Multivariate truncated moments problems and maximum entropy

We characterize the existence of the Lebesgue integrable solutions of the truncated problem of moments in several variables on unbounded supports by the existence of some maximum entropy -- type representing densities and discuss a few topics on their approximation in a particular case, of two variables and 4th order moments.Comment: Revised version, to appear in Analysis and Mathematical Physic

Avalanche amplification of a single exciton in a semiconductor nanowire

Interfacing single photons and electrons is a crucial ingredient for sharing quantum information between remote solid-state qubits. Semiconductor nanowires offer the unique possibility to combine optical quantum dots with avalanche photodiodes, thus enabling the conversion of an incoming single photon into a macroscopic current for efficient electrical detection. Currently, millions of excitation events are required to perform electrical read-out of an exciton qubit state. Here we demonstrate multiplication of carriers from only a single exciton generated in a quantum dot after tunneling into a nanowire avalanche photodiode. Due to the large amplification of both electrons and holes (> 10^4), we reduce by four orders of magnitude the number of excitation events required to electrically detect a single exciton generated in a quantum dot. This work represents a significant step towards single-shot electrical read-out and offers a new functionality for on-chip quantum information circuits

Neurofibromatosis

Neurofibromatosis (NF) is one of the most common genetic disorders. Inherited in an autosomal dominant fashion, this phacomatosis is classified into two genetically distinct subtypes characterized by multiple cutaneous lesions and tumors of the peripheral and central nervous system. Neurofibromatosis type 1 (NF1), also referred to as Recklinghausen's disease, affects about 1 in 3500 individuals and presents with a variety of characteristic abnormalities of the skin and the peripheral nervous system. Neurofibromatosis type 2 (NF2), previously termed central neurofibromatosis, is much more rare occurring in less than 1 in 25 000 individuals. Often first clinical signs of NF2 become apparent in the late teens with a sudden loss of hearing due to the development of bi-or unilateral vestibular schwannomas. In addition NF2 patients may suffer from further nervous tissue tumors such as meningiomas or gliomas. This review summarizes the characteristic features of the two forms of NF and outlines commonalities and distinctions between NF1 and NF2

Some geometric invariants from resolutions of Hilbert modules

The model theory of Sz.-Nagy and Foias for contractions was reformulated in [15, chapter 3]. The existence of a unique minimal unitary dilation amounts to the exis-tence of a Silov resolution for contractive Hilbert modulesM over the disc algebra A(D) along with the fact that any two minimal Silov resolutions are isomorphic

Planck intermediate results. XIX. An overview of the polarized thermal emission from Galactic dust

This paper presents an overview of the polarized sky as seen by Planck HFI at 353GHz, which is the most sensitive Planck channel for dust polarization. We construct and analyse maps of dust polarization fraction and polarization angle at 1 degrees resolution, taking into account noise bias and possible systematic effects. The sensitivity of the Planck HFI polarization measurements allows for the first time a mapping of Galactic dust polarized emission on large scales, including low column density regions. We find that the maximum observed dust polarization fraction is high (p(max) = 19.8%), in particular in some regions of moderate hydrogen column density (N-H <2 x 10(21) cm(-2)). The polarization fraction displays a large scatter at NH below a few 10(21) cm(-2). There is a general decrease in the dust polarization fraction with increasing column density above N-H similar or equal to 1 x 10(21) cm(-2) and in particular a sharp drop above N-H similar or equal to 1.5 x 10(22) cm(-2). We characterize the spatial structure of the polarization angle using the angle dispersion function. We find that the polarization angle is ordered over extended areas of several square degrees, separated by filamentary structures of high angle dispersion function. These appear as interfaces where the sky projection of the magnetic field changes abruptly without variations in the column density. The polarization fraction is found to be anti-correlated with the dispersion of polarization angles. These results suggest that, at the resolution of 1 degrees, depolarization is due mainly to fluctuations in the magnetic field orientation along the line of sight, rather than to the loss of grain alignment in shielded regions. We also compare the polarization of thermal dust emission with that of synchrotron measured with Planck, low-frequency radio data, and Faraday rotation measurements toward extragalactic sources. These components bear resemblance along the Galactic plane and in some regions such as the Fan and North Polar Spur regions. The poor match observed in other regions shows, however, that dust, cosmic-ray electrons, and thermal electrons generally sample different parts of the line of sight.Peer reviewe