Related papers: Optimal quantization for a probability measure on …
This work is concerned with the quantification of the epistemic uncertainties induced the discretization of partial differential equations. Following the paradigm of probabilistic numerics, we quantify this uncertainty probabilistically.…
Ergodic optimization aims to single out dynamically invariant Borel probability measures which maximize the integral of a given "performance" function. For a continuous self-map of a compact metric space and a dense set of continuous…
Let $K\subset R^n$ be a compact basic semi-algebraic set. We provide a necessary and sufficient condition (with no a priori bounding parameter) for a real sequence $y=(y_\alpha)$, $\alpha\in N^n$, to have a finite representing Borel measure…
This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer…
A Borel probability measure $\mu$ on a locally compact group is called a spectral measure if there exists a subset of continuous group characters which forms an orthogonal basis of the Hilbert space $L^2(\mu)$. In this paper, we…
Probabilistic metrology attempts to improve parameter estimation by occasionally reporting an excellent estimate and the rest of the time either guessing or doing nothing at all. Here we show that probabilistic metrology can never improve…
In this paper, we have studied various mixed distributions generated by two uniform distributions: first, where the supports are two connected line segments, and second, where the supports are two disconnected line segments. For these mixed…
We study the continuity and the measurability of the solution to Schr\"odinger's functional equation, with respect to space, kernel and marginals, provided the space of all Borel probability measures is endowed with the weak topology. This…
Bell's inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell's inequalities are only possible because the precision of any joint measurement of these observables…
This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets of the sphere, emphasizing both continuous and discrete settings. We…
In this paper, the quantization dimensions of the Borel probability measures supported on the limit sets of the bi-Lipschitz recurrent iterated function systems under the strong open set condition in terms of the spectral radius have been…
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…
Quantum nonlocality offers a secure way to produce random numbers: their unpredictability is intrinsic and can be certified just by observing the statistic of the measurement outcomes, without assumptions on how they are produced. To do…
We first define the coarse-graining of probability measures in terms of stochastic kernels. We define when a probability measure is part of another probability measure and say that two probability measures coexist if they are both parts of…
This paper presents a detailed study of constrained quantization for both finite and infinite discrete probability distributions supported on subsets of the real line. Under specific geometric constraints - namely, a semicircular arc and…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a…
We consider the problem of unambiguous (error-free) discrimination of N linearly independent pure quantum states with prior probabilities, where the goal is to find a measurement that maximizes the average probability of success. We derive…
This paper develops a systematic and geometric theory of optimal quantization on the unit sphere $\mathbb S^2$, focusing on finite uniform probability distributions supported on the spherical surface - rather than on lower-dimensional…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…