Related papers: Uncertainty in time--frequency representations on …
The Cahill-Glauber approach for quantum mechanics on phase-space is extended to the finite dimensional case through the use of discrete coherent states. All properties and features of the continuous formalism are appropriately generalized.…
We establish that temporal averaging over multiple observations is the degenerate case of algebraic group action with the trivial group $G=\{e\}$. A General Replacement Theorem proves that a group-averaged estimator from one snapshot…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
We study in detail the time behavior of classical fidelity for chaotic systems. We show in particular that the asymptotic decay, depending on system dynamical properties, can be either exponential, with a rate determined by the gap in the…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
We consider sums of oscillating functions on intervals in cyclic groups of size close to the square root of the size of the group. We first prove non-trivial estimates for intervals of length slightly larger than this square root (bridging…
In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude…
We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…
Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary state. Supposing that during a certain, long…
The celebrated Fefferman's theorems on the general form of linear functionals on the Hardy space $H^1$ over the circle group is generalized to the case of an arbitrary compact Abelian group with totally ordered dual. Several corollaries…
We show that standard identities and theorems for lattice models with $U(1)$ symmetry get re-expressed discretely in the tensorial formulation of these models. We explain the geometrical analogy between the continuous lattice equations of…
We investigate a certain well-established generalization of the Davenport constant. For $j$ a positive integer (the case $j=1$, is the classical one) and a finite Abelian group $(G,+,0)$, the invariant $\Dav_j(G)$ is defined as the smallest…
In 2007, Carlet and Ding introduced two parameters, denoted by $Nb_F$ and $NB_F$, quantifying respectively the balancedness of general functions $F$ between finite Abelian groups and the (global) balancedness of their derivatives $D_a…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…
It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We…
Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…
The existence of a minimum time uncertainty is usually argued to be a consequence of the combination of quantum mechanics and general relativity. Most of the studies that point to this result are nonetheless based on perturbative…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
In high energy physics, a widely used method to treat systematic uncertainties in confidence interval calculations is based on combining a frequentist construction of confidence belts with a Bayesian treatment of systematic uncertainties.…
We derive the extended fluctuation theorems in presence of multiple measurements and feedback, when the system is governed by Hamiltonian dynamics. We use only the forward phase space trajectories in the derivation. However, to obtain an…