5,647 research outputs found
Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine
Finding the ground states of the Ising Hamiltonian [1] maps to various
combinatorial optimization problems in biology, medicine, wireless
communications, artificial intelligence, and social network. So far no
efficient classical and quantum algorithm is known for these problems, and
intensive research is focused on creating physical systems - Ising machines -
capable of finding the absolute or approximate ground states of the Ising
Hamiltonian [2-6]. Here we report a novel Ising machine using a network of
degenerate optical parametric oscillators (OPOs). Spins are represented with
above-threshold binary phases of the OPOs and the Ising couplings are realized
by mutual injections [7]. The network is implemented in a single OPO ring
cavity with multiple trains of femtosecond pulses and configurable mutual
couplings, and operates at room temperature. We programed the smallest
non-deterministic polynomial time (NP)- hard Ising problem on the machine, and
in 1000 runs of the machine no computational error was detected
Distributed stochastic optimization via matrix exponential learning
In this paper, we investigate a distributed learning scheme for a broad class
of stochastic optimization problems and games that arise in signal processing
and wireless communications. The proposed algorithm relies on the method of
matrix exponential learning (MXL) and only requires locally computable gradient
observations that are possibly imperfect and/or obsolete. To analyze it, we
introduce the notion of a stable Nash equilibrium and we show that the
algorithm is globally convergent to such equilibria - or locally convergent
when an equilibrium is only locally stable. We also derive an explicit linear
bound for the algorithm's convergence speed, which remains valid under
measurement errors and uncertainty of arbitrarily high variance. To validate
our theoretical analysis, we test the algorithm in realistic
multi-carrier/multiple-antenna wireless scenarios where several users seek to
maximize their energy efficiency. Our results show that learning allows users
to attain a net increase between 100% and 500% in energy efficiency, even under
very high uncertainty.Comment: 31 pages, 3 figure
Synchronization in a neuronal feedback loop through asymmetric temporal delays
We consider the effect of asymmetric temporal delays in a system of two
coupled Hopfield neurons. For couplings of opposite signs, a limit cycle
emerges via a supercritical Hopf bifurcation when the sum of the delays reaches
a critical value. We show that the angular frequency of the limit cycle is
independent of an asymmetry in the delays. However, the delay asymmetry
determines the phase difference between the periodic activities of the two
components. Specifically, when the connection with negative coupling has a
delay much larger than the delay for the positive coupling, the system
approaches in-phase synchrony between the two components. Employing variational
perturbation theory (VPT), we achieve an approximate analytical evaluation of
the phase shift, in good agreement with numerical results.Comment: 5 pages, 4 figure
Delay-induced patterns in a two-dimensional lattice of coupled oscillators
We show how a variety of stable spatio-temporal periodic patterns can be
created in 2D-lattices of coupled oscillators with non-homogeneous coupling
delays. A "hybrid dispersion relation" is introduced, which allows studying the
stability of time-periodic patterns analytically in the limit of large delay.
The results are illustrated using the FitzHugh-Nagumo coupled neurons as well
as coupled limit cycle (Stuart-Landau) oscillators
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