Related papers: Scaled Oscillation and Level Sets
A scalar valued random field is called operator-scaling if it satisfies a self-similarity property for some matrix E with positive real parts of the eigenvalues. We present a moving average and a harmonizable representation of stable…
In the present paper we study two-dimensional maximal surfaces with harmonic level-sets. As a corollary we obtain a new class of one-periodic maximal surfaces.
This article establishes several remarkably simple identities relating certain metric invariants of level curves of real and complex functions. In particular, we relate lengths of level curves to their curvature and to the gradient field of…
We present a class of systems for which the signal-to-noise ratio as a function of the noise level may display a multiplicity of maxima. This phenomenon, referred to as stochastic multiresonance, indicates the possibility that periodic…
Our objective is to determine which subsets of $\mathbb{R}^d$ arise as escaping sets of continuous functions from $\mathbb{R}^d$ to itself. We obtain partial answers to this problem, particularly in one dimension, and in the case of open…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.
Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.
We use scaling results to identify the crossover to mean-field behavior of equilibrium statistical mechanics models on a variant of the small world network. The results are generalizable to a wide-range of equilibrium systems. Anomalous…
Allometric scaling can reflect underlying mechanisms, dynamics and structures in complex systems; examples include typical scaling laws in biology, ecology and urban development. In this work, we study allometric scaling in scientific…
We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving…
The scaling relations for solar-like oscillations provide a translation of the features of the stochastic low-degree modes of oscillation in the Sun to predict the features of solar-like oscillations in other stars with convective outer…
We are going to classify sets by a given mean in two ways. Firstly we study small and big sets regarding a given mean. Secondly we study sets that have the same weight according to a mean. We also generalize the notion of roundness and get…
In this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension. In particular we determine numerically the order parameter, its fluctuations as well as the susceptibility as a function…
We study a model for the movement of surfaces, namely the conserved, restricted solid-on-solid model. The surface configurations are restricted such that the difference between the heights at adjacent sites is no more than one. In addition…
Families of hypersurfaces that are level-set families of harmonic functions free of critical points are characterized by a local differential-geometric condition. Harmonic functions with a specified level-set family are constructed from…
We study by Monte Carlo techniques the evolution of finite two-dimensional Ising systems in oscillating magnetic fields. The phenomenon of stochastic resonance is observed. The characteristic peak obtained for the correlation function…
We analytically and numerically investigate the evolutions of the scalar perturbations through the cycles with nonsingular bounce. It is found that the amplitude of the curvature perturbation on large scale will be amplified cycle by cycle,…
We study previously un-researched second order statistics - correlation function of spectral staircase and global level number variance - in generic integrable systems with no extra degeneracies. We show that the global level number…
We study the pattern formation in a lattice of coupled phase oscillators with quenched disorder. In the synchronized regime concentric waves can arise, which are induced and increase in regularity by the disorder of the system. Maximal…