391 research outputs found
Episodic synchronization in dynamically driven neurons
We examine the response of type II excitable neurons to trains of synaptic
pulses, as a function of the pulse frequency and amplitude. We show that the
resonant behavior characteristic of type II excitability, already described for
harmonic inputs, is also present for pulsed inputs. With this in mind, we study
the response of neurons to pulsed input trains whose frequency varies
continuously in time, and observe that the receiving neuron synchronizes
episodically to the input pulses, whenever the pulse frequency lies within the
neuron's locking range. We propose this behavior as a mechanism of rate-code
detection in neuronal populations. The results are obtained both in numerical
simulations of the Morris-Lecar model and in an electronic implementation of
the FitzHugh-Nagumo system, evidencing the robustness of the phenomenon.Comment: 7 pages, 8 figure
A New View on Worst-Case to Average-Case Reductions for NP Problems
We study the result by Bogdanov and Trevisan (FOCS, 2003), who show that
under reasonable assumptions, there is no non-adaptive worst-case to
average-case reduction that bases the average-case hardness of an NP-problem on
the worst-case complexity of an NP-complete problem. We replace the hiding and
the heavy samples protocol in [BT03] by employing the histogram verification
protocol of Haitner, Mahmoody and Xiao (CCC, 2010), which proves to be very
useful in this context. Once the histogram is verified, our hiding protocol is
directly public-coin, whereas the intuition behind the original protocol
inherently relies on private coins
Nonuniversal spectral properties of the Luttinger model
The one electron spectral functions for the Luttinger model are discussed for
large but finite systems. The methods presented allow a simple interpretation
of the results. For finite range interactions interesting nonunivesal spectral
features emerge for momenta which differ from the Fermi points by the order of
the inverse interaction range or more. For a simplified model with interactions
only within the branches of right and left moving electrons analytical
expressions for the spectral function are presented which allows to perform the
thermodynamic limit. As in the general spinless model and the model including
spin for which we present mainly numerical results the spectral functions do
not approach the noninteracting limit for large momenta. The implication of our
results for recent high resolution photoemission measurements on quasi
one-dimensional conductors are discussed.Comment: 19 pages, Revtex 2.0, 5 ps-figures, to be mailed on reques
Transition from regular to complex behaviour in a discrete deterministic asymmetric neural network model
We study the long time behaviour of the transient before the collapse on the
periodic attractors of a discrete deterministic asymmetric neural networks
model. The system has a finite number of possible states so it is not possible
to use the term chaos in the usual sense of sensitive dependence on the initial
condition. Nevertheless, at varying the asymmetry parameter, , one observes
a transition from ordered motion (i.e. short transients and short periods on
the attractors) to a ``complex'' temporal behaviour. This transition takes
place for the same value at which one has a change for the mean
transient length from a power law in the size of the system () to an
exponential law in . The ``complex'' behaviour during the transient shows
strong analogies with the chaotic behaviour: decay of temporal correlations,
positive Shannon entropy, non-constant Renyi entropies of different orders.
Moreover the transition is very similar to that one for the intermittent
transition in chaotic systems: scaling law for the Shannon entropy and strong
fluctuations of the ``effective Shannon entropy'' along the transient, for .Comment: 18 pages + 6 figures, TeX dialect: Plain TeX + IOP macros (included
Measurement of molecular mixing at a conjugated polymer interface by specular and off-specular neutron scattering
Measurements have been performed on thermally equilibrated conjugated-polymer/insulating-polymer bilayers, using specular and off-specular neutron reflectivity. While specular reflectivity is only sensitive to the structure normal to the sample, off-specular measurements can probe the structure of the buried polymer/polymer interface in the plane of the sample. Systematic analysis of the scattering from a set of samples with varying insulating-polymer-thickness, using the distorted-wave Born approximation (DWBA), has allowed a robust determination of the intrinsic width at the buried polymer/polymer interface. The quantification of this width (12 Ă
± 4 Ă
) allows us to examine aspects of the conjugated polymer conformation at the interface, by appealing to self-consistent field theory (SCFT) predictions for equilibrium polymer/polymer interfaces in the cases of flexible and semi-flexible chains. This analysis enables us to infer that mixing at this particular interface cannot be described in terms of polymer chain segments that adopt conformations similar to a random walk. Instead, a more plausible explanation is that the conjugated polymer chain segments become significantly oriented in the plane of the interface. It is important to point out that we are only able to reach this conclusion following the extensive analysis of reflectivity data, followed by comparison with SCFT predictions. It is not simply the case that conjugated polymers would be expected to adopt this kind of oriented conformation at the interface, because of their relatively high chain stiffness. It is the combination of a high stiffness and a relatively narrow intrinsic interfacial width that results in a deviation from flexible chain behaviour
Attractors in fully asymmetric neural networks
The statistical properties of the length of the cycles and of the weights of
the attraction basins in fully asymmetric neural networks (i.e. with completely
uncorrelated synapses) are computed in the framework of the annealed
approximation which we previously introduced for the study of Kauffman
networks. Our results show that this model behaves essentially as a Random Map
possessing a reversal symmetry. Comparison with numerical results suggests that
the approximation could become exact in the infinite size limit.Comment: 23 pages, 6 figures, Latex, to appear on J. Phys.
Stochastic transitions of attractors in associative memory models with correlated noise
We investigate dynamics of recurrent neural networks with correlated noise to
analyze the noise's effect. The mechanism of correlated firing has been
analyzed in various models, but its functional roles have not been discussed in
sufficient detail. Aoyagi and Aoki have shown that the state transition of a
network is invoked by synchronous spikes. We introduce two types of noise to
each neuron: thermal independent noise and correlated noise. Due to the effects
of correlated noise, the correlation between neural inputs cannot be ignored,
so the behavior of the network has sample dependence. We discuss two types of
associative memory models: one with auto- and weak cross-correlation
connections and one with hierarchically correlated patterns. The former is
similar in structure to Aoyagi and Aoki's model. We show that stochastic
transition can be presented by correlated rather than thermal noise. In the
latter, we show stochastic transition from a memory state to a mixture state
using correlated noise. To analyze the stochastic transitions, we derive a
macroscopic dynamic description as a recurrence relation form of a probability
density function when the correlated noise exists. Computer simulations agree
with theoretical results.Comment: 21 page
How universal is the one-particle Green's function of a Luttinger liquid?
The one-particle Green's function of the Tomonaga-Luttinger model for
one-dimensional interacting Fermions is discussed. Far away from the origin of
the plane of space-time coordinates the function falls off like a power law.
The exponent depends on the direction within the plane. For a certain form of
the interaction potential or within an approximated cut-off procedure the
different exponents only depend on the strength of the interaction at zero
momentum and can be expressed in terms of the Luttinger liquid parameters
and of the model at hand. For a more general
interaction and directions which are determined by the charge velocity
and spin velocity the exponents also depend on the
smoothness of the interaction at zero momentum and the asymptotic behavior of
the Green's function is not given by the Luttinger liquid parameters alone.
This shows that the physics of large space-time distances in Luttinger liquids
is less universal than is widely believed.Comment: 5 pages with 2 figure
Hydration and Ordering of Lamellar Block Copolymer Films under Controlled Water Vapor
Amphiphilic block copolymers within a range of volume fraction spontaneously form vesicles in aqueous solution, where a water core is enclosed by a polymer bilayer. Thin-film rehydration is a method used to produce vesicles routinely; a thin film is immersed in water, the film swells, and vesicles are formed which bleb off from the film surface. We have studied the early stages of hydration for PEOâPBO block copolymer thin films under controlled water vapor conditions to understand this formation mechanism and so enable more efficient ways to encapsulate molecules using this method. Neutron and X-ray measurements show that the initial film exhibits weakly ordered structure with isotropic parallel and vertical orientation; the films initially swell and maintain the same orientation. At a critical point the layer swells rapidly and makes highly ordered lamellae structure at the same time. The lamellae are almost exclusively oriented parallel to the substrate and swell with increasing water absorption
Relaxation, closing probabilities and transition from oscillatory to chaotic attractors in asymmetric neural networks
Attractors in asymmetric neural networks with deterministic parallel dynamics
were shown to present a "chaotic" regime at symmetry eta < 0.5, where the
average length of the cycles increases exponentially with system size, and an
oscillatory regime at high symmetry, where the typical length of the cycles is
2. We show, both with analytic arguments and numerically, that there is a sharp
transition, at a critical symmetry \e_c=0.33, between a phase where the
typical cycles have length 2 and basins of attraction of vanishing weight and a
phase where the typical cycles are exponentially long with system size, and the
weights of their attraction basins are distributed as in a Random Map with
reversal symmetry. The time-scale after which cycles are reached grows
exponentially with system size , and the exponent vanishes in the symmetric
limit, where . The transition can be related to the dynamics
of the infinite system (where cycles are never reached), using the closing
probabilities as a tool.
We also study the relaxation of the function ,
where is the local field experienced by the neuron . In the symmetric
system, it plays the role of a Ljapunov function which drives the system
towards its minima through steepest descent. This interpretation survives, even
if only on the average, also for small asymmetry. This acts like an effective
temperature: the larger is the asymmetry, the faster is the relaxation of ,
and the higher is the asymptotic value reached. reachs very deep minima in
the fixed points of the dynamics, which are reached with vanishing probability,
and attains a larger value on the typical attractors, which are cycles of
length 2.Comment: 24 pages, 9 figures, accepted on Journal of Physics A: Math. Ge
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