The Faint End Slopes Of Galaxy Luminosity Functions In The COSMOS 2-Square Degree Field

We examine the faint-end slope of the rest-frame V-band luminosity function (LF), with respect to galaxy spectral type, of field galaxies with redshift z<0.5, using a sample of 80,820 galaxies with photometric redshifts in the Cosmic Evolution Survey (COSMOS) field. For all galaxy spectral types combined, the LF slope, alpha, ranges from -1.24 to -1.12, from the lowest redshift bin to the highest. In the lowest redshift bin (0.02<z<0.1), where the magnitude limit is M(V) ~ -13, the slope ranges from ~ -1.1 for galaxies with early-type spectral energy distributions (SEDs), to ~ -1.9 for galaxies with low-extinction starburst SEDs. In each galaxy SED category (Ell, Sbc, Scd/Irr, and starburst), the faint-end slopes grow shallower with increasing redshift; in the highest redshift bin (0.4<z<0.5), the slope is ~ -0.5 and ~ -1.3 for early-types and starbursts respectively. The steepness of alpha at lower redshift could be qualitatively explained by large numbers of faint dwarf galaxies, perhaps of low surface brightness, which are not detected at higher redshifts.Comment: 24 pages including 5 figures, accepted to ApJ

A comparison of animal output and nitrogen leaching losses recorded from drained fertilized grass and grass/clover pasture

Annual liveweight gain of beef cattle (steers) grazing grass pasture fertilized with 200 kg N/ha was compared over a period of 7 years (1989–95) with that of steers grazing grass/white clover pasture given no artificial N fertilizer at North Wyke, Devon, UK. Nitrogen lost by leaching over the ensuing winter drainage periods was monitored from both pastures. Nitrogen leaching loss from the fertilized pasture over an extended period of 13 years (1983–95) is also reported.The average annual liveweight gain of the steers grazing the grass/clover pasture (0·81 t/ha) was 19% lower than that of the steers grazing the N-fertilized grass pasture (1·00 t/ha). The average annual loss of nitrate-N by leaching in winter drainage from the grass/clover pasture (13 kg/ha) was only 26% of that recorded from the fertilized grass (50 kg/ha). A possible reason for this difference may arise from the previous history of the grass/clover pasture which had been ploughed in 1982, causing a flush of N mineralization and consequently greater immobilization of N in the soil in subsequent years.Losses of N each winter by leaching measured over a 13-year period from the fertilized grass were highly correlated (P&lt;0·001) with the preceding summer's soil moisture deficit, with the highest losses following dry summers. The nitrate-N concentration in the drainage water exceeded the European Union limit in drinking water (11·3 mg/l) in the initial 25 mm of drainage during 11 of the 13 autumns. The average loss of N each winter (53 kg/ha) was equivalent to 26% of the fertilizer-N applied annually. Immediate losses of N by leaching of fertilizer applied in early spring and throughout one very wet summer (1993) were minimal.</jats:p

Blending and obscuration in weak lensing magnification

We test the impact of some systematic errors in weak lensing magnification measurements with the COSMOS 30-band photo-$z$ Survey flux limited to $I_{auto}<25.0$ using correlations of both source galaxy counts and magnitudes. Systematic obscuration effects are measured by comparing counts and magnification correlations. We use the ACS-HST catalogs to identify potential blending objects (close pairs) and perform the magnification analyses with and without blended objects. We find that blending effects start to be important ($\sim$ 0.04~mag obscuration) at angular scales smaller than 0.1 arcmin. Extinction and other systematic obscuration effects can be as large as 0.10~mag (U-band) but are typically smaller than 0.02~mag depending on the band. After applying these corrections, we measure a $3.9\sigma$ magnification signal that is consistent for both counts and magnitudes. The corresponding projected mass profiles of galaxies at redshift $z \simeq 0.6$ ($M_I \simeq -21$) is $\Sigma= 25\pm 6 M_{sun}h^3/pc^2$ at 0.1 Mpc/h, consistent with NFW type profile with $M_{200} \simeq 2 \times 10^{12} M_{sun} h/pc^2$. Tangential shear and flux-size magnification over the same lenses show similar mass profiles. We conclude that magnification from counts and fluxes using photometric redshifts has the potential to provide complementary weak lensing information in future wide field surveys once we carefully take into account systematic effects, such as obscuration and blending.Comment: matches version accepted in MNRA

Theory of Spike Spiral Waves in a Reaction-Diffusion System

We discovered a new type of spiral wave solutions in reaction-diffusion systems --- spike spiral wave, which significantly differs from spiral waves observed in FitzHugh-Nagumo-type models. We present an asymptotic theory of these waves in Gray-Scott model. We derive the kinematic relations describing the shape of this spiral and find the dependence of its main parameters on the control parameters. The theory does not rely on the specific features of Gray-Scott model and thus is expected to be applicable to a broad range of reaction-diffusion systems.Comment: 4 pages (REVTeX), 2 figures (postscript), submitted to Phys. Rev. Let

Synoptic Sky Surveys and the Diffuse Supernova Neutrino Background: Removing Astrophysical Uncertainties and Revealing Invisible Supernovae

The cumulative (anti)neutrino production from all core-collapse supernovae within our cosmic horizon gives rise to the diffuse supernova neutrino background (DSNB), which is on the verge of detectability. The observed flux depends on supernova physics, but also on the cosmic history of supernova explosions; currently, the cosmic supernova rate introduces a substantial (+/-40%) uncertainty, largely through its absolute normalization. However, a new class of wide-field, repeated-scan (synoptic) optical sky surveys is coming online, and will map the sky in the time domain with unprecedented depth, completeness, and dynamic range. We show that these surveys will obtain the cosmic supernova rate by direct counting, in an unbiased way and with high statistics, and thus will allow for precise predictions of the DSNB. Upcoming sky surveys will substantially reduce the uncertainties in the DSNB source history to an anticipated +/-5% that is dominated by systematics, so that the observed high-energy flux thus will test supernova neutrino physics. The portion of the universe (z < 1) accessible to upcoming sky surveys includes the progenitors of a large fraction (~ 87%) of the expected 10-26 MeV DSNB event rate. We show that precision determination of the (optically detected) cosmic supernova history will also make the DSNB into a strong probe of an extra flux of neutrinos from optically invisible supernovae, which may be unseen either due to unexpected large dust obscuration in host galaxies, or because some core-collapse events proceed directly to black hole formation and fail to give an optical outburst.Comment: 11 pages, 6 figure

Schwarzschild black hole lensing

We study strong gravitational lensing due to a Schwarzschild black hole. Apart from the primary and the secondary images we find a sequence of images on both sides of the optic axis; we call them {\em relativistic images}. These images are formed due to large bending of light near r = 3M (the closest distance of approach r_o is greater than 3M). The sources of the entire universe are mapped in the vicinity of the black hole by these images. For the case of the Galactic supermassive ``black hole'' they are formed at about 17 microarcseconds from the optic axis. The relativistic images are not resolved among themselves, but they are resolved from the primary and secondary images. However the relativistic images are very much demagnified unless the observer, lens and source are very highly aligned. Due to this and some other difficulties the observation of these images does not seem to be feasible in near future. However, it would be a great success of the general theory of relativity in a strong gravitational field if they ever were observed and it would also give an upper bound, r_o = 3.21 M, to the compactness of the lens, which would support the black hole interpretation of the lensing object.Comment: RevTex, 5 eps files are included, observational difficulties are discussed and there are some changes in presentatio

Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds

We prove a concise factor-of-2 estimate for the failure rate of optimally distinguishing an arbitrary ensemble of mixed quantum states, generalizing work of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis, MIT, 1979]. A modification to the minimal principle of Cocha and Poor [Proceedings of the 6th International Conference on Quantum Communication, Measurement, and Computing (Rinton, Princeton, NJ, 2003)] is used to derive a suboptimal measurement which has an error rate within a factor of 2 of the optimal by construction. This measurement is quadratically weighted and has appeared as the first iterate of a sequence of measurements proposed by Jezek et al. [Phys. Rev. A 65, 060301 (2002)]. Unlike the so-called pretty good measurement, it coincides with Holevo's asymptotically optimal measurement in the case of nonequiprobable pure states. A quadratically weighted version of the measurement bound by Barnum and Knill [J. Math. Phys. 43, 2097 (2002)] is proven. Bounds on the distinguishability of syndromes in the sense of Schumacher and Westmoreland [Phys. Rev. A 56, 131 (1997)] appear as a corollary. An appendix relates our bounds to the trace-Jensen inequality.Comment: It was not realized at the time of publication that the lower bound of Theorem 10 has a simple generalization using matrix monotonicity (See [J. Math. Phys. 50, 062102]). Furthermore, this generalization is a trivial variation of a previously-obtained bound of Ogawa and Nagaoka [IEEE Trans. Inf. Theory 45, 2486-2489 (1999)], which had been overlooked by the autho

Movie Pirates of the Caribbean: Exploring Illegal Streaming Cyberlockers

Online video piracy (OVP) is a contentious topic, with strong proponents on both sides of the argument. Recently, a number of illegal websites, called streaming cyberlockers, have begun to dominate OVP. These websites specialise in distributing pirated content, underpinned by third party indexing services offering easy-to-access directories of content. This paper performs the first exploration of this new ecosystem. It characterises the content, as well the streaming cyberlockers' individual attributes. We find a remarkably centralised system with just a few networks, countries and cyberlockers underpinning most provisioning. We also investigate the actions of copyright enforcers. We find they tend to target small subsets of the ecosystem, although they appear quite successful. 84% of copyright notices see content removed

A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy

The analysis of data from gravitational wave detectors can be divided into three phases: search, characterization, and evaluation. The evaluation of the detection - determining whether a candidate event is astrophysical in origin or some artifact created by instrument noise - is a crucial step in the analysis. The on-going analyses of data from ground based detectors employ a frequentist approach to the detection problem. A detection statistic is chosen, for which background levels and detection efficiencies are estimated from Monte Carlo studies. This approach frames the detection problem in terms of an infinite collection of trials, with the actual measurement corresponding to some realization of this hypothetical set. Here we explore an alternative, Bayesian approach to the detection problem, that considers prior information and the actual data in hand. Our particular focus is on the computational techniques used to implement the Bayesian analysis. We find that the Parallel Tempered Markov Chain Monte Carlo (PTMCMC) algorithm is able to address all three phases of the anaylsis in a coherent framework. The signals are found by locating the posterior modes, the model parameters are characterized by mapping out the joint posterior distribution, and finally, the model evidence is computed by thermodynamic integration. As a demonstration, we consider the detection problem of selecting between models describing the data as instrument noise, or instrument noise plus the signal from a single compact galactic binary. The evidence ratios, or Bayes factors, computed by the PTMCMC algorithm are found to be in close agreement with those computed using a Reversible Jump Markov Chain Monte Carlo algorithm.Comment: 19 pages, 12 figures, revised to address referee's comment

Validation and Calibration of Models for Reaction-Diffusion Systems

Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps ($\Delta x$ and $\Delta t$) are varied independently. On the other hand, anisotropy effects due to the symmetries of the discretization lattice prevent the quantitative calibration of models. We introduce a new class of explicit difference methods for numerical integration of diffusion and reaction-diffusion equations, where the dependence on space and time scales occurs naturally. Numerical solutions approach the exact solution of the continuous diffusion equation for finite $\Delta x$ and $\Delta t$, if the parameter $\gamma_N=D \Delta t/(\Delta x)^2$ assumes a fixed constant value, where $N$ is an odd positive integer parametrizing the alghorithm. The error between the solutions of the discrete and the continuous equations goes to zero as $(\Delta x)^{2(N+2)}$ and the values of $\gamma_N$ are dimension independent. With these new integration methods, anisotropy effects resulting from the finite differences are minimized, defining a standard for validation and calibration of numerical solutions of diffusion and reaction-diffusion equations. Comparison between numerical and analytical solutions of reaction-diffusion equations give global discretization errors of the order of $10^{-6}$ in the sup norm. Circular patterns of travelling waves have a maximum relative random deviation from the spherical symmetry of the order of 0.2%, and the standard deviation of the fluctuations around the mean circular wave front is of the order of $10^{-3}$.Comment: 33 pages, 8 figures, to appear in Int. J. Bifurcation and Chao