An unexpectedly low-redshift excess of Swift gamma-ray burst rate

Gamma-ray bursts (GRBs) are the most violent explosions in the Universe and can be used to explore the properties of high-redshift universe. It is believed that the long GRBs are associated with the deaths of massive stars. So it is possible to use GRBs to investigate the star formation rate (SFR). In this paper, we use Lynden-Bell's $c^-$ method to study the luminosity function and rate of \emph{Swift} long GRBs without any assumptions. We find that the luminosity of GRBs evolves with redshift as $L(z)\propto g(z)=(1+z)^k$ with $k=2.43_{-0.38}^{+0.41}$. After correcting the redshift evolution through $L_0(z)=L(z)/g(z)$, the luminosity function can be expressed as $\psi(L_0)\propto L_0^{-0.14\pm0.02}$ for dim GRBs and $\psi(L_0)\propto L_0^{-0.70\pm0.03}$ for bright GRBs, with the break point $L_{0}^{b}=1.43\times10^{51}~{\rm erg~s^{-1}}$. We also find that the formation rate of GRBs is almost constant at $z<1.0$ for the first time, which is remarkably different from the SFR. At $z>1.0$, the formation rate of GRB is consistent with the SFR. Our results are dramatically different from previous studies. Some possible reasons for this low-redshift excess are discussed. We also test the robustness of our results with Monte Carlo simulations. The distributions of mock data (i.e., luminosity-redshift distribution, luminosity function, cumulative distribution and $\log N-\log S$ distribution) are in good agreement with the observations. Besides, we also find that there are remarkable difference between the mock data and the observations if long GRB are unbiased tracers of SFR at $z<1.0$.Comment: 33 pages, 10 figures, 1 table, accepted by ApJ

Effect of long range forces on the interfacial profiles in thin binary polymer films

We study the effect of surface fields on the interfacial properties of a binary polymer melt confined between two parallel walls. Each wall attracts a different component of the blend by a non-retarded van der Waals potential. An interface which runs parallel to the surfaces is stabilized in the center of the film. Using extensive Monte Carlo simulations we study the interfacial properties as a function of the film thickness, the strength of the surface forces and the lateral size over which the profiles across the film are averaged. We find evidence for capillary wave broadening of the apparent interfacial profiles. However, the apparent interfacial width cannot be described quantitatively by a simple logarithmic dependence on the film thickness. The Monte Carlo simulations reveal that the surface fields give rise to an additional reduction of the intrinsic interfacial width and an increase of the effective interfacial tension upon decreasing the film thickness. These modifications of the intrinsic interfacial properties are confirmed by self-consistent field calculations. Taking account of the thickness dependence of the intrinsic interfacial properties and the capillary wave broadening, we can describe our simulation results quantitatively.Comment: to appear in J.Chem.Phy

On data skewness, stragglers, and MapReduce progress indicators

We tackle the problem of predicting the performance of MapReduce applications, designing accurate progress indicators that keep programmers informed on the percentage of completed computation time during the execution of a job. Through extensive experiments, we show that state-of-the-art progress indicators (including the one provided by Hadoop) can be seriously harmed by data skewness, load unbalancing, and straggling tasks. This is mainly due to their implicit assumption that the running time depends linearly on the input size. We thus design a novel profile-guided progress indicator, called NearestFit, that operates without the linear hypothesis assumption and exploits a careful combination of nearest neighbor regression and statistical curve fitting techniques. Our theoretical progress model requires fine-grained profile data, that can be very difficult to manage in practice. To overcome this issue, we resort to computing accurate approximations for some of the quantities used in our model through space- and time-efficient data streaming algorithms. We implemented NearestFit on top of Hadoop 2.6.0. An extensive empirical assessment over the Amazon EC2 platform on a variety of real-world benchmarks shows that NearestFit is practical w.r.t. space and time overheads and that its accuracy is generally very good, even in scenarios where competitors incur non-negligible errors and wide prediction fluctuations. Overall, NearestFit significantly improves the current state-of-art on progress analysis for MapReduce

A rapid cosmic-ray increase in BC 3372-3371 from ancient buried tree rings in China

Cosmic rays interact with the Earth's atmosphere to produce $^{14}$C, which can be absorbed by trees. Therefore, rapid increases of $^{14}$C in tree rings can be used to probe previous cosmic-ray events. By this method, three $^{14}$C rapidly increasing events have been found. Plausible causes of these events include large solar proton events, supernovae or short gamma-ray bursts. However, due to the lack of measurements of $^{14}$C by year, the occurrence frequency of such $^{14}$C rapidly increasing events is poorly known. In addition, rapid increases may be hidden in the IntCal13 data with five-year resolution. Here we report the result of $^{14}$C measurements using an ancient buried tree during the period between BC 3388 and 3358. We find a rapid increase of about 9\textperthousand~ in the $^{14}$C content from BC 3372 to BC 3371. We suggest that this event could originate from a large solar proton event.Comment: 23 pages, 3 figures, 2 tables, published in Nature Communication

The equation of state for two-dimensional hard-sphere gases: Hard-sphere gases as ideal gases with multi-core boundaries

The equation of state for a two-dimensional hard-sphere gas is difficult to calculate by usual methods. In this paper we develop an approach for calculating the equation of state of hard-sphere gases, both for two- and three-dimensional cases. By regarding a hard-sphere gas as an ideal gas confined in a container with a multi-core (excluded sphere) boundary, we treat the hard-sphere interaction in an interacting gas as the boundary effect on an ideal quantum gas; this enables us to treat an interacting gas as an ideal one. We calculate the equation of state for a three-dimensional hard-sphere gas with spin $j$, and compare it with the results obtained by other methods. By this approach the equation of state for a two-dimensional hard-sphere gas can be calculated directly.Comment: 9 pages, 1 figur

Magnetic Coherence as a Universal Feature of Cuprate Superconductors

Recent inelastic neutron scattering (INS) experiments on La$_{2-x}$Sr$_x$CuO$_4$ have established the existence of a {\it magnetic coherence effect}, i.e., strong frequency and momentum dependent changes of the spin susceptibility, $\chi''$, in the superconducting phase. We show, using the spin-fermion model for incommensurate antiferromagnetic spin fluctuations, that the magnetic coherence effect establishes the ability of INS experiments to probe the electronic spectrum of the cuprates, in that the effect arises from the interplay of an incommensurate magnetic response, the form of the underlying Fermi surface, and the opening of the d-wave gap in the fermionic spectrum. In particular, we find that the magnetic coherence effect observed in INS experiments on La$_{2-x}$Sr$_x$CuO$_4$ requires that the Fermi surface be closed around $(\pi,\pi)$ up to optimal doping. We present several predictions for the form of the magnetic coherence effect in YBa$_2$Cu$_3$O$_{6+x}$ in which an incommensurate magnetic response has been observed in the superconducting state.Comment: 9 pages, 12 figures; extended version of Phys. Rev B, R6483 (2000

Fluid and Diffusion Limits for Bike Sharing Systems

Bike sharing systems have rapidly developed around the world, and they are served as a promising strategy to improve urban traffic congestion and to decrease polluting gas emissions. So far performance analysis of bike sharing systems always exists many difficulties and challenges under some more general factors. In this paper, a more general large-scale bike sharing system is discussed by means of heavy traffic approximation of multiclass closed queueing networks with non-exponential factors. Based on this, the fluid scaled equations and the diffusion scaled equations are established by means of the numbers of bikes both at the stations and on the roads, respectively. Furthermore, the scaling processes for the numbers of bikes both at the stations and on the roads are proved to converge in distribution to a semimartingale reflecting Brownian motion (SRBM) in a $N^{2}$-dimensional box, and also the fluid and diffusion limit theorems are obtained. Furthermore, performance analysis of the bike sharing system is provided. Thus the results and methodology of this paper provide new highlight in the study of more general large-scale bike sharing systems.Comment: 34 pages, 1 figure