Near-Optimal Quantum Algorithms for Multivariate Mean Estimation

We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian estimators to the quantum setting. Unlike classically, where any univariate estimator can be turned into a multivariate estimator with at most a logarithmic overhead in the dimension, no similar result can be proved in the quantum setting. Indeed, Heinrich ruled out the existence of a quantum advantage for the mean estimation problem when the sample complexity is smaller than the dimension. Our main result is to show that, outside this low-precision regime, there is a quantum estimator that outperforms any classical estimator. Our approach is substantially more involved than in the univariate setting, where most quantum estimators rely only on phase estimation. We exploit a variety of additional algorithmic techniques such as amplitude amplification, the Bernstein-Vazirani algorithm, and quantum singular value transformation. Our analysis also uses concentration inequalities for multivariate truncated statistics. We develop our quantum estimators in two different input models that showed up in the literature before. The first one provides coherent access to the binary representation of the random variable and it encompasses the classical setting. In the second model, the random variable is directly encoded into the phases of quantum registers. This model arises naturally in many quantum algorithms but it is often incomparable to having classical samples. We adapt our techniques to these two settings and we show that the second model is strictly weaker for solving the mean estimation problem. Finally, we describe several applications of our algorithms, notably in measuring the expectation values of commuting observables and in the field of machine learning.Comment: 35 pages, 1 figure; v2: minor change

Human Gamma Oscillations during Slow Wave Sleep

Neocortical local field potentials have shown that gamma oscillations occur spontaneously during slow-wave sleep (SWS). At the macroscopic EEG level in the human brain, no evidences were reported so far. In this study, by using simultaneous scalp and intracranial EEG recordings in 20 epileptic subjects, we examined gamma oscillations in cerebral cortex during SWS. We report that gamma oscillations in low (30–50 Hz) and high (60–120 Hz) frequency bands recurrently emerged in all investigated regions and their amplitudes coincided with specific phases of the cortical slow wave. In most of the cases, multiple oscillatory bursts in different frequency bands from 30 to 120 Hz were correlated with positive peaks of scalp slow waves (“IN-phase” pattern), confirming previous animal findings. In addition, we report another gamma pattern that appears preferentially during the negative phase of the slow wave (“ANTI-phase” pattern). This new pattern presented dominant peaks in the high gamma range and was preferentially expressed in the temporal cortex. Finally, we found that the spatial coherence between cortical sites exhibiting gamma activities was local and fell off quickly when computed between distant sites. Overall, these results provide the first human evidences that gamma oscillations can be observed in macroscopic EEG recordings during sleep. They support the concept that these high-frequency activities might be associated with phasic increases of neural activity during slow oscillations. Such patterned activity in the sleeping brain could play a role in off-line processing of cortical networks

Management and Outcome of Cardiac and Endovascular Cystic Echinococcosis

Cardiac and vascular involvement are infrequent in classical cystic echinococcosis (CE), but when they occur they tend to present earlier and are associated with complications that may be life threatening. Cardiovascular CE usually requires complex surgery, so in low-income countries the outcome is frequently fatal. This case series describes the characteristics of cardiovascular CE in patients diagnosed and treated at a Tropical Medicine & Clinical Parasitology Center in Spain. A retrospective case series of 11 patients with cardiac and/or endovascular CE, followed-up over a period of 15 years (1995–2009) is reported. The main clinical manifestations included thoracic pain or dyspnea, although 2 patients were asymptomatic. The clinical picture and complications vary according to cyst location. Isolated cardiac CE may be cured after surgery, while endovascular extracardiac involvement is associated with severe chronic complications. CE should be included in the differential diagnosis of cardiovascular disease in patients from endemic areas. CE is a neglected disease and further studies are necessary in order to make more definite management recommendations for this rare and severe form of the disease. The authors propose a general approach based on cyst location: exclusively cardiac, endovascular or both

-MAD - MODULE D'ANALYSE DYSFONCTIONNELLE D'AIDE A LA REALISATION DES AMDEC D'EQUIPEMENTS ELECTRONIQUES

International audienceSummary MAD (Dysfunctional Analysis Module) was developed to help the engineer in charge of electronic board FMECA at Technical Function (TF) level. The module allowed to fill semi-automatically the "Failure Mode" and "% Failure Mode (% FM)" columns. MAD uses electronic circuit simulator to simulate the same function in nominal state then in fail state (only one fail component each time) and to compare the resulting graphs. Compiling the analysis results, weighted by the TF component failure rate, gives the Technical Function Failure Mode ratio (% FM)Nous avons développé MAD (Module d'Analyse Dysfonctionnelle) dans le but d'aider le réalisateur d'AMDEC de cartes électroniques au niveau Fonction Technique (FT). Le module permet de remplir semi-automatiquement les colonnes « Mode de Défaillance » et leur pourcentage associé. Le principe de fonctionnement de MAD est d'utiliser un outil de simulation de circuits électroniques pour simuler la même fonction à l'état « nominal » puis à l'état « défaillant » (un composant défaillant à chaque fois) et de comparer ensuite les courbes obtenues. La compilation des résultats d'analyses, pondérée par le taux de défaillance des composants de la FT permet de calculer les « % Mode de défaillance » de la FT