1,734 research outputs found
Dynamical Entropy Production in Spiking Neuron Networks in the Balanced State
We demonstrate deterministic extensive chaos in the dynamics of large sparse
networks of theta neurons in the balanced state. The analysis is based on
numerically exact calculations of the full spectrum of Lyapunov exponents, the
entropy production rate and the attractor dimension. Extensive chaos is found
in inhibitory networks and becomes more intense when an excitatory population
is included. We find a strikingly high rate of entropy production that would
limit information representation in cortical spike patterns to the immediate
stimulus response.Comment: 4 pages, 4 figure
Unstable attractors induce perpetual synchronization and desynchronization
Common experience suggests that attracting invariant sets in nonlinear
dynamical systems are generally stable. Contrary to this intuition, we present
a dynamical system, a network of pulse-coupled oscillators, in which
\textit{unstable attractors} arise naturally. From random initial conditions,
groups of synchronized oscillators (clusters) are formed that send pulses
alternately, resulting in a periodic dynamics of the network. Under the
influence of arbitrarily weak noise, this synchronization is followed by a
desynchronization of clusters, a phenomenon induced by attractors that are
unstable. Perpetual synchronization and desynchronization lead to a switching
among attractors. This is explained by the geometrical fact, that these
unstable attractors are surrounded by basins of attraction of other attractors,
whereas the full measure of their own basin is located remote from the
attractor. Unstable attractors do not only exist in these systems, but moreover
dominate the dynamics for large networks and a wide range of parameters.Comment: 14 pages, 12 figure
Impact of membrane bistability on dynamical response of neuronal populations
Neurons in many brain areas can develop pronounced depolarized state of
membrane potential (up state) in addition to the normal hyperpolarized down
state near the resting potential. The influence of the up state on signal
encoding, however, is not well investigated. Here we construct a
one-dimensional bistable neuron model and calculate the linear response to
noisy oscillatory inputs analytically. We find that with the appearance of an
up state, the transmission function is enhanced by the emergence of a local
maximum at some optimal frequency and the phase lag relative to the input
signal is reduced. We characterize the dependence of the enhancement of
frequency response on intrinsic dynamics and on the occupancy of the up state
Spike Onset Dynamics and Response Speed in Neuronal Populations
Recent studies of cortical neurons driven by fluctuating currents revealed
cutoff frequencies for action potential encoding of several hundred Hz.
Theoretical studies of biophysical neuron models have predicted a much lower
cutoff frequency of the order of average firing rate or the inverse membrane
time constant. The biophysical origin of the observed high cutoff frequencies
is thus not well understood. Here we introduce a neuron model with dynamical
action potential generation, in which the linear response can be analytically
calculated for uncorrelated synaptic noise. We find that the cutoff frequencies
increase to very large values when the time scale of action potential
initiation becomes short
Long Chaotic Transients in Complex Networks
We show that long chaotic transients dominate the dynamics of randomly
diluted networks of pulse-coupled oscillators. This contrasts with the rapid
convergence towards limit cycle attractors found in networks of globally
coupled units. The lengths of the transients strongly depend on the network
connectivity and varies by several orders of magnitude, with maximum transient
lengths at intermediate connectivities. The dynamics of the transient exhibits
a novel form of robust synchronization. An approximation to the largest
Lyapunov exponent characterizing the chaotic nature of the transient dynamics
is calculated analytically.Comment: 4 pages; 5 figure
Can retinal ganglion cell dipoles seed iso-orientation domains in the visual cortex?
It has been argued that the emergence of roughly periodic orientation
preference maps (OPMs) in the primary visual cortex (V1) of carnivores and
primates can be explained by a so-called statistical connectivity model. This
model assumes that input to V1 neurons is dominated by feed-forward projections
originating from a small set of retinal ganglion cells (RGCs). The typical
spacing between adjacent cortical orientation columns preferring the same
orientation then arises via Moir\'{e}-Interference between hexagonal ON/OFF RGC
mosaics. While this Moir\'{e}-Interference critically depends on long-range
hexagonal order within the RGC mosaics, a recent statistical analysis of RGC
receptive field positions found no evidence for such long-range positional
order. Hexagonal order may be only one of several ways to obtain spatially
repetitive OPMs in the statistical connectivity model. Here, we investigate a
more general requirement on the spatial structure of RGC mosaics that can seed
the emergence of spatially repetitive cortical OPMs, namely that angular
correlations between so-called RGC dipoles exhibit a spatial structure similar
to that of OPM autocorrelation functions. Both in cat beta cell mosaics as well
as primate parasol receptive field mosaics we find that RGC dipole angles are
spatially uncorrelated. To help assess the level of these correlations, we
introduce a novel point process that generates mosaics with realistic nearest
neighbor statistics and a tunable degree of spatial correlations of dipole
angles. Using this process, we show that given the size of available data sets,
the presence of even weak angular correlations in the data is very unlikely. We
conclude that the layout of ON/OFF ganglion cell mosaics lacks the spatial
structure necessary to seed iso-orientation domains in the primary visual
cortex.Comment: 9 figures + 1 Supplementary figure and 1 Supplementary tabl
Ontology, Epistemology, Consciousness; And Closed, Timelike Curves
How should we think about subjective states vs. objective states? Is it a question of the meaning associated with a state? Recent work on this question arose in consideration of closed timelike curves (CTCs) and their possible role in quantum computers. The issue of ontic and epistemic states is particularly important when considering CTCs because, as one may argue, the interpretation of quantum states as either ontic or epistemic will naturally lead to different assumptions about how quantum systems behave in the presence of CTCs. For example, David Deutsch studied various time travel scenarios in a classical model and then in a quantum model motivated by a strictly ontic interpretation of quantum states. While in the classical model, CTCs could produce paradoxes, however Deutsch argued that no paradoxes can occur in his parallel universes (modified Everett interpretation) quantum treatment. Although all paradoxes are resolved in this way, the resulting theory is not standard quantum theory, but a new nonlinear theory. Many implications can arise using Deutsch's model and I shall discuss some of them in particular. These assumptions are particularly unconventional in part because they require that mixed quantum states are ontic. Pure quantum states can be interpreted as ontic, however most interpretations view mixed states as epistemic, i.e., reflecting an observer's lack of knowledge. I shall here consider an alternative proposal-pure quantum states, represented by density matrices containing off-diagonal elements, are possibly epistemic (since we never actually see them) while mixed quantum states arising in CTCs are always ontic representing the action of consciousness in observers (we do see them). Paradoxically my argument is based on the well-known experiences of gaining knowledge in classical physics; couching this in quantum physics terms, classical mixed states (represented by diagonal density matrices in quantum physics) are just what arise when an "observation" is said to occur resulting in a so-called reduction of the quantum wave function and the appearance of a classical world. In brief, Deutsch's CTC nonlinear post quantum physics model may represent the action of a conscious mind
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