Related papers: Measuring the QCD Gell Mann-Low $\Psi$-function
In this paper, we present a collection of results on the observability of quantum mechanical systems, in the case the output is the result of a discrete nonselective measurement. By defining an effective observable we extend previous…
Quadratic discriminant analysis (QDA) is a widely used statistical tool to classify observations from different multivariate Normal populations. The generalized quadratic discriminant analysis (GQDA) classification rule/classifier, which…
We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the…
This paper studies the asymptotic behavior of penalized spline estimates of derivatives. In particular, we show that simply differentiating the penalized spline estimator of the mean regression function itself to estimate the corresponding…
We consider fluctuations of error terms $\Delta(x)$ appearing in the asymptotic formula for a summatory function of coefficients of the Dirichlet series. These are quantified via $\Omega$ and $\Omega_{\pm}$ estimates. We obtain $\Omega$…
We derive the Callan-Symanzik equation of the electroweak Standard Model in the QED-like on-shell parameterization. The various coefficient functions, the $\beta$-functions and anomalous dimensions, are determined in one-loop order in the…
We establish a generic formula for the generalised q-dimensions of measures supported by almost self-affine sets, for all q>1. These q-dimensions may exhibit phase transitions as q varies. We first consider general measures and then…
Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…
This paper proposes a density-weighted average derivative estimator based on two noisy measures of a latent regressor. Both measures have classical errors with possibly asymmetric distributions. We show that the proposed estimator achieves…
We provide a rigorous derivation of the Landau-Pekar equations from the Fr\"ohlich Hamiltonian in the mean-field limit using Wigner measure techniques. On the classical side, we extend the global well-posedness results up to $L^2 \oplus…
We propose a generic protocol to experimentally measure the quantum metric tensor, a fundamental geometric property of quantum states. Our method is based on the observation that the excitation rate of a quantum state directly relates to…
We propose a test for a change in the mean for a sequence of functional observations that are only partially observed on subsets of the domain, with no information available on the complement. The framework accommodates important scenarios,…
We give a representation of the classical Riemann $\zeta$-function in the half plane $\Re s>0$ in terms of a Mellin transform involving the real part of the dilogarithm function with an argument on the unit circle (associated Clausen…
A novel application of lattice QCD spectral reconstruction is presented, in which euclidean correlation function data in a fixed time range are used to infer values outside the range, enabling a model-independent investigation of the…
Linear Quadratic Gaussian (LQG) systems are well-understood and methods to minimize the expected cost are readily available. Less is known about the statistical properties of the resulting cost function. The contribution of this paper is a…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
In this paper we propose a general methodology, based on multiple testing, for testing that the mean of a Gaussian vector in R^n belongs to a convex set. We show that the test achieves its nominal level, and characterize a class of vectors…
We derive approximate formulas for the logarithmic de- rivative of the Selberg and Ruelle zeta functions over compact, even- dimensional, locally symmetric spaces of rank one. The obtained for- mulas are given in terms of the…
We establish discrete and continuous log-concavity results for a biparametric extension of the $q$-numbers and of the $q$-binomial coefficients. By using classical results for the Jacobi theta function we are able to lift some of our…
In this paper we give criteria about estimation of derivatives of the Riemann Zeta Function on the line $\sigma=1$.