231,519 research outputs found
The identification of complex spatiotemporal patterns using Coupled map lattice model
Many complex and interesting spatiotemporal patterns have been observed in a wide range of scienti¯c areas. In this paper, two kinds of spatiotemporal patterns including spot replication and Turing systems are investigated and new identi¯cation methods are proposed to obtain Coupled Map Lattice (CML) models for this class of systems. Initially, a new correlation analysis method is introduced to determine an appropriate temporal and spatial data sampling step procedure for the identification of spatiotemporal systems. A new combined Orthogonal Forward Regression and Bayesian Learning algorithm with Laplace priors is introduced to identify sparse and robust CML models for complex spatiotemporal patterns. The final identified CML models are validated using correlation based model validation tests for spatiotemporal systems. Numerical re-sults illustrate the identification procedure and demonstrate the validity of the identified models
Non-universal dependence of spatiotemporal regularity on randomness in coupling connections
We investigate the spatiotemporal dynamics of a network of coupled nonlinear
oscillators, modeled by sine circle maps, with varying degrees of randomness in
coupling connections. We show that the change in the basin of attraction of the
spatiotemporal fixed point due to varying fraction of random links , is
crucially related to the nature of the local dynamics. Even the qualitative
dependence of spatiotemporal regularity on changes drastically as the
angular frequency of the oscillators change, ranging from monotonic increase or
monotonic decrease, to non-monotonic variation. Thus it is evident here that
the influence of random coupling connections on spatiotemporal order is highly
non-universal, and depends very strongly on the nodal dynamics.Comment: 9 pages, 4 figure
A canonical space-time state space model: state and parameter estimation
The maximum likelihood estimation of a dynamic spatiotemporal model is introduced, centred around the inclusion of a prior arbitrary spatiotemporal neighborhood description. The neighborhood description defines a specific parameterization of the state transition matrix, chosen on the basis of prior knowledge about the system. The model used is inspired by the spatiotemporal ARMA (STARMA) model, but the representation used is based on the standard state-space model. The inclusion of the neighborhood into an expectation-maximization based joint state and parameter estimation algorithm allows for accurate characterization of the spatiotemporal model. The process of including the neighborhood, and the effect it has on the maximum likelihood parameter estimate is described and demonstrated in this paper
Forecasting confined spatiotemporal chaos with genetic algorithms
A technique to forecast spatiotemporal time series is presented. it uses a
Proper Ortogonal or Karhunen-Lo\`{e}ve Decomposition to encode large
spatiotemporal data sets in a few time-series, and Genetic Algorithms to
efficiently extract dynamical rules from the data. The method works very well
for confined systems displaying spatiotemporal chaos, as exemplified here by
forecasting the evolution of the onedimensional complex Ginzburg-Landau
equation in a finite domain.Comment: 4 pages, 5 figure
Spatiotemporal Barcodes for Image Sequence Analysis
Taking as input a time-varying sequence of two-dimensional
(2D) binary images, we develop an algorithm for computing a spatiotemporal
0–barcode encoding lifetime of connected components on the image
sequence over time. This information may not coincide with the one provided
by the 0–barcode encoding the 0–persistent homology, since the
latter does not respect the principle that it is not possible to move backwards
in time. A cell complex K is computed from the given sequence,
being the cells of K classified as spatial or temporal depending on whether
they connect two consecutive frames or not. A spatiotemporal path is
defined as a sequence of edges of K forming a path such that two edges
of the path cannot connect the same two consecutive frames. In our
algorithm, for each vertex v ∈ K, a spatiotemporal path from v to the
“oldest” spatiotemporally-connected vertex is computed and the corresponding
spatiotemporal 0–bar is added to the spatiotemporal 0–barcode.Junta de Andalucía FQM-369Ministerio de Economía y Competitividad MTM2012-3270
Spatiotemporal heterodyne detection
We describe a scheme into which a camera is turned into an efficient tunable
frequency filter of a few Hertz bandwidth in an off-axis, heterodyne optical
mixing configuration, enabling to perform parallel, high-resolution coherent
spectral imaging. This approach is made possible through the combination of a
spatial and temporal modulation of the signal to reject noise contributions.
Experimental data obtained with dynamically scattered light by a suspension of
particles in brownian motion is interpreted
- …