Related papers: Mean Euler characteristic of stationary random clo…
We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. After introducing a general formalism for describing such systems, we consider here the mean-field…
We perform numerical studies including Monte Carlo simulations of high rotational symmetry random tilings. For computational convenience, our tilings obey fixed boundary conditions in regular polygons. Such tilings are put in correspondence…
A stationary rotating surface is a compact surface in Euclidean space whose mean curvature $H$ at each point $x$ satisfies $2H(x)=a r^2+b$, where $r$ is the distance from $x$ to a fixed straight-line $L$, and $a$ and $b$ are constants.…
This work demonstrates that the popular arithmetic mean conformation tensor frequently used in the analysis of turbulent viscoelastic flows is not a good representative of the ensemble. Alternative means based on recent developments in the…
We introduce the universal Euler characteristic of orbit space definable groupoids, a class of groupoids containing cocompact proper Lie groupoids as well as translation groupoids associated to proper definable group actions. We show that…
We give an overview of results on irregular complex surfaces of general type, discussing in particular the distribution of the numerical invariants self-intersection of a canonical divisor and holomorphic Euler characteristic for the…
A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…
For polyhedral convex cones in ${\mathbb R}^d$, we give a proof for the conic kinematic formula for conic curvature measures, which avoids the use of characterization theorems. For the random cones defined as typical cones of an isotropic…
The behaviour of the mean Euler-Poincar\'{e} characteristic and mean Betti's numbers in the Ising model with arbitrary spin on $\mathbbm{Z}^2$ as functions of the temperature is investigated through intensive Monte Carlo simulations. We…
The Euler characteristic transform (ECT) is an integral transform used widely in topological data analysis. Previous efforts by Curry et al. and Ghrist et al. have independently shown that the ECT is injective on all compact definable sets.…
The notion of multivariate upcrossings index of a stationary sequence ${\bf{X}}=\{(X_{n,1},\ldots,X_{n,d})\}_{n\geq 1}$ is introduced and its main properties are derived, namely the relations with the multivariate extremal index and the…
In this work a relation between topology and thermodynamical features of gravitational instantons is shown. The expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for the entropy of gravitational…
For $m\geq n$, Let $K$ be an algebraic closed base field, and define $\tau_{m,n,k}$ to be the set of $m\times n$ matrices over $K$ with kernel dimension $\geq k$. This is a projective subvariety of $\mathbb{P}^{mn-1}$, and is usually called…
Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…
Let M be a bounded domain of a Euclidian space with smooth boundary. We relate the Cheeger constant of M and the conductance of a neighborhood graph defined on a random sample from M. By restricting the minimization defining the latter over…
We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. In Part I, we introduced a general formalism for describing such systems and presented the mean…
New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.
This paper resolves the characteristic initial data problem for the three-dimensional compressible Euler equations - an open problem analogous to Christodoulou's characteristic initial value formulation for the vacuum Einstein field…
Some statistical properties of finite-time stability exponents in the standard map can be estimated analytically. The mean exponent averaged over the entire phase space behaves quite differently from all the other cumulants. Whereas the…
Fluctuations of observables provide unique insights into the nature of physical systems, and their study stands as a cornerstone of both theoretical and experimental science. Generalized fluctuations, or cumulants, provide information…