Phase transitions and self-organized criticality in networks of stochastic spiking neurons.

Phase transitions and critical behavior are crucial issues both in theoretical and experimental neuroscience. We report analytic and computational results about phase transitions and self-organized criticality (SOC) in networks with general stochastic neurons. The stochastic neuron has a firing probability given by a smooth monotonic function Φ(V) of the membrane potential V, rather than a sharp firing threshold. We find that such networks can operate in several dynamic regimes (phases) depending on the average synaptic weight and the shape of the firing function Φ. In particular, we encounter both continuous and discontinuous phase transitions to absorbing states. At the continuous transition critical boundary, neuronal avalanches occur whose distributions of size and duration are given by power laws, as observed in biological neural networks. We also propose and test a new mechanism to produce SOC: the use of dynamic neuronal gains - a form of short-term plasticity probably located at the axon initial segment (AIS) - instead of depressing synapses at the dendrites (as previously studied in the literature). The new self-organization mechanism produces a slightly supercritical state, that we called SOSC, in accord to some intuitions of Alan Turing.

A uniform grid structure to speed up example-based photometric stereo.

In this paper, we describe a data structure and an algorithm to accelerate the table lookup step in example-based multiimage photometric stereo. In that step, one must find a pixel of a reference object, of known shape and color, whose appearance under m different illumination fields is similar to that of a given scene pixel. This search reduces to finding the closest match to a given m-vector in a table with a thousand or more m-vectors. Our method is faster than previously known solutions for this problem but, unlike some of them, is exact, i.e., always yields the best matching entry in the table, and does not assume point-like sources. Our solution exploits the fact that the table is in fact a fairly flat 2-D manifold in m-dimensional space so that the search can be efficiently solved with a uniform 2-D grid structure.

Mutual information content of homologous DNA sequences.

The necessary information to reproduce and keep an organism is codified in acid nucleic molecules. Deepening the knowledge about how the information is stored in these bio-sequences can lead to more efficient methods of comparing genomic sequences. In the present study, we analyzed the quantity of information contained in a DNA sequence that can be useful to identify sequences homologous to it. To reach it, we used signal processing techniques, specially spectral analysis and information theory.

The image foresting transform: theory, algorithms, and applications.

The image foresting transform (IFT) is a graph-based approach to the design of image processing operators based on connectivity. It naturally leads to correct and efficient implementations and to a better understanding of how different operators relate to each other. We give here a precise definition of the IFT, and a procedure to compute it-a generalization of Dijkstra's algorithm-with a proof of correctness. We also discuss implementation issues and illustrate the use of the IFT in a few applications.