相关论文: On Symmetric Sensitivity

The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: how are gauge transformations and spacetime diffeomorphisms understood as symmetries, in which ways are they similar, and in…

Symmetry plays a crucial role in understanding the properties of mathematical structures and optimization problems. Recent work has explored this phenomenon in the context of neural networks, where the loss function is invariant under…

Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…

What can one do with a given tunable quantum device? We provide complete symmetry criteria deciding whether some effective target interaction(s) can be simulated by a set of given interactions. Symmetries lead to a better understanding of…

In this paper we investigate the role of symmetry in visual stimuli designed to probe human sensitivity to image statistics. Our starting point is a recently published parameter space, a point in which defines a family of binary texture…

Within a category $\mathtt{C}$, having objects $\mathtt{C}_0$, it may be instructive to know not only that two objects are non-isomorphic, but also how far from being isomorphic they are. We introduce pseudo-metrics $d:\mathtt{C}_0 \times…

We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…

We prove that a symmetric nonnegative function of two variables on a Lebesgue space that satisfies the triangle inequality for almost all triples of points is equivalent to some semimetric. Some other properties of metric triples (spaces…

The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…

We classify complex projective surfaces with an automorphism of positive entropy for which the unique invariant measure of maximal entropy is absolutely continuous with respect to Lebesgue measure.

Uncertainty relations are among the unique fingerprints of quantum physics, being direct expression of non-commutativity and complementarity. Entropic uncertainty relations arise in quantum information theory as the most natural expression…

Symmetry is often treated in philosophy of physics as an interpretive problem. A particularly lively dispute concerns local symmetries: do they indicate surplus structure that ought to be expunged, or are they merely a harmless redundancy?…

Combining quantum and Bayesian principles leads to optimality in metrology, but the optimisation equations involved are often hard to solve. This work mitigates this problem with a novel class of measurement strategies for quantities…

Critical quantum metrology relies on the extreme sensitivity of a system's eigenstates near the critical point of a quantum phase transition to Hamiltonian perturbations. This means that these eigenstates are extremely sensitive to all the…

Entanglement asymmetry is an observable in quantum systems, constructed using quantum-information methods, suited to detecting symmetry breaking in states -- possibly out of equilibrium -- relative to a subsystem. In this paper we define…

We initiate the rigorous study of classification in semimetric spaces, which are point sets with a distance function that is non-negative and symmetric, but need not satisfy the triangle inequality. For metric spaces, the doubling dimension…

A system of four globally coupled doubling maps is studied in this paper. It is known that such systems have a unique absolutely continuous invariant measure (acim) for weak interaction, but the case of stronger coupling is still…

We study locally compact metric spaces that enjoy various forms of homogeneity with respect to M\"obius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with…

A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…

This paper studies the properties of convergence of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semi-cyclic impulsive self-mappings on the union of a number of nonempty…