286 research outputs found
Nonlinear regression of stable random variables
Let (X1,X2) be an α-stable random vector, not necessarily symmetric, with 0<α<2. This article investigates the regression E(X2∣X1=x) for all values of α. We give conditions for the existence of the conditional moment E(|X2|p|X1=x) when p≥α, and we obtain an explicit form of the regression E(X2∣X1=x) as a function of x. Although this regression is, in general, not linear, it can be linear even when the vector (X1,X2) is skewed. We give a necessary and sufficient condition for linearity and characterize the asymptotic behavior of the regression as x→±∞. The behavior of the regression functions is also illustrated graphically
Rosenblatt distribution subordinated to gaussian random fields with long-range dependence
The Karhunen-Lo\`eve expansion and the Fredholm determinant formula are used
to derive an asymptotic Rosenblatt-type distribution of a sequence of integrals
of quadratic functions of Gaussian stationary random fields on R^d displaying
long-range dependence. This distribution reduces to the usual Rosenblatt
distribution when d=1. Several properties of this new distribution are
obtained. Specifically, its series representation in terms of independent
chi-squared random variables is given, the asymptotic behavior of the
eigenvalues, its L\`evy-Khintchine representation, as well as its membership to
the Thorin subclass of self-decomposable distributions. The existence and
boundedness of its probability density is then a direct consequence.Comment: This paper has 40 pages and it has already been submitte
Observation of Long-Lived Muonic Hydrogen in the 2S State
The kinetic energy distribution of ground state muonic hydrogen atoms
mu-p(1S) is determined from time-of-flight spectra measured at 4, 16, and 64
hPa H2 room-temperature gas. A 0.9 keV-component is discovered and attributed
to radiationless deexcitation of long-lived mu-p(2S) atoms in collisions with
H2 molecules. The analysis reveals a relative population of about 1%, and a
pressure-dependent lifetime (e.g. (30.4 +21.4 -9.7) ns at 64 hPa) of the
long-lived mu-p(2S) population, equivalent to a 2S-quench rate in mu-p(2S) + H2
collisions of (4.4 +2.1 -1.8) 10^11 s^-1 at liquid hydrogen density.Comment: 4 pages, 2 figures, accepted for publication in Physical Review
Letter
Rosenblatt distribution subordinated to Gaussian fields with long-range dependence
The Karhunen-Lo`eve expansion and the Fredholm determinant formula are used, to derive
an asymptotic Rosenblatt-type distribution of a sequence of integrals of quadratic functions of
Gaussian stationary random fields on R
d displaying long-range dependence. This distribution
reduces to the usual Rosenblatt distribution when d = 1. Several properties of this new distribution
are obtained. Specifically, its series representation, in terms of independent chi-squared
random variables, is established. Its L´evy-Khintchine representation, and membership to the
Thorin subclass of self-decomposable distributions are obtained as well. The existence and
boundedness of its probability density then follow as a direct consequence
Thin-disk laser pump schemes for large number of passes and moderate pump source quality
Novel thin-disk laser pump layouts are proposed yielding an increased number
of passes for a given pump module size and pump source quality. These novel
layouts result from a general scheme which bases on merging two simpler pump
optics arrangements. Some peculiar examples can be realized by adapting
standard commercially available pump optics simply by intro ducing an
additional mirror-pair. More pump passes yield better efficiency, opening the
way for usage of active materials with low absorption. In a standard multi-pass
pump design, scaling of the number of beam passes brings ab out an increase of
the overall size of the optical arrangement or an increase of the pump source
quality requirements. Such increases are minimized in our scheme, making them
eligible for industrial applicationsComment: 16 pages, 9 figure
muCool: A novel low-energy muon beam for future precision experiments
Experiments with muons () and muonium atoms () offer
several promising possibilities for testing fundamental symmetries. Examples of
such experiments include search for muon electric dipole moment, measurement of
muon and experiments with muonium from laser spectroscopy to gravity
experiments. These experiments require high quality muon beams with small
transverse size and high intensity at low energy.
At the Paul Scherrer Institute, Switzerland, we are developing a novel device
that reduces the phase space of a standard beam by a factor of
with efficiency. The phase space compression is achieved by
stopping a standard beam in a cryogenic helium gas. The stopped
are manipulated into a small spot with complex electric and magnetic
fields in combination with gas density gradients. From here, the muons are
extracted into the vacuum and into a field-free region. Various aspects of this
compression scheme have been demonstrated. In this article the current status
will be reported.Comment: 8 pages, 5 figures, TCP 2018 conference proceeding
Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen
The sixth-order electron-loop vacuum-polarization contribution to the
Lamb shift of the muonic hydrogen ( bound
state) has been evaluated numerically. Our result is 0.007608(1) meV. This
eliminates the largest uncertainty in the theoretical calculation. Combined
with the proposed precision measurement of the Lamb shift it will lead to a
very precise determination of the proton charge radius.Comment: 4 pages, 5 figures the totoal LS number is change
Variance fluctuations in nonstationary time series: a comparative study of music genres
An important problem in physics concerns the analysis of audio time series
generated by transduced acoustic phenomena. Here, we develop a new method to
quantify the scaling properties of the local variance of nonstationary time
series. We apply this technique to analyze audio signals obtained from selected
genres of music. We find quantitative differences in the correlation properties
of high art music, popular music, and dance music. We discuss the relevance of
these objective findings in relation to the subjective experience of music.Comment: 13 pages, 4 fig
Rosenblatt distribution subordinated to Gaussian fields with long-range dependence
The Karhunen-Lo`eve expansion and the Fredholm determinant formula are used, to derive
an asymptotic Rosenblatt-type distribution of a sequence of integrals of quadratic functions of
Gaussian stationary random fields on R
d displaying long-range dependence. This distribution
reduces to the usual Rosenblatt distribution when d = 1. Several properties of this new distribution
are obtained. Specifically, its series representation, in terms of independent chi-squared
random variables, is established. Its L´evy-Khintchine representation, and membership to the
Thorin subclass of self-decomposable distributions are obtained as well. The existence and
boundedness of its probability density then follow as a direct consequence
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