510 research outputs found
Longitudinal Response of Confined Semiflexible Polymers
The longitudinal response of single semiflexible polymers to sudden changes
in externally applied forces is known to be controlled by the propagation and
relaxation of backbone tension. Under many experimental circumstances,
realized, e.g., in nano-fluidic devices or in polymeric networks or solutions,
these polymers are effectively confined in a channel- or tube-like geometry. By
means of heuristic scaling laws and rigorous analytical theory, we analyze the
tension dynamics of confined semiflexible polymers for various generic
experimental setups. It turns out that in contrast to the well-known linear
response, the influence of confinement on the non-linear dynamics can largely
be described as that of an effective prestress. We also study the free
relaxation of an initially confined chain, finding a surprising superlinear
t^(9/8) growth law for the change in end-to-end distance at short times.Comment: 18 pages, 1 figur
Escalation of error catastrophe for enzymatic self-replicators
It is a long-standing question in origin-of-life research whether the
information content of replicating molecules can be maintained in the presence
of replication errors. Extending standard quasispecies models of non-enzymatic
replication, we analyze highly specific enzymatic self-replication mediated
through an otherwise neutral recognition region, which leads to
frequency-dependent replication rates. We find a significant reduction of the
maximally tolerable error rate, because the replication rate of the fittest
molecules decreases with the fraction of functional enzymes. Our analysis is
extended to hypercyclic couplings as an example for catalytic networks.Comment: 6 pages, 4 figures; accepted at Europhys. Let
Analyzing Short-Term Noise Dependencies of Spike-Counts in Macaque Prefrontal Cortex Using Copulas and the Flashlight Transformation
Simultaneous spike-counts of neural populations are typically modeled by a Gaussian distribution. On short time scales, however, this distribution is too restrictive to describe and analyze multivariate distributions of discrete spike-counts. We present an alternative that is based on copulas and can account for arbitrary marginal distributions, including Poisson and negative binomial distributions as well as second and higher-order interactions. We describe maximum likelihood-based procedures for fitting copula-based models to spike-count data, and we derive a so-called flashlight transformation which makes it possible to move the tail dependence of an arbitrary copula into an arbitrary orthant of the multivariate probability distribution. Mixtures of copulas that combine different dependence structures and thereby model different driving processes simultaneously are also introduced. First, we apply copula-based models to populations of integrate-and-fire neurons receiving partially correlated input and show that the best fitting copulas provide information about the functional connectivity of coupled neurons which can be extracted using the flashlight transformation. We then apply the new method to data which were recorded from macaque prefrontal cortex using a multi-tetrode array. We find that copula-based distributions with negative binomial marginals provide an appropriate stochastic model for the multivariate spike-count distributions rather than the multivariate Poisson latent variables distribution and the often used multivariate normal distribution. The dependence structure of these distributions provides evidence for common inhibitory input to all recorded stimulus encoding neurons. Finally, we show that copula-based models can be successfully used to evaluate neural codes, e. g., to characterize stimulus-dependent spike-count distributions with information measures. This demonstrates that copula-based models are not only a versatile class of models for multivariate distributions of spike-counts, but that those models can be exploited to understand functional dependencies
Cellular Structures for Computation in the Quantum Regime
We present a new cellular data processing scheme, a hybrid of existing
cellular automata (CA) and gate array architectures, which is optimized for
realization at the quantum scale. For conventional computing, the CA-like
external clocking avoids the time-scale problems associated with ground-state
relaxation schemes. For quantum computing, the architecture constitutes a novel
paradigm whereby the algorithm is embedded in spatial, as opposed to temporal,
structure. The architecture can be exploited to produce highly efficient
algorithms: for example, a list of length N can be searched in time of order
cube root N.Comment: 11 pages (LaTeX), 3 figure
A freely relaxing polymer remembers how it was straightened
The relaxation of initially straight semiflexible polymers has been discussed
mainly with respect to the longest relaxation time. The biologically relevant
non-equilibrium dynamics on shorter times is comparatively poorly understood,
partly because "initially straight" can be realized in manifold ways. Combining
Brownian dynamics simulations and systematic theory, we demonstrate how
different experimental preparations give rise to specific short-time and
universal long-time dynamics. We also discuss boundary effects and the onset of
the stretch--coil transition.Comment: 14 pages, 5 figures, 3 table
Pinwheel stabilization by ocular dominance segregation
We present an analytical approach for studying the coupled development of
ocular dominance and orientation preference columns. Using this approach we
demonstrate that ocular dominance segregation can induce the stabilization and
even the production of pinwheels by their crystallization in two types of
periodic lattices. Pinwheel crystallization depends on the overall dominance of
one eye over the other, a condition that is fulfilled during early cortical
development. Increasing the strength of inter-map coupling induces a transition
from pinwheel-free stripe solutions to intermediate and high pinwheel density
states.Comment: 10 pages, 4 figure
Asymptotic Level Density of the Elastic Net Self-Organizing Feature Map
Whileas the Kohonen Self Organizing Map shows an asymptotic level density
following a power law with a magnification exponent 2/3, it would be desired to
have an exponent 1 in order to provide optimal mapping in the sense of
information theory. In this paper, we study analytically and numerically the
magnification behaviour of the Elastic Net algorithm as a model for
self-organizing feature maps. In contrast to the Kohonen map the Elastic Net
shows no power law, but for onedimensional maps nevertheless the density
follows an universal magnification law, i.e. depends on the local stimulus
density only and is independent on position and decouples from the stimulus
density at other positions.Comment: 8 pages, 10 figures. Link to publisher under
http://link.springer.de/link/service/series/0558/bibs/2415/24150939.ht
On the shape of barchan dunes
Barchans are crescent-shaped sand dunes forming in aride regions with
unidirectional wind and limited sand supply. We report analytical and numerical
results for dune shapes under different environmental conditions as obtained
from the so-called `minimal model' of aeolian sand dunes. The profiles of
longitudinal vertical slices (i.e. along the wind direction) are analyzed as a
function of wind speed and sand supply. Shape transitions can be induced by
changes of mass, wind speed and sand supply. Within a minimal extension of the
model to the transverse direction the scale-invariant profile of transverse
vertical cuts can be derived analytically.Comment: to appear in J. Phys.: Condens. Matter 17 (2005
Reorganization of columnar architecture in the growing visual cortex
Many cortical areas increase in size considerably during postnatal
development, progressively displacing neuronal cell bodies from each other. At
present, little is known about how cortical growth affects the development of
neuronal circuits. Here, in acute and chronic experiments, we study the layout
of ocular dominance (OD) columns in cat primary visual cortex (V1) during a
period of substantial postnatal growth. We find that despite a considerable
size increase of V1, the spacing between columns is largely preserved. In
contrast, their spatial arrangement changes systematically over this period.
While in young animals columns are more band-like, layouts become more
isotropic in mature animals. We propose a novel mechanism of growth-induced
reorganization that is based on the `zigzag instability', a dynamical
instability observed in several inanimate pattern forming systems. We argue
that this mechanism is inherent to a wide class of models for the
activity-dependent formation of OD columns. Analyzing one member of this class,
the Elastic Network model, we show that this mechanism can account for the
preservation of column spacing and the specific mode of reorganization of OD
columns that we observe. We conclude that neurons systematically shift their
selectivities during normal development and that this reorganization is induced
by the cortical expansion during growth. Our work suggests that cortical
circuits remain plastic for an extended period in development in order to
facilitate the modification of neuronal circuits to adjust for cortical growth.Comment: 8+13 pages, 4+8 figures, paper + supplementary materia
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