Margareth Lanzingerand Raffaella Sarti (eds) (2006) Nubili e celibi tra scelta e costrizione(secoli XVI–XX)

Review of 'Nubili e celibi tra scelta e costrizione (secoli XVI-XX)', ed. Margareth Lanzinger and Raffaella Sarti (Udine: Forum, 2006) in the Journal of Modern Italian Studies, 15 (2) (2010

The constitution of visual perceptual units in the functional architecture of V1

Scope of this paper is to consider a mean field neural model which takes into account the functional neurogeometry of the visual cortex modelled as a group of rotations and translations. The model generalizes well known results of Bressloff and Cowan which, in absence of input, accounts for hallucination patterns. The main result of our study consists in showing that in presence of a visual input, the eigenmodes of the linearized operator which become stable represent perceptual units present in the image. The result is strictly related to dimensionality reduction and clustering problems

Local and global gestalt laws: A neurally based spectral approach

A mathematical model of figure-ground articulation is presented, taking into account both local and global gestalt laws. The model is compatible with the functional architecture of the primary visual cortex (V1). Particularly the local gestalt law of good continuity is described by means of suitable connectivity kernels, that are derived from Lie group theory and are neurally implemented in long range connectivity in V1. Different kernels are compatible with the geometric structure of cortical connectivity and they are derived as the fundamental solutions of the Fokker Planck, the Sub-Riemannian Laplacian and the isotropic Laplacian equations. The kernels are used to construct matrices of connectivity among the features present in a visual stimulus. Global gestalt constraints are then introduced in terms of spectral analysis of the connectivity matrix, showing that this processing can be cortically implemented in V1 by mean field neural equations. This analysis performs grouping of local features and individuates perceptual units with the highest saliency. Numerical simulations are performed and results are obtained applying the technique to a number of stimuli.Comment: submitted to Neural Computatio

A semidiscrete version of the Citti-Petitot-Sarti model as a plausible model for anthropomorphic image reconstruction and pattern recognition

In his beautiful book [66], Jean Petitot proposes a sub-Riemannian model for the primary visual cortex of mammals. This model is neurophysiologically justified. Further developments of this theory lead to efficient algorithms for image reconstruction, based upon the consideration of an associated hypoelliptic diffusion. The sub-Riemannian model of Petitot and Citti-Sarti (or certain of its improvements) is a left-invariant structure over the group $SE(2)$ of rototranslations of the plane. Here, we propose a semi-discrete version of this theory, leading to a left-invariant structure over the group $SE(2,N)$, restricting to a finite number of rotations. This apparently very simple group is in fact quite atypical: it is maximally almost periodic, which leads to much simpler harmonic analysis compared to $SE(2).$ Based upon this semi-discrete model, we improve on previous image-reconstruction algorithms and we develop a pattern-recognition theory that leads also to very efficient algorithms in practice.Comment: 123 pages, revised versio

Vortex state microwave response in superconducting cuprates and MgB2_2

We investigate the physics of the microwave response in YBa$_{2}$Cu$_{3}$O$_{7-\delta}$, SmBa$_{2}$Cu$_{3}$O$_{7-\delta}$ and MgB$_{2}$ in the vortex state. We first recall the theoretical basics of vortex-state microwave response in the London limit. We then present a wide set of measurements of the field, temperature, and frequency dependences of the vortex state microwave complex resistivity in superconducting thin films, measured by a resonant cavity and by swept-frequency Corbino disk. The combination of these techniques allows for a comprehensive description of the microwave response in the vortex state in these innovative superconductors. In all materials investigated we show that flux motion alone cannot take into account all the observed experimental features, neither in the frequency nor in the field dependence. The discrepancy can be resolved by considering the (usually neglected) contribution of quasiparticles to the response in the vortex state. The peculiar, albeit different, physics of the superconducting materials here considered, namely two-band superconductivity in MgB$_{2}$ and superconducting gap with lines of nodes in cuprates, give rise to a substantially increased contribution of quasiparticles to the field-dependent microwave response. With careful combined analysis of the data it is possible to extract or infer many interesting quantities related to the vortex state, such as the temperature-dependent characteristic vortex frequency and vortex viscosity, the field dependence of the quasiparticle density, the temperature dependence of the $\sigma$-band superfluid density in MgB$_{2}$Comment: 51 pages, 27 figures, to appear as a book chapter (Nova Science

A geometric model of multi-scale orientation preference maps via Gabor functions

In this paper we present a new model for the generation of orientation preference maps in the primary visual cortex (V1), considering both orientation and scale features. First we undertake to model the functional architecture of V1 by interpreting it as a principal fiber bundle over the 2-dimensional retinal plane by introducing intrinsic variables orientation and scale. The intrinsic variables constitute a fiber on each point of the retinal plane and the set of receptive profiles of simple cells is located on the fiber. Each receptive profile on the fiber is mathematically interpreted as a rotated Gabor function derived from an uncertainty principle. The visual stimulus is lifted in a 4-dimensional space, characterized by coordinate variables, position, orientation and scale, through a linear filtering of the stimulus with Gabor functions. Orientation preference maps are then obtained by mapping the orientation value found from the lifting of a noise stimulus onto the 2-dimensional retinal plane. This corresponds to a Bargmann transform in the reducible representation of the $\text{SE}(2)=\mathbb{R}^2\times S^1$ group. A comparison will be provided with a previous model based on the Bargman transform in the irreducible representation of the $\text{SE}(2)$ group, outlining that the new model is more physiologically motivated. Then we present simulation results related to the construction of the orientation preference map by using Gabor filters with different scales and compare those results to the relevant neurophysiological findings in the literature