Related papers: Linear encoding of the spatiotemporal cat
Hamiltonian tridiagonal matrices characterized by multi-fractal spectral measures in the family of Iterated Function Systems can be constructed by a recursive technique here described. We prove that these Hamiltonians are almost-periodic.…
In this paper we show that the analysis of the dynamics in localized regions, i.e., sub-systems can be used to characterize the chaotic dynamics and the synchronization ability of the spatiotemporal systems. Using noisy scalar time-series…
Spatio-temporal feature encoding is essential for encoding facial expression dynamics in video sequences. At test time, most spatio-temporal encoding methods assume that a temporally segmented sequence is fed to a learned model, which could…
The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the…
We study the spatial distributions of two randomly interacting species, in the presence of an external multiplicative colored noise. The dynamics of the ecosystem is described by a coupled map lattice model. We find a nonmonotonic behavior…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
Spatiotemporal chaos of a two-dimensional one-way coupled map lattice is used for chaotic cryptography. The chaotic outputs of many space units are used for encryption simultaneously. This system shows satisfactory cryptographic properties…
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a ``no go'' for simulating the original continuum classical gauge fields over a long time…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
Multicolor cell spatio-temporal image data have become important to investigate organ development and regeneration, malignant growth or immune responses by tracking different cell types both in vivo and in vitro. Statistical modeling of…
Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to…
High resolution satellite image sequences are multidimensional signals composed of spatio-temporal patterns associated to numerous and various phenomena. Bayesian methods have been previously proposed in (Heas and Datcu, 2005) to code the…
From biological systems to cyber-physical systems, monitoring the behavior of such dynamical systems often requires to reason about complex spatio-temporal properties of physical and/or computational entities that are dynamically…
We consider systems of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
Localised defect modes generated by a finite line defect composed of several masses, embedded an infinite square cell lattice, are analysed using the linear superposition of Green's function for a single mass defect. Several representations…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
A new complexity measure named as Lattice Complexity is presented for finite symbolic sequences. This measure is based on the symbolic dynamics of one-dimensional iterative maps and Lempel-Ziv Complexity. To make Lattice Complexity…
In this paper we study the evolution of the wave function with the system size in a locally periodic structure. In particular we analyse the dependence of the wave function with the number of unit cells, which also reflects information…