composition nature is in sharp disagreement with earlier AUGER claim of a heavy nuclei dominance at 40 EeV. Therefore we interpret here the signals as mostly UHECR light nuclei (He, Be, B, C, O), very possibly mostly the lightest (He,Be) ones, ejected from nearest AGN Cen-A, UHECR smeared by galactic magnetic fields, whose random vertical bending is overlapping with super-galactic arm. The eventual AUGER misunderstanding took place because of such a rare coincidence between the Super Galactic Plane (arm) and the smeared (randomized) signals from Cen-A, bent orthogonally to the Galactic fields. Our derivation verify the consistence of the random smearing angles for He, Be and B, C, O, in reasonable agreement with the AUGER main group events around Cen-A. Only few other rare events are spread elsewhere. The most collimated from Cen-A are the lightest. The most spread the heavier. Consequently Cen-A is the best candidate UHE neutrino tau observable by HEAT and AMIGA as enhanced AUGER array at tens-hundred PeV energy. This model maybe soon tested by new events clustering around the Cen-A and by composition imprint study.Comment: 4 pages, 5 figures

Inference of the Cold Dark Matter substructure mass function at z=0.2 using strong gravitational lenses

We present the results of a search for galaxy substructures in a sample of 11 gravitational lens galaxies from the Sloan Lens ACS Survey. We find no significant detection of mass clumps, except for a luminous satellite in the system SDSS J0956+5110. We use these non-detections, in combination with a previous detection in the system SDSS J0946+1006, to derive constraints on the substructure mass function in massive early-type host galaxies with an average redshift z ~ 0.2 and an average velocity dispersion of 270 km/s. We perform a Bayesian inference on the substructure mass function, within a median region of about 32 kpc squared around the Einstein radius (~4.2 kpc). We infer a mean projected substructure mass fraction $f = 0.0076^{+0.0208}_{-0.0052}$ at the 68 percent confidence level and a substructure mass function slope $\alpha$ < 2.93 at the 95 percent confidence level for a uniform prior probability density on alpha. For a Gaussian prior based on Cold Dark Matter (CDM) simulations, we infer $f = 0 .0064^{+0.0080}_{-0.0042}$ and a slope of $\alpha$ = 1.90$^{+0.098}_{-0.098}$ at the 68 percent confidence level. Since only one substructure was detected in the full sample, we have little information on the mass function slope, which is therefore poorly constrained (i.e. the Bayes factor shows no positive preference for any of the two models).The inferred fraction is consistent with the expectations from CDM simulations and with inference from flux ratio anomalies at the 68 percent confidence level.Comment: Accepted for publication on MNRAS, some typos corrected and some important references adde