Related papers: Fractal uncertainty in higher dimensions
Scaling properties of Yang-Mills fields are used to show that fractal structures are expected to be present in system described by those theories. We show that the fractal structure leads to recurrence formulas that allow the determination…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
The fractal dimension of a liquid column is a crucial parameter in several models describing the main features of the primary break-up occurring at the interface of a liquid phase surrounded by the gas-flow. In this work, the deformation of…
Measurements from galaxies spanning a broad range of morphology reveal a linear scaling of enclosed dark to luminous mass that is not anticipated by standard galaxy formation cosmology. The linear scaling is found to extend from the inner…
We develop a new approach to estimate the uncertainty due to missing higher orders in perturbative predictions (the perturbative "theory uncertainty"), which overcomes many inherent limitations of the currently prevalent methods based on…
The hypothesis that the causal properties of space-time, as well as other properties of physical systems like unitarity, charge conservation, etc., might be decided by the higher dimensional structure (in particular, higher-dimensional…
Fabry's theorem on the singularities of power series is improved: the maximum density in the assumptions of this theorem is replaced by an interior density of Beurling--Malliavin type.
Mutually unbiased measurements (MUMs) are generalized from the concept of mutually unbiased bases (MUBs) and include the complete set of MUBs as a special case, but they are superior to MUBs as they do not need to be rank one projectors. We…
Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel…
The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work which is recovered in the…
Notions of (pointwise) tangential dimension are considered, for measures of R^n. Under regularity conditions (volume doubling), the upper resp. lower dimension at a point x of a measure can be defined as the supremum, resp. infimum, of…
We introduce a new concept called uncertainty spaces which is an extended concept of probability spaces. Then, we express n-layer uncertainty which we call hierarchical uncertainty by a hierarchically constructed sequence of uncertainty…
Complexity measures are designed to capture complex behavior and quantify *how* complex, according to that measure, that particular behavior is. It can be expected that different complexity measures from possibly entirely different fields…
We show that each limiting semiclassical measure obtained from a sequence of eigenfunctions of the Laplacian on a compact hyperbolic surface is supported on the entire cosphere bundle. The key new ingredient for the proof is the fractal…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
Let $f: B^n \rightarrow {\mathbb R}$ be a $d+1$ times continuously differentiable function on the unit ball $B^n$, with $\max_{z\in B^n} \| f(z) \|=1$. A well-known fact is that if $f$ vanishes on a set $Z\subset B^n$ with a non-empty…
We establish pointwise and distributional fractal tube formulas for a large class of compact subsets of Euclidean spaces of arbitrary dimensions. These formulas are expressed as sums of residues of suitable meromorphic functions over the…
Given subsets of uncertain values, we study the problem of identifying the subset of minimum total value (sum of the uncertain values) by querying as few values as possible. This set selection problem falls into the field of explorable…
There is no known fundamental reason to demand as a cosmological initial condition that the bulk possess an SO(3,1) isometry. On the contrary, one expects bulk curvature terms that violate the SO(3,1) isometry at early epochs, leading to a…
We introduce a new technique to bound the fluctuations exhibited by a physical system, based on the Euclidean geometry of the space of observables. Through a simple unifying argument, we derive a sweeping generalization of so-called…