Related papers: On Symmetric Sensitivity
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…
What kind of dynamics do we observe in general on the circle? It depends somehow on the interpretation of "in general". Everything is quite well understood in the topological (Baire) setting, but what about the probabilistic sense? The main…
A sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding. While sensitivity analyses in matched observational studies have been well addressed when there is a single outcome…
We present a family of entropic uncertainty relations for pointer-based simultaneous measurements of conjugate observables. The lower bounds of these relations explicitly incorporate the influence of the measurement apparatus. We achieve…
We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for…
We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…
For a $C^{r}$ $(r>1)$ diffeomorphism on a compact manifold that admits a dominated splitting, this paper establishes the upper semi-continuity of the entropy map. More precisely, this paper establishes the upper semi-continuity of the…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
\noindent In our contribution to this volume we deal with \emph{discrete} symmetries: these are symmetries based upon groups with a discrete set of elements (generally a set of elements that can be enumerated by the positive integers). In…
In this article we study some statistical aspects of surface diffeomorphisms. We first show that for a $C^1$ generic diffeomorphism, a Dirac invariant measure whose \emph{statistical basin of attraction} is dense in some open set and has…
In this work, we investigate the dynamics of homeomorphisms through the lens of the local shadowing theory. We study the influence of positively shadowable points and positively shadowable measures into the local entropy theory of…
We explore the information-theoretic phases of monitored quantum circuits subject to dynamics that conserves both charge and dipole moment, as well as measurements of the local charge density. Explicitly, both charge and dipole-moment…
Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…
We continue our previous work studying critical exponent semilinear elliptic (and subelliptic) problems which generalize the classical Yamabe problem. In [3] the focus was on metric-measure spaces with an `almost smooth' structure, with…
We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…
In mixed states of quantum systems, symmetries come in two types: strong and weak. Furthermore, it has been argued that in quantum many-body systems, strong symmetries can be "spontaneously broken" down to weak symmetries. An issue is that…
We study homeomorphisms of compact metric spaces whose restriction to the nonwandering set has the pseudo-orbit tracing property. We prove that if there are positively expansive measures, then the topological entropy is positive. Some short…
Commutator-based entropic uncertainty relations in multidimensional position and momentum spaces are derived, twofold generalizing previous entropic uncertainty relations for one-mode states. They provide optimal lower bounds and imply the…
Statistical data depth plays an important role in the analysis of multivariate data sets. The main outcome is a center-outward ordering of the observations that can be used both to highlight features of the underlying distribution of the…
We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the…