3,419 research outputs found
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 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
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