Related papers: A Linear Programming Approach to Attainable Cram\'…
A wide variety of imaging systems have been designed to measure phase variations, with applications from physics to biology and medicine. In this work, we theoretically compare the precision of phase estimations achievable with classical…
In this paper, new methodology -- direct approach -- for the determination of the attainable CR type bound of the pure state model, is proposed and successfully applied to the wide variety of pure state models, for example, the…
Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage, however, relies on refined data postprocessing, assessed based on the variance of the estimated…
This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…
This paper aims at providing a fresh look at semiparametric estimation theory and, in particular, at the Semiparametric Cram\'{e}r-Rao Bound (SCRB). Semiparametric models are characterized by a finite-dimensional parameter vector of…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…
Neural networks are increasingly used to estimate parameters in quantitative MRI, in particular in magnetic resonance fingerprinting. Their advantages over the gold standard non-linear least square fitting are their superior speed and their…
Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or that of low signal-to-noise ratios, the meaning of common frequentist…
A Cramer-Rao bound (CRB) for semi-blind channel estimators in redundant block transmission systems is derived. The derived CRB is valid for any system adopting a full-rank linear redundant precoder, including the popular cyclic-prefixed…
The quantum Cram\'er-Rao bound sets a fundamental limit on the accuracy of unbiased parameter estimation in quantum systems, relating the uncertainty in determining a parameter to the inverse of the quantum Fisher information. We…
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…
In his 2005 paper, S.T. Smith proposed an intrinsic Cram\'er-Rao bound on the variance of estimators of a parameter defined on a Riemannian manifold. In the present technical note, we consider the special case where the parameter lives in a…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…
The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical…
Artificial neural networks have become important tools to harness the complexity of disordered or random photonic systems. Recent applications include the recovery of information from light that has been scrambled during propagation through…
The best possible precision is one of the key figures in metrology, but this is established by the exact response of the detection apparatus, which is often unknown. There exist techniques for detector characterisation, that have been…
We derive Cram\'{e}r type moderate deviations for stationary sequences of bounded random variables. Our results imply the moderate deviation principles and a Berry-Esseen bound. Applications to quantile coupling inequalities, functions of…
Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints C on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and…