Note on the super inflation in loop quantum cosmology

Phenomenological effect of the super-inflation in loop quantum cosmology (LQC) is discussed. We investigate the case that the Universe is filled with the interacting field between massive scalar field and radiation. Considering the damping coefficient $\Gamma$ as a constant, the changes of the scale factor during super-inflation with four different initial conditions are discussed, and we find that the changes of the scale factor depends on the initial values of energy density of the scalar field and radiation at the bounce point. But no matter which initial condition is chosen, the radiation always dominated at the late time. Moreover, we investigate whether the super-inflation can provide enough e-folding number. For the super-inflation starts from the quantum bounce point, the initial value of Hubble parameter $H(t_i)\sim0$, then it is possible to solve the flatness problem and horizon problem. As an example, following the method of \cite{Amoros-prd} to calculate particle horizon on the condition that the radiation dominated at bounce point, and we find that the Universe has had enough time to be homogeneous and isotopic.Comment: 9 pages, 4 figures. Physics Letters B, online publication complete: 13-NOV-201

Evaluating Robustness of Neural Networks with Mixed Integer Programming

Neural networks have demonstrated considerable success on a wide variety of real-world problems. However, networks trained only to optimize for training accuracy can often be fooled by adversarial examples - slightly perturbed inputs that are misclassified with high confidence. Verification of networks enables us to gauge their vulnerability to such adversarial examples. We formulate verification of piecewise-linear neural networks as a mixed integer program. On a representative task of finding minimum adversarial distortions, our verifier is two to three orders of magnitude quicker than the state-of-the-art. We achieve this computational speedup via tight formulations for non-linearities, as well as a novel presolve algorithm that makes full use of all information available. The computational speedup allows us to verify properties on convolutional networks with an order of magnitude more ReLUs than networks previously verified by any complete verifier. In particular, we determine for the first time the exact adversarial accuracy of an MNIST classifier to perturbations with bounded $l_\infty$ norm $\epsilon=0.1$: for this classifier, we find an adversarial example for 4.38% of samples, and a certificate of robustness (to perturbations with bounded norm) for the remainder. Across all robust training procedures and network architectures considered, we are able to certify more samples than the state-of-the-art and find more adversarial examples than a strong first-order attack.Comment: Accepted as a conference paper at ICLR 201

Eccentricity is not the only source of elliptic flow fluctuations

Sources of event-by-event elliptic flow fluctuations in relativistic heavy-ion collisions are investigated in a multiphase transport model. Besides the well-known initial eccentricity fluctuations, several other sources of dynamical fluctuations are identified. One is fluctuations in initial parton configurations at a given eccentricity. Second is quantum fluctuations in parton interactions during system evolution. Third is fluctuations caused by hadronization and final-state hadronic scatterings. The magnitudes of these fluctuations are investigated relative to eccentricity fluctuations and average flow magnitude. The fluctuations from the latter two sources are found to be negative. The results may have important implications to the interpretation of elliptic flow data.Comment: 5 pages, 3 figure

Online Algorithms Modeled After Mousehunt

In this paper we study a variety of novel online algorithm problems inspired by the game Mousehunt. We consider a number of basic models that approximate the game, and we provide solutions to these models using Markov Decision Processes, deterministic online algorithms, and randomized online algorithms. We analyze these solutions' performance by deriving results on their competitive ratios.Comment: 14 pages, 2 figure

Non-Fermi liquid behavior in Bose-Fermi mixtures at two dimensions

In this paper we study the low temperature behaviors of a system of Bose-Fermi mixtures at two dimensions. Within a self-consistent ladder diagram approximation, we show that at nonzero temperatures $T\rightarrow0$ the fermions exhibit non-fermi liquid behavior. We propose that this is a general feature of Bose-Fermi mixtures at two dimensions. An experimental signature of this new state is proposed.Comment: 4 pages, 2 figures. supplementary materia

Factorization of event-plane correlations over transverse momentum in relativistic heavy ion collisions in a multi-phase transport model

Momentum-space azimuthal harmonic event planes (EP) are constructed from final-state midrapidity particles binned in transverse momentum (pT ) in sqrt(s_NN) = 200 GeV Au+Au collisions in a multi-phase transport (AMPT) model. The EP correlations between pT bins, corrected by EP resolutions, are smaller than unity. This indicates that the EP's decorrelate over pT in AMPT, qualitatively consistent with data and hydrodynamic calculations. It is further found that the EP correlations approximately factorize into single pT-bin EP correlations to a common plane. This common plane appears to be the momentum-space EP integrated over all pT, not the configuration space participant plane (PP).Comment: 7 pages, 2 tables, 2 figure

Phenomenology analysis of duration inflation for Tachyon field in loop quantum cosmology

Assuming that the e-folding number is just determined by the change of the scale factor, the tachyonic inflation theory in LQC has been discussed. Considering the tachyon field with exponential potential and inverse quadratic potential, we find that the evolutionary pictures of super inflation are affected by the potentials and the initial conditions. However it cannot provide enough e-folding number, no matter which condition is chosen. Therefore a slow-rolling inflation is necessary. The e-folding number for slow-rolling inflation depends on the values of the parameter $\alpha$ of the exponential potential and the initial conditions. To get enough e-folding number, $\alpha$ should be small. Based on the slow-rolling inflation happens immediately when the super inflation ends, and the scale factor is continuously growing during the whole inflation stage, we consider an e-folding number provided by the whole inflationary stage, and we find that it is easier to get enough e-folding number when the scale factor increases during all the inflation phase.Comment: 8 pages, 6 figure

Direct numerical study of speed of sound in dispersed air-water two-phase flow

Speed of sound is a key parameter for the compressibility effects in multiphase flow. We present a new approach to do direct numerical simulations on the speed of sound in compressible two-phase flow, based on the stratified multiphase flow model (Chang & Liou, JCP 2007). In this method, each face is divided into gas-gas, gas-liquid, and liquid-liquid parts via reconstruction of volume fraction, and the corresponding fluxes are calculated by Riemann solvers. Viscosity and heat transfer models are included. The effects of frequency (below the natural frequency of bubbles), volume fraction, viscosity and heat transfer are investigated. With frequency 1 kHz, under viscous and isothermal conditions, the simulation results satisfy the experimental ones very well. The simulation results show that the speed of sound in air-water bubbly two-phase flow is larger when the frequency is higher. At lower frequency, for the phasic velocities, the homogeneous condition is better satisfied. Considering the phasic temperatures, during the wave propagation an isothermal bubble behavior is observed. Finally, the dispersion relation of acoustics in two-phase flow is compared with analytical results below the natural frequency. This work for the first time presents an approach to the direct numerical simulations of speed of sound and other compressibility effects in multiphase flow, which can be applied to study more complex situations, especially when it is hard to do experimental study

Four paradoxes about the special theory of relativity

Various paradoxes about the relativity theory have been developed since the birth of this theory. Each paradox somewhat shows people's query about the relativity theory, and solving of each paradox demonstrates the correctness of relativity theory once again. In this paper, four paradoxes about the special theory of relativity are brought forward: displacement paradox, electromagnetic transformation paradox, Doppler paradox and magnetic force paradox. We hope some researchers can reasonably explain these paradoxes, and then knowledge of the relativity theory will become more abundant.Comment: 12 pages, 7 figure

Optical quasi-periodic oscillation and color behavior of blazar PKS 2155-304

PKS 2155-304 is a well studied BL Lac object in the southern sky. The historical optical data during different period have been collected and compiled. Light curves with a time span of 35 years have been constructed. The R-band light curve has been analyzed by means of three methods: epoch folding method, Jurkevich method and discrete correlation function (DCF) method. It is derived that there is an evident periodic component of 317 days (i.e. 0.87 yr) superposed on a long-term trend with large-amplitude variation in the light curve. The variability of this source is accompanied by a slight color variation, and the brightness and color index are correlated with each other. On the long time-scale, PKS 2155-304 exhibits a tendency of bluer-when-brighter, which means the spectrum becomes flatter when the source brightens.Comment: 9 pages, 4 figures. Accepted for publication in RAA (Research in Astronomy and Astrophysics