495 research outputs found
Actions for Vacuum Einstein's Equation with a Killing Symmetry
In a space-time with a Killing vector field which is either
everywhere timelike or everywhere spacelike, the collection of all trajectories
of gives a 3-dimension space . Besides the symmetry-reduced action
from that of Einstein-Hilbert, an alternative action of the fields on is
also proposed, which gives the same fields equations as those reduced from the
vacuum Einstein equation on .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
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