A tree-ensemble method, referred to as time series forest (TSF), is proposed for time series classification. TSF employs a combination of entropy gain and a distance measure, referred to as the Entrance (entropy and distance) gain, for evaluating the splits. Experimental studies show that the Entrance gain improves the accuracy of TSF. TSF randomly samples features at each tree node and has computational complexity linear in the length of time series, and can be built using parallel computing techniques. The temporal importance curve is proposed to capture the temporal characteristics useful for classification. Experimental studies show that TSF using simple features such as mean, standard deviation and slope is computationally efficient and outperforms strong competitors such as one-nearest-neighbor classifiers with dynamic time warping.

The most-studied classes of exact solutions to Vlasov–Maxwell equations for stationary neutral current structures in a collisionless relativistic plasma, which allow the particle distribution functions (PDFs) to be chosen at will, are reviewed. A general classification is presented of the current sheets and filaments described by the method of invariants of motion of particles whose PDF is symmetric in a certain way in coordinate and momentum spaces. The possibility is discussed of using these explicit solutions to model the observed and/or expected features of current structures in cosmic and laboratory plasmas. Also addressed are how the magnetic field forms and the analytical description of the so-called Weibel instability in a plasma with an arbitrary PDF.

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