A metric model for the functional architecture of the visual cortex

open3siThis work was supported by the Horizon 2020 Project, ref. 777822: GHAIA, PRIN 2015 ``Variational and perturbative aspects of nonlinear differential problems,"" and by the European Union's Seventh Framework Programme, ref. 607643: MAnET.The purpose of this work is to construct a model for the functional architecture of the primary visual cortex (V1), based on a structure of metric measure space induced by the underlying organization of receptive profiles (RPs) of visual cells. In order to account for the horizontal connectivity of V1 in such a context, a diffusion process compatible with the geometry of the space is defined following the classical approach of K.-T. Sturm [Ann. Probab., 26 (1998), pp. 1-55]. The construction of our distance function neither requires any group parameterization of the family of RPs nor involves any differential structure. As such, it adapts to nonparameterized sets of RPs, possibly obtained through numerical procedures; it also allows us to model the lateral connectivity arising from nondifferential metrics such as the one induced on a pinwheel surface by a family of filters of vanishing scale. On the other hand, when applied to the classical framework of Gabor filters, this construction yields a distance approximating the sub-Riemannian structure proposed as a model for V1 by Citti and Sarti [J. Math. Imaging Vision Archive, 24 (2006), pp. 307-326], thus showing itself to be consistent with existing cortex models.openMontobbio N.; Sarti A.; Citti G.Montobbio N.; Sarti A.; Citti G

From receptive profiles to a metric model of V1

In this work we show how to construct connectivity kernels induced by the receptive profiles of simple cells of the primary visual cortex (V1). These kernels are directly defined by the shape of such profiles: this provides a metric model for the functional architecture of V1, whose global geometry is determined by the reciprocal interactions between local elements. Our construction adapts to any bank of filters chosen to represent a set of receptive profiles, since it does not require any structure on the parameterization of the family. The connectivity kernel that we define carries a geometrical structure consistent with the well-known properties of long-range horizontal connections in V1, and it is compatible with the perceptual rules synthesized by the concept of association field. These characteristics are still present when the kernel is constructed from a bank of filters arising from an unsupervised learning algorithm

Predictions for Nongaussianity from Nonlocal Inflation

In our previous work the nonlinearity parameter f_NL, which characterizes nongaussianity in the cosmic microwave background, was estimated for a class of inflationary models based on nonlocal field theory. These models include p-adic inflation and generically have the remarkable property that slow roll inflation can proceed even with an extremely steep potential. Previous calculations found that large nongaussianity is possible; however, the technical complications associated with studying perturbations in theories with infinitely many derivatives forced us to provide only an order of magnitude estimate for f_NL. We reconsider the problem of computing f_NL in nonlocal inflation models, showing that a particular choice of field basis and recent progress in cosmological perturbation theory makes an exact computation possible. We provide the first quantitatively accurate computation of the bispectrum in nonlocal inflation, confirming our previous claim that it can be observably large. We show that the shape of the bispectrum in this class of models makes it observationally distinguishable from Dirac-Born-Infeld inflation models.Comment: 26 pages, 5 figures; references added, sign convention for f_NL clarified, minor correction

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Use of thermodynamic orientors for the management of aquatic systems

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The writing room: writing helps healing

It is described the project and actuation of a room for writing inside of Alessandria's Hospital. The idea was organized from know out matured by doctors and nurses who have participated in training curses in narrative medicine in these years. The realization was asked by the head of the Neurology Department and his assistant where is located. The writing room is thinking on the base of typology of the emerging needs of their patients. In a simple and practical way it is detailed the instruction of this rooms model with the purpose to make writing, in this contest, an effective behavioral resource in the adaptation to illness. In the base of the first results, the strategies are suggested to make initiated practical effectively