arXiv subjects

Vasileios Basios

Publications and source records attributed to Vasileios Basios.

17 recordsLinked to original sources

arXiv2023

Extending the Bayesian Framework from Information to Action

In this review, we examine an extended Bayesian inference method and its relation to biological information processing. We discuss the idea of combining two modes of Bayesian inference. The first is the standard Bayesian inference, which contracts probability space. The second is its inverse, which extends and enriches the probability space of latent and observable variables. Their combination has been observed that, greatly, facilitates discovery. Moreover, this dual search during the updating process elucidates a crucial difference between biological and artificial information processing. The latter is restricted due to nonlinearities, while the former utilizes it. This duality is ubiquitous in biological information process dynamics (`flee-or-fight', `explore-or-exploit' etc.) as is the role of fractality and chaos in its underlying nonequilibrium, nonlinear dynamics. We also propose a new experimental set up that stems from testing these ideas.

stat.OT↗

arXiv2022

A generic model for pandemics in networks of communities and the role of vaccination

The slogan "nobody is safe until everybody is safe" is a dictum to raise awareness that in an interconnected world, pandemics such as COVID-19, require a global approach. Motivated by the ongoing COVID-19 pandemic, we model here the spread of a virus in interconnected communities and explore different vaccination scenarios, assuming that the efficacy of the vaccination wanes over time. We start with susceptible populations and consider a susceptible-vaccinated-infected-recovered model with unvaccinated ("Bronze"), moderately vaccinated ("Silver") and very well vaccinated ("Gold") communities, connected through different types of networks via a diffusive linear coupling for local spreading. We show that when considering interactions in "Bronze"-"Gold" and "Bronze"-"Silver" communities, the "Bronze" community is driving an increase in infections in the "Silver" and "Gold" communities. This shows a detrimental, unidirectional effect of non-vaccinated to vaccinated communities. Regarding the interactions between "Gold", "Silver" and "Bronze" communities in a network, we find that two factors play central role: the coupling strength in the dynamics and network density. When considering the spread of a virus in Barabási-Albert networks, infections in "Silver" and "Gold" communities are lower than in "Bronze" communities. We find that the "Gold" communities are the best in keeping their infection levels low. However, a small number of "Bronze" communities are enough to give rise to an increase in infections in moderately and well-vaccinated communities. When studying the spread of a virus in a dense Erdős-Rényi, and sparse Watts-Strogatz and Barabási-Albert networks, the communities reach the disease-free state in the dense Erdős-Rényi networks, but not in the sparse Watts-Strogatz and Barabási-Albert networks. However, we also find that if all these networks...

physics.soc-ph↗

arXiv2020

Labyrinth chaos: Revisiting the elegant, chaotic and hyperchaotic walks

Labyrinth chaos was discovered by Otto Rössler and René Thomas in their endeavour to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, we celebrate their discovery by considering a single labyrinth walks system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behaviour, reminiscent of chimera-like states, a peculiar synchronisation phenomenon. We discuss the properties of the single labyrinth walks system and review the ability of coupled labyrinth chaos systems to exhibit chimera-like states due to the unique properties of their space-filling, chaotic trajectories, what amounts to elegant, hyperchaotic walks. Finally, we discuss further implications in relation to the labyrinth walks system by showing that even though it is volume-preserving, it is not force-conservative.

nlin.CD↗

arXiv2020

Labyrinth walks: An elegant chaotic conservative non-Hamiltonian system

In this paper, we show that "Labyrinth walks", the conservative version of "Labyrinth chaos" and member of the Thomas-Rössler class of systems, does not admit an autonomous Hamiltonian as a constant function in time, and as a consequence, does not admit a symplectic structure. However, it is conservative, and thus admits a vector potential, being at the same time chaotic. This exceptional set of properties makes "Labyrinth walks" an elegant example of a chaotic, conservative, non-Hamiltonian system, with only unstable stationary points in its phase space, arranged in a 3-dimensional grid. As a consequence, "Labyrinth walks", even though is a deterministic system, it exhibits motion reminiscent of fractional Brownian motion in stochastic systems!

nlin.CD↗

arXiv2020

Labyrinth Chaos is not Hamiltonian but still has a Vector Potential

We provide here a comprehensive proof that the so-called Labyrinth chaos systems, a member of the Thomas-Rössler (TR) class of systems do not admit a Hamiltonian; yet they admit a vector potential. The proof starts from the general case of TR systems, which are in general non-conservative and we show that this is also true for the conservative (volume-preserving) case known as `Labyrinth chaos'. To our knowledge, this is the first instance reported where a conservative chaotic system does not, in principle, admit a Hamiltonian symplectic structure. Still, a vector potential is readily admissible and thus, constructed.

nlin.CD↗

arXiv2018

Hyperchaos & Labyrinth chaos: Revisiting Thomas-Rössler systems

We consider a multi-dimensional extension of the Thomas-Rössler (TR) systems, that was inspired by Thomas' earlier work on biological feedback circuits, and we report on our first results that shows its ability to sustain a spatio-temporal behaviour, reminiscent of chimera states. The novelty here being that its underlying mechanism is based on "chaotic walks" discovered by René Thomas during the course of his investigations on what he called Labyrinth Chaos. We briefly review the main properties of TR systems and their chaotic and hyperchaotic dynamics and discuss the simplest way of coupling, necessary for this spatio-temporal behaviour that allows the emergence of complex dynamical behaviours. We also recall René Thomas' memorable influence and interaction with the authors as we dedicate this work to his memory.

nlin.CD↗

arXiv2018

Symbolic Dynamics of Music from Europe and Japan

After a brief introduction to the theory underlying block-entropy, and its relation to the dynamics of complex systems as well as certain information theory aspects, we study musical texts coming from two distinct musical traditions (Japanese and Western European) encoded via symbolic dynamics. We quantify their information content or also known as the degree of "non-randomness" which essentially defines the complexity of the text. We analyse the departure of "total randomness" to the constrains underlying the dynamics of the symbol generating process. Following Shannon on his attribution to these constraints as the emergence of complexity, we observe that it can be accurately assessed by the texts' block-entropy versus block-length scaling laws.

nlin.CD↗

arXiv2015

Quantum Cognition based on an Ambiguous Representation Derived from a Rough Set Approximation

Over the last years, in a series papers by Arrechi and others, a model for the cognitive processes involved in decision making has been proposed and investigated. The key element of this model is the expression of apprehension and judgement, basic cognitive process of decision making, as an inverse Bayes inference classifying the information content of neuron spike trains. For successive plural stimuli, it has been shown that this inference, equipped with basic non-algorithmic jumps, is affected by quantum-like characteristics. We show here that such a decision making process is related consistently with ambiguous representation by an observer within a universe of discourse. In our work ambiguous representation of an object or a stimuli is defined by a pair of maps from objects of a set to their representations, where these two maps are interrelated in a particular structure. The a priori and a posteriori hypotheses in Bayes inference are replaced by the upper and lower approximation, correspondingly, for the initial data sets each derived with respect to a map. We show further that due to the particular structural relation between the two maps, the logical structure of such combined approximations can only be expressed as an orthomodular lattice and therefore can be represented by a quantum rather than a Boolean logic. To our knowledge, this is the first investigation aiming to reveal the concrete logic structure of inverse Bayes inference in cognitive processes.

q-bio.NC↗

arXiv2014

Goedel's other legacy and the imperative of a self-reflective science

The Goedelian approach is discussed as a prime example of a science towards the origins. While mere selfreferential objectification locks in to its own byproducts, self-releasing objectification informs the formation of objects at hand and their different levels of interconnection. Guided by the spirit of Goedel's work a self-reflective science can open the road where old tenets see only blocked paths. "This is, as it were, an analysis of the analysis itself, but if that is done it forms the fundamental of human science, as far as this kind of things is concerned." G. Leibniz, ('Methodus Nova ...', 1673)

physics.hist-ph↗

arXiv2013

Linear And Nonlinear Arabesques: A Study Of Closed Chains Of Negative 2-Element Circuits

In this paper we consider a family of dynamical systems that we call "arabesques", defined as closed chains of 2-element negative circuits. An $n$-dimensional arabesque system has $n$ 2-element circuits, but in addition, it displays by construction, two $n$-element circuits which are both positive vs one positive and one negative, depending on the parity (even or odd) of the dimension $n$. In view of the absence of diagonal terms in their Jacobian matrices, all these dynamical systems are conservative and consequently, they can not possess any attractor. First, we analyze a linear variant of them which we call "arabesque 0" or for short "A0". For increasing dimensions, the trajectories are increasingly complex open tori. Next, we inserted a single cubic nonlinearity that does not affect the signs of its circuits (that we call "arabesque 1" or for short "A1"). These systems have three steady states, whatever the dimension is, in agreement with the order of the nonlinearity. All three are unstable, as there can not be any attractor in their state-space. The 3D variant (that we call for short "A1\_3D") has been analyzed in some detail and found to display a complex mixed set of quasi-periodic and chaotic trajectories. Inserting $n$ cubic nonlinearities (one per equation) in the same way as above, we generate systems "A2\_$n$D". A2\_3D behaves essentially as A1\_3D, in agreement with the fact that the signs of the circuits remain identical. A2\_4D, as well as other arabesque systems with even dimension, has two positive $n$-circuits and nine steady states. Finally, we investigate and compare the complex dynamics of this family of systems in terms of their symmetries.

nlin.CD↗

arXiv2011

Emergence of coherent motion in aggregates of motile coupled maps

In this paper we study the emergence of coherence in collective motion described by a system of interacting motiles endowed with an inner, adaptative, steering mechanism. By means of a nonlinear parametric coupling, the system elements are able to swing along the route to chaos. Thereby, each motile can display different types of behavior, i.e. from ordered to fully erratic motion, accordingly with its surrounding conditions. The appearance of patterns of collective motion is shown to be related to the emergence of interparticle synchronization and the degree of coherence of motion is quantified by means of a graph representation. The effects related to the density of particles and to interparticle distances are explored. It is shown that the higher degrees of coherence and group cohesion are attained when the system elements display a combination of ordered and chaotic behaviors, which emerges from a collective self-organization process.

nlin.CD↗

arXiv2011

Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems

We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-$β$) oscillator chains with different boundary conditions and numbers of particles and a microplasma of identical ions confined in a Penning trap and repelled by mutual Coulomb interactions. For the FPU systems we show that, when chaos is limited within "small size" phase space regions, statistical distributions of sums of chaotic variables are well approximated for surprisingly long times (typically up to $t\approx10^6$) by a $q$-Gaussian ($1<q<3$) distribution and tend to a Gaussian ($q=1$) for longer times, as the orbits eventually enter into "large size" chaotic domains. However, in agreement with other studies, we find in certain cases that the $q$-Gaussian is not the only possible distribution that can fit the data, as our sums may be better approximated by a different so-called "crossover" function attributed to finite-size effects. In the case of the microplasma Hamiltonian, we make use of these $q$-Gaussian distributions to identify two energy regimes of "weak chaos"-one where the system melts and one where it transforms from liquid to a gas state-by observing where the $q$-index of the distribution increases significantly above the $q=1$ value of strong chaos.

nlin.CD↗

arXiv2010

Kinetics of intermediate-mediated self-assembly in nano-sized materials: a generic model

We propose in this paper a generic model of a non-standard aggregation mechanism for self-assembly processes of a class of materials involving the mediation of intermediates consisting of a polydisperse population of nano-sized particles. The model accounts for a long induction period in the process. The proposed mechanism also gives insight on future experiments aiming at a more comprehensive picture of the role of self-organization in self-assembly processes.

cond-mat.mes-hall↗

arXiv2010

Kinetic roughening-like transition with finite nucleation barrier

Recent observations of the growth of protein crystals have identified two different growth regimes. At low supersaturation, the surface of the crystal is smooth and increasing in size due to the nucleation of steps at defects and the subsequent growth of the steps. At high supersaturation, nucleation occurs at many places simultaneously, the crystal surface becomes rough and the growth velocity increases more rapidly with increasing supersaturation than in the smooth regime. Kinetic roughening transitions are typically assumed to be due to the vanishing of the barrier for two-dimension nucleation on the surface of the crystal. We show here, by means of both analytic mean field models and kinetic Monte Carlo simulations that a transition between different growth modes reminiscent of kinetic roughening can also arise as a kinetic effect occurring at finite nucleation barriers.

cond-mat.soft↗

arXiv2009

Weak Chaos and the "Melting Transition" in a Confined Microplasma System

We present results demonstrating the occurrence of changes in the collective dynamics of a Hamiltonian system which describes a confined microplasma characterized by long--range Coulomb interactions. In its lower energy regime, we first detect macroscopically, the transition from a "crystalline--like" to a "liquid--like" behavior, which we call the "melting transition". We then proceed to study this transition using a microscopic chaos indicator called the \emph{Smaller Alignment Index} (SALI), which utilizes two deviation vectors in the tangent dynamics of the flow and is nearly constant for ordered (quasi--periodic) orbits, while it decays exponentially to zero for chaotic orbits as $\exp(-(λ_{1}-λ_{2})t)$, where $λ_{1}>λ_{2}>0$ are the two largest Lyapunov exponents. During the "melting phase", SALI exhibits a peculiar, stair--like decay to zero, reminiscent of "sticky" orbits of Hamiltonian systems near the boundaries of resonance islands. This alerts us to the importance of the $Δλ=λ_{1}-λ_{2}$ variations in that regime and helps us identify the energy range over which "melting" occurs as a multi--stage diffusion process through weakly chaotic layers in the phase space of the microplasma. Additional evidence supporting further the above findings is given by examining the $GALI_{k}$ indices, which generalize SALI (=$GALI_{2}$) to the case of $k>2$ deviation vectors and depend on the complete spectrum of Lyapunov exponents of the tangent flow about the reference orbit.

nlin.CD↗

arXiv2008

Statistical properties of time-reversible triangular maps of the square

Time reversal symmetric triangular maps of the unit square are introduced with the property that the time evolution of one of their two variables is determined by a piecewise expanding map of the unit interval. We study their statistical properties and establish the conditions under which their equilibrium measures have a product structure, i.e. factorises in a symmetric form. When these conditions are not verified, the equilibrium measure does not have a product form and therefore provides additional information on the statistical properties of theses maps. This is the case of anti-symmetric cusp maps, which have an intermittent fixed point and yet have uniform invariant measures on the unit interval. We construct the invariant density of the corresponding two-dimensional triangular map and prove that it exhibits a singularity at the intermittent fixed point.

nlin.CD↗

arXiv2006

Symbolic Dynamics Generated by a Combination of Graphs

In this paper we investigate the growth rate of the number of all possible paths in graphs with respect to their length in an exact analytical way. Apart from the typical rates of growth, i.e. exponential or polynomial, we identify conditions for a stretched exponential type of growth. This is made possible by combining two or more graphs over the same alphabet, in order to obtain a discrete dynamical system generated by a triangular map, which can also be interpreted as a discrete non-autonomous system. Since the vertices and the edges of a graph usually are used to depict the states and transitions between states of a discrete dynamical system, the combination of two (or more) graphs can be interpreted as the driving, or perturbation, of one system by another.

math.DS↗