4,686 research outputs found
Topological transversals to a family of convex sets
Let be a family of compact convex sets in . We say
that has a \emph{topological -transversal of index }
(, ) if there are, homologically, as many transversal
-planes to as -planes containing a fixed -plane in
.
Clearly, if has a -transversal plane, then
has a topological -transversal of index for and . The converse is not true in general.
We prove that for a family of compact convex sets in
a topological -transversal of index implies an
ordinary -transversal. We use this result, together with the
multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann
category of the Grassmannian, and different versions of the colorful Helly
theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences
Ultraviolet and Infrared Divergences in Implicit Regularization: a Consistent Approach
Implicit Regularization is a 4-dimensional regularization initially conceived
to treat ultraviolet divergences. It has been successfully tested in several
instances in the literature, more specifically in those where Dimensional
Regularization does not apply. In the present contribution we extend the method
to handle infrared divergences as well. We show that the essential steps which
rendered Implicit Regularization adequate in the case of ultraviolet
divergences have their counterpart for infrared ones. Moreover we show that a
new scale appears, typically an infrared scale which is completely independent
of the ultraviolet one. Examples are given.Comment: 9 pages, version to appear in Mod. Phys. Lett.
Tunka-Rex: the Cost-Effective Radio Extension of the Tunka Air-Shower Observatory
Tunka-Rex is the radio extension of the Tunka cosmic-ray observatory in
Siberia close to Lake Baikal. Since October 2012 Tunka-Rex measures the radio
signal of air-showers in coincidence with the non-imaging air-Cherenkov array
Tunka-133. Furthermore, this year additional antennas will go into operation
triggered by the new scintillator array Tunka-Grande measuring the secondary
electrons and muons of air showers. Tunka-Rex is a demonstrator for how
economic an antenna array can be without losing significant performance: we
have decided for simple and robust SALLA antennas, and we share the existing
DAQ running in slave mode with the PMT detectors and the scintillators,
respectively. This means that Tunka-Rex is triggered externally, and does not
need its own infrastructure and DAQ for hybrid measurements. By this, the
performance and the added value of the supplementary radio measurements can be
studied, in particular, the precision for the reconstructed energy and the
shower maximum in the energy range of approximately eV. Here
we show first results on the energy reconstruction indicating that radio
measurements can compete with air-Cherenkov measurements in precision.
Moreover, we discuss future plans for Tunka-Rex.Comment: Proceeding of UHECR 2014, Springdale, Utah, USA, accepted by JPS
Conference Proceeding
Radio measurements of the energy and the depth of the shower maximum of cosmic-ray air showers by Tunka-Rex
We reconstructed the energy and the position of the shower maximum of air
showers with energies PeV applying a method using radio
measurements performed with Tunka-Rex. An event-to-event comparison to
air-Cherenkov measurements of the same air showers with the Tunka-133
photomultiplier array confirms that the radio reconstruction works reliably.
The Tunka-Rex reconstruction methods and absolute scales have been tuned on
CoREAS simulations and yield energy and values consistent
with the Tunka-133 measurements. The results of two independent measurement
seasons agree within statistical uncertainties, which gives additional
confidence in the radio reconstruction. The energy precision of Tunka-Rex is
comparable to the Tunka-133 precision of , and exhibits a
uncertainty on the absolute scale dominated by the amplitude calibration of the
antennas. For , this is the first direct experimental
correlation of radio measurements with a different, established method. At the
moment, the resolution of Tunka-Rex is approximately g/cm. This resolution can probably be improved by deploying additional
antennas and by further development of the reconstruction methods, since the
present analysis does not yet reveal any principle limitations.Comment: accepted for publication by JCA
Fourier-Space Crystallography as Group Cohomology
We reformulate Fourier-space crystallography in the language of cohomology of
groups. Once the problem is understood as a classification of linear functions
on the lattice, restricted by a particular group relation, and identified by
gauge transformation, the cohomological description becomes natural. We review
Fourier-space crystallography and group cohomology, quote the fact that
cohomology is dual to homology, and exhibit several results, previously
established for special cases or by intricate calculation, that fall
immediately out of the formalism. In particular, we prove that {\it two phase
functions are gauge equivalent if and only if they agree on all their
gauge-invariant integral linear combinations} and show how to find all these
linear combinations systematically.Comment: plain tex, 14 pages (replaced 5/8/01 to include archive preprint
number for reference 22
Signal recognition and background suppression by matched filters and neural networks for Tunka-Rex
The Tunka Radio Extension (Tunka-Rex) is a digital antenna array, which
measures the radio emission of the cosmic-ray air-showers in the frequency band
of 30-80 MHz. Tunka-Rex is co-located with TAIGA experiment in Siberia and
consists of 63 antennas, 57 of them are in a densely instrumented area of about
1 km\textsuperscript{2}. In the present work we discuss the improvements of the
signal reconstruction applied for the Tunka-Rex. At the first stage we
implemented matched filtering using averaged signals as template. The
simulation study has shown that matched filtering allows one to decrease the
threshold of signal detection and increase its purity. However, the maximum
performance of matched filtering is achievable only in case of white noise,
while in reality the noise is not fully random due to different reasons. To
recognize hidden features of the noise and treat them, we decided to use
convolutional neural network with autoencoder architecture. Taking the recorded
trace as an input, the autoencoder returns denoised trace, i.e. removes all
signal-unrelated amplitudes. We present the comparison between standard method
of signal reconstruction, matched filtering and autoencoder, and discuss the
prospects of application of neural networks for lowering the threshold of
digital antenna arrays for cosmic-ray detection.Comment: ARENA2018 proceeding
Current Status and New Challenges of The Tunka Radio Extension
The Tunka Radio Extension (Tunka-Rex) is an antenna array spread over an area
of about 1~km. The array is placed at the Tunka Advanced Instrument for
cosmic rays and Gamma Astronomy (TAIGA) and detects the radio emission of air
showers in the band of 30 to 80~MHz. During the last years it was shown that a
sparse array such as Tunka-Rex is capable of reconstructing the parameters of
the primary particle as accurate as the modern instruments. Based on these
results we continue developing our data analysis. Our next goal is the
reconstruction of cosmic-ray energy spectrum observed only by a radio
instrument. Taking a step towards it, we develop a model of aperture of our
instrument and test it against hybrid TAIGA observations and Monte-Carlo
simulations. In the present work we give an overview of the current status and
results for the last five years of operation of Tunka-Rex and discuss prospects
of the cosmic-ray energy estimation with sparse radio arrays.Comment: Proceedings of E+CRS 201
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