Actions for Vacuum Einstein's Equation with a Killing Symmetry

In a space-time $M$ with a Killing vector field $\xi^a$ which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of $\xi^a$ gives a 3-dimension space $S$. Besides the symmetry-reduced action from that of Einstein-Hilbert, an alternative action of the fields on $S$ is also proposed, which gives the same fields equations as those reduced from the vacuum Einstein equation on $M$.Comment: 8 pages, the difference between the action we proposed and the symmetry-reduced action is clarifie

Distributed Linear Regression with Compositional Covariates

With the availability of extraordinarily huge data sets, solving the problems of distributed statistical methodology and computing for such data sets has become increasingly crucial in the big data area. In this paper, we focus on the distributed sparse penalized linear log-contrast model in massive compositional data. In particular, two distributed optimization techniques under centralized and decentralized topologies are proposed for solving the two different constrained convex optimization problems. Both two proposed algorithms are based on the frameworks of Alternating Direction Method of Multipliers (ADMM) and Coordinate Descent Method of Multipliers(CDMM, Lin et al., 2014, Biometrika). It is worth emphasizing that, in the decentralized topology, we introduce a distributed coordinate-wise descent algorithm based on Group ADMM(GADMM, Elgabli et al., 2020, Journal of Machine Learning Research) for obtaining a communication-efficient regularized estimation. Correspondingly, the convergence theories of the proposed algorithms are rigorously established under some regularity conditions. Numerical experiments on both synthetic and real data are conducted to evaluate our proposed algorithms.Comment: 35 pages,2 figure

Research on Industry Alliance Knowledge Transfer Network Modeling and Simulation Based on Complex Networks

The booming of the complex network research provides new avenues of research and support for various types of complex systems. And a large number of studies have shown that industrial technology innovation coalition belongs to the scope of complex system, so it is available to use the complex network theory to study it. This paper first describes the theory of complex networks. Second, the use of complex network theory in the industry alliance knowledge transfer is probed in terms of the overall network structure, network node centrality and network subgroup. Finally, the industry alliances knowledge transfer network model is constructed and the quantitative analysis of the simulation example is done with the network analysis tool, reflecting the effectiveness of analyzing knowledge transfer from a complex network perspective