In this work, we propose a novel method to transform a time series into a weighted and directed network. For a given time series, we first generate a set of segments via a sliding window, and then use a doubly symbolic scheme to characterize every windowed segment by combining absolute amplitude information with an ordinal pattern characterization. Based on this construction, a network can be directly constructed from the given time series: segments corresponding to different symbol-pairs are mapped to network nodes and the temporal succession between nodes is represented by directed links. With this conversion, dynamics underlying the time series has been encoded into the network structure. We illustrate the potential of our networks with a well-studied dynamical model as a benchmark example. Results show that network measures for characterizing global properties can detect the dynamical transitions in the underlying system. Moreover, we employ a random walk algorithm to sample loops in our networks, and find that time series with different dynamics exhibits distinct cycle structure. That is, the relative prevalence of loops with different lengths can be used to identify the underlying dynamics.
A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicia complex preserves all pertinent topological features of the reconstructed phase space and it may be analyzed from topological, combinatorial and algebraic aspects. In focus of this study is computation of homology of the invariant set of some well known dynamical systems which display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examined by studying the
We generate time series from scale-free networks based on a finite-memory random walk traversing the network. These time series reveal topological and functional properties of networks via their temporal correlations. Remarkably, networks with different node-degree mixing patterns exhibit distinct self-similar characteristics. In particular, assortative networks are transformed into time series with long-range correlation, while disassortative networks are transformed into time series exhibiting anticorrelation. These relationships are consistent across a diverse variety of real networks. Moreover, we show that multiscale analysis of these time series can describe and classify various physical networks ranging from social and technological to biological networks according to their functional origin. These results suggest that there is a unified dynamical mechanism that governs the structural organization of many seemingly different networks.
Abstract.A new algorithm is presented for the automatic segmentation and classification of brain tissue from 3D MR scans. It uses discriminative Random Decision Forest classification and takes into account partial volume effects. This is combined with correction of intensities for the MR bias field, in conjunction with a learned model of spatial context, to achieve accurate voxel-wise classification. Our quantitative validation, carried out on existing labelled datasets, demonstrates improved results over the state of the art, especially for the cerebro-spinal fluid class which is the most difficult to label accurately.
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