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Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
A mathematical extension of the weak value formalism to the simultaneous measurement of multiple parameters is presented in the context of an optical focused vector beam scatterometry experiment. In this example, preselection and…
Weak measurements performed between quantum state preparation and post-selection result in complex values for self-adjoint operators, corresponding to complex conditional probabilities for the projections on specific eigenstates. In this…
Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements in particular, through their back-action on the system, may enable…
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…
The aim of this note is to show that weak relative hyperbolicity of a group relative to a subgroup (or relative hyperbolicity in the sense of Farb) does not imply any natural analogues of some well-known algebraic properties of ordinary…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
Using a coupling argument, we establish a general weak law of large numbers for functionals of binomial point processes in d-dimensional space, with a limit that depends explicitly on the (possibly non-uniform) density of the point process.…
Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algorithm has been developed to determine implications…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
This paper investigates the generalizations and applications of weakly $p$-K\"ahler hyperbolic manifolds.
The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio metric.
In this paper, we study physical measures for partially hyperbolic diffeomorphisms with multi one-dimensional centers under the condition that all Gibbs $u$-states are hyperbolic. We prove the finiteness of ergodic physical measures. Then…
It has been proposed that the ability to perform joint weak measurements on post-selected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the…
The random measures on the space of continuous functions are considered. Stationary random measures are described. The weak solutions of the stochastic equations are substituted by the strong measure-valued solutions.
We will consider here some dynamics of the tangent map, weaker than hyperbolicity, and we will discuss if these structures are rich enough to provide a good description of the dynamics from a topological and geometrical point of view. This…
We consider the possibility of obtaining emergent properties of physical spaces endowed with structures analogous to that of collective models put forward by classical statistical physics. We show that, assuming that a so-called "metric…
Quantum mechanics does not permit joint measurements of non-commuting observables. However, it is possible to measure the weak value of a projection operator, followed by the precise measurement of a different property. The results can be…
We study the measure theoretic properties of typical C 0 maps of the interval. We prove that any ergodic measure is pseudo-physical, and conversely, any pseudo-physical measure is in the closure of the ergodic measures, as well as in the…
Some aspects of weak sufficiency of quantum statistics are investigated. In particular, we give necessary and sufficient conditions for the existence of a weakly sufficient statistic for a given family of vector states, investigate the…