Ioannis Antoniou

Intrinsic irreversibility and integrability of dynamics

Irreversibility as the emergence of a priviledged direction of time arises in an intrinsic way at the fundamental level for highly unstable dynamical systems, such as Kolmogorov systems or large Poincare systems. The presence of resonances in large Poincare systems causes a breakdown of the conventional perturbation methods analytic in the coupling parameter. These difficulties are manifestations of general limitations to computability for unstable dynamical systems. However, a natural ordering of the dynamical states leads to a well-defined prescription for the regularization of the propagators which lifts the divergence and gives rise to an extension of the eigenvalue problem to the complex plane. The extension acquires meaning in suitable rigged Hilbert spaces which are constructed explicitly for the Friedrichs model. We show that the unitary evolution group, when extended, splits into two semigroups, one decaying in the future and the other in the past. Irreversibility emerges as the selection of the semigroup compatible with our future observations. In this way the problems of integration and irreversibility both enjoy a common solution in the extended space.

Spectral decomposition of the Renyi map

The authors construct a generalized spectral decomposition of the Frobenius-Perron operator of the general beta -adic Renyi map using a general iterative operator method applicable in principle to any mixing dynamical system. They also explicitly define appropriate rigged Hilbert spaces, which provide mathematical meaning to the formally obtained spectral decomposition. The explicit construction of the eigenvalues and eigenvectors allows one to show that the essential spectral radius of the Frobenius-Perron operator decreases as the smoothness of the domain increases. The reason for the change of the spectrum from the unit disk to isolated eigenvalues, is the existence of coherent states of the Frobenius-Perron operator, which are not infinitely differentiable.

Generalized spectral decomposition of the β-adic baker's transformation and intrinsic irreversibility

Abstract We construct a generalized spectral decomposition of the Frobenius-Perron operator of the β-adic bakers transformation using a general iterative operator method applicable in principle for any mixing dynamical system. The eigenvalues in the decomposition are related to the decay rates of the autocorrelation functions and have magnitudes less than one. We explicitly define appropriate generalized function spaces, which provide mathematical meaning to the formally obtained spectral decomposition. The unitary Frobenius-Perron evolution of densities, when extended to the generalized function spaces, splits into two semigroups, one decaying in the future and the other in the past. This split, which reflects the asymptotic evolution of the forward and backward K-partitions, shows the instrinsic irreversibility of the bakers transformation.

Solitons and chaos

I General Questions on Chaos and Integrability.- Integration of Non-Integrable Systems.- Order and Chaos in the Statistical Mechanics of the Integrable Models in 1+1 Dimensions.- Soliton Dynamics and Chaos Transition in a Microstructured Lattice Model.- What is the Role of Dynamical Chaos in Irreversible Processes?.- A Propositional Lattice for the Logic of Temporal Predictions.- Damping, Quantum Field Theory and Thermodynamics.- Quasi-Monomial Transformations and Decoupling of Systems of ODEs.- II Physical Systems with Soliton Ingredients.- Solitons in Optical Fibers: First- and Second-Order Perturbations.- Similarity Solutions of Equations of Nonlinear Optics.- Heisenberg Ferromagnet, Generalized Coherent States and Nonlinear Behaviour.- Integrable Supersymmetric Models and Phase Transitions in One Dimension.- Denaturation of DNA in a Toda Lattice Model.- III Dissipative Systems.- A Simple Method to Obtain First Integrals of Dynamical Systems.- Transition to Turbulence in 1-D Rayleigh-Benard Convection.- Modelling of Low-Dimensional, Incompressible, Viscous, Rotating Fluid Flow.- Spatial Coherent Structures in Dissipative Systems.- Hierarchies of (1+1)-Dimensional Multispeed Discrete Boltzmann Model Equations.- IV Hamiltonian Systems.- Universality of the Long Time Tail in Hamiltonian Dynamics.- Why some Henon-Heiles Potentials are Integrable.- Chaotic Pulsations in Variable Stars with Harmonic Mode Coupling.- Canonical Forms for Compatible BiHamiltonian Systems.- V Maps and Cascades.- Transitions from Chaotic to Brownian Motion Behaviour.- Kinetic Theory for the Standard Map.- Probabilistic Description of Deterministic Chaos: A Local Equilibrium Approach.- State Prediction for Chaotic 1-D-Maps.- Exact and Approximate Reconstruction of Multifractal Coding Measures.- Conservative Versus Reversible Dynamical Systems.- A Simple Method to Generate Integrable Symplectic Maps.- Integrable Mappings and Soliton Lattices.- VI Direct Methods Applicable to Soliton Systems.- Integrable Higher Nonlinear Schrodinger Equations.- Nonclassical Symmetry Reductions of a Generalized Nonlinear Schrodinger Equation.- Direct Methods in Soliton Theories.- Trilinear Form - an Extension of Hirotas Bilinear Form.- On the Use of Bilinear Forms for the Search of Families of Integrable Nonlinear Evolution Equations.- From Periodic Processes to Solitons and Vice-Versa.- VII Inverse Methods Related to a Linearization Scheme.- The Crum Transformation for a Third Order Scattering Problem.- Darboux Theorems Connected to Dym Type Equations.- Forced Initial Boundary Value Problems for Burgers Equation.- Creation and Annihilation of Solitons in Nonlinear Integrable Systems.- VIII Nonlinear Excitations in more than one Space Dimension.- Multidimensional Nonlinear Schrodinger Equations Showing Localized Solutions.- New Soliton Solutions for the Davey-Stewartson Equation.- 2+1 Dimensional Dromions and Hirotas Bilinear Method.- Skyrmions Scattering in (2+1) Dimensions.- Index of Contributors.

Internationalization of Linked Data: The case of the Greek DBpedia edition

This paper describes the deployment of the Greek DBpedia and the contribution to the DBpedia information extraction framework with regard to internationalization (I18n) and multilingual support. I18n filters are proposed as pluggable components in order to address issues when extracting knowledge from non-English Wikipedia editions. We report on our strategy for supporting the International Resource Identifier (IRI) and introduce two new extractors to complement the I18n filters. Additionally, the paper discusses the definition of Transparent Content Negotiation (TCN) rules for IRIs to address de-referencing and IRI serialization problems. The aim of this research is to establish best practices (complemented by software) to allow the DBpedia community to easily generate, maintain and properly interlink language-specific DBpedia editions. Furthermore, these best practices can be applied for the publication of Linked Data in non-Latin languages in general.

Intrinsic irreversibility of quantum systems with diagonal singularity

The work of the Brussels-Austin group on irreversibility over the last years has shown that quantum large Poincare systems with diagonal singularity lead to an extension of quantum theory beyond the conventional Hilbert space framework and logic. We characterize the algebra of observables, the states and the logic of the extended quantum theory of intrinsically irreversible systems with diagonal singularity. We illustrate the general ideas for the Friedrichs model.

Statistical Analysis of Weighted Networks

The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely, average path length, degree distribution, and clustering coefficient. Although the degree distribution and the average path length admit straightforward generalizations, for the clustering coefficient several different definitions have been proposed in the literature. We examined the different definitions and identified the similarities and differences between them. In order to elucidate the significance of different definitions of the weighted clustering coefficient, we studied their dependence on the weights of the connections. For this purpose, we introduce the relative perturbation norm of the weights as an index to assess the weight distribution. This study revealed new interesting statistical regularities in terms of the relative perturbation norm useful for the statistical characterization of weighted graphs.

Wavelets and stochastic processes

Wavelets are known to have intimate connections to several other parts of mathematics, notably phase-space analysis of signal processing, reproducing kernel Hilbert spaces, coherent states in quantum mechanics, spline approximation theory, windowed Fourier transforms, and filter banks. Here, we establish and survey a new connection, namely to stochastic processes. Key to this link are the Kolmogorov systems of ergodic theory.

Relativistic Gamow Vectors

The Friedrichs model has often been used in order to obtain explicit formulas for eigenvectors associated to complex eigenvalues corresponding to lifetimes. Such eigenvectors are called Gamow vectors and they acquire meaning in extensions of the conventional Hilbert space of quantum theory to the so-called rigged Hilbert space. In this paper, Gamow vectors are constructed for a solvable model of an unstable relativistic field. As a result, we obtain a time asymmetric relativistic extension of the Fock space. This extension leads to two distinct Poincare semigroups. The time reversal transformation maps one semigroup to the other. As a result, the usual PCT invariance should be extended. We show that irreversibility as expressed by dynamical semigroups is compatible with the requirements of relativity.

A quantum mechanical arrow of time and the semigroup time evolution of Gamow vectors

The exponential decay (or growth) of resonances provides an arrow of time which is described as the semigroup time evolution of Gamow vector in a new formulation of quantum mechanics. Another direction of time follows from the fact that a state must first be prepared before observables can be measured in it. Applied to scattering experiments, this produces another quantum mechanical arrow of time. The mathematical statements of these two arrows of time are shown to be equivalent. If the semigroup arrow is interpreted as microphysical irreversibility and if the arrow of time from the prepared in‐state to its effect on the detector of a scattering experiment is interpreted as causality, then the equivalence of their mathematical statements implies that causality and irreversibility are interrelated.