Congruent families and invariant tensors

Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only $2$-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant $3$-tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree $n$, showing that any family of $n$-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in an earlier paper

Combining spatial and parametric working memory in a dynamic neural field model

We present a novel dynamic neural field model consisting of two coupled fields of Amari-type which supports the existence of localized activity patterns or “bumps” with a continuum of amplitudes. Bump solutions have been used in the past to model spatial working memory. We apply the model to explain input-specific persistent activity that increases monotonically with the time integral of the input (parametric working memory). In numerical simulations of a multi-item memory task, we show that the model robustly memorizes the strength and/or duration of inputs. Moreover, and important for adaptive behavior in dynamic environments, the memory strength can be changed at any time by new behaviorally relevant information. A direct comparison of model behaviors shows that the 2-field model does not suffer the problems of the classical Amari model when the inputs are presented sequentially as opposed to simultaneously

A spatially extended model for macroscopic spike-wave discharges

Spike-wave discharges are a distinctive feature of epileptic seizures. So far, they have not been reported in spatially extended neural field models. We study a space-independent version of the Amari neural field model with two competing inhibitory populations. We show that this competition leads to robust spike-wave dynamics if the inhibitory populations operate on different time-scales. The spike-wave oscillations present a fold/homoclinic type bursting. From this result we predict parameters of the extended Amari system where spike-wave oscillations produce a spatially homogeneous pattern. We propose this mechanism as a prototype of macroscopic epileptic spike-wave discharges. To our knowledge this is the first example of robust spike-wave patterns in a spatially extended neural field model

3D magnetic configuration of the Halpha filament and X-ray sigmoid in NOAA AR 8151

We investigate the structure and relationship of an H $\alpha$ filament and an X-ray sigmoid observed in active region NOAA 8151. We first examine the presence of such structures in the reconstructed 3D coronal magnetic field obtained from the non-constant- $\alpha$ force-free field hypothesis using a photospheric vector magnetogram (IVM, Mees Solar Observatory). This method allows us to identify several flux systems: a filament (height 30 Mm, aligned with the polarity inversion line (PIL), magnetic field strength at the apex 49 G, number of turns 0.5-0.6), a sigmoid (height 45 Mm, aligned with the PIL, magnetic field strength at the apex 56 G, number of turns 0.5-0.6) and a highly twisted flux tube (height 60 Mm, magnetic field strength at the apex 36 G, number of turns 1.1-1.2). By searching for magnetic dips in the configuration, we identify a filament structure which is in good agreement with the H $\alpha$ observations. We find that both filament and sigmoidal structures can be described by a long twisted flux tube with a number of turns less than 1 which means that these structures are stable against kinking. The filament and the sigmoid have similar absolute values of $\alpha$ and Jz in the photosphere. However, the electric current density is positive in the filament and negative in the sigmoid: the filament is right-handed whereas the sigmoid is left-handed. This fact can explain the discrepancies between the handedness of magnetic clouds (twisted flux tubes ejected from the Sun) and the handedness of their solar progenitors (twisted flux bundles in the low corona). The mechanism of eruption in AR 8151 is more likely not related to the development of instability in the filament and/or the sigmoid but is associated with the existence of the highly twisted flux tube (~1.1-1.2 turns)

Coordinated analysis of two graphite grains from the CO3.0 LAP 031117 meteorite: First identification of a CO Nova graphite and a presolar iron sulfide subgrain

Presolar grains constitute remnants of stars that existed before the formation of the solar system. In addition to providing direct information on the materials from which the solar system formed, these grains provide ground-truth information for models of stellar evolution and nucleosynthesis. Here we report the in-situ identification of two unique presolar graphite grains from the primitive meteorite LaPaz Icefield 031117. Based on these two graphite grains, we estimate a bulk presolar graphite abundance of 5-3+7 ppm in this meteorite. One of the grains (LAP-141) is characterized by an enrichment in 12C and depletions in 33,34S, and contains a small iron sulfide subgrain, representing the first unambiguous identification of presolar iron sulfide. The other grain (LAP-149) is extremely 13C-rich and 15N-poor, with one of the lowest 12C/13C ratios observed among presolar grains. Comparison of its isotopic compositions with new stellar nucleosynthesis and dust condensation models indicates an origin in the ejecta of a low-mass CO nova. Grain LAP-149 is the first putative nova grain that quantitatively best matches nova model predictions, providing the first strong evidence for graphite condensation in nova ejecta. Our discovery confirms that CO nova graphite and presolar iron sulfide contributed to the original building blocks of the solar system.Peer ReviewedPostprint (author's final draft

Coronal mass ejection initiation: On the nature of the Flux Cancellation Model

We consider a three-dimensional bipolar force-free magnetic field with non zero magnetic helicity, occupying a half-space, and study the problem of its evolution driven by an imposed photospheric flux decrease. For this specific setting of the Flux Cancellation Model describing coronal mass ejections occuring in active regions, we address the issues of the physical meaning of flux decrease, of the influence on field evolution of the size of the domain over which this decrease is imposed, and of the existence of an energetic criterion characterizing the possible onset of disruption of the configuration. We show that: (1) The imposed flux disappearance can be interpreted in terms of transport of positive and negative fluxes towards the inversion line, where they get annihilated. (2) For the particular case actually computed, in which the initial state is quite sheared, the formation of a twisted flux rope and the subsequent global disruption of the configuration are obtained when the flux has decreased by only a modest amount over a limited part of the whole active region. (3) The disruption is produced when the magnetic energy becomes of the order of the decreasing energy of a semi-open field, and then before reaching the energy of the associated fully open field. This suggests that the mechanism leading to the disruption is nonequilibrium as in the case where flux is imposed to decrease over the whole region.Comment: In press in ApJ Letter

The physical mechanisms that initiate and drive solar eruptions

Solar eruptions are due to a sudden destabilization of force-free coronal magnetic fields. But the detailed mechanisms which can bring the corona towards an eruptive stage, then trigger and drive the eruption, and finally make it explosive, are not fully understood. A large variety of storage-and-release models have been developed and opposed to each other since 40 years. For example, photospheric flux emergence vs. flux cancellation, localized coronal reconnection vs. large-scale ideal instabilities and loss of equilibria, tether-cutting vs. breakout reconnection, and so on. The competition between all these approaches has led to a tremendous drive in developing and testing all these concepts, by coupling state-of-the-art models and observations. Thanks to these developments, it now becomes possible to compare all these models with one another, and to revisit their interpretation in light of their common and their different behaviors. This approach leads me to argue that no more than two distinct physical mechanisms can actually initiate and drive prominence eruptions: the magnetic breakout and the torus instability. In this view, all other processes (including flux emergence, flux cancellation, flare reconnection and long-range couplings) should be considered as various ways that lead to, or that strengthen, one of the aforementioned driving mechanisms.Comment: 13 pages, 0 figure, to appear in proceedings of the IAUS300 meetin

Power spectrum and diffusion of the Amari neural field

We study the power spectrum of a space-time dependent neural field which describes the average membrane potential of neurons in a single layer. This neural field is modelled by a dissipative integro-differential equation, the so-called Amari equation. By considering a small perturbation with respect to a stationary and uniform configuration of the neural field we derive a linearized equation which is solved for a generic external stimulus by using the Fourier transform into wavevector-freqency domain, finding an analytical formula for the power spectrum of the neural field. In addition, after proving that for large wavelengths the linearized Amari equation is equivalent to a diffusion equation which admits space-time dependent analytical solutions, we take into account the nonlinearity of the Amari equation. We find that for large wavelengths a weak nonlinearity in the Amari equation gives rise to a reaction-diffusion equation which can be formally derived from a neural action functional by introducing a dual neural field. For some initial conditions, we discuss analytical solutions of this reaction-diffusion equation.Comment: 8 pages, 2 figures, improved version with inclusion of reaction-diffusion equation and dual neural field. To be published in the open access journal Symmetr

Nonlinear force-free and potential field models of active-region and global coronal fields during the Whole Heliospheric Interval

Between 2008/3/24 and 2008/4/2, the three active regions NOAA active regions 10987, 10988 and 10989 were observed daily by the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) while they traversed the solar disk. We use these measurements and the nonlinear force-free magnetic field code XTRAPOL to reconstruct the coronal magnetic field for each active region and compare model field lines with images from the Solar Terrestrial RElations Observatory (STEREO) and Hinode X-ray Telescope (XRT) telescopes. Synoptic maps made from continuous, round-the-clock Global Oscillations Network Group (GONG) magnetograms provide information on the global photospheric field and potential-field source-surface models based on these maps describe the global coronal field during the Whole Heliospheric Interval (WHI) and its neighboring rotations. Features of the modeled global field, such as the coronal holes and streamer belt locations, are discussed in comparison with extreme ultra-violet and coronagraph observations from STEREO. The global field is found to be far from a minimum, dipolar state. From the nonlinear models we compute physical quantities for the active regions such as the photospheric magnetic and electric current fluxes, the free magnetic energy and the relative helicity for each region each day where observations permit. The interconnectivity of the three regions is addressed in the context of the potential-field source-surface model. Using local and global quantities derived from the models, we briefly discuss the different observed activity levels of the regions.Comment: Accepted for publication in the Solar Physics Whole Heliospheric Interval (WHI) topical issue. We had difficulty squeezing this paper into arXiv's 15 Mb limit. The full paper is available here ftp://gong2.nso.edu/dsds_user/petrie/PetrieCanouAmari.pd