arXiv subjects

N. Parga

Publications and source records attributed to N. Parga.

7 recordsLinked to original sources

arXiv2002

Response of Spiking Neurons to Correlated Inputs

The effect of a temporally correlated afferent current on the firing rate of a leaky integrate-and-fire (LIF) neuron is studied. This current is characterized in terms of rates, auto and cross-correlations, and correlation time scale $τ_c$ of excitatory and inhibitory inputs. The output rate $ν_{out}$ is calculated in the Fokker-Planck (FP) formalism in the limit of both small and large $τ_c$ compared to the membrane time constant $τ$ of the neuron. By simulations we check the analytical results, provide an interpolation valid for all $τ_c$ and study the neuron's response to rapid changes in the correlation magnitude.

cond-mat.dis-nn↗

arXiv2001

Scene dependence of the non-gaussian scaling properties of natural images

We report results on the scaling properties of changes in contrast of natural images in different visual environments. This study confirms the existence, in a vast class of images, of a multiplicative process relating the variations in contrast seen at two different scales, as was found in \cite{NIPS97,TuMaPaNa98}. But it also shows that the scaling exponents are not universal: Even if most images follow the same type of statistics, they do it with different values of the distribution parameters. Motivated by these results, we also present the analysis of a generative model of images that reproduces those properties and that has the correct power spectrum. Possible implications for visual processing are also discussed.

cond-mat.stat-mech↗

arXiv2001

Multiscaling and information content of natural color images

Naive scale invariance is not a true property of natural images. Natural monochrome images posses a much richer geometrical structure, that is particularly well described in terms of multiscaling relations. This means that the pixels of a given image can be decomposed into sets, the fractal components of the image, with well-defined scaling exponents (Turiel & Parga, submitted). Here it is shown that multispectral representations of natural scenes also exhibit multiscaling properties, observing the same kind of behavior. A precise measure of the informational relevance of the fractal components is also given, and it is shown that there are important differences between the intrinsically redundant RGB system and the decorrelated one defined in (Ruderman, Cronin & Chiao, 1998).

cond-mat.stat-mech↗

arXiv2001

Multifractal wavelet filter of natural images

Natural images are characterized by the multiscaling properties of their contrast gradient, in addition to their power spectrum. In this work we show that those properties uniquely define an {\em intrinsic wavelet} and present a suitable technique to obtain it from an ensemble of images. Once this wavelet is known, images can be represented as expansions in the associated wavelet basis. The resulting code has the remarkable properties that it separates independent features at different resolution level, reducing the redundancy, and remains essentially unchanged under changes in the power spectrum. The possible generalization of this representation to other systems is discussed.

cond-mat.stat-mech↗

arXiv2001

The multi-fractal structure of contrast changes in natural images: from sharp edges to textures

We present a formalism that leads very naturally to a hierarchical description of the different contrast structures in images, providing precise definitions of sharp edges and other texture components. Within this formalism, we achieve a decomposition of pixels of the image in sets, the fractal components of the image, such that each set only contains points characterized by a fixed stregth of the singularity of the contrast gradient in its neighborhood. A crucial role in this description of images is played by the behavior of contrast differences under changes in scale. Contrary to naive scaling ideas where the image is thought to have uniform transformation properties \cite{Fie87}, each of these fractal components has its own transformation law and scaling exponents. A conjecture on their biological relevance is also given.

cond-mat.stat-mech↗

arXiv2001

The self-similarity properties of natural images resemble those of turbulent flows

We show that the statistics of an edge type variable in natural images exhibits self-similarity properties which resemble those of local energy dissipation in turbulent flows. Our results show that extended self-similarity remarkably holds for the statistics of the local edge variance, and that the very same models can be used to predict all the associated exponents. These results suggest to use natural images as a laboratory for testing scaling models of interest for the statistical description of turbulent flows. The properties we have exhibited are relevant for the modeling of the early visual system: they should be included in models designed for the prediction of receptive fiel$

cond-mat.stat-mech↗

arXiv2001

Numerical simulation of a binary communication channel: Comparison between a replica calculation and an exact solution

The mutual information of a single-layer perceptron with $N$ Gaussian inputs and $P$ deterministic binary outputs is studied by numerical simulations. The relevant parameters of the problem are the ratio between the number of output and input units, $α= P/N$, and those describing the two-point correlations between inputs. The main motivation of this work refers to the comparison between the replica computation of the mutual information and an analytical solution valid up to $α\sim O(1)$. The most relevant results are: (1) the simulation supports the validity of the analytical prediction, and (2) it also verifies a previously proposed conjecture that the replica solution interpolates well between large and small values of $α$.

cond-mat.stat-mech↗