Related papers: Exact Minimax Estimation for Phase Synchronization
We consider an $\ell_2$-regularized non-convex optimization problem for recovering signals from their noisy phaseless observations. We design and study the performance of a message passing algorithm that aims to solve this optimization…
Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…
We prove that the Sinkhorn algorithm converges at a rate of $O(k^{-1} \log k)$ in $\ell_1$-norm marginal error, in the asymptotically scalable case. This almost closes the gap between the lower bound $\Omega(k^{-1})$ (Qu et al., 2025) and…
In this paper we study observation problem for linear 2-point BVP Dx=Bf assuming that information about system input f and random noise \eta in system state observation model y=Hx+\eta$ is incomplete (f and M\eta\eta' are some arbitrary…
Channel measurements in MIMO systems hinge on precise synchronization. While methods for time and frequency synchronization are well established, maintaining real-time phase coherence remains an open requirement for many MIMO systems. Phase…
High statistics measurements of the photon asymmetry $\mathrm{\Sigma}$ for the $\overrightarrow{\gamma}$p$\rightarrow\pi^{0}$p reaction have been made in the center of mass energy range W=1214-1450 MeV. The data were measured with the MAMI…
It is well known that a minimum error quantum measurement for arbitrary binary optical coherent states can be realized by a receiver that comprises interfering with a coherent reference light, photon counting, and feedback control. We show…
We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial…
Estimating the second frequency moment of a stream up to $(1\pm\varepsilon)$ multiplicative error requires at most $O(\log n / \varepsilon^2)$ bits of space, due to a seminal result of Alon, Matias, and Szegedy. It is also known that at…
A recently proposed phase-estimation protocol that is based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that Cram\'{e}r-Rao bound sensitivity can be obtained [P.\ M.\…
In a circular convolution model, we aim to infer on the density of a circular random variable using observations contaminated by an additive measurement error. We highlight the interplay of the two problems: optimal testing and quadratic…
We study the detection of a change in the covariance matrix of $n$ independent sub-Gaussian random variables of dimension $p$. Our first contribution is to show that $\log\log(8n)$ is the exact minimax testing rate for a change in variance…
We present a new method for high precision measurements of polarization rotation in the frequency range from 0.2 to 2.2 THz using a fiber coupled time-domain THz spectrometer. A free standing wire-grid polarizer splits THz light into…
In this paper we are concerned with the plane wave method for the discretization of time-harmonic Maxwell's equations in three dimensions. As pointed out in [6], it is difficult to derive a satisfactory L2 error estimate of the standard…
We analyze the problem of discrete distribution estimation under $\ell_1$ loss. We provide non-asymptotic upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in…
We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…
We complete the effective potential calculation of the two-loop, top/bottom Yukawa corrections to the Higgs boson masses in the Minimal Supersymmetric Standard Model, by computing the O(at^2 + at*ab + ab^2) contributions for arbitrary…
For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the…
The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance and analyzed under highly simplified…
Within the Constrained Minimal Supersymmetric Standard Model it is possible to predict the low energy gauge couplings and masses of the 3. generation particles from a few parameters at the GUT scale. In addition the MSSM predicts…