Figure of Merit for Dark Energy Constraints from Current Observational Data

Choosing the appropriate figure of merit (FoM) for dark energy (DE) constraints is key in comparing different DE experiments. Here we show that for a set of DE parameters {f_i}, it is most intuitive to define FoM = 1/\sqrt{Cov(f1,f2,f3,...)}, where Cov(f1,f2,f3,...) is the covariance matrix of {f_i}. The {f_i} should be minimally correlated. We demonstrate two useful choices of {f_i} using 182 SNe Ia (compiled by Riess et al. 2007), [R(z_*), l_a(z_*), \Omega_b h^2] from the five year Wilkinson Microwave Anisotropy Probe (WMAP) observations, and SDSS measurement of the baryon acoustic oscillation (BAO) scale, assuming the HST prior of H_0=72+/-8 km/s Mpc^{-1} and without assuming spatial flatness. We find that the correlation of (w_0,w_{0.5}) [w_0=w_X(z=0), w_{0.5}=w_X(z=0.5), w_X(a) = 3w_{0.5}-2w_0+3(w_0-w_{0.5})a] is significantly smaller than that of (w_0,w_a) [w_X(a)=w_0+(1-a)w_a]. In order to obtain model-independent constraints on DE, we parametrize the DE density function X(z)=\rho_X(z)/\rho_X(0) as a free function with X_{0.5}, X_{1.0}, and X_{1.5} [values of X(z) at z=0.5, 1.0, and 1.5] as free parameters estimated from data. If one assumes a linear DE equation of state, current data are consistent with a cosmological constant at 68% C.L. If one assumes X(z) to be a free function parametrized by (X_{0.5}, X_{1.0}, X_{1.5}), current data deviate from a cosmological constant at z=1 at 68% C.L., but are consistent with a cosmological constant at 95% C.L.. Future DE experiments will allow us to dramatically increase the FoM of constraints on (w_0,w_{0.5}) and of (X_{0.5}, X_{1.0}, X_{1.5}). This will significantly shrink the DE parameter space to enable the discovery of DE evolution, or the conclusive evidence for a cosmological constant.Comment: 7 pages, 3 color figures. Submitte

Observational Bounds on Modified Gravity Models

Modified gravity provides a possible explanation for the currently observed cosmic accelaration. In this paper, we study general classes of modified gravity models. The Einstein-Hilbert action is modified by using general functions of the Ricci and the Gauss-Bonnet scalars, both in the metric and in the Palatini formalisms. We do not use an explicit form for the functions, but a general form with a valid Taylor expansion up to second order about redshift zero in the Riemann-scalars. The coefficients of this expansion are then reconstructed via the cosmic expansion history measured using current cosmological observations. These are the quantities of interest for theoretical considerations relating to ghosts and instabilities. We find that current data provide interesting constraints on the coefficients. The next-generation dark energy surveys should shrink the allowed parameter space for modifed gravity models quite dramatically.Comment: 23 pages, 5 figures, uses RevTe

A Comparative Study of Dark Energy Constraints from Current Observational Data

We examine how dark energy constraints from current observational data depend on the analysis methods used: the analysis of Type Ia supernovae (SNe Ia), and that of galaxy clustering data. We generalize the flux-averaging analysis method of SNe Ia to allow correlated errors of SNe Ia, in order to reduce the systematic bias due to weak lensing of SNe Ia. We find that flux-averaging leads to larger errors on dark energy and cosmological parameters if only SN Ia data are used. When SN Ia data (the latest compilation by the SNLS team) are combined with WMAP 7 year results (in terms of our Gaussian fits to the probability distributions of the CMB shift parameters), the latest Hubble constant (H_0) measurement using the Hubble Space Telescope (HST), and gamma ray burst (GRB) data, flux-averaging of SNe Ia increases the concordance with other data, and leads to significantly tighter constraints on the dark energy density at z=1, and the cosmic curvature \Omega_k. The galaxy clustering measurements of H(z=0.35)r_s(z_d) and r_s(z_d)/D_A(z=0.35) (where H(z) is the Hubble parameter, D_A(z) is the angular diameter distance, and r_s(z_d) is the sound horizon at the drag epoch) by Chuang & Wang (2011) are consistent with SN Ia data, given the same pirors (CMB+H_0+GRB), and lead to significantly improved dark energy constraints when combined. Current data are fully consistent with a cosmological constant and a flat universe.Comment: 11 pages, 9 figures. Slightly revised version, to appear in PRD. Supernova flux-averaging code available at http://www.nhn.ou.edu/~wang/SNcode

Planck priors for dark energy surveys

Although cosmic microwave background (CMB) anisotropy data alone cannot constrain simultaneously the spatial curvature and the equation of state of dark energy, CMB data provide a valuable addition to other experimental results. However computing a full CMB power spectrum with a Boltzmann code is quite slow; for instance if we want to work with many dark energy and/or modified gravity models, or would like to optimize experiments where many different configurations need to be tested, it is possible to adopt a quicker and more efficient approach. In this paper we consider the compression of the projected Planck CMB data into four parameters, R (scaled distance to last scattering surface), l_a (angular scale of sound horizon at last scattering), Omega_b h^2 (baryon density fraction) and n_s (powerlaw index of primordial matter power spectrum), all of which can be computed quickly. We show that, although this compression loses information compared to the full likelihood, such information loss becomes negligible when more data is added. We also demonstrate that the method can be used for scalar field dark energy independently of the parametrisation of the equation of state, and discuss how this method should be used for other kinds of dark energy models.Comment: 8 pages, 3 figures, 4 table

Uncorrelated Measurements of the Cosmic Expansion History and Dark Energy from Supernovae

We present a method for measuring the cosmic expansion history H(z) in uncorrelated redshift bins, and apply it to current and simulated type Ia supernova data assuming spatial flatness. If the matter density parameter Omega_m can be accurately measured from other data, then the dark energy density history X(z)=rho_X(z)/rho_X(0) can trivially be derived from this expansion history H(z). In contrast to customary ``black box'' parameter fitting, our method is transparent and easy to interpret: the measurement of H(z)^{-1} in a redshift bin is simply a linear combination of the measured comoving distances for supernovae in that bin, making it obvious how systematic errors propagate from input to output. We find the Riess et al. (2004) ``gold'' sample to be consistent with the ``vanilla'' concordance model where the dark energy is a cosmological constant. We compare two mission concepts for the NASA/DOE Joint Dark Energy Mission (JDEM), the Joint Efficient Dark-energy Investigation (JEDI), and the Supernova Accelaration Probe (SNAP), using simulated data including the effect of weak lensing (based on numerical simulations) and a systematic bias from K-corrections. Estimating H(z) in seven uncorrelated redshift bins, we find that both provide dramatic improvements over current data: JEDI can measure H(z) to about 10% accuracy and SNAP to 30-40% accuracy.Comment: 7 pages, 4 color figures. Expanded and revised version; PRD in pres

Object Contour and Edge Detection with RefineContourNet

A ResNet-based multi-path refinement CNN is used for object contour detection. For this task, we prioritise the effective utilization of the high-level abstraction capability of a ResNet, which leads to state-of-the-art results for edge detection. Keeping our focus in mind, we fuse the high, mid and low-level features in that specific order, which differs from many other approaches. It uses the tensor with the highest-levelled features as the starting point to combine it layer-by-layer with features of a lower abstraction level until it reaches the lowest level. We train this network on a modified PASCAL VOC 2012 dataset for object contour detection and evaluate on a refined PASCAL-val dataset reaching an excellent performance and an Optimal Dataset Scale (ODS) of 0.752. Furthermore, by fine-training on the BSDS500 dataset we reach state-of-the-art results for edge-detection with an ODS of 0.824.Comment: Keywords: Object Contour Detection, Edge Detection, Multi-Path Refinement CN

Comment on "Single-mode excited entangled coherent states"

In Xu and Kuang (\textit{J. Phys. A: Math. Gen.} 39 (2006) L191), the authors claim that, for single-mode excited entangled coherent states $| \Psi_{\pm}(\alpha,m)>$, \textquotedblleft the photon excitations lead to the decrease of the concurrence in the strong field regime of $| \alpha | ^{2}$ and the concurrence tends to zero when $| \alpha | ^{2}\to \infty$". This is wrong.Comment: 4 apges, 2 figures, submitted to JPA 15 April 200

A Fair and Secure Cluster Formation Process for Ad Hoc Networks

An efficient approach for organizing large ad hoc networks is to divide the nodes into multiple clusters and designate, for each cluster, a clusterhead which is responsible for holding intercluster control information. The role of a clusterhead entails rights and duties. On the one hand, it has a dominant position in front of the others because it manages the connectivity and has access to other node¿s sensitive information. But on the other hand, the clusterhead role also has some associated costs. Hence, in order to prevent malicious nodes from taking control of the group in a fraudulent way and avoid selfish attacks from suitable nodes, the clusterhead needs to be elected in a secure way. In this paper we present a novel solution that guarantees the clusterhead is elected in a cheat-proof manner

Quark mass density- and temperature- dependent model for strange quark matter

It is found that the radius of a stable strangelet decreases as the temperature increases in a quark mass density-dependent model. To overcome this difficulty, we extend this model to a quark mass density- and temperature- dependent model in which the vacuum energy density at zero baryon density limit B depends on temperature. An ansatz is introduced and the regions for the best choice of the parameters are studied.Comment: 5 pages, 4 figure