Resolution of Nested Neuronal Representations Can Be Exponential in the Number of Neurons

Collective computation is typically polynomial in the number of computational elements, such as transistors or neurons, whether one considers the storage capacity of a memory device or the number of floating-point operations per second of a CPU. However, we show here that the capacity of a computational network to resolve real-valued signals of arbitrary dimensions can be exponential in N, even if the individual elements are noisy and unreliable. Nested, modular codes that achieve such high resolutions mirror the properties of grid cells in vertebrates, which underlie spatial navigation

The Warm Ionized Medium in the Milky Way and Other Galaxies

Observations of the "Warm Ionized Medium" (or, equivalently, the "Diffuse Ionized Gas") of the local ISM, the Perseus arm in the Milky Way, and also in several other galaxies show strong [NII]6563 (~H-alpha in some cases) and [SII]6717/[NII]6583 = 0.6 - 0.7 in all locations and objects. Other line ratios (e.g., [O III]5007/H-beta) vary considerably. Simple photoionization models reproduce the observed spectra, providing extra heating beyond that supplied by photoionization is assumed (Reynolds, Haffner, & Tufte 1999). With observed gas-phase abundances (not solar), the line ratios in the local arm at b = 0 deg are fitted with no extra heating and (S/H) = 13 ppm (solar is 20 ppm). Local gas observed at b = -35 deg requires extra heating of about gamma = 0.75, where gamma is the extra heating in units of 10^{-25} erg H^{-1} s^{-1}. In the Perseus arm, there are similar results, with a domposition consistent with the Galactic abundance gradient. The requirements for NGC 891 are similar to the Perseus arm: little or no extra heating at |z| = 1 kpc and gamma 3 at 2 kpc. In NGC 891 there is also an increase of 5007/H-alpha with |z| that can only come about if most of the ionizing radiation is supplied by stars with T~50000 K. Either their radiation must propagate from the plane to high |z| through very little intervening matter, or else the stars are located at high |z|. The total power requirement of the extra heating is <15% of the photoionization power. [O~II]3727/H-beta can serve as a useful diagnostic of extra heating, but [S~III] 9065,9531/H-alpha is not useful in this regard.Comment: 32 pages, including 2 figures. To appear in November 20 Ap

Edaq530: a transparent, open-end and open-source measurement solution in natural science education

We present Edaq530, a low-cost, compact and easy-to-use digital measurement solution consisting of a thumb-sized USB-to-sensor interface and a measurement software. The solution is fully open-source, our aim being to provide a viable alternative to professional solutions. Our main focus in designing Edaq530 has been versatility and transparency. In this paper, we shall introduce the capabilities of Edaq530, complement it by showing a few sample experiments, and discuss the feedback we have received in the course of a teacher training workshop in which the participants received personal copies of Edaq530 and later made reports on how they could utilise Edaq530 in their teaching

Transition between Two Oscillation Modes

A model for the symmetric coupling of two self-oscillators is presented. The nonlinearities cause the system to vibrate in two modes of different symmetries. The transition between these two regimes of oscillation can occur by two different scenarios. This might model the release of vortices behind circular cylinders with a possible transition from a symmetric to an antisymmetric Benard-von Karman vortex street.Comment: 12 pages, 0 figure

Perspectives on Interstellar Dust Inside and Outside of the Heliosphere

Measurements by dust detectors on interplanetary spacecraft appear to indicate a substantial flux of interstellar particles with masses exceeding 10^{-12}gram. The reported abundance of these massive grains cannot be typical of interstellar gas: it is incompatible with both interstellar elemental abundances and the observed extinction properties of the interstellar dust population. We discuss the likelihood that the Solar System is by chance located near an unusual concentration of massive grains and conclude that this is unlikely, unless dynamical processes in the ISM are responsible for such concentrations. Radiation pressure might conceivably drive large grains into "magnetic valleys". If the influx direction of interstellar gas and dust is varying on a ~10 yr timescale, as suggested by some observations, this would have dramatic implications for the small-scale structure of the interstellar medium.Comment: 13 pages. To appear in Space Science Review

Infrared High-Resolution Spectroscopy of Post-AGB Circumstellar Disks. I. HR 4049 - The Winnowing Flow Observed?

High-resolution infrared spectroscopy in the 2.3-4.6 micron region is reported for the peculiar A supergiant, single-lined spectroscopic binary HR 4049. Lines from the CO fundamental and first overtone, OH fundamental, and several H2O vibration-rotation transitions have been observed in the near-infrared spectrum. The spectrum of HR 4049 appears principally in emission through the 3 and 4.6 micron region and in absorption in the 2 micron region. The 4.6 micron spectrum shows a rich 'forest' of emission lines. All the spectral lines observed in the 2.3-4.6 micron spectrum are shown to be circumbinary in origin. The presence of OH and H2O lines confirm the oxygen-rich nature of the circumbinary gas which is in contrast to the previously detected carbon-rich material. The emission and absorption line profiles show that the circumbinary gas is located in a thin, rotating layer near the dust disk. The properties of the dust and gas circumbinary disk and the spectroscopic orbit yield masses for the individual stars, M_AI~0.58 Msolar and M_MV~0.34 Msolar. Gas in the disk also has an outward flow with a velocity of $\gtrsim$ 1 km/s. The severe depletion of refractory elements but near-solar abundances of volatile elements observed in HR 4049 results from abundance winnowing. The separation of the volatiles from the grains in the disk and the subsequent accretion by the star are discussed. Contrary to prior reports, the HR 4049 carbon and oxygen isotopic abundances are typical AGB values: 12C/13C=6^{+9}_{-4} and 16O/17O>200.Comment: 42 pages, 14 figures, Accepted by Ap

How chemistry controls electron localization in 3d1 perovskites: A Wannier-function study

In the series of 3d1 t2g perovskites, SrVO3--CaVO3--LaTiO3--YTiO3 the transition-metal d electron becomes increasingly localized and undergoes a Mott transition between CaVO3 and LaTiO3. By defining a low-energy Hubbard Hamiltonian in the basis of Wannier functions for the t2g LDA band and solving it in the single-site DMFT approximation, it was recently shown[1] that simultaneously with the Mott transition there occurs a strong suppression of orbital fluctuations due to splitting of the t2g levels. The present paper reviews and expands this work, in particular in the direction of exposing the underlying chemical mechanisms by means of ab initio LDA Wannier functions generated with the NMTO method. The Wannier functions for the t2g band exhibit covalency between the transition-metal t2g, the large cation-d, and the oxygen-p states; this covalency, which increases along the series, turns out to be responsible not only for the splittings of the t2g levels, but also for non-cubic perturbations of the hopping integrals, both of which are decisive for the Mott transition. We find good agreement with the optical and photoemission spectra, with the crystal-field splittings and orbital polarizations recently measured for the titanates, and with the metallization volume for LaTiO3. The metallization volume for YTiO3 is predicted. Using super-exchange theory, we reproduce the observed magnetic orders in LaTiO3 and YTiO3, but the results are sensitive to detail, in particular for YTiO3 which, without the Jahn-Teller distortion, would be AFM C- or A-type, rather than FM. Finally, we show that it possible to unfold the orthorhombic t2g LDA bandstructure to a pseudocubic zone. In this zone, the lowest band is separated from the two others by a direct gap and has a width, W_I, which is significantly smaller than that, W, of the entire t2g band. The progressive GdFeO3-type distortion favours electron localization by decreasing W, by increasing the splitting of the t2g levels and by decreasing W_I. Our conclusions concerning the roles of GdFeO3-type and JT distortions agree with those of Mochizuki and Imada [2].Comment: Published version, final. For high resolution figures see http://www.fkf.mpg.de/andersen/docs/pub/abstract2004+/pavarini_02.pd

The Thermal Structure of Gas in Pre-Stellar Cores: A Case Study of Barnard 68

We present a direct comparison of a chemical/physical model to multitransitional observations of C18O and 13CO towards the Barnard 68 pre-stellar core. These observations provide a sensitive test for models of low UV field photodissociation regions and offer the best constraint on the gas temperature of a pre-stellar core. We find that the gas temperature of this object is surprisingly low (~7-8 K), and significantly below the dust temperature, in the outer layers (Av < 5 mag) that are traced by C18O and 13CO emission. As shown previously, the inner layers (Av > 5 mag) exhibit significant freeze-out of CO onto grain surfaces. Because the dust and gas are not fully coupled, depletion of key coolants in the densest layers raises the core (gas) temperature, but only by ~1 K. The gas temperature in layers not traced by C18O and 13CO emission can be probed by NH3 emission, with a previously estimated temperature of ~10-11 K. To reach these temperatures in the inner core requires an order of magnitude reduction in the gas to dust coupling rate. This potentially argues for a lack of small grains in the densest gas, presumably due to grain coagulation.Comment: 33 pages, 11 figures, accepted by Astrophysical Journa

The BinaMIcS project: understanding the origin of magnetic fields in massive stars through close binary systems

It is now well established that a fraction of the massive (M>8 Msun) star population hosts strong, organised magnetic fields, most likely of fossil origin. The details of the generation and evolution of these fields are still poorly understood. The BinaMIcS project takes an important step towards the understanding of the interplay between binarity and magnetism during the stellar formation and evolution, and in particular the genesis of fossil fields, by studying the magnetic properties of close binary systems. The components of such systems are most likely formed together, at the same time and in the same environment, and can therefore help us to disentangle the role of initial conditions on the magnetic properties of the massive stars from other competing effects such as age or rotation. We present here the main scientific objectives of the BinaMIcS project, as well as preliminary results from the first year of observations from the associated ESPaDOnS and Narval spectropolarimetric surveys.Comment: To appear in New Windows on Massive Stars, proceedings of the IAU Symposium 30