Estimation of the Jump Size Density in a Mixed Compound Poisson Process

International audienceIn this paper, we consider a mixed compound Poisson process, i.e. a random sum of i.i.d. random variables where the number of terms is a Poisson process with random intensity. We study nonparametric estimators of the jump density by specific deconvolution methods. First, assuming that the random intensity has exponential distribution with unknown expectation , we propose two types of estimators based on the observation of an i.i.d. sample. Risks bounds and adaptive procedures are provided. Then, with no assumption on the distribution of the random intensity, we propose two nonparametric estimators of the jump density based on the joint observation of the number of jumps and the random sum of jumps. Risks bounds are provided, leading to unusual rates for one of the two estimators. The methods are implemented and compared via simulations. February 25, 201

Random Fibonacci Sequences

Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1} decrease (increase) exponentially, x_{n} = exp(lambda n), for sufficiently small (large) B. In the limits B --> 0 and B --> infinity, we expand the Lyapunov exponent lambda(B) in powers of B and B^{-1}, respectively. For the classical case of $\beta=1$ we obtain exact non-perturbative results. In particular, an invariant measure associated with Ricatti variable r_n=x_{n+1}/x_{n} is shown to exhibit plateaux around all rational.Comment: 11 Pages (Multi-Column); 3 EPS Figures ; Submitted to J. Phys.

Tectonomagmatic Evolution of Southwestern Laurentia: Insights from Zircon U-Pb Geochronology and Hafnium Isotopic Composition of the Red Bluff Granite Suite, West Texas, USA

We provide laser ablation–multicollector–inductively coupled plasma–mass spectrometry (LA-MC-ICP-MS) and high-precision chemical abrasion–isotope dilution–thermal ionization mass spectrometry (CA-ID-TIMS) U-Pb ages and Hf isotopic compositions of zircons from the Red Bluff Granite Suite and mafic dikes in the Franklin Mountains of El Paso, Texas, USA. Granitoids exposed in the Franklin Mountains were previously divided into five magmatic stages based on cross-cutting relationships. Major and trace element compositions showed that these granitoids are ferroan, alkaline, and A2 type. Homogeneity in the whole-rock geochemistry suggests that the granite stages are genetically related and share similar petrogenetic histories. Weighted mean zircon 206Pb/238U dates from the older magmatic stage 1 alkali-feldspar quartz syenite and stage 2 alkali-feldspar granite are 1112.36 ± 0.35 and 1112.46 ± 0.37 Ma, respectively. The weighted mean εHf(t) values varying from +5.3 to +7.2 are similar to those of other regional ca. 1.1 Ga magmatic rocks throughout southwestern Laurentia. Geochemical characteristics, petrological modeling, and enriched Hf isotopic composition suggest fractional crystallization of a basaltic magma that was produced by melting of an enriched mantle reservoir. However, zircon inheritance ages of ca. 1.3 Ga and 1.26–1.15 Ga are consistent with a minor contribution from felsic crustal basement. Our data and regional geology are consistent with a post-collisional slab break-off that facilitated asthenospheric upwelling and partial melting of the enriched mantle, possibly subcontinental lithospheric mantle, extending from Llano Uplift, Texas, in the southeast to California to the northwest. Magma thus generated upon differentiation produced ferroan and A-type granitoids

A model of linear chain submonolayer structures. Application to Li/W(112) and Li/Mo(112)

We propose a lattice gas model to account for linear chain structures adsorbed on (112) faces of W and Mo. The model includes a dipole-dipole interaction as well as a long-ranged indirect interaction. We have explicitly demonstrated that the periodic ground states depend on a competition between dipole-dipole and indirect interaction. The effect of temperature is studied within the molecular-field approximation. The numerical results show that for dipole-dipole interaction only, all long periodic linear chain phases are suppressed to low temperatures. However, when the long-range indirect interaction becomes important, the long-periodic linear chain phases start to fill up the phase diagram and develop a high thermal stability. Model parameters are chosen to reconstruct a sequence of long-periodic phases as observed experimentally for Li/Mo(112) and Li/W(112).Comment: RevTeX 9 pages + 5 Postscript figures (included), uses newdoc.sty (included), to be published in Surface Scienc

Single parameter scaling in one-dimensional localization revisited

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We find a new significant scaling parameter in the system, and derive an exact analytical criterion for single parameter scaling which differs from the commonly used condition of phase randomization. The results obtained are applied to the Kronig-Penney model with the potential in the form of periodically positioned $\delta$-functions with random strength.Comment: Phys. Rev. Lett. 84, 2678 (2000

Failure of single-parameter scaling of wave functions in Anderson localization

We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the origin of $L^{d-1} \times \infty$ disordered systems. For $d=1$ our approach is shown to reproduce exact diagonalization results available in the literature. In $d=2$, where strips of width $L \leq 64$ sites were used, attempted fits of gaussian (log-normal) forms to the wavefunction amplitude distributions result in effective localization lengths growing with distance, contrary to the prediction from single-parameter scaling theory. We also show that the distributions possess a negative skewness $S$, which is invariant under the usual histogram-collapse rescaling, and whose absolute value increases with distance. We find $0.15 \lesssim -S \lesssim 0.30$ for the range of parameters used in our study, .Comment: RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be published

Decay Rate Distributions of Disordered Slabs and Application to Random Lasers

We compute the distribution of the decay rates (also referred to as residues) of the eigenstates of a disordered slab from a numerical model. From the results of the numerical simulations, we are able to find simple analytical formulae that describe those results well. This is possible for samples both in the diffusive and in the localised regime. As example of a possible application, we investigate the lasing threshold of random lasers.Comment: 11 pages, 11 figure

Frailty in liver transplantation: An expert opinion statement from the American Society of Transplantation Liver and Intestinal Community of Practice

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149699/1/ajt15392_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149699/2/ajt15392.pd

Anderson-localization versus delocalization of interacting fermions in one dimension

Using the density matrix renormalization group algorithm, we investigate the lattice model for spinless fermions in one dimension in the presence of a strong interaction and disorder. The phase sensitivity of the ground state energy is determined with high accuracy for systems up to a size of 60 lattice constants. This quantity is found to be log-normally distributed. The fluctuations grow algebraically with system size with a universal exponent of ~2/3 in the localized region of the phase diagram. Surprizingly, we find, for an attractive interaction, a delocalized phase of finite extension. The boundary of this delocalized phase is determined.Comment: 5 pages, 6 figures, revte