Related papers: Complexity in some Physical Systems
We study in limit law the complexity of some anticipated rejection random sampling algorithms. We express this complexity in terms of a probabilistic process, the threshold sum process. We show that, under the right conditions, the…
In the last two decades, the linear model of coregionalization (LMC) has been widely used to model multivariate spatial processes. However, it can be a challenging task to conduct likelihood-based inference for such models because of the…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
The complex version of Bohr-Sommerfeld conditions is proposed. The BPU-construction (see [D.Borthwick, T. Paul and A. Uribe, Legendrian distributions with applications to the non-vanishing of Poincar\'e series of large weight, Invent. math,…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
We review and investigate some new problems and results in the field of dynamical systems generated by iteration of maps, {\beta}-transformations, partitions, group actions, bundle dynamical systems, Hasse-Kloosterman maps, and some aspects…
The best way to model, understand, and quantify the information contained in complex systems is an open question in physics, mathematics, and computer science. The uncertain relationship between entropy and complexity further complicates…
We derive semiclassical laser equations valid in all orders of nonlinearity. With the help of a diagrammatic representation, the perturbation series in powers of electric field can be resummed in terms of a certain class of diagrams. The…
We present several known formalizations of theorems from computational complexity in bounded arithmetic and formalize the PCP theorem in the theory PV1 (no formalization of this theorem was known). This includes a formalization of the…
The recently introduced mixed time-averaging semiclassical initial value representation molecular dynamics method for spectroscopic calculations [M. Buchholz, F. Grossmann, and M. Ceotto, J. Chem. Phys. 144, 094102 (2016)] is applied to…
The emergence of a complex, large-scale organisation of cosmic matter into the Cosmic Web is a beautiful exemplification of how complexity can be produced by simple initial conditions and simple physical laws. In the epoch of Big Data in…
It is declared that the aim of simplifying representations of coefficients of power series of classical statistical mechanics is to simplify a process of obtaining estimates of the coefficients using their simplified representations. The…
We will review some of the theoretical progresses that have been in the study of complex systems in physics and of their applications to biology.
We survey the diverse approaches to the notion of information content: from Shannon entropy to Kolmogorov complexity. The main applications of Kolmogorov complexity are presented namely, the mathematical notion of randomness (which goes…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
It is declared that the aim of simplifying representations of coefficients of power series of classical statistical mechanics is to simplify a process of obtaining estimates of the coefficients using their simplified representations. The…
Matrix permanents arise naturally in the context of linear optical networks fed with nonclassical states of light. In this letter we tie the computational complexity of a class of multi-dimensional integrals to the permanents of large…
Finite mixture models are used in statistics and other disciplines, but inference for mixture models is challenging due, in part, to the multimodality of the likelihood function and the so-called label switching problem. We propose…
A model to simulate the phenomenon of random lasing is presented. It couples Maxwell's equations with the rate equations of electronic population in a disordered system. Finite difference time domain methods are used to obtain the field…