A quasi three dimensional model of water flow in the subsurface of Milano (Italy): the stationary flow

International audienceA quasi three-dimensional model is developed to simulate the behaviour of the aquifer system which is the resource of drinkable water for the town of Milano (Italy). Non continuous semipermeable layers locally separate permeable levels in a multilayered system, consisting of a phreatic and three confined aquifers. The numerical model is a conservative finite difference scheme based on the discretisation of the water balance equation for stationary flow. The grid spacing is 500 m and has been chosen, taking into account the distribution of the data in an area of about 400 km2. The model has been calibrated with a "trial and error" procedure, by comparison of the results of the model with the observations for three years (1950, 1974 and 1982) which correspond to different flow situations. Once calibrated, the model has been used as a predictive tool, to forecast the behaviour of the aquifer system for other years of the 20th century; the comparison between the model forecasts and observations is good. The model is capable of describing both the strong drawdown of the water table in the 1970s, when the water demand for domestic and industrial needs was very high, and the rise of the water table in the 1990s, when water extraction decreased. The results of the model confirm that the phreatic level is controlled largely by the local extraction of water; moreover, the aquifer system reacts to an increasing water demand with a small increase of the inflow and with a strong decrease of the outflow from its boundaries

Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table

Self-organization and the selection of pinwheel density in visual cortical development

Self-organization of neural circuitry is an appealing framework for understanding cortical development, yet its applicability remains unconfirmed. Models for the self-organization of neural circuits have been proposed, but experimentally testable predictions of these models have been less clear. The visual cortex contains a large number of topological point defects, called pinwheels, which are detectable in experiments and therefore in principle well suited for testing predictions of self-organization empirically. Here, we analytically calculate the density of pinwheels predicted by a pattern formation model of visual cortical development. An important factor controlling the density of pinwheels in this model appears to be the presence of non-local long-range interactions, a property which distinguishes cortical circuits from many nonliving systems in which self-organization has been studied. We show that in the limit where the range of these interactions is infinite, the average pinwheel density converges to $\pi$. Moreover, an average pinwheel density close to this value is robustly selected even for intermediate interaction ranges, a regime arguably covering interaction-ranges in a wide range of different species. In conclusion, our paper provides the first direct theoretical demonstration and analysis of pinwheel density selection in models of cortical self-organization and suggests to quantitatively probe this type of prediction in future high-precision experiments.Comment: 22 pages, 3 figure

Using high angular resolution diffusion imaging data to discriminate cortical regions

Brodmann's 100-year-old summary map has been widely used for cortical localization in neuroscience. There is a pressing need to update this map using non-invasive, high-resolution and reproducible data, in a way that captures individual variability. We demonstrate here that standard HARDI data has sufficiently diverse directional variation among grey matter regions to inform parcellation into distinct functional regions, and that this variation is reproducible across scans. This characterization of the signal variation as non-random and reproducible is the critical condition for successful cortical parcellation using HARDI data. This paper is a first step towards an individual cortex-wide map of grey matter microstructure, The gray/white matter and pial boundaries were identified on the high-resolution structural MRI images. Two HARDI data sets were collected from each individual and aligned with the corresponding structural image. At each vertex point on the surface tessellation, the diffusion-weighted signal was extracted from each image in the HARDI data set at a point, half way between gray/white matter and pial boundaries. We then derived several features of the HARDI profile with respect to the local cortical normal direction, as well as several fully orientationally invariant features. These features were taken as a fingerprint of the underlying grey matter tissue, and used to distinguish separate cortical areas. A support-vector machine classifier, trained on three distinct areas in repeat 1 achieved 80-82% correct classification of the same three areas in the unseen data from repeat 2 in three volunteers. Though gray matter anisotropy has been mostly overlooked hitherto, this approach may eventually form the foundation of a new cortical parcellation method in living humans. Our approach allows for further studies on the consistency of HARDI based parcellation across subjects and comparison with independent microstructural measures such as ex-vivo histology

Roles of contour and surface processing in microgenesis of object perception and visual consciousness

Developments in visual neuroscience and neural-network modeling indicate the existence of separate pathways for the processing of form and surface attributes of a visual object. In line with prior theoretical proposals, it is assumed that the processing of form can be explicit or conscious only as or after the surface property such as color is filled in. In conjunction with extant psychophysical findings, these developments point to interesting distinctions between nonconscious and conscious processing of these attributes, specifically in relation to distinguishable temporal dynamics. At nonconscious levels form processing proceeds faster than surface processing, whereas in contrast, at conscious levels form processing proceeds slower than surface processing. I mplications of separate form and surface processing for current and future psychophysical and neuroscientific research, particularly that relating cortical oscillations to conjunctions of surface and form features, and for cognitive science and philosophy of mind and consciousness are discussed

Mapping Human Whole-Brain Structural Networks with Diffusion MRI

Understanding the large-scale structural network formed by neurons is a major challenge in system neuroscience. A detailed connectivity map covering the entire brain would therefore be of great value. Based on diffusion MRI, we propose an efficient methodology to generate large, comprehensive and individual white matter connectional datasets of the living or dead, human or animal brain. This non-invasive tool enables us to study the basic and potentially complex network properties of the entire brain. For two human subjects we find that their individual brain networks have an exponential node degree distribution and that their global organization is in the form of a small world

Encoding of Temporal Information by Timing, Rate, and Place in Cat Auditory Cortex

A central goal in auditory neuroscience is to understand the neural coding of species-specific communication and human speech sounds. Low-rate repetitive sounds are elemental features of communication sounds, and core auditory cortical regions have been implicated in processing these information-bearing elements. Repetitive sounds could be encoded by at least three neural response properties: 1) the event-locked spike-timing precision, 2) the mean firing rate, and 3) the interspike interval (ISI). To determine how well these response aspects capture information about the repetition rate stimulus, we measured local group responses of cortical neurons in cat anterior auditory field (AAF) to click trains and calculated their mutual information based on these different codes. ISIs of the multiunit responses carried substantially higher information about low repetition rates than either spike-timing precision or firing rate. Combining firing rate and ISI codes was synergistic and captured modestly more repetition information. Spatial distribution analyses showed distinct local clustering properties for each encoding scheme for repetition information indicative of a place code. Diversity in local processing emphasis and distribution of different repetition rate codes across AAF may give rise to concurrent feed-forward processing streams that contribute differently to higher-order sound analysis

Spatio-Temporal Brain Mapping of Motion-Onset VEPs Combined with fMRI and Retinotopic Maps

Neuroimaging studies have identified several motion-sensitive visual areas in the human brain, but the time course of their activation cannot be measured with these techniques. In the present study, we combined electrophysiological and neuroimaging methods (including retinotopic brain mapping) to determine the spatio-temporal profile of motion-onset visual evoked potentials for slow and fast motion stimuli and to localize its neural generators. We found that cortical activity initiates in the primary visual area (V1) for slow stimuli, peaking 100 ms after the onset of motion. Subsequently, activity in the mid-temporal motion-sensitive areas, MT+, peaked at 120 ms, followed by peaks in activity in the more dorsal area, V3A, at 160 ms and the lateral occipital complex at 180 ms. Approximately 250 ms after stimulus onset, activity fast motion stimuli was predominant in area V6 along the parieto-occipital sulcus. Finally, at 350 ms (100 ms after the motion offset) brain activity was visible again in area V1. For fast motion stimuli, the spatio-temporal brain pattern was similar, except that the first activity was detected at 70 ms in area MT+. Comparing functional magnetic resonance data for slow vs. fast motion, we found signs of slow-fast motion stimulus topography along the posterior brain in at least three cortical regions (MT+, V3A and LOR)

Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates

In this paper we will review the main results concerning the issue of stability for the determination unknown boundary portion of a thermic conducting body from Cauchy data for parabolic equations. We give detailed and selfcontained proofs. We prove that such problems are severely ill-posed in the sense that under a priori regularity assumptions on the unknown boundaries, up to any finite order of differentiability, the continuous dependence of unknown boundary from the measured data is, at best, of logarithmic type

Synchronous chaos and broad band gamma rhythm in a minimal multi-layer model of primary visual cortex

Visually induced neuronal activity in V1 displays a marked gamma-band component which is modulated by stimulus properties. It has been argued that synchronized oscillations contribute to these gamma-band activity [... however,] even when oscillations are observed, they undergo temporal decorrelation over very few cycles. This is not easily accounted for in previous network modeling of gamma oscillations. We argue here that interactions between cortical layers can be responsible for this fast decorrelation. We study a model of a V1 hypercolumn, embedding a simplified description of the multi-layered structure of the cortex. When the stimulus contrast is low, the induced activity is only weakly synchronous and the network resonates transiently without developing collective oscillations. When the contrast is high, on the other hand, the induced activity undergoes synchronous oscillations with an irregular spatiotemporal structure expressing a synchronous chaotic state. As a consequence the population activity undergoes fast temporal decorrelation, with concomitant rapid damping of the oscillations in LFPs autocorrelograms and peak broadening in LFPs power spectra. [...] Finally, we argue that the mechanism underlying the emergence of synchronous chaos in our model is in fact very general. It stems from the fact that gamma oscillations induced by local delayed inhibition tend to develop chaos when coupled by sufficiently strong excitation.Comment: 49 pages, 11 figures, 7 table