Related papers: Emergence via non-existence of averages
We introduce a novel model of affine gravity, which implements the no-scale scenario. Namely, Planck mass and Hubble constant emerge dynamically, through the mechanism of spontaneous breaking of scale-invariance. Moreover, in our model the…
In order to bypass the big bang singularity, we develop an emergent universe scenario within a covariant extension of General Relativity known as \emph{"Energy-Momentum Squared Gravity"}. The extra terms of the model emerge in the high…
In this paper we consider the problem of detecting a change in the parameters of an autoregressive process, where the moments of the innovation process do not necessarily exist. An empirical likelihood ratio test for the existence of a…
Microbial ecosystems exhibit a surprising amount of functionally relevant diversity at all levels of taxonomic resolution, presenting a significant challenge for most modeling frameworks. A long-standing hope of theoretical ecology is that…
We consider a large class of exponential random graph models and prove the existence of a region of parameter space corresponding to multipartite structure, separated by a phase transition from a region of disordered graphs.
In change-point analysis, one aims at finding the locations of abrupt distributional changes (if any) in a sequence of multivariate observations. In this article, we propose some nonparametric methods based on averages of pairwise distances…
Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena, which can be fundamentally traced back to non-unitarity and is much more fundamental and universal than complex energy spectrum. In this…
We show that for any topological dynamical system with approximate product property, the set of points whose forward orbits do not accumulate to any point in a large set carries full topological pressure.
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
We suggest a quantitative and objective notion of emergence. Our proposal uses algorithmic information theory as a basis for an objective framework in which a bit string encodes observational data. A plurality of drops in the Kolmogorov…
The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…
In these notes we review emergent phenomena in complex systems, emphasizing ways to identify potential underlying universal mechanisms that generates complexity. The discussion is centered around the emergence of collective behavior in…
Emergent behavior that appears at a given level of organization may be characterized as arising from an organizationally lower level in such a way that it transcends a mere increase in the behavioral degree of complexity. It is therefore to…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
This paper seeks to advance the theory of nonexpansive mappings by introducing and exploring a novel class of nonexpansive type mappings, which we aptly designate as perimetric nonexpansive mappings. We establish that the collection of…
According to the principle of emergence, the expansion of the universe can be explained as the emergence of space with the progress of cosmic time. We have analytically solved the equation of emergence proposed by Padmanabhan by assuming…
In 1977 L.T. Ramsey showed that any sequence in $\mathbb{Z}^2$ with bounded gaps contains arbitrarily many collinear points. Thereafter, in 1980, C. Pomerance provided a density version of this result, relaxing the condition on the sequence…
The theory of regular model sets is highly developed, but does not cover examples such as the visible lattice points, the k-th power-free integers, or related systems. They belong to the class of weak model sets, where the window may have a…
In 2018, Cook, Harbourne, Migliore and Nagel introduced the concept of unexpected hypersurfaces, which connects the study of Lefschetz properties of artinian algebras defined by powers of linear forms, to a family of interpolation problems.…