2,947 research outputs found
Information Storage in the Stochastic Ising Model
Most information systems store data by modifying the local state of matter,
in the hope that atomic (or sub-atomic) local interactions would stabilize the
state for a sufficiently long time, thereby allowing later recovery. In this
work we initiate the study of information retention in locally-interacting
systems. The evolution in time of the interacting particles is modeled via the
stochastic Ising model (SIM). The initial spin configuration serves as
the user-controlled input. The output configuration is produced by
running steps of the Glauber chain. Our main goal is to evaluate the
information capacity when the time
scales with the size of the system . For the zero-temperature SIM on the
two-dimensional grid and free boundary conditions, it
is easy to show that for . In addition, we show
that on the order of bits can be stored for infinite time in striped
configurations. The achievability is optimal when and
is fixed.
One of the main results of this work is an achievability scheme that stores
more than bits (in orders of magnitude) for superlinear (in )
times. The analysis of the scheme decomposes the system into
independent Z-channels whose crossover probability is found via the (recently
rigorously established) Lifshitz law of phase boundary movement. We also
provide results for the positive but small temperature regime. We show that an
initial configuration drawn according to the Gibbs measure cannot retain more
than a single bit for . On the other hand,
when scaling time with , the stripe-based coding scheme (that stores for
infinite time at zero temperature) is shown to retain its bits for time that is
exponential in
Retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks
The retrieval behavior and thermodynamic properties of symmetrically diluted
Q-Ising neural networks are derived and studied in replica-symmetric mean-field
theory generalizing earlier works on either the fully connected or the
symmetrical extremely diluted network. Capacity-gain parameter phase diagrams
are obtained for the Q=3, Q=4 and state networks with uniformly
distributed patterns of low activity in order to search for the effects of a
gradual dilution of the synapses. It is shown that enlarged regions of
continuous changeover into a region of optimal performance are obtained for
finite stochastic noise and small but finite connectivity. The de
Almeida-Thouless lines of stability are obtained for arbitrary connectivity,
and the resulting phase diagrams are used to draw conclusions on the behavior
of symmetrically diluted networks with other pattern distributions of either
high or low activity.Comment: 21 pages, revte
Thouless-Anderson-Palmer equation for analog neural network with temporally fluctuating white synaptic noise
Effects of synaptic noise on the retrieval process of associative memory
neural networks are studied from the viewpoint of neurobiological and
biophysical understanding of information processing in the brain. We
investigate the statistical mechanical properties of stochastic analog neural
networks with temporally fluctuating synaptic noise, which is assumed to be
white noise. Such networks, in general, defy the use of the replica method,
since they have no energy concept. The self-consistent signal-to-noise analysis
(SCSNA), which is an alternative to the replica method for deriving a set of
order parameter equations, requires no energy concept and thus becomes
available in studying networks without energy functions. Applying the SCSNA to
stochastic network requires the knowledge of the Thouless-Anderson-Palmer (TAP)
equation which defines the deterministic networks equivalent to the original
stochastic ones. The study of the TAP equation which is of particular interest
for the case without energy concept is very few, while it is closely related to
the SCSNA in the case with energy concept. This paper aims to derive the TAP
equation for networks with synaptic noise together with a set of order
parameter equations by a hybrid use of the cavity method and the SCSNA.Comment: 13 pages, 3 figure
Synchronous versus sequential updating in the three-state Ising neural network with variable dilution
The three-state Ising neural network with synchronous updating and variable
dilution is discussed starting from the appropriate Hamiltonians. The
thermodynamic and retrieval properties are examined using replica mean-field
theory. Capacity-temperature phase diagrams are derived for several values of
the pattern activity and different gradations of dilution, and the information
content is calculated. The results are compared with those for sequential
updating. The effect of self-coupling is established. Also the dynamics is
studied using the generating function technique for both synchronous and
sequential updating. Typical flow diagrams for the overlap order parameter are
presented. The differences with the signal-to-noise approach are outlined.Comment: 21 pages Latex, 12 eps figures and 1 ps figur
Near-optimal protocols in complex nonequilibrium transformations
The development of sophisticated experimental means to control nanoscale
systems has motivated efforts to design driving protocols which minimize the
energy dissipated to the environment. Computational models are a crucial tool
in this practical challenge. We describe a general method for sampling an
ensemble of finite-time, nonequilibrium protocols biased towards a low average
dissipation. We show that this scheme can be carried out very efficiently in
several limiting cases. As an application, we sample the ensemble of
low-dissipation protocols that invert the magnetization of a 2D Ising model and
explore how the diversity of the protocols varies in response to constraints on
the average dissipation. In this example, we find that there is a large set of
protocols with average dissipation close to the optimal value, which we argue
is a general phenomenon.Comment: 6 pages and 3 figures plus 4 pages and 5 figures of supplemental
materia
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