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