2,588 research outputs found
Scalable Kernel Methods via Doubly Stochastic Gradients
The general perception is that kernel methods are not scalable, and neural
nets are the methods of choice for nonlinear learning problems. Or have we
simply not tried hard enough for kernel methods? Here we propose an approach
that scales up kernel methods using a novel concept called "doubly stochastic
functional gradients". Our approach relies on the fact that many kernel methods
can be expressed as convex optimization problems, and we solve the problems by
making two unbiased stochastic approximations to the functional gradient, one
using random training points and another using random functions associated with
the kernel, and then descending using this noisy functional gradient. We show
that a function produced by this procedure after iterations converges to
the optimal function in the reproducing kernel Hilbert space in rate ,
and achieves a generalization performance of . This doubly
stochasticity also allows us to avoid keeping the support vectors and to
implement the algorithm in a small memory footprint, which is linear in number
of iterations and independent of data dimension. Our approach can readily scale
kernel methods up to the regimes which are dominated by neural nets. We show
that our method can achieve competitive performance to neural nets in datasets
such as 8 million handwritten digits from MNIST, 2.3 million energy materials
from MolecularSpace, and 1 million photos from ImageNet.Comment: 32 pages, 22 figure
Efficient calculation of the robustness measure R for complex networks
In a recent work, Schneider et al. (2011) proposed a new measure R for network robustness, where the value of R is calculated within the entire process of malicious node attacks. In this paper, we present an approach to improve the calculation efficiency of R, in which a computationally efficient robustness measure R' is introduced when the fraction of failed nodes reaches to a critical threshold qc. Simulation results on three different types of network models and three real networks show that these networks all exhibit a computationally efficient robustness measure R'. The relationships between R' and the network size N and the network average degree are also explored. It is found that the value of R' decreases with N while increases with . Our results would be useful for improving the calculation efficiency of network robustness measure R for complex networks.Peer ReviewedPostprint (author's final draft
Hawking radiation-quasinormal modes correspondence for large AdS black holes
It is well-known that the non-strictly thermal character of the Hawking
radiation spectrum generates a natural correspondence between Hawking radiation
and black hole quasinormal modes. This main issue has been analyzed in the
framework of Schwarzschild black holes, Kerr black holes and nonextremal
Reissner-Nordstrom black holes. In this paper, by introducing the effective
temperature, we reanalysis the non-strictly thermal character of large AdS
black holes. The results show that the effective mass corresponding to the
effective temperature is approximatively the average one in any dimension. And
the other effective quantities can also be obtained. Based on the known forms
of frequency in quasinormal modes, we reanalysis the asymptotic frequencies of
the large AdS black hole in three and five dimensions. Then we get the formulas
of the Bekenstein-Hawking entropy and the horizon's area quantization with
functions of the quantum "overtone" number .Comment: 6 page
LS-DTKMS: A Local Search Algorithm for Diversified Top-k MaxSAT Problem
The Maximum Satisfiability (MaxSAT), an important optimization problem, has a range of applications, including network routing, planning and scheduling, and combinatorial auctions. Among these applications, one usually benefits from having not just one single solution, but k diverse solutions. Motivated by this, we study an extension of MaxSAT, named Diversified Top-k MaxSAT (DTKMS) problem, which is to find k feasible assignments of a given formula such that each assignment satisfies all hard clauses and all of them together satisfy the maximum number of soft clauses. This paper presents a local search algorithm, LS-DTKMS, for DTKMS problem, which exploits novel scoring functions to select variables and assignments. Experiments demonstrate that LS-DTKMS outperforms the top-k MaxSAT based DTKMS solvers and state-of-the-art solvers for diversified top-k clique problem
Efficient manganese luminescence induced by Ce3+-Mn2+ energy transfer in rare earth fluoride and phosphate nanocrystals
Manganese materials with attractive optical properties have been proposed for applications in such areas as photonics, light-emitting diodes, and bioimaging. In this paper, we have demonstrated multicolor Mn2+ luminescence in the visible region by controlling Ce3+-Mn2+ energy transfer in rare earth nanocrystals [NCs]. CeF3 and CePO4 NCs doped with Mn2+ have been prepared and can be well dispersed in aqueous solutions. Under ultraviolet light excitation, both the CeF3:Mn and CePO4:Mn NCs exhibit Mn2+ luminescence, yet their output colors are green and orange, respectively. By optimizing Mn2+ doping concentrations, Mn2+ luminescence quantum efficiency and Ce3+-Mn2+ energy transfer efficiency can respectively reach 14% and 60% in the CeF3:Mn NCs
- …