The Statistics of the Cross-Spectrum and the Spectrum Average: Generalization to Multiple Instruments.

This article addresses the measurement of the power spectrum of red noise processes at the lowest frequencies, where the minimum acquisition time is so long that it is impossible to average on a sequence of data record. Therefore, averaging is possible only on simultaneous observation of multiple instruments. This is the case of radio astronomy, which we take as the paradigm, but examples may be found in other fields such as climatology and geodesy.

Cross-Spectrum Measurement Statistics: Uncertainties and Detection Limit.

The cross-spectrum method consists in measuring a signal c(t) simultaneously with two independent instruments. Each of these instruments contributes to the global noise by its intrinsic (white) noise, whereas the signal c(t) that we want to characterize could be a (red) noise. We first define the real part of the cross spectrum as a relevant estimator.

Advancing Fourier: space-time concepts in ultrafast optics, imaging, and photonic neural networks.

The concepts of Fourier optics were established in France in the 1940s by Pierre-Michel Duffieux, and laid the foundations of an extensive series of activities in the French research community that have touched on nearly every aspect of contemporary optics and photonics. In this paper, we review a selection of results where applications of the Fourier transform and transfer functions in optics have been applied to yield significant advances in unexpected areas of optics, including the spatial shaping of complex laser beams in amplitude and in phase, real-time ultrafast measurements, novel ghost imaging techniques, and the development of parallel processing methodologies for photonic artificial intelligence.

Grand challenges in the science of wind energy.

Harvested by advanced technical systems honed over decades of research and development, wind energy has become a mainstream energy resource. However, continued innovation is needed to realize the potential of wind to serve the global demand for clean energy. Here, we outline three interdependent, cross-disciplinary grand challenges underpinning this research endeavor.

Effect of saw blade geometry on crack initiation and propagation on the lateral cortical hinge for HTO: Finite element analysis.

Introduction: The hinge plays a primary role in the hold and healing of a high tibial osteotomy (HTO). Weakening of the hinge is a risk factor for failure. The aim of our study was to determine whether the geometry of the saw blade's cutting edge impacts crack initiation or propagation on the hinge.

KLTS: A Rigorous Method to Compute the Confidence Intervals for the Three-Cornered Hat and for Groslambert Covariance.

The three-cornered hat/Groslambert Covariance (GCov) methods are widely used to estimate the stability of each individual clock in a set of three, but no method gives reliable confidence intervals for large integration times. We propose a new KLTS (Karhunen-Loève Tansform using Sufficient statistics) method which uses these estimators to consider the statistics of all the measurements between the pairs of clocks in a Bayesian way. The resulting cumulative density function (CDF) yields confidence intervals for each clock Allan variance (AVAR).

Three-Cornered Hat and Groslambert Covariance: A First Attempt to Assess the Uncertainty Domains.

The three-cornered hat method and the Groslambert covariance are very often used to estimate the frequency stability of each individual oscillator in a set of three oscillators by comparing them in pairs. However, no rigorous method to assess the uncertainties over their estimates has yet been formulated. In order to overcome this lack, this paper will first study the direct problem, i.

Einstein-Podolsky-Rosen paradox in single pairs of images.

Spatially entangled twin photons provide a test of the Einstein-Podolsky-Rosen (EPR) paradox in its original form of position (image plane) versus impulsion (Fourier plane). We show that recording a single pair of images in each plane is sufficient to safely demonstrate an EPR paradox. On each pair of images, we have retrieved the fluctuations by subtracting the fitted deterministic intensity shape and then have obtained an intercorrelation peak with a sufficient signal to noise ratio to safely distinguish this peak from random fluctuations.

Einstein-Podolsky-Rosen paradox in twin images.

Spatially entangled twin photons provide both promising resources for modern quantum information protocols, because of the high dimensionality of transverse entanglement, and a test of the Einstein-Podolsky-Rosen paradox in its original form of position versus impulsion. Usually, photons in temporal coincidence are selected and their positions recorded, resulting in a priori assumptions on their spatiotemporal behavior. In this Letter, we record, on two separate electron-multiplying charge coupled devices cameras, twin images of the entire flux of spontaneous down-conversion.

Privacy in Pharmacogenetics: An End-to-End Case Study of Personalized Warfarin Dosing.

We initiate the study of privacy in pharmacogenetics, wherein machine learning models are used to guide medical treatments based on a patient's genotype and background. Performing an in-depth case study on privacy in personalized warfarin dosing, we show that suggested models carry privacy risks, in particular because attackers can perform what we call : an attacker, given the model and some demographic information about a patient, can predict the patient's genetic markers. As differential privacy (DP) is an oft-proposed solution for medical settings such as this, we evaluate its effectiveness for building private versions of pharmacogenetic models.

Traumatic aortic injury: CT findings, mimics, and therapeutic options.

Objective: Traumatic aortic injury (TAI) is rare, but frequently lethal. However, with prompt diagnosis, patients can undergo life-saving open or endovascular repair. Unfortunately, because these injuries are relatively rare, subtle forms of these injuries may be missed, and normal variants may mimic TAI leading to misdiagnosis.

3D-PSTD simulation and polarization analysis of a light pulse transmitted through a scattering medium.

A tridimensional pseudo-spectral time domain (3D-PSTD) algorithm, that solves the full-wave Maxwell's equations by using Fourier transforms to calculate the spatial derivatives, has been applied to determine the time characteristics of the propagation of electromagnetic waves in inhomogeneous media. Since the 3D simulation gives access to the full-vector components of the electromagnetic fields, it allowed us to analyse the polarization state of the scattered light with respect to the characteristics of the scattering medium and the polarization state of the incident light. We show that, while the incident light is strongly depolarized on the whole, the light that reaches the output face of the scattering medium is much less depolarized.

Real-time suppression of turbidity of biological tissues in motion by three-wave mixing phase-conjugation.

We show that phase-conjugation by three-wave mixing allows turbidity suppression through biological tissues with thicknesses up to 5 mm, at a near-infrared wavelength included in the therapeutic window. Because of the ultrafast character of the imaging process, a motion of the tissue, which mimics in vivo imaging, can be exploited to significantly improve the signal-to-noise ratio and the resolution of the restored images.

Beam steering using optical parametric amplification in Kerr medium: a space-time analogy of parametric slow-light.

In a way analogous to a light pulse that can be optically delayed via slow light propagation in Kerr-type nonlinear media, we theoretically demonstrate that beam steering and spatial walk-off compensation can be achieved in noncollinear optical parametric amplification. We identify this effect as a result of the quadratic phase shift induced by parametric amplification that leads to the cancellation of the spatial walk-off and collinear propagation of all beams though they have different wavevectors. Experimental evidence is reported of a soliton array steering in a Kerr slab waveguide.

Statistical biases and very-long-term time stability analysis.

The prediction of very-long-term time stability is a key issue in various fields, such as time keeping, obviously, but also navigation and spatial applications. This is usually performed by extrapolating the measurement data obtained by estimators such as the Allan variance, modified Allan variance, Hadamard variance, etc. This extrapolation may be assessed from a fit over the variance estimates.

Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime.

We have measured sub-shot-noise quantum correlations of spatial fluctuations in the far-field image of the parametric fluorescence created in a type I beta-barium-borate nonlinear crystal. Imaging is performed at very low light level (0.15 photons per pixel) with an electron multiplying charge coupled device camera.

Investigation of gain ripple in two-pump fiber optical parametric amplifiers.

By using the four-sideband theory, we analyze the gain spectrum in wideband two-pump fiber optical parametric amplifiers and predict gain ripples over the flat gain region. We derive an approximation of their pseudo-periods and discuss methods for reducing their amplitudes.

Absolute radiance imaging using parametric image amplification.

We show that parametric image amplification can be used to achieve a 2D radiance map directly expressed in photons per spatiotemporal mode. Radiance images of incoherent signals with less than one photon per mode (typically 10(-2)) are resolved.

Effective signal-to-noise ratio improvement by parametric image amplification.

We show experimentally that parametric optical preamplification greatly improves the signal-to-noise ratio of an image if the detector has a poor quantum efficiency and/or a great level of readout noise. Results are fully consistent with the theory of quantum-noise-limited amplification.

Spatially noiseless optical amplification of images.

We present the first experimental demonstration of noiseless amplification of images, where noise refers to spatial quantum fluctuations on the pixels of single shot images. Phase-sensitive and phase-insensitive schemes are compared and the noise figures are in good agreement with theory, inasmuch this theory includes the quantum efficiency of the whole system and the pixel size.

Weak-wave advancement in nearly collinear four-wave mixing: comment.

The exponential gain predicted in "Weak-wave advancement in nearly collinear four-wave mixing" [Opt. Express 10, 581 (2002)], disappears when all interacting sidebands are properly taken into account. The demonstration closely follows well-established literature in the formally equivalent temporal domain.

Spatiotemporal dynamics of soliton arrays generated from spatial noise in a planar waveguide with relaxing Kerr nonlinearity.

Quasi-periodic arrays of bright soliton-like beams are obtained experimentally in the picosecond regime as a result of the transverse modulational instability of a noisy continuous background in a planar CS2 waveguide. For a given propagation length, the array is stable from a laser shot to another and for a wide range of input intensities. The experimental period corresponds to the maximum gain of modulational instability only for the intensity just sufficient for soliton formation.