456 research outputs found
Robust chaos generation by a perceptron
The properties of time series generated by a perceptron with monotonic and
non-monotonic transfer function, where the next input vector is determined from
past output values, are examined. Analysis of the parameter space reveals the
following main finding: a perceptron with a monotonic function can produce
fragile chaos only whereas a non-monotonic function can generate robust chaos
as well. For non-monotonic functions, the dimension of the attractor can be
controlled monotonically by tuning a natural parameter in the model.Comment: 7 pages, 5 figures (reduced quality), accepted for publication in
EuroPhysics Letter
Mean First Passage Time in Periodic Attractors
The properties of the mean first passage time in a system characterized by
multiple periodic attractors are studied. Using a transformation from a high
dimensional space to 1D, the problem is reduced to a stochastic process along
the path from the fixed point attractor to a saddle point located between two
neighboring attractors. It is found that the time to switch between attractors
depends on the effective size of the attractors, , the noise, ,
and the potential difference between the attractor and an adjacent saddle point
as: ; the
ratio between the sizes of the two attractors affects . The
result is obtained analytically for small and confirmed by numerical
simulations. Possible implications that may arise from the model and results
are discussed.Comment: 14 pages, 3 figures, submitted to journal of physics
Learning and generation of long-range correlated sequences
We study the capability to learn and to generate long-range, power-law
correlated sequences by a fully connected asymmetric network. The focus is set
on the ability of neural networks to extract statistical features from a
sequence. We demonstrate that the average power-law behavior is learnable,
namely, the sequence generated by the trained network obeys the same
statistical behavior. The interplay between a correlated weight matrix and the
sequence generated by such a network is explored. A weight matrix with a
power-law correlation function along the vertical direction, gives rise to a
sequence with a similar statistical behavior.Comment: 5 pages, 3 figures, accepted for publication in Physical Review
On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories
Symmetries of three-dimensional topological field theories are naturally
defined in terms of invertible topological surface defects. Symmetry groups are
thus Brauer-Picard groups. We present a gauge theoretic realization of all
symmetries of abelian Dijkgraaf-Witten theories. The symmetry group for a
Dijkgraaf-Witten theory with gauge group a finite abelian group , and with
vanishing 3-cocycle, is generated by group automorphisms of , by
automorphisms of the trivial Chern-Simons 2-gerbe on the stack of -bundles,
and by partial e-m dualities.
We show that transmission functors naturally extracted from extended
topological field theories with surface defects give a physical realization of
the bijection between invertible bimodule categories of a fusion category and
braided auto-equivalences of its Drinfeld center. The latter provides the
labels for bulk Wilson lines; it follows that a symmetry is completely
characterized by its action on bulk Wilson lines.Comment: 21 pages, 9 figures. v2: Minor changes, typos corrected and
references added. v3: Typos correcte
The Forces Applied by Cilia Depend Linearly on Their Frequency Due to Constant Geometry of the Effective Stroke
AbstractMucus propelling cilia are excitable by many stimulants, and have been shown to increase their beating frequency up to threefold, by physiological extracellular stimulants, such as adenosine-triphosphate, acetylcholine, and others. This is thought to represent the evolutionary adaptation of mucociliary systems to the need of rapid and efficient cleansing the airways of foreign particles. However, the mucus transport velocity depends not only on the beat frequency of the cilia, but on their beat pattern as well, especially in the case of mucus bearing cilia that beat in a complex, three-dimensional fashion. In this study, we directly measured the force applied by live ciliary tissues with an atomic force microscope, and found that it increases linearly with the beating frequency. This implies that the arc swept by the cilia during their effective stroke remains unchanged during frequency increase, thus leading to a linear dependence of transport velocity on the beat frequency. Combining the atomic force microscope measurements with optical measurements, we have indications that the recovery stroke is performed on a less inclined plane, leading to an effective shortening of the overall path traveled by the cilia tip during this nontransporting phase of their beat pattern. This effect is observed to be independent of the type of stimulant (temperature or chemical), chemical (adenosine-triphosphate or acetylcholine), or concentration (1μM–100μM), indicating that this behavior may result from internal details of the cilium mechanical structure
Learning and predicting time series by neural networks
Artificial neural networks which are trained on a time series are supposed to
achieve two abilities: firstly to predict the series many time steps ahead and
secondly to learn the rule which has produced the series. It is shown that
prediction and learning are not necessarily related to each other. Chaotic
sequences can be learned but not predicted while quasiperiodic sequences can be
well predicted but not learned.Comment: 5 page
Model of ionic currents through microtubule nanopores and the lumen
It has been suggested that microtubules and other cytoskeletal filaments may
act as electrical transmission lines. An electrical circuit model of the
microtubule is constructed incorporating features of its cylindrical structure
with nanopores in its walls. This model is used to study how ionic conductance
along the lumen is affected by flux through the nanopores when an external
potential is applied across its two ends. Based on the results of Brownian
dynamics simulations, the nanopores were found to have asymmetric inner and
outer conductances, manifested as nonlinear IV curves. Our simulations indicate
that a combination of this asymmetry and an internal voltage source arising
from the motion of the C-terminal tails causes a net current to be pumped
across the microtubule wall and propagate down the microtubule through the
lumen. This effect is demonstrated to enhance and add directly to the
longitudinal current through the lumen resulting from an external voltage
source, and could be significant in amplifying low-intensity endogenous
currents within the cellular environment or as a nano-bioelectronic device.Comment: 43 pages, 6 figures, revised versio
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