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. We compare the Bayesian confidence interval of the red noise parameter using two estimators, the spectrum average and the cross-spectrum. While the spectrum average is widely used, the cross-spectrum using multiple instruments is rather uncommon. With two instruments, the cross-spectrum estimator leads to the Variance-Gamma distribution. A generalization to q devices based on the Fourier transform of characteristic functions is provided, with the example of the observation of millisecond pulsars with five radio telescopes (RTs). The simulations show that the spectrum average is by a small amount more efficient than the cross-spectrum, chiefly when the background exceeds the signal. However, some notable differences between their upper limit indicate that it should be wiser to compute both estimators.

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. Then, we characterize the probability density function (pdf) of this estimator knowing the noise level (direct problem) as a Variance-gamma (VG) distribution. Next, we solve the "inverse problem" due to Bayes' theorem to obtain an upper limit of the noise level knowing the estimate. Checked by massive Monte Carlo simulations, VG proves to be perfectly reliable for any number of degrees of freedom (DOFs). Finally, we compare this method with another method using the Karhunen-Loève transform (KLT). We find an upper limit of the signal level slightly different as the one of VG since KLT better considers the available information.

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. The first is the need for a deeper understanding of the physics of atmospheric flow in the critical zone of plant operation. The second involves science and engineering of the largest dynamic, rotating machines in the world. The third encompasses optimization and control of fleets of wind plants working synergistically within the electricity grid. Addressing these challenges could enable wind power to provide as much as half of our global electricity needs and perhaps beyond.

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. HYPOTHESIS: A certain cutting edge geometry exists that will reduce this risk. MATERIALS AND METHODS: A finite element model with transverse isotropic elastic bone properties was created. A 1.27-mm thick saw cut (full thickness in anteroposterior direction) was made leaving a 1cm lateral cortical hinge. Three different cutting edge geometries were compared: rectangular, U-shaped, V-shaped. Opening of the osteotomy was done over 1mm for 1 s by a load applied distally with the proximal portion fixed. In the first simulation, no crack was initiated at the hinge, while in the second simulation, the beginnings of a 2mm crack angled upward at 15° was added. These two simulations were used to identify whether a local stress riser was present at the hinge. This information was used to calculate the energy release rate to the hinge, which corresponds to the energy needed to initiate and propagate a crack on the hinge. RESULTS: In the first simulation (no crack initiation), a rectangular saw blade geometry resulted in the lowest local stress concentration. In the second simulation (with crack initiation), the U-shaped geometry resulted in the lowest local stress concentration. The U-shaped geometry had the lowest energy release rate, meaning that it was the least likely to initiate and propagate a crack on the lateral cortical hinge. DISCUSSION/CONCLUSION: Keeping the inherent limitations related to computer modelling in mind, our findings show that a U-shaped cutting edge is least likely to initiate or propagate a crack since it has the lowest energy release rate. This confirms our hypothesis. LEVEL OF EVIDENCE: V, expert opinion.

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). This CDF provides also a stability estimator that is always positive. Checked by massive Monte Carlo simulations, KLTS proves to be perfectly reliable even for one degree of freedom. An example of experimental measurement is given.

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.e., the calculation of the statistics of the clock stability estimates by assuming known values of the true clock stabilities and then will propose a first attempt to solve the inverse problem, i.e., the assessment of a confidence interval over the true clock stabilities by assuming known values of the clock stability estimates. We show that this method is reliable from 5 equivalent degrees of freedom (EDF) and beyond.

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. A 95% confidence interval has been determined, confirming a high degree of paradox whatever the considered single pairs. Last, we have verified that the value of the variance of the difference between twin images is always below the quantum (poissonian) limit, in order to ensure the particle character of the demonstration. Our demonstration shows that a single image pattern can reveal the quantum and non-local behavior of light.

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. This ensures a strict equivalence between the subsystems corresponding to the detection of either position (image or near-field plane) or momentum (Fourier or far-field plane). We report the highest degree of paradox ever reported and show that this degree corresponds to the number of independent degrees of freedom, or resolution cells, of the images.

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. CONCLUSIONS: We will discuss computed tomography findings of typical injury patterns of traumatic aortic injuries as well as treatment options, diagnostic pitfalls and injury mimics. These are highlighted with clinical case examples.

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 model inversion: 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. We show that DP mechanisms prevent our model inversion attacks when the privacy budget is carefully selected. We go on to analyze the impact on utility by performing simulated clinical trials with DP dosing models. We find that for privacy budgets effective at preventing attacks, patients would be exposed to increased risk of stroke, bleeding events, and mortality. We conclude that current DP mechanisms do not simultaneously improve genomic privacy while retaining desirable clinical efficacy, highlighting the need for new mechanisms that should be evaluated in situ using the general methodology introduced by our work.

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. This fact is consistent with our recently reported experimental results, where a rotation of the polarization does not preclude the restoration of an image by phase conjugation.

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. However, this fit should be performed on the log-log graph of the estimates, which corresponds to a least-squares minimization of the relative difference between the variance estimates and the fitting curve. However, a bias exists between the average of the log of the estimates and the log of the true value of the estimated variance. This paper presents the theoretical calculation of this log-log bias based on the number of equivalent degrees of freedom of the estimates, shows simulations over a large number of realizations, and provides a reliable method of unbiased logarithmic fit. Extrapolating this fit yields a more confident assessment of the very-long-term time stability.

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. Experimental results overcome the standard quantum limit shot-noise level without subtraction of the variance of the detection noise.

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.