Roland Köberle

Synergy in a Neural Code

We show that the information carried by compound events in neural spike trainspatterns of spikes across time or across a population of cellscan be measured, independent of assumptions about what these patterns might represent. By comparing the information carried by a compound pattern with the information carried independently by its parts, we directly measure the synergy among these parts. We illustrate the use of these methods by applying them to experiments on the motion-sensitive neuron H1 of the flys visual system, where we confirm that two spikes close together in time carry far more than twice the information carried by a single spike. We analyze the sources of this synergy and provide evidence that pairs of spikes close together in time may be especially important patterns in the code of H1.

Factorized Scattering in the Presence of Reflecting Boundaries

We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the W-matrix, which encodes the reflection of a particle off a wall. This set of equations is sufficient to derive explicit formulas for W, which we illustrate in the case of some particular affine Toda field theories.

Affine Toda Field Theory in the Presence of Reflecting Boundaries

We show that the “boundary crossing-unitarity equation” recently proposed by Ghoshal and Zamolodchikov is a consequence of the boundary bootstrap equation for the S-matrix and the wall-bootstrap equation. We solve this set of equations for all affine Toda theories related to simply laced Lie algebras, obtaining explicit formulas for the W-matrix which encodes the scattering of a particle with the boundary in the ground state. For each theory there are two solutions to these equations, related by CDD-ambiguities, each giving rise to different kind of physics.

A new technique to construct a wavelet transform matching a specified signal with applications to digital, real time, spike, and overlap pattern recognition

This work describes a new and different path to create a wavelet transform that can match a specified discrete-time signal. Called Spikelet, it is designed and optimized to spike and overlap pattern recognition in the digitalized signal that comes from H1, a motion-sensitive neuron of the flys visual system. The technique proposed here and the associated algorithm, implemented in real time using a digital signal processor (DSP), are fully detailed. The results obtained matching the signal under analysis show an improvement over all other transforms, including the Daubechies transform. This reassures the efficacy of our transform. rm.

Boundary Bound States in Affine Toda Field Theory

We demonstrate that the generalization of the Coleman-Thun mechanism may be applied to the situation, when considering scattering processes in 1+1-dimensions in the presence of reflecting boundaries. For affine Toda field theories we find that the binding energies of the bound states are always half the sum over a set of masses having the same colour with respect to the bicolouration of the Dynkin diagram. For the case of E6-affine Toda field theory we compute explicitly the spectrum of all higher boundary bound states. The complete set of states constitutes a closed bootstrap.

Recording from two neurons: Second-order stimulus reconstruction from spike trains and population coding

We study the reconstruction of visual stimuli from spike trains, representing the reconstructed stimulus by a Volterra series up to second order. We illustrate this procedure in a prominent example of spiking neurons, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. Second-order reconstructions require the manipulation of potentially very large matrices, which obstructs the use of this approach when there are many neurons. We avoid the computation and inversion of these matrices using a convenient set of basis functions to expand our variables in. This requires approximating the spike train four-point functions by combinations of two-point functions similar to relations, which would be true for gaussian stochastic processes. In our test case, this approximation does not reduce the quality of the reconstruction. The overall contribution to stimulus reconstruction of the second-order kernels, measured by the mean squared error, is only about 5 of the first-order contribution. Yet at specific stimulus-dependent instants, the addition of second-order kernels represents up to 100 improvement, but only for rotational stimuli. We present a perturbative scheme to facilitate the application of our method to weakly correlated neurons.

Dynamically Multilayered Visual System of the Multifractal Fly

We dynamically analyze our experimental results on the motion sensitive spiking H1 neuron of the flys visual system. We find that the fly uses an alphabet composed of a few letters to encode the information contained in the stimulus. The {\em alphabet dynamics} is multifractal both with and without stimulus, though the multifractality increases with the stimulus entropy. This is in sharp contrast to models generating independent spike-intervals, whose dynamics is monofractal.

A complex biological system: the fly's visual module

Is the characterization of biological systems as complex systems in the mathematical sense a fruitful assertion? In this paper we argue in the affirmative, although obviously we do not attempt to confront all the issues raised by this question. We use the flys visual system as an example and analyse our experimental results of one particular neuron in the flys visual system from this point of view. We find that the motion-sensitive ‘H1’ neuron, which converts incoming signals into a sequence of identical pulses or ‘spikes’, encodes the information contained in the stimulus into an alphabet composed of a few letters. This encoding occurs on multilayered sets, one of the features attributed to complex systems. The conversion of intervals between consecutive occurrences of spikes into an alphabet requires us to construct a generating partition. This entails a one-to-one correspondence between sequences of spike intervals and words written in the alphabet. The alphabet dynamics is multifractal both with and without stimulus, though the multifractality increases with the stimulus entropy. This is in sharp contrast to models generating independent spike intervals, such as models using Poisson statistics, whose dynamics is monofractal. We embed the support of the probability measure, which describes the distribution of words written in this alphabet, in a two-dimensional space, whose topology can be reproduced by an M-shaped map. This map has positive Lyapunov exponents, indicating a chaotic-like encoding.

VSImG: A high frame rate bitmap based display system for neuroscience research

This paper describes a visual stimulus generator (VSImG) capable of displaying a gray-scale, 256x256x8bitmap image with a frame rate of 500Hz using a boustrophedonic scanning technique. It is designed for experiments with motion-sensitive neurons of the flys visual system, where the flicker fusion frequency of the photoreceptors can reach up to 500Hz. Devices with such a high frame rate are not commercially available, but are required, if sensory systems with high flicker fusion frequency are to be studied. The implemented hardware approach gives us complete real-time control of the displacement sequence and provides all the signals needed to drive an electrostatic deflection display. With the use of analog signals, very small high-resolution displacements, not limited by the images pixel size can be obtained. Very slow image displacements with visually imperceptible steps can also be generated. This can be of interest for other vision research experiments. Two different stimulus files can be used simultaneously, allowing the system to generate X-Y displacements on one display or independent movements on two displays as long as they share the same bitmap image.

Exact solution of the deformed biquadratic spin-1 chain

Remarks about highest weight states of the underlying quantum group are corrected.