相关论文: Low Correlation Noise Stability of Symmetric Sets

In this paper, we study the strong consistency of the sparse K-means clustering for high dimensional data. We prove the consistency in both risk and clustering for the Euclidean distance. We discuss the characterization of the limit of the…

Geometric description of quantum correlations are favored for their distinct physical significance. Geometric discord based on the trace distance and the Bures distance are shown to be well-defined quantum correlation measures. Here, we…

This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…

Gaussian quantum discord is a measure of quantum correlations in Gaussian systems. Using Gaussian discord we quantify the quantum correlations of a bipartite entangled state and a separable two-mode mixture of coherent states. We…

Imaging, detection and ranging of objects in the presence of significant background noise is a fundamental challenge in optical sensing. Overcoming the limitations imposed in conventional methods, quantum light sources show higher…

The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…

We consider the range-based localization problem, which involves estimating an object's position by using $m$ sensors, hoping that as the number $m$ of sensors increases, the estimate converges to the true position with the minimum…

This paper investigates the theoretical guarantees of L1-analysis regularization when solving linear inverse problems. Most of previous works in the literature have mainly focused on the sparse synthesis prior where the sparsity is measured…

We address the metrological problem of estimating collective stochastic properties imprinted on a network of quantum sensors. Canonical examples include center-of-mass quadrature fluctuations in a system of bosonic modes and correlated…

Let $g$ be a Riemannian metric for $\mathbf{R}^d$ ($d\geq 3$) which differs from the Euclidean metric only in a smooth and strictly convex bounded domain $M$. The lens rigidity problem is concerned with recovering the metric $g$ inside $M$…

Poisson distributed shot noise is normally considered in the Gaussian limit in cosmology. However, if the shot noise is large enough and the correlation function/power spectrum conspires, the Gaussian approximation mis-estimates the errors…

The usual interpretation of noise is represented by a sum of many independent two-level elementary random signals with a distribution of relaxation times. In this paper it is demonstrated that also the superposition of many similar…

Generalizations of the classic Bell inequality to higher dimensional quantum systems known as qudits are reputed to exhibit a higher degree of robustness to noise, but such claims are based on one particular noise model. We analyze the…

The problem of structured noise suppression is addressed by i)modelling the subspaces hosting the components of the signal conveying the information and ii)applying a non-extensive nonlinear technique for effecting the right separation.…

We consider the complex case of the so-called S-inequality. It concerns the behaviour of the Gaussian measures of dilations of convex and rotationally symmetric sets in C^n (rotational symmetry is invariance under the multiplication by…

We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed…

Gaussian comparison theorems are useful tools in probability theory; they are essential ingredients in the classical proofs of many results in empirical processes and extreme value theory. More recently, they have been used extensively in…

We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…

The investigation of samples with a spatial resolution in the nanometer range relies on the precise and stable positioning of the sample. Due to inherent mechanical instabilities of typical sample stages in optical microscopes, it is…

The most common error models for quantum computers assume the independence of errors on different qubits. However, most noise mechanisms have some correlations in space. We show how to improve quantum information processing for few-qubit…