相关论文: On Symmetric Sensitivity

We propose a semantic similarity metric for image registration. Existing metrics like euclidean distance or normalized cross-correlation focus on aligning intensity values, giving difficulties with low intensity contrast or noise. Our…

We consider the nonconvex optimization problem associated with the decomposition of a real symmetric tensor into a sum of rank-one terms. Use is made of the rich symmetry structure to construct infinite families of critical points…

We use the inverse pressure concept to estimate the stable dimension for hyperbolic non-invertible maps which are conformal in the stable fibers. The non-invertible case is different than the diffeomorphism case. In particular we show that…

Motivated by proving the loss of ergodicity in expanding systems of piecewise affine coupled maps with arbitrary number of units, all-to-all coupling and inversion symmetry, we provide ad-hoc substitutes - namely inversion-symmetric maps of…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…

The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…

We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries and the group of symmetries are not finite, in contrast with…

This paper is an introduction to soft cone metric spaces. We define the concept of soft cone metric via soft element, investigate soft converges in soft cone metric spaces and prove some fixed point theorems for contractive mappings on soft…

The problem of finding an appropriate geometrical/physical index for measuring a degree of inhomogeneity for a given space-time manifold is posed. Interrelations with the problem of understanding the gravitational/informational entropy are…

For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric…

Starting from the De Witt supermetric and limiting ourselves to a family of geometries characterized by a finite number of geometric invariants we extract the unique integration measure. Such a measure turns out to be a geometric invariant,…

We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…

The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…

We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…

The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the…

We construct inequalities between R\'{e}nyi entropy and the indexes of coincidence of probability distributions, based on which we obtain improved state-dependent entropic uncertainty relations for general symmetric informationally complete…

We propose an alternative measure of quantum uncertainty for pairs of arbitrary observables in the 2-dimensional case, in terms of collision entropies. We derive the optimal lower bound for this entropic uncertainty relation, which results…

Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…

High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…

Coarse geometry studies metric spaces on the large scale. The recently introduced notion of coarse entropy is a tool to study dynamics from the coarse point of view. We prove that all isometries of a given metric space have the same coarse…