Non-parametric reconstruction of dark energy and cosmic expansion from the Pantheon compilation of type Ia supernovae

The equation of state (EoS) of dark energy plays an important role in the evolution of the universe and arouses great interests in recent years. With the progress on observational technique, precise constraint on the EoS of dark energy becomes possible. In this paper, we reconstruct the EoS of dark energy and cosmic expansion using Gaussian processes (GP) from the most up-to-date Pantheon compilation of type Ia supernovae (SNe Ia), which consists of 1048 finely calibrated SNe Ia. The reconstructed EoS of dark energy has large uncertainty due to its dependence on the second order derivative of the construction. Adding the direct measurements of Hubble parameters $H(z)$ as an additional constraint on the first order derivative can partially reduce the uncertainty, but is still not precise enough to distinguish between evolving and constant dark energy. Besides, the results heavily rely on the prior of Hubble constant $H_0$. The $H_0$ value inferred from SNe+$H(z)$ without prior is $H_0=70.5\pm 0.5~{\textrm{km}~\textrm{s}^{-1}~\textrm{Mpc}^{-1}}$. Moreover, the matter density $\Omega_M$ has an unnegligible effect on the reconstruction of dark energy. Therefore, more accurate determinations on $H_0$ and $\Omega_M$ are needed to tightly constrain the EoS of dark energy.Comment: 7 pages, 7 figure

Comparing the dark matter models, modified Newtonian dynamics and modified gravity in accounting for the galaxy rotation curves

We compare six models (including the baryonic model, two dark matter models, two modified Newtonian dynamics models and one modified gravity model) in accounting for the galaxy rotation curves. For the dark matter models, we assume NFW profile and core-modified profile for the dark halo, respectively. For the modified Newtonian dynamics models, we discuss Milgrom's MOND theory with two different interpolation functions, i.e. the standard and the simple interpolation functions. As for the modified gravity, we focus on Moffat's MSTG theory. We fit these models to the observed rotation curves of 9 high-surface brightness and 9 low-surface brightness galaxies. We apply the Bayesian Information Criterion and the Akaike Information Criterion to test the goodness-of-fit of each model. It is found that non of the six models can well fit all the galaxy rotation curves. Two galaxies can be best fitted by the baryonic model without involving the nonluminous dark matter. MOND can fit the largest number of galaxies, and only one galaxy can be best fitted by MSTG model. Core-modified model can well fit about one half LSB galaxies but no HSB galaxy, while NFW model can fit only a small fraction of HSB galaxies but no LSB galaxy. This may imply that the oversimplified NFW and Core-modified profiles couldn't well mimic the postulated dark matter halo.Comment: 12 pages, 3 figure

Testing the anisotropy of the Universe with the distance duality relation

The distance duality relation (DDR) is valid in Riemannian spacetime. The astronomical data hint that the universe may have certain preferred direction. If the universe is described by anisotropic cosmological models based on Riemannian spacetime, then DDR still valid. If the anisotropy universe is described by other models which are not based on Riemannian spacetime, then DDR is violated. Thus, DDR could be used to test the validity of these anisotropic cosmological models. In this paper, we perform anisotropic DDR parametrization with the dipolar structures. The DDR is tested by comparing the luminosity distance from type-Ia supernovae (Union 2.1 and JLA compilations) and the angular diameter distance from strong gravitational lensing (SL) systems at the same redshift. It is shown that, the DDR is valid with the Union2.1 compilation, while is violated more than 1$\sigma$ confidence level with the JLA compilation. Additionally, we verify the statistical signification of our method with Monte Carlo simulations. Due to the large uncertainty of available data, no strong evidence is found to violate the DDR in the anisotropic models.Comment: 10 pages,2 table

Efficient Discriminative Nonorthogonal Binary Subspace with its Application to Visual Tracking

One of the crucial problems in visual tracking is how the object is represented. Conventional appearance-based trackers are using increasingly more complex features in order to be robust. However, complex representations typically not only require more computation for feature extraction, but also make the state inference complicated. We show that with a careful feature selection scheme, extremely simple yet discriminative features can be used for robust object tracking. The central component of the proposed method is a succinct and discriminative representation of the object using discriminative non-orthogonal binary subspace (DNBS) which is spanned by Haar-like features. The DNBS representation inherits the merits of the original NBS in that it efficiently describes the object. It also incorporates the discriminative information to distinguish foreground from background. However, the problem of finding the DNBS bases from an over-complete dictionary is NP-hard. We propose a greedy algorithm called discriminative optimized orthogonal matching pursuit (D-OOMP) to solve this problem. An iterative formulation named iterative D-OOMP is further developed to drastically reduce the redundant computation between iterations and a hierarchical selection strategy is integrated for reducing the search space of features. The proposed DNBS representation is applied to object tracking through SSD-based template matching. We validate the effectiveness of our method through extensive experiments on challenging videos with comparisons against several state-of-the-art trackers and demonstrate its capability to track objects in clutter and moving background.Comment: 15 page

Classification of seven-vertex solutions of the coloured Yang-Baxter equation

In this paper all seven-vertex type solutions of the coloured Yang-Baxter equation dependent on spectral as well as coloured parameters are given. It is proved that they are composed of five groups of basic solutions, two groups of their degenerate forms up to five solution transformations. Moreover, all solutions can be claasified into two types called Baxter type and free-fermion type.Comment: 29 page

Estimation of inverse autocovariance matrices for long memory processes

This work aims at estimating inverse autocovariance matrices of long memory processes admitting a linear representation. A modified Cholesky decomposition is used in conjunction with an increasing order autoregressive model to achieve this goal. The spectral norm consistency of the proposed estimate is established. We then extend this result to linear regression models with long-memory time series errors. In particular, we show that when the objective is to consistently estimate the inverse autocovariance matrix of the error process, the same approach still works well if the estimated (by least squares) errors are used in place of the unobservable ones. Applications of this result to estimating unknown parameters in the aforementioned regression model are also given. Finally, a simulation study is performed to illustrate our theoretical findings.Comment: Published at http://dx.doi.org/10.3150/14-BEJ692 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource

Recently using entanglement as resource to distinguish orthogonal product states by local operations and classical communication (LOCC) has been studied intensively. Zhang. et al. presented protocols to use entanglement to distinguish certain classes of orthogonal product states in $\mathbb{C}^m\otimes \mathbb{C}^n$\cite{Zhang016}. In this paper, we study local distinguishability of multipartite orthogonal product states and provide a practical solution. Our method relies upon a special class of locally indistinguishable multipartite product states introduced by Wang et. al. to build a protocol to distinguishes perfectly multipartitie quantum states by LOCC using an entangled state as a resource for implementing quantum measurements.Comment: 13p

The Kondo Temperature of a Two-dimensional Electron Gas with Rashba Spin-orbit Coupling

We use the Hirsch-Fye quantum Monte Carlo method to study the single magnetic impurity problem in a two-dimensional electron gas with Rashba spin-orbit coupling. We calculate the spin susceptibility for various values of spin-orbit coupling, Hubbard interaction, and chemical potential. The Kondo temperatures for different parameters are estimated by fitting the universal curves of spin susceptibility. We find that the Kondo temperature is almost a linear function of Rashba spin-orbit energy when the chemical potential is close to the edge of the conduction band. When the chemical potential is far away from the band edge, the Kondo temperature is independent of the spin-orbit coupling. These results demonstrate that, for single impurity problem in this system, the most important reason to change the Kondo temperature is the divergence of density of states near the band edge, and the divergence is induced by the Rashba spin-orbit coupling.Comment: 5 pages, 4 figures, 2 references adde

Dynamics of social contagions with memory of non-redundant information

A key ingredient in social contagion dynamics is reinforcement, as adopting a certain social behavior requires verification of its credibility and legitimacy. Memory of non-redundant information plays an important role in reinforcement, which so far has eluded theoretical analysis. We first propose a general social contagion model with reinforcement derived from non-redundant information memory. Then, we develop a unified edge-based compartmental theory to analyze this model, and a remarkable agreement with numerics is obtained on some specific models. Using a spreading threshold model as a specific example to understand the memory effect, in which each individual adopts a social behavior only when the cumulative pieces of information that the individual received from his/her neighbors exceeds an adoption threshold. Through analysis and numerical simulations, we find that the memory characteristic markedly affects the dynamics as quantified by the final adoption size. Strikingly, we uncover a transition phenomenon in which the dependence of the final adoption size on some key parameters, such as the transmission probability, can change from being discontinuous to being continuous. The transition can be triggered by proper parameters and structural perturbations to the system, such as decreasing individuals' adoption threshold, increasing initial seed size, or enhancing the network heterogeneity.Comment: 13 pages, 9 figure

Preferential imitation of vaccinating behavior can invalidate the targeted subsidy on complex network

We consider the effect of inducement to vaccinate during the spread of an infectious disease on complex networks. Suppose that public resources are finite and that only a small proportion of individuals can be vaccinated freely (complete subsidy), for the remainder of the population vaccination is a voluntary behavior --- and each vaccinated individual carries a perceived cost. We ask whether the classical targeted subsidy strategy is definitely better than the random strategy: does targeting subsidy at individuals perceived to be with the greatest risk actually help? With these questions, we propose a model to investigate the \emph{interaction effects} of the subsidy policies and individuals responses when facing subsidy policies on the epidemic dynamics on complex networks. In the model, a small proportion of individuals are freely vaccinated according to either the targeted or random subsidy policy, the remainder choose to vaccinate (or not) based on voluntary principle and update their vaccination decision via an imitation rule. Our findings show that the targeted strategy is only advantageous when individuals prefer to imitate the subsidized individuals' strategy. Otherwise, the effect of the targeted policy is worse than the random immunization, since individuals preferentially select non-subsidized individuals as the imitation objects. More importantly, we find that under the targeted subsidy policy, increasing the proportion of subsidized individuals may increase the final epidemic size. We further define social cost as the sum of the costs of vaccination and infection, and study how each of the two policies affect the social cost. Our result shows that there exist some optimal intermediate regions leading to the minimal social cost.Comment: 8 pages, 7 figure