A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and proximal updates, respectively. The proposed algorithm is closely related to a previous algorithm, PG-EXTRA \cite{shi2015proximal}, but has a few advantages. First of all, agents use uncoordinated step-sizes, and the stable upper bounds on step-sizes are independent of network topologies. The step-sizes depend on local objective functions, and they can be as large as those of the gradient descent. Secondly, for the special case without non-smooth terms, linear convergence can be achieved under the strong convexity assumption. The dependence of the convergence rate on the objective functions and the network are separated, and the convergence rate of the new algorithm is as good as one of the two convergence rates that match the typical rates for the general gradient descent and the consensus averaging. We provide numerical experiments to demonstrate the efficacy of the introduced algorithm and validate our theoretical discoveries

Fukushima's decomposition for diffusions associated with semi-Dirichlet forms

Diffusion processes associated with semi-Dirichlet forms are studied in the paper. The main results are Fukushima's decomposition for the diffusions and a transformation formula for the corresponding martingale part of the decomposition. The results are applied to some concrete examples

Fukushima type decomposition for semi-Dirichlet forms

We present a Fukushima type decomposition in the setting of general quasi-regular semi-Dirichlet forms. The decomposition is then employed to give a transformation formula for martingale additive functionals. Applications of the results to some concrete examples of semi-Dirichlet forms are given at the end of the paper. We discuss also the uniqueness question about Doob-Meyer decomposition on optional sets of interval type.Comment: arXiv admin note: text overlap with arXiv:1104.295

The magnetization degree of the outflow powering the highly-polarized reverse shock emission of GRB 120308A

GRB 120308A, a long duration $\gamma-$ray burst detected by {\it Swift}, was distinguished by a highly-polarized early optical afterglow emission that strongly suggests an ordered magnetic field component in the emitting region. In this work we model the optical and X-ray emission in the reverse and forward shock scenario and show that the strength of the magnetic field in reverse shock region is $\sim 10$ times stronger than that in the forward shock region. Consequently the outflow powering the highly-polarized reverse shock optical emission was mildly-magnetized at a degree $\sigma \sim$ a few percent. Considering the plausible magnetic energy dissipation in both the acceleration and prompt emission phases of the Gamma-ray Burst (GRB) outflow, the afterglow data of GRB 120308A provides us the compelling evidence that at least for some GRBs a non-ignorable fraction of the energy was released in the form of Poynting-flux, confirming the finding firstly made in the reverse-forward shock emission modeling of the optical afterglow of GRB 990123 (Fan et al. 2002; Zhang et al. 2003)

The bulk Lorentz factor of outflow powering X-ray flare in GRB afterglow

We develop two methods to estimate the bulk Lorentz factor of X-ray flare outflow. In the first method the outflow is assumed to be baryonic and is accelerated by the thermal pressure, for which the final bulk Lorentz factor is limited by the outflow luminosity as well as the initial radius of the outflow getting accelerated. Such a method may be applied to a considerable fraction of flares. The second method, based on the curvature effect interpretation of the quick decline of the flare, can give a tightly constrained estimate of the bulk Lorentz factor but can only be applied to a few giant flares. The results obtained in these two different ways are consistent with each other. The obtained bulk Lorentz factor (or just upper limit) of the X-ray flare outflows, ranging from ten to a few hundred, is generally smaller than that of the Gamma-ray Burst (GRB) outflows.Comment: 6 pages, 3 figures, ApJ in pres

Statistical properties of world investment networks

We have performed a detailed investigation on the world investment networks constructed from the Coordinated Portfolio Investment Survey (CPIS) data of the International Monetary Fund, ranging from 2001 to 2006. The distributions of degrees and node strengthes are scale-free. The weight distributions can be well modeled by the Weibull distribution. The maximum flow spanning trees of the world investment networks possess two universal allometric scaling relations, independent of time and the investment type. The topological scaling exponent is $1.17\pm0.02$ and the flow scaling exponent is $1.03\pm0.01$.Comment: 8 pages + an Appendi

Finite Sample Analysis of the GTD Policy Evaluation Algorithms in Markov Setting

In reinforcement learning (RL) , one of the key components is policy evaluation, which aims to estimate the value function (i.e., expected long-term accumulated reward) of a policy. With a good policy evaluation method, the RL algorithms will estimate the value function more accurately and find a better policy. When the state space is large or continuous \emph{Gradient-based Temporal Difference(GTD)} policy evaluation algorithms with linear function approximation are widely used. Considering that the collection of the evaluation data is both time and reward consuming, a clear understanding of the finite sample performance of the policy evaluation algorithms is very important to reinforcement learning. Under the assumption that data are i.i.d. generated, previous work provided the finite sample analysis of the GTD algorithms with constant step size by converting them into convex-concave saddle point problems. However, it is well-known that, the data are generated from Markov processes rather than i.i.d. in RL problems.. In this paper, in the realistic Markov setting, we derive the finite sample bounds for the general convex-concave saddle point problems, and hence for the GTD algorithms. We have the following discussions based on our bounds. (1) With variants of step size, GTD algorithms converge. (2) The convergence rate is determined by the step size, with the mixing time of the Markov process as the coefficient. The faster the Markov processes mix, the faster the convergence. (3) We explain that the experience replay trick is effective by improving the mixing property of the Markov process. To the best of our knowledge, our analysis is the first to provide finite sample bounds for the GTD algorithms in Markov setting

Large solar energetic particle event that occurred on 2012 March 7 and its VDA analysis

On 2012 March 7, the STEREO Ahead and Behind spacecraft, along with the near-earth spacecraft (e.g. SOHO, Wind) situated between the two STEREO spacecraft, observed an extremely large global solar energetic particle (SEP) event in Solar Cycle 24. Two successive coronal mass ejections (CMEs) have been detected close in time. From the multi-point in-situ observations, it can be found that this SEP event was caused by the first CME, and the second one was not involved. Using the velocity dispersion analysis (VDA), we find that for well magnetically connected point, the energetic protons and electrons are released nearly at the same time. The path lengths to STEREO-B(STB) of protons and electrons have distinct difference and deviate remarkably from the nominal Parker spiral path length, which is likely due to the presence of interplanetary magnetic structures situated between the source and the STB. Also the VDA method seems only to obtain reasonable results at well-connected locations and the inferred energetic particles release times in different energy channels are similar. We suggest that good-connection is crucial for obtaining both accurate release time and path length simultaneously, agreeing with the modeling result of Wang & Qin (2015)

TeV-PeV neutrinos over the atmospheric background: originating from two groups of sources?

In addition to the two ~1 PeV neutrinos, the IceCube Collaboration recently reported a detection of 26 neutrino candidates at energies from 30 TeV to 250 TeV, implying a confidence level of 4.3\sigma over the atmospheric background. We suggest that these TeV-PeV non-atmospheric neutrinos may originate from two groups of sources, motivated by the non-detection of neutrinos in the energy range 250 TeV- 1 PeV in current data. If intrinsic, the non-detection of 250 TeV-1 PeV neutrinos disfavors the single power-law spectrum model for the TeV-PeV non-atmospheric neutrinos at a confidence level of ~ 2\sigma. We then interpret the current neutrino data with a two-component spectrum model. One has a flat spectrum with a cutoff at the energy ~ 250 TeV and the other has a sharp peak at ~1 PeV. The former is likely via pp collision while the latter may be generated by the photomeson interaction.Comment: 5 pages, 1 figur

Communication cliques in mobile phone calling networks

People in modern societies form different social networks through numerous means of communication. These communication networks reflect different aspects of human's societal structure. The billing records of calls among mobile phone users enable us to construct a directed calling network (DCN) and its Bonferroni network (SVDCN) in which the preferential communications are statistically validated. Here we perform a comparative investigation of the cliques of the original DCN and its SVDCN constructed from the calling records of more than nine million individuals in Shanghai over a period of 110 days. We find that the statistical properties of the cliques of the two calling networks are qualitatively similar and the clique members in the DCN and the SVDCN exhibit idiosyncratic behaviors quantitatively. Members in large cliques are found to be spatially close to each other. Based on the clique degree profile of each mobile phone user, the most active users in the two calling networks can be classified in to several groups. The users in different groups are found to have different calling behaviors. Our study unveils interesting communication behaviors among mobile phone users that are densely connected to each other.Comment: 18 pages, 10 figure