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Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…
Turbulence modeling within the Lattice Boltzmann Method (LBM) framework has long relied on traditional algebraic sub-grid scale (SGS) models, which often suffer from over-dissipation and lack of spatial selectivity near solid boundaries. In…
Examples of one-dimensional lattice systems are considered, in which patterns of different spatial scales arise alternately, so that the spatial phase over a full cycle undergo transformation according to expanding circle map that implies…
The scaling hypothesis for the coupled chotic map lattices (CML) is formulated. Scaling properties of the CML in the regime of extensive chaos observed numerically before is justified analytically. The asymptotic Liapunov exponents spectrum…
In this work, inspired in the symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is…
In this paper it is shown that a generalized circulant matrix underlies every weakly Coupled Map Lattice (CML), independently of the form of the coupling term. Therefore, this matrix will appear always perturbative methods are used to get…
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…
In presence of unstable dimension variability numerical solutions of chaotic systems are valid only for short periods of observation. For this reason, analytical results for systems that exhibit this phenomenon are needed. Aiming to go one…
The dynamics of coupled 2D chaotic maps with time-delay on a scalefree-tree is studied, with different types of the collective behaviors already been reported for various values of coupling strength [1]. In this work we focus on the…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
In this article, we have studied a 1D map, which is formed by combining the two well-known maps i.e. the tent and the logistic maps in the unit interval i.e. [0, 1]. The proposed map can behave as the piecewise smooth or non-smooth maps…
The intermediate dynamics of composed one-dimensional maps is used to multiply attractors in phase space and create multiple independent bifurcation diagrams which can split apart. Results are shown for the composition of k-paradigmatic…
We study the spatio-temporal behavior of simple coupled map lattices with periodic boundary conditions. The local dynamics is governed by two maps, namely, the sine circle map and the logistic map respectively. It is found that even though…
Many real-world decision-theoretic planning problems can be naturally modeled with discrete and continuous state Markov decision processes (DC-MDPs). While previous work has addressed automated decision-theoretic planning for DCMDPs,…
The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…
Inferring latent interaction structures from observed dynamics is a fundamental inverse problem in many-body interacting systems. Most neural approaches rely on black-box surrogates over trainable graphs, achieving accuracy at the expense…
We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed in [1,2]. The algorithms for computation of the time averages of observables on phase space are developed and…
This research investigates the dynamic behavior of one dimensional discrete systems using two computational algorithms, the numerical transitivity and the numerical locally eventually onto (LEO) tests. Both algorithms are systematically…
The dynamics of physical systems that require high-dimensional representation can often be captured in a few meaningful degrees of freedom called collective variables (CVs). However, identifying CVs is challenging and constitutes a…
A diagrammatic method is presented for averaging over the circular ensemble of random-matrix theory. The method is applied to phase-coherent conduction through a chaotic cavity (a ``quantum dot'') and through the interface between a normal…