101,540 research outputs found
An elementary approach to toy models for D. H. Lehmer's conjecture
In 1947, Lehmer conjectured that the Ramanujan's tau function
never vanishes for all positive integers , where is the -th
Fourier coefficient of the cusp form of weight 12. The theory of
spherical -design is closely related to Lehmer's conjecture because it is
shown, by Venkov, de la Harpe, and Pache, that is equivalent to
the fact that the shell of norm of the -lattice is a spherical
8-design. So, Lehmer's conjecture is reformulated in terms of spherical
-design.
Lehmer's conjecture is difficult to prove, and still remains open. However,
Bannai-Miezaki showed that none of the nonempty shells of the integer lattice
\ZZ^2 in \RR^2 is a spherical 4-design, and that none of the nonempty
shells of the hexagonal lattice is a spherical 6-design. Moreover, none
of the nonempty shells of the integer lattices associated to the algebraic
integers of imaginary quadratic fields whose class number is either 1 or 2,
except for \QQ(\sqrt{-1}) and \QQ(\sqrt{-3}) is a spherical 2-design. In
the proof, the theory of modular forms played an important role.
Recently, Yudin found an elementary proof for the case of \ZZ^{2}-lattice
which does not use the theory of modular forms but uses the recent results of
Calcut. In this paper, we give the elementary (i.e., modular form free) proof
and discuss the relation between Calcut's results and the theory of imaginary
quadratic fields.Comment: 18 page
The HH34 outflow as seen in [FeII]1.64um by LBT-LUCI
Dense atomic jets from young stars copiously emit in [FeII] IR lines, which
can, therefore, be used to trace the immediate environments of embedded
protostars. We want to investigate the morphology of the bright [FeII] 1.64um
line in the jet of the source HH34 IRS and compare it with the most commonly
used optical tracer [SII]. We analyse a 1.64um narrow-band filter image
obtained with the Large Binocular Telescope (LBT) LUCI instrument, which covers
the HH34 jet and counterjet. A Point Spread Function (PSF) deconvolution
algorithm was applied to enhance spatial resolution and make the IR image
directly comparable to a [SII] HST image of the same source. The [FeII]
emission is detected from both the jet, the (weak) counter-jet, and from the
HH34-S and HH34-N bow shocks. The deconvolved image allows us to resolve jet
knots close to about 1\arcsec from the central source. The morphology of the
[FeII] emission is remarkably similar to that of the [SII] emission, and the
relative positions of [FeII] and [SII] peaks are shifted according to proper
motion measurements, which were previously derived from HST images. An analysis
of the [FeII]/[SII] emission ratio shows that Fe gas abundance is much lower
than the solar value with up to 90% of Fe depletion in the inner jet knots.
This confirms previous findings on dusty jets, where shocks are not efficient
enough to remove refractory species from grains.Comment: 5 pages, 4 figures, note accepted by A&
Human brain distinctiveness based on EEG spectral coherence connectivity
The use of EEG biometrics, for the purpose of automatic people recognition,
has received increasing attention in the recent years. Most of current analysis
rely on the extraction of features characterizing the activity of single brain
regions, like power-spectrum estimates, thus neglecting possible temporal
dependencies between the generated EEG signals. However, important
physiological information can be extracted from the way different brain regions
are functionally coupled. In this study, we propose a novel approach that fuses
spectral coherencebased connectivity between different brain regions as a
possibly viable biometric feature. The proposed approach is tested on a large
dataset of subjects (N=108) during eyes-closed (EC) and eyes-open (EO) resting
state conditions. The obtained recognition performances show that using brain
connectivity leads to higher distinctiveness with respect to power-spectrum
measurements, in both the experimental conditions. Notably, a 100% recognition
accuracy is obtained in EC and EO when integrating functional connectivity
between regions in the frontal lobe, while a lower 97.41% is obtained in EC
(96.26% in EO) when fusing power spectrum information from centro-parietal
regions. Taken together, these results suggest that functional connectivity
patterns represent effective features for improving EEG-based biometric
systems.Comment: Key words: EEG, Resting state, Biometrics, Spectral coherence, Match
score fusio
Comment on `Strong Vortex Liquid Correlation' from Multiterminal Measurements on Untwinned YBaCuO Single Crystals'
A.Rydh and \"O.Rapp [Phys. Rev. Lett. {\bf 86}, 1873 (2001).] claim that the
vortex liquid in untwinned YBaCuO crystals is correlated
above the melting transition, in striking contrast to previous work [D.L\'opez
{\it et al.}, Phys. Rev. Lett. {\bf 76}, 4034 (1996).]. In this Comment we
present new measurements using the same experimental technique on twinned and
untwinned YBaCuO crystals with similar overall
characteristics as those reported by Rydh and Rapp . The comparison of the
vortex correlation response in both cases indicates that the central conclusion
of their work is not correct. Our results reconfirm the work by L\'opez {\it et
al.} and points on the origin of the misinterpretation in the work of Rydh and
Rapp.Comment: comment on A.Rydh and \"O.Rapp, Phys. Rev. Lett. {\bf 86}, 1873
(2001). accepted in Phys. Rev. Let
Molecular collisions. 16: Comparison of GPS with classical trajectory calculations of rotational inelasticity for the Ar-N2 system
Comparison of generalized phase shift treatment with classical trajectory calculations of rotational inelasticity cross sections of Ar-N2 scatterin
Generation of two-photon states with arbitrary degree of entanglement via nonlinear crystal superlattices
We demonstrate a general method of engineering the joint quantum state of
photon pairs produced in spontaneous parametric downconversion (PDC). The
method makes use of a superlattice structure of nonlinear and linear materials,
in conjunction with a broadband pump, to manipulate the group delays of the
signal and idler photons relative to the pump pulse, and realizes a joint
spectral amplitude with arbitrary degree of entanglement for the generated
pairs. This method of group delay engineering has the potential of synthesizing
a broad range of states including factorizable states crucial for quantum
networking and states optimized for Hong-Ou-Mandel interferometry. Experimental
results for the latter case are presented, illustrating the principles of this
approach.Comment: 4 pages, 4 figures, accepted Phys. Rev. Let
Quantum diffusion on a cyclic one dimensional lattice
The quantum diffusion of a particle in an initially localized state on a
cyclic lattice with N sites is studied. Diffusion and reconstruction time are
calculated. Strong differences are found for even or odd number of sites and
the limit N->infinit is studied. The predictions of the model could be tested
with micro - and nanotechnology devices.Comment: 17 pages, 5 figure
The antenna DSA 3 and its potential use for Radio Astronomy
The European Space Agency (ESA) will inaugurate its third Deep Space Antenna
(DSA 3) by the end of 2012. DSA 3 will be located in Argentina near the city of
Malarg"ue in the Mendoza province. While the instrument will be primarily
dedicated to communications with interplanetary missions, the characteristics
of its antenna and receivers will also enable standalone leading scientific
contributions, with a high scientific-technological return. We outline here
scientific proposals for a radio astronomical use of DSA 3.Comment: 4 pages, submitted as Proceedings for the BAA
DC-Prophet: Predicting Catastrophic Machine Failures in DataCenters
When will a server fail catastrophically in an industrial datacenter? Is it
possible to forecast these failures so preventive actions can be taken to
increase the reliability of a datacenter? To answer these questions, we have
studied what are probably the largest, publicly available datacenter traces,
containing more than 104 million events from 12,500 machines. Among these
samples, we observe and categorize three types of machine failures, all of
which are catastrophic and may lead to information loss, or even worse,
reliability degradation of a datacenter. We further propose a two-stage
framework-DC-Prophet-based on One-Class Support Vector Machine and Random
Forest. DC-Prophet extracts surprising patterns and accurately predicts the
next failure of a machine. Experimental results show that DC-Prophet achieves
an AUC of 0.93 in predicting the next machine failure, and a F3-score of 0.88
(out of 1). On average, DC-Prophet outperforms other classical machine learning
methods by 39.45% in F3-score.Comment: 13 pages, 5 figures, accepted by 2017 ECML PKD
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