Testing non-uniform k-wise independent distributions over product spaces (extended abstract)

A distribution D over Σ1× ⋯ ×Σ n is called (non-uniform) k-wise independent if for any set of k indices {i 1, ..., i k } and for any z1zki1ik, PrXD[Xi1Xik=z1zk]=PrXD[Xi1=z1]PrXD[Xik=zk]. We study the problem of testing (non-uniform) k-wise independent distributions over product spaces. For the uniform case we show an upper bound on the distance between a distribution D from the set of k-wise independent distributions in terms of the sum of Fourier coefficients of D at vectors of weight at most k. Such a bound was previously known only for the binary field. For the non-uniform case, we give a new characterization of distributions being k-wise independent and further show that such a characterization is robust. These greatly generalize the results of Alon et al. [1] on uniform k-wise independence over the binary field to non-uniform k-wise independence over product spaces. Our results yield natural testing algorithms for k-wise independence with time and sample complexity sublinear in terms of the support size when k is a constant. The main technical tools employed include discrete Fourier transforms and the theory of linear systems of congruences.National Science Foundation (U.S.) (NSF grant 0514771)National Science Foundation (U.S.) (grant 0728645)National Science Foundation (U.S.) (Grant 0732334)Marie Curie International Reintegration Grants (Grant PIRG03-GA-2008-231077)Israel Science Foundation (Grant 1147/09)Israel Science Foundation (Grant 1675/09)Massachusetts Institute of Technology (Akamai Presidential Fellowship

Information and Discriminability as Measures of Reliability of Sensory Coding

Response variability is a fundamental issue in neural coding because it limits all information processing. The reliability of neuronal coding is quantified by various approaches in different studies. In most cases it is largely unclear to what extent the conclusions depend on the applied reliability measure, making a comparison across studies almost impossible. We demonstrate that different reliability measures can lead to very different conclusions even if applied to the same set of data: in particular, we applied information theoretical measures (Shannon information capacity and Kullback-Leibler divergence) as well as a discrimination measure derived from signal-detection theory to the responses of blowfly photoreceptors which represent a well established model system for sensory information processing. We stimulated the photoreceptors with white noise modulated light intensity fluctuations of different contrasts. Surprisingly, the signal-detection approach leads to a safe discrimination of the photoreceptor response even when the response signal-to-noise ratio (SNR) is well below unity whereas Shannon information capacity and also Kullback-Leibler divergence indicate a very low performance. Applying different measures, can, therefore, lead to very different interpretations concerning the system's coding performance. As a consequence of the lower sensitivity compared to the signal-detection approach, the information theoretical measures overestimate internal noise sources and underestimate the importance of photon shot noise. We stress that none of the used measures and, most likely no other measure alone, allows for an unbiased estimation of a neuron's coding properties. Therefore the applied measure needs to be selected with respect to the scientific question and the analyzed neuron's functional context

Distributed Dendritic Processing Facilitates Object Detection: A Computational Analysis on the Visual System of the Fly

Hennig P, Möller R, Egelhaaf M. Distributed Dendritic Processing Facilitates Object Detection: A Computational Analysis on the Visual System of the Fly. PLoS ONE. 2008;3(8): e3092.Background: Detecting objects is an important task when moving through a natural environment. Flies, for example, may land on salient objects or may avoid collisions with them. The neuronal ensemble of Figure Detection cells (FD-cells) in the visual system of the fly is likely to be involved in controlling these behaviours, as these cells are more sensitive to objects than to extended background structures. Until now the computations in the presynaptic neuronal network of FD-cells and, in particular, the functional significance of the experimentally established distributed dendritic processing of excitatory and inhibitory inputs is not understood. Methodology/Principal Findings: We use model simulations to analyse the neuronal computations responsible for the preference of FD-cells for small objects. We employed a new modelling approach which allowed us to account for the spatial spread of electrical signals in the dendrites while avoiding detailed compartmental modelling. The models are based on available physiological and anatomical data. Three models were tested each implementing an inhibitory neural circuit, but differing by the spatial arrangement of the inhibitory interaction. Parameter optimisation with an evolutionary algorithm revealed that only distributed dendritic processing satisfies the constraints arising from electrophysiological experiments. In contrast to a direct dendro-dendritic inhibition of the FD-cell (Direct Distributed Inhibition model), an inhibition of its presynaptic retinotopic elements (Indirect Distributed Inhibition model) requires smaller changes in input resistance in the inhibited neurons during visual stimulation. Conclusions/Significance: Distributed dendritic inhibition of retinotopic elements as implemented in our Indirect Distributed Inhibition model is the most plausible wiring scheme for the neuronal circuit of FD-cells. This microcircuit is computationally similar to lateral inhibition between the retinotopic elements. Hence, distributed inhibition might be an alternative explanation of perceptual phenomena currently explained by lateral inhibition networks

Synaptic transfer of dynamic motion information between identified neurons in the visual system of the blowfly

Warzecha A-K, Kurtz R, Egelhaaf M. Synaptic transfer of dynamic motion information between identified neurons in the visual system of the blowfly. Neuroscience. 2003;119(4):1103-1112.Synaptic transmission is usually studied in vitro with electrical stimulation replacing the natural input of the system. In contrast, we analyzed in vivo transfer of visual motion information from graded-potential presynaptic to spiking postsynaptic neurons in the fly. Motion in the null direction leads to hyperpolarization of the presynaptic neuron but does not much influence the postsynaptic cell, because its firing rate is already low during rest, giving only little scope for further reductions. In contrast, preferred-direction motion leads to presynaptic depolarizations and increases the postsynaptic spike rate. Signal transfer to the postsynaptic cell is linear and reliable for presynaptic graded membrane potential fluctuations of up to approximately 10 Hz. This frequency range covers the dynamic range of velocities that is encoded with a high gain by visual motion-sensitive neurons. Hence, information about preferred-direction motion is transmitted largely undistorted ensuring a consistent dependency of neuronal signals on stimulus parameters, such as motion velocity. Postsynaptic spikes are often elicited by rapid presynaptic spike-like depolarizations which superimpose the graded membrane potential. Although the timing of most of these spike-like depolarizations is set by noise and not by the motion stimulus, it is preserved at the synapse with millisecond precision. (C) 2003 IBRO. Published by Elsevier Science Ltd. All rights reserved

Elastosis in chronic radiodermatitis. An ultrastructural study

SCOPUS: ar.jFLWNAinfo:eu-repo/semantics/publishe

Pinguecula and Actinic Elastosis. An Ultrastructural Study

Three cases of pinguecula (conjunctival elastosis) were ultrastructurally investigated. Findings were compared with the features described in cutaneous actinic elastosis. Changes observed were not uniform. In both diseases, numerous elastotic fibers were present with a finely granular matrix and masses of dense grains. The degenerative changes of the elastotic fibers evolved differently in conjunctival stroma and in dermis. The superficial extracellular concretions observed in pinguecula seemed to be an ultimate stage of elastotic degeneration. Like actinic elastosis and elastosis observed in chronic radiodermatitis, pinguecula is believed to result from a dystrophic increased elastogenesis induced by chronic irradiation, with secondary degenerative changes.SCOPUS: ar.jFLWNAinfo:eu-repo/semantics/publishe