5 research outputs found
A layered neural network with three-state neurons optimizing the mutual information
The time evolution of an exactly solvable layered feedforward neural network
with three-state neurons and optimizing the mutual information is studied for
arbitrary synaptic noise (temperature). Detailed stationary
temperature-capacity and capacity-activity phase diagrams are obtained. The
model exhibits pattern retrieval, pattern-fluctuation retrieval and spin-glass
phases. It is found that there is an improved performance in the form of both a
larger critical capacity and information content compared with three-state
Ising-type layered network models. Flow diagrams reveal that saddle-point
solutions associated with fluctuation overlaps slow down considerably the flow
of the network states towards the stable fixed-points.Comment: 17 pages Latex including 6 eps-figure
Phase variance of squeezed vacuum states
We consider the problem of estimating the phase of squeezed vacuum states
within a Bayesian framework. We derive bounds on the average Holevo variance
for an arbitrary number of uncorrelated copies. We find that it scales with
the mean photon number, , as dictated by the Heisenberg limit, i.e., as
, only for . For this fundamental scaling breaks down
and it becomes . Thus, a single squeezed vacuum state performs worse
than a single coherent state with the same energy. We find the optimal
splitting of a fixed given energy among various copies. We also compute the
variance for repeated individual measurements (without classical communication
or adaptivity) and find that the standard Heisenberg-limited scaling
is recovered for large samples.Comment: Minor changes, version to appear in PRA, 8 pages, 2 figure
Reexamination of the long-range Potts model: a multicanonical approach
We investigate the critical behavior of the one-dimensional q-state Potts
model with long-range (LR) interaction , using a multicanonical
algorithm. The recursion scheme initially proposed by Berg is improved so as to
make it suitable for a large class of LR models with unequally spaced energy
levels. The choice of an efficient predictor and a reliable convergence
criterion is discussed. We obtain transition temperatures in the first-order
regime which are in far better agreement with mean-field predictions than in
previous Monte Carlo studies. By relying on the location of spinodal points and
resorting to scaling arguments, we determine the threshold value
separating the first- and second-order regimes to two-digit precision within
the range . We offer convincing numerical evidence supporting
$\sigma_c(q)Comment: 18 pages, 18 figure