Kernel reconstruction for delayed neural field equations

Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues. In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Frechet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience

Standing and travelling waves in a spherical brain model: the Nunez model revisited

The Nunez model for the generation of electroencephalogram (EEG) signals is naturally described as a neural field model on a sphere with space-dependent delays. For simplicity, dynamical realisations of this model either as a damped wave equation or an integro- differential equation, have typically been studied in idealised one dimensional or planar settings. Here we revisit the original Nunez model to specifically address the role of spherical topology on spatio-temporal pattern generation. We do this using a mixture of Turing instability analysis, symmetric bifurcation theory, center manifold reduction and direct simulations with a bespoke numerical scheme. In particular we examine standing and travelling wave solutions using normal form computation of primary and secondary bifurcations from a steady state. Interestingly, we observe spatio-temporal patterns which have counterparts seen in the EEG patterns of both epileptic and schizophrenic brain conditions

A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics

Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either (1) top-­down and interpretable, but not flex- ible enough to account for experimental data, or (2) bottom-­up and biologically realistic, but too intricate to interpret and hard to fit to data. To avoid the shortcomings of these approaches, we present a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to predict plasticity outcomes. We apply this readout to a multi-­timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-­timing and frequency-­dependent plasticity induction proto- cols, animal ages, and experimental conditions. Our model also predicts that in vivo-­like spike timing irregularity strongly shapes plasticity outcome. This geometrical readout modelling approach can be readily applied to other excitatory or inhibitory synapses to discover their synaptic plasticity rules

Estimation of the Tilt of the Stellar Velocity Ellipsoid from RAVE and Implications for Mass Models

We present a measure of the inclination of the velocity ellipsoid at 1 kpc below the Galactic plane using a sample of red clump giants from the RAVE DR2 release. We find that the velocity ellipsoid is tilted towards the Galactic plane with an inclination of 7.3 +/-1.8 degree. We compare this value to computed inclinations for two mass models of the Milky Way. We find that our measurement is consistent with a short scale length of the stellar disc (Rd ~2 kpc) if the dark halo is oblate or with a long scale length (Rd~3 kpc) if the dark halo is prolate. Once combined with independent constraints on the flattening of the halo, our measurement suggests that the scale length is approximately halfway between these two extreme values, with a preferred range [2.5-2.7] kpc for a nearly spherical halo. Nevertheless, no model can be clearly ruled out. With the continuation of the RAVE survey, it will be possible to provide a strong constraint on the mass distribution of the Milky Way using refined measurements of the orientation of the velocity ellipsoid.Comment: Accepted for publication in MNRAS, 10 pages, 9 figures, 2 table

Galactic kinematics from RAVE to Gaia-RVS Data

RAVE data has provided new results on Galactic kinematics like the kinematical decomposition of the Galactic disk. This decomposition permits to identify the different components of the disk and to characterize them in terms of scale height and scale length. With the data provided by Gaia and in particular the RVS, we will have a completly renewed view of the Galaxy. The precision of the RVS will permit to undertake a precise analysis of the kinematics of the Galactic disks. This knowledge will provide significant clues to constrain the scenarios of the Galactic disk formation

Chemical gradients in the Milky Way from the RAVE data

Aims. We aim at measuring the chemical gradients of the elements Mg, Al, Si, and Fe along the Galactic radius to provide new constraints on the chemical evolution models of the Galaxy and Galaxy models such as the Besancon model. Thanks to the large number of stars of our RAVE sample we can study how the gradients vary as function of the distance from the Galactic plane. Methods. We analysed three different samples selected from three independent datasets: a sample of 19 962 dwarf stars selected from the RAVE database, a sample of 10 616 dwarf stars selected from the Geneva-Copenhagen Survey (GCS) dataset, and a mock sample (equivalent to the RAVE sample) created by using the GALAXIA code, which is based on the Besancon model. The three samples were analysed by using the very same method for comparison purposes. We integrated the Galactic orbits and obtained the guiding radii (R-g) and the maximum distances from the Galactic plane reached by the stars along their orbits (Z(max)). We measured the chemical gradients as functions of R-g at different Z(max). Results. We found that the chemical gradients of the RAVE and GCS samples are negative and show consistent trends, although they are not equal: at Z(max) < 0.4 kpc and 4.5 < R-g(kpc) < 9.5, the iron gradient for the RAVE sample is d[Fe/H]/dR(g) = -0.065 dex kpc(-1), whereas for the GCS sample it is d[Fe/H]/dR(g) = -0.043 dex kpc(-1) with internal errors of +/-0.002 and +/-0.004 dex kpc(-1), respectively. The gradients of the RAVE and GCS samples become flatter at larger Z(max). Conversely, the mock sample has a positive iron gradient of d[Fe/H]/dR(g) = +0.053 +/- 0.003 dex kpc(-1) at Z(max) < 0.4 kpc and remains positive at any Z(max). These positive and unrealistic values originate from the lack of correlation between metallicity and tangential velocity in the Besancon model. In addition, the low metallicity and asymmetric drift of the thick disc causes a shift of the stars towards lower R-g and metallicity which, together with the thin-disc stars with a higher metallicity and R-g, generates a fictitious positive gradient of the full sample. The flatter gradient at larger Z(max) found in the RAVE and the GCS samples may therefore be due to the superposition of thin-and thick-disc stars, which mimicks a flatter or positive gradient. This does not exclude the possibility that the thick disc has no chemical gradient. The discrepancies between the observational samples and the mock sample can be reduced by i) decreasing the density; ii) decreasing the vertical velocity; and iii) increasing the metallicity of the thick disc in the Besancon model

Reversal of economic fortunes: institutions and the changing ascendancy of Barcelona and Madrid as economic hubs

This paper looks at the divergent economic trajectories of Barcelona and Madrid since Spain's transition to democracy. It highlights how Barcelona, the city that was better positioned four decades ago to emerge as the main Spanish economic hub, has lost out to Madrid. We argue that the contrasting trajectories of the two cities have less to do with the pull of Madrid as the capital of Spain, with the development of new infrastructure in the country, or with agglomeration economies, and more with institutional factors. A growing societal divide in Barcelona along economic, social, and identity lines has led to a greater breakdown of trust and to the development of strong groups with limited capacity to bridge with one another than in Madrid. This has entailed the emergence of negative externalities that have limited the economic potential for growth in Barcelona and facilitated the rise of Madrid as the main economic hub within Spain

<i>Gaia</i> Data Release 1. Summary of the astrometric, photometric, and survey properties

Context. At about 1000 days after the launch of Gaia we present the first Gaia data release, Gaia DR1, consisting of astrometry and photometry for over 1 billion sources brighter than magnitude 20.7. Aims. A summary of Gaia DR1 is presented along with illustrations of the scientific quality of the data, followed by a discussion of the limitations due to the preliminary nature of this release. Methods. The raw data collected by Gaia during the first 14 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium (DPAC) and turned into an astrometric and photometric catalogue. Results. Gaia DR1 consists of three components: a primary astrometric data set which contains the positions, parallaxes, and mean proper motions for about 2 million of the brightest stars in common with the HIPPARCOS and Tycho-2 catalogues – a realisation of the Tycho-Gaia Astrometric Solution (TGAS) – and a secondary astrometric data set containing the positions for an additional 1.1 billion sources. The second component is the photometric data set, consisting of mean G-band magnitudes for all sources. The G-band light curves and the characteristics of ∼3000 Cepheid and RR-Lyrae stars, observed at high cadence around the south ecliptic pole, form the third component. For the primary astrometric data set the typical uncertainty is about 0.3 mas for the positions and parallaxes, and about 1 mas yr−1 for the proper motions. A systematic component of ∼0.3 mas should be added to the parallax uncertainties. For the subset of ∼94 000 HIPPARCOS stars in the primary data set, the proper motions are much more precise at about 0.06 mas yr−1. For the secondary astrometric data set, the typical uncertainty of the positions is ∼10 mas. The median uncertainties on the mean G-band magnitudes range from the mmag level to ∼0.03 mag over the magnitude range 5 to 20.7. Conclusions. Gaia DR1 is an important milestone ahead of the next Gaia data release, which will feature five-parameter astrometry for all sources. Extensive validation shows that Gaia DR1 represents a major advance in the mapping of the heavens and the availability of basic stellar data that underpin observational astrophysics. Nevertheless, the very preliminary nature of this first Gaia data release does lead to a number of important limitations to the data quality which should be carefully considered before drawing conclusions from the data

Bifurcation study of a neural field competition model with an application to perceptual switching in motion integration.

Perceptual multistability is a phenomenon in which alternate interpretations of a fixed stimulus are perceived intermittently. Although correlates between activity in specific cortical areas and perception have been found, the complex patterns of activity and the underlying mechanisms that gate multistable perception are little understood. Here, we present a neural field competition model in which competing states are represented in a continuous feature space. Bifurcation analysis is used to describe the different types of complex spatio-temporal dynamics produced by the model in terms of several parameters and for different inputs. The dynamics of the model was then compared to human perception investigated psychophysically during long presentations of an ambiguous, multistable motion pattern known as the barberpole illusion. In order to do this, the model is operated in a parameter range where known physiological response properties are reproduced whilst also working close to bifurcation. The model accounts for characteristic behaviour from the psychophysical experiments in terms of the type of switching observed and changes in the rate of switching with respect to contrast. In this way, the modelling study sheds light on the underlying mechanisms that drive perceptual switching in different contrast regimes. The general approach presented is applicable to a broad range of perceptual competition problems in which spatial interactions play a role