Related papers: Statistics as a dynamical attractor
We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…
Highlights: \begin{itemize} \item Relativistic effect of crystal dynamics "freezing". \item Non-statistical model of thermodynamic equilibration. \end{itemize} The dynamics of oscillations of a one-dimensional atomic chain is investigated…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the…
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical…
The state of a classical point-particle system may often be specified by giving the position and momentum for each constituent particle. For non-pointlike particles, the center-of-mass position may be augmented by an additional coordinate…
Turbulent flows present rich dynamics originating from non-trivial energy fluxes across scales, non-stationary forcings and geometrical constraints. This complexity manifests in non-hyperbolic chaos, randomness, state-dependent persistence…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
We argue that statistical mechanics of systems with relaxation implies breaking the energy function of systems into two having different transformation rules. With this duality the energy approach incorporates the generalized vortex forces.…
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
The theory of evolution by natural selection cannot be used to evaluate the truth value of the following proposition: Through evolution, there exists at least one species that can adapt to any one given environment. To address this issue,…
Many statistics are based on functions of sample moments. Important examples are the sample variance $s_{n-1}^2$, the sample coefficient of variation SV(n), the sample dispersion SD(n) and the non-central $t$-statistic $t(n)$. The…
The MaxEnt solutions are shown to display a variety of behaviors (beyond the traditional and customary exponential one) if adequate dynamical information is inserted into the concomitant entropic-variational principle. In particular, we…
We study the dynamics of the periodically-forced May-Leonard system. We extend previous results on the field and we identify different dynamical regimes depending on the strength of attraction $\delta$ of the network and the frequency…
The second law of thermodynamics, which deals with irreversibility and makes the theory so special, is usually considered empirical. The definition of equilibrium as an attractor, on the other hand, requires a postulate. This article shows…
An analyst observes an agent take a sequence of actions. The analyst does not have access to the agent's information and ponders whether the observed actions could be justified through a rational Bayesian model with a known utility…
The Log-Poisson phenomenological description of the turbulent energy cascade is evoked to discuss high-order statistics of velocity derivatives and the mapping between their probability distribution functions at different Reynolds numbers.…
In special relativity the mathematical expressions, defining physical observables as the momentum, the energy etc, emerge as one parameter (light speed) continuous deformations of the corresponding ones of the classical physics. Here, we…