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

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

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

muCool: A novel low-energy muon beam for future precision experiments

Experiments with muons ($\mu^{+}$) and muonium atoms ($\mu^{+}e^{-}$) offer several promising possibilities for testing fundamental symmetries. Examples of such experiments include search for muon electric dipole moment, measurement of muon $g-2$ 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 $\mu^{+}$ beam by a factor of $10^{10}$ with $10^{-3}$ efficiency. The phase space compression is achieved by stopping a standard $\mu^{+}$ beam in a cryogenic helium gas. The stopped $\mu^{+}$ 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 $2P_{1/2} - 2S_{1/2}$ Lamb shift of the muonic hydrogen ($\mu^{-} p^+$ 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