相关论文: Improving Cram\'er-Rao Bound And Its Variants: An …

Motivated by a M\"obius invariant subdivision scheme for polygons, we study a curvature notion for discrete curves where the cross-ratio plays an important role in all our key definitions. Using a particular M\"obius invariant…

A framework to boost the efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation. We call it the refined variational approximation. Its strength lies both…

We derive extrinsic curvature estimates for compact disks embedded in $\mathbb{R}^3$ with nonzero constant mean curvature.

Discrete forms of the mean and directed curvature are constructed on piecewise flat manifolds, providing local curvature approximations for smooth manifolds embedded in both Euclidean and non-Euclidean spaces. The resulting expressions take…

We consider the problem of carrier frequency offset (CFO) estimation for a two-way relaying system based on the amplify-and-forward (AF) protocol. Our contributions are in designing an optimal preamble, and the corresponding estimator, to…

We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for…

In this work we propose a simple but effective high order polynomial correction allowing to enhance the consistency of all kind of boundary conditions for the Euler equations (Dirichlet, characteristic far-field and slip-wall), both in 2D…

In this paper we consider surfaces which are critical points of the Willmore functional subject to constrained area. In the case of small area we calculate the corrections to the intrinsic geometry induced by the ambient curvature. These…

Precision and accuracy, as two crucial criteria for quantum metrology, have previously lacked rigorous definitions and distinctions. In this paper, we provide a unified definition of precision and accuracy from the perspective of…

In this paper, we prove the existence of $H^2$-regular coordinates on Riemannian $3$-manifolds with boundary, assuming only $L^2$-bounds on the Ricci curvature, $L^4$-bounds on the second fundamental form of the boundary, and a positive…

The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables has…

Nonparametric regression and regression-discontinuity designs suffer from smoothing bias that distorts conventional confidence intervals. Solutions based on robust bias correction (RBC) are now central to the economist's toolbox. In this…

Outlier-robust estimation is a fundamental problem and has been extensively investigated by statisticians and practitioners. The last few years have seen a convergence across research fields towards "algorithmic robust statistics", which…

We explore the cosmological implications provided by the geodetic brane gravity action corrected by an extrinsic curvature brane term, describing a codimension-1 brane embedded in a 5D fixed Minkowski spacetime. In the geodetic brane…

We investigate the geometric implications of spectral curvature bounds, extending classical rigidity results in scalar curvature geometry to the spectral setting. By systematically employing the warped $\mu$-bubble method, we show…

This study revisits the problem of identifying the unknown interior Robin boundary of a connected domain using Cauchy data from the exterior region of a harmonic function. It investigates two shape optimization reformulations employing…

Magnetic induction (MI) enables communication in RF-denied environments (underground, underwater, in-body), where the medium conductivity imprints a deterministic signature on the channel. This letter derives a closed-form Cram\'{e}r--Rao…

We consider the problem of quantum phase estimation with access to arbitrary measurements in a single suboptimal basis. The achievable sensitivity limit in this case is determined by the classical Cram\'{e}r-Rao bound with respect to the…

A combinatorial optimization problem is to find an optimal solution under the constraints. This is one of the potential applications for quantum computers. Quantum Random Access Optimization (QRAO) is the quantum optimization algorithm that…

We investigate the interaction between systolic geometry and positive scalar curvature through spinorial methods. Our main theorem establishes an upper bound for the two-dimensional stable systole on certain high-dimensional manifolds with…