3,263 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
Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability
Distributed consensus and other linear systems with system stochastic
matrices emerge in various settings, like opinion formation in social
networks, rendezvous of robots, and distributed inference in sensor networks.
The matrices are often random, due to, e.g., random packet dropouts in
wireless sensor networks. Key in analyzing the performance of such systems is
studying convergence of matrix products . In this paper, we
find the exact exponential rate for the convergence in probability of the
product of such matrices when time grows large, under the assumption that
the 's are symmetric and independent identically distributed in time.
Further, for commonly used random models like with gossip and link failure, we
show that the rate is found by solving a min-cut problem and, hence, easily
computable. Finally, we apply our results to optimally allocate the sensors'
transmission power in consensus+innovations distributed detection
Randomized Consensus with Attractive and Repulsive Links
We study convergence properties of a randomized consensus algorithm over a
graph with both attractive and repulsive links. At each time instant, a node is
randomly selected to interact with a random neighbor. Depending on if the link
between the two nodes belongs to a given subgraph of attractive or repulsive
links, the node update follows a standard attractive weighted average or a
repulsive weighted average, respectively. The repulsive update has the opposite
sign of the standard consensus update. In this way, it counteracts the
consensus formation and can be seen as a model of link faults or malicious
attacks in a communication network, or the impact of trust and antagonism in a
social network. Various probabilistic convergence and divergence conditions are
established. A threshold condition for the strength of the repulsive action is
given for convergence in expectation: when the repulsive weight crosses this
threshold value, the algorithm transits from convergence to divergence. An
explicit value of the threshold is derived for classes of attractive and
repulsive graphs. The results show that a single repulsive link can sometimes
drastically change the behavior of the consensus algorithm. They also
explicitly show how the robustness of the consensus algorithm depends on the
size and other properties of the graphs
Spatial networks with wireless applications
Many networks have nodes located in physical space, with links more common
between closely spaced pairs of nodes. For example, the nodes could be wireless
devices and links communication channels in a wireless mesh network. We
describe recent work involving such networks, considering effects due to the
geometry (convex,non-convex, and fractal), node distribution,
distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina
- …