4,494 research outputs found
Bayesian recovery of the initial condition for the heat equation
We study a Bayesian approach to recovering the initial condition for the heat
equation from noisy observations of the solution at a later time. We consider a
class of prior distributions indexed by a parameter quantifying "smoothness"
and show that the corresponding posterior distributions contract around the
true parameter at a rate that depends on the smoothness of the true initial
condition and the smoothness and scale of the prior. Correct combinations of
these characteristics lead to the optimal minimax rate. One type of priors
leads to a rate-adaptive Bayesian procedure. The frequentist coverage of
credible sets is shown to depend on the combination of the prior and true
parameter as well, with smoother priors leading to zero coverage and rougher
priors to (extremely) conservative results. In the latter case credible sets
are much larger than frequentist confidence sets, in that the ratio of
diameters diverges to infinity. The results are numerically illustrated by a
simulated data example.Comment: 17 pages, 4 figures. Published in Comm. Statist. Theory Methods. This
version differs from the original in pagination and typographic detail. arXiv
admin note: text overlap with arXiv:1103.269
Entropic Interactions in Suspensions of Semi-Flexible Rods: Short-Range Effects of Flexibility
We compute the entropic interactions between two colloidal spheres immersed
in a dilute suspension of semi-flexible rods. Our model treats the
semi-flexible rod as a bent rod at fixed angle, set by the rod contour and
persistence lengths. The entropic forces arising from this additional
rotational degree of freedom are captured quantitatively by the model, and
account for observations at short range in a recent experiment. Global fits to
the interaction potential data suggest the persistence length of fd-virus is
about two to three times smaller than the commonly used value of .Comment: 4 pages, 5 figures, submitted to PRE rapid communication
The energy of waves in the photosphere and lower chromosphere: III. Inversion setup for Ca II H spectra in local thermal equilibrium
The Ca II H line is one of the strongest lines in the solar spectrum and
provides continuous information on the solar atmosphere from the photosphere to
the lower chromosphere. We describe an inversion approach that reproduces
observed Ca II H spectra assuming LTE. We developed an inversion strategy based
on the SIR code. The approach uses a two-step procedure with an archive of
pre-calculated spectra to fit the line core and a subsequent iterative
modification to improve the fit in the line wing. Simultaneous spectra in the
630nm range can optionally be used to fix the continuum temperature. The method
retrieves 1D temperature stratifications neglecting lateral radiative
transport. LOS velocities are included by an empirical approach. An archive of
about 300.000 pre-calculated spectra is more than sufficient to reproduce the
line core of observed Ca II H spectra both in quiet Sun and in active regions.
The final thermodynamical stratifications match observed and best-fit spectra
to a level of about 0.5 (1) % of Ic in the line wing (core). Inversion schemes
based on pre-calculated spectra allow one a reliable and relatively fast
retrieval of solar properties from observed chromospheric spectra. The approach
can be easily extended to an 1D NLTE case by a simple exchange of the
pre-calculated archive spectra.Comment: 15 pages, 15 figures, accepted for publication in A&A. The animation
will only be provided in the A&A online sectio
The energy of waves in the photosphere and lower chromosphere: IV. Inversion results of Ca II H spectra
Most static 1D atmosphere models in the quiet Sun predict a rise of the gas
temperature at chromospheric layers, but numerical simulations only yield an
increase in the brightness temperature. We investigate the thermal structure in
the solar chromosphere as derived from an LTE inversion of Ca II H spectra in
QS and active regions. We investigate the temperature stratifications on
differences between magnetic and field-free regions in the QS, and between QS
and ARs. We determine the energy content of individual calcium bright grains
(BGs). The rms temperature fluctuations are below 100 K in the photosphere and
200-300 K in the chromosphere. The average temperature stratification in the QS
does not exhibit a clear chromospheric temperature rise, opposite to the AR
case. We find an energy content of about 7*10E18 J for BGs that repeat with a
cadence of about 160 secs. The precursors of BGs have a vertical extent of
about 200 km and a horizontal extent of about 1 Mm. The comparison of observed
with synthetic NLTE profiles confirms that the solar chromosphere in the QS
oscillates between an atmosphere in radiative equilibrium and one with a
moderate chromospheric temperature rise. Two-dimensional x-z temperature maps
exhibit nearly horizontal canopy-like structures with a few Mm extent around
photospheric magnetic field concentrations at a height of about 600 km. The
large difference between QS regions and ARs, and the better match of AR and
non-LTE reference spectra suggest that magnetic heating processes are more
important than commonly assumed. The temperature fluctuations in QS derived by
the LTE inversion do not suffice on average to maintain a stationary
chromospheric temperature rise. The spatially and vertically resolved
information on the temperature structure allows one to investigate in detail
the topology and evolution of the thermal structure in the lower solar
atmosphere.Comment: 16 pages, 16 figures + 1 page Appendix, accepted by A&
Continuum Surface Energy from a Lattice Model
We investigate connections between the continuum and atomistic descriptions
of deformable crystals, using certain interesting results from number theory.
The energy of a deformed crystal is calculated in the context of a lattice
model with general binary interactions in two dimensions. A new bond counting
approach is used, which reduces the problem to the lattice point problem of
number theory. The main contribution is an explicit formula for the surface
energy density as a function of the deformation gradient and boundary normal.
The result is valid for a large class of domains, including faceted (polygonal)
shapes and regions with piecewise smooth boundaries.Comment: V. 1: 10 pages, no fig's. V 2: 23 pages, no figures. Misprints
corrected. Section 3 added, (new results). Intro expanded, refs added.V 3: 26
pages. Abstract changed. Section 2 split into 2. Section (4) added material.
V 4, 28 pages, Intro rewritten. Changes in Sec.5 (presentation only). Refs
added.V 5,intro changed V.6 address reviewer's comment
Polarized point sources in the LOFAR Two-meter Sky Survey: A preliminary catalog
The polarization properties of radio sources at very low frequencies (h45mâ15h30m right ascension, 45°â57° declination, 570 square degrees). We have produced a catalog of 92 polarized radio sources at 150 MHz at 4.âČ3 resolution and 1 mJy rms sensitivity, which is the largest catalog of polarized sources at such low frequencies. We estimate a lower limit to the polarized source surface density at 150 MHz, with our resolution and sensitivity, of 1 source per 6.2 square degrees. We find that our Faraday depth measurements are in agreement with previous measurements and have significantly smaller errors. Most of our sources show significant depolarization compared to 1.4 GHz, but there is a small population of sources with low depolarization indicating that their polarized emission is highly localized in Faraday depth. We predict that an extension of this work to the full LOTSS data would detect at least 3400 polarized sources using the same methods, and probably considerably more with improved data processing
The association between depressive symptoms and executive control impairments in response to emotional and non-emotional information
Depression has been linked with impaired executive control and specific impairments in inhibition of negative material. To date, only a few studies have examined the relationship between depressive symptoms and executive functions in response to emotional information. Using a new paradigm, the Affective Shift Task (AST), the present study examined whether depressive symptoms in general, and rumination specifically, are related to impairments in inhibition and set shifting in response to emotional and non-emotional material. The main finding was that depressive symptoms in general were not related to inhibition. Set-shifting impairments were only observed in moderate to severely depressed individuals. Interestingly, rumination was related to inhibition impairments, specifically when processing negative information, as well as impaired set shifting as reflected in a larger shift cost. These results are discussed in relation to cognitive views on vulnerability for depression
- âŠ