182 research outputs found
Cellular neural networks for NP-hard optimization problems
Nowadays, Cellular Neural Networks (CNN) are practically implemented in
parallel, analog computers, showing a fast developing trend. Physicist must be
aware that such computers are appropriate for solving in an elegant manner
practically important problems, which are extremely slow on the classical
digital architecture. Here, CNN is used for solving NP-hard optimization
problems on lattices. It is proved, that a CNN in which the parameters of all
cells can be separately controlled, is the analog correspondent of a
two-dimensional Ising type (Edwards-Anderson) spin-glass system. Using the
properties of CNN computers a fast optimization method can be built for such
problems. Estimating the simulation time needed for solving such NP-hard
optimization problems on CNN based computers, and comparing it with the time
needed on normal digital computers using the simulated annealing algorithm, the
results are astonishing: CNN computers would be faster than digital computers
already at 10*10 lattice sizes. Hardwares realized nowadays are of 176*144
size. Also, there seems to be no technical difficulties adapting CNN chips for
such problems and the needed local control is expected to be fully developed in
the near future
Perspectives for Monte Carlo simulations on the CNN Universal Machine
Possibilities for performing stochastic simulations on the analog and fully
parallelized Cellular Neural Network Universal Machine (CNN-UM) are
investigated. By using a chaotic cellular automaton perturbed with the natural
noise of the CNN-UM chip, a realistic binary random number generator is built.
As a specific example for Monte Carlo type simulations, we use this random
number generator and a CNN template to study the classical site-percolation
problem on the ACE16K chip. The study reveals that the analog and parallel
architecture of the CNN-UM is very appropriate for stochastic simulations on
lattice models. The natural trend for increasing the number of cells and local
memories on the CNN-UM chip will definitely favor in the near future the CNN-UM
architecture for such problems.Comment: 14 pages, 6 figure
Centrality scaling in large networks
Betweenness centrality lies at the core of both transport and structural
vulnerability properties of complex networks, however, it is computationally
costly, and its measurement for networks with millions of nodes is near
impossible. By introducing a multiscale decomposition of shortest paths, we
show that the contributions to betweenness coming from geodesics not longer
than L obey a characteristic scaling vs L, which can be used to predict the
distribution of the full centralities. The method is also illustrated on a
real-world social network of 5.5*10^6 nodes and 2.7*10^7 links
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