Trajectory analysis time series

Another recent trend is to show the importance of hydrophobic profiles rather than molecular hydrophobicity. Giuliani et al. (2002) suggested nonlinear signal analysis methods in the elucidation of protein sequence-structure relationships. The major algorithm used for analyzing hydrophobicity sequences or profiles was recurrence quantification analysis (RQA), in which a recurrence plot depicted a single trajectory as a two-dimensional representation of experimental time-series data. Examples of the global properties used in this... 

Short-range diffusion (SRD) analysis is the method used to obtain the distribution of diffusion coefficients of target molecules. In this method, short trajectories with constant time duration are successively extracted from one trajectory, and diffusion coefficients are determined for individual short trajectories, producing a time series of diffusion coefficients. This analysis can be used to detect temporal changes in the mobility of individual molecules (14,15). In this section, we suppose that the images were acquired at 33-ms intervals (i.e., 30 frames per second (fps), = 33 ms). 

In this chapter, we briefly review some of our recent studies on structure and dynamics of normal and supercritical water based on first principles simulations. The work reviewed here was based on the methods of ab initio molecular dynamics for trajectory generation and time series analysis for frequency calculations. We consider normal water at room temperature and also supercritical water at three different densities ranging from 1.0 to 0.35 g cm at a temperature of 673 K. More details of the work reviewed here can be found in [16,17]. The next section of this chapter contains a brief account of the ab initio simulations and time series analysis. The results of the hydrogen-bonded structures and their relations to the vibrational frequencies and also the dynamics of the hydrogen bond and vibrational frequency fluctuations in normal and supercritical water are discussed in Section 14.4. This chapter is concluded in Section 14.5. 

HANUSSE - In fact the morphology analysis is performed on the complete trajectory given by the simulation of the full model. One interesting result is that the results do not seem to depend on the space in which you work (concentrations, reaction rates, combinations of them). You obtain the same essential dynamical features. This stability of the solution is to be compared to that of the reconstruction procedure of three dimensional attractors from a unique time series, in studies of chaotic behaviour. 

For quasi-periodic trajectories, like those for the normal-mode Hamiltonian in Eq. (69), I to) consists of a series of lines at the frequencies for the normal modes of vibration. In contrast, a Fourier analysis of a chaotic trajectory results in a multitude of peaks, without identifiable frequencies for particular modes. An inconvenience in this approach is that for a large molecule with many modes, a trajectory may have to be integrated for a long time T to resolve the individual lines in a power spectrum for a quasi-periodic trajectory. Moreover, in the presence of a resonance between different modes, the interpretation of the power spectrum may become misleading. 

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