Timely detection of unusual and/or unexpected events in natural and man-made systems has deep scientific and practical relevance. We show that the recently proposed conceptually simple and easily calculated measure of permutation entropy can be effectively used to detect qualitative and quantitative dynamical changes. We illustrate our results on two model systems as well as on clinically characterized brain wave data from epileptic patients.

Due to the ubiquity of time series with long-range correlation in many areas of science and engineering, analysis and modeling of such data is an important problem. While the field seems to be mature, three major issues have not been satisfactorily resolved. ͑i͒ Many methods have been proposed to assess long-range correlation in time series. Under what circumstances do they yield consistent results? ͑ii͒ The mathematical theory of long-range correlation concerns the behavior of the correlation of the time series for very large times. A measured time series is finite, however. How can we relate the fractal scaling break at a specific time scale to important parameters of the data? ͑iii͒ An important technique in assessing long-range correlation in a time series is to construct a random walk process from the data, under the assumption that the data are like a stationary noise process. Due to the difficulty in determining whether a time series is stationary or not, however, one cannot be 100% sure whether the data should be treated as a noise or a random walk process. Is there any penalty if the data are interpreted as a noise process while in fact they are a random walk process, and vice versa? In this paper, we seek to gain important insights into these issues by examining three model systems, the autoregressive process of order 1, on-off intermittency, and Lévy motions, and considering an important engineering problem, target detection within sea-clutter radar returns. We also provide a few rules of thumb to safeguard against misinterpretations of long-range correlation in a time series, and discuss relevance of this study to pattern recognition.

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Homologs of the Yersinia virulence factor YopJ are found in both animal and plant bacterial pathogens, as well as in plant symbionts. The conservation of this effector family indicates that several pathogens may use YopJ-like proteins to regulate bacteria-host interactions during infection. YopJ and YopJ-like proteins share structural homology with cysteine proteases and are hypothesized to functionally mimic small ubiquitin-like modifier (SUMO) proteases in eukaryotic cells. Strains of the phytopathogenic bacterium Xanthomonas campestris pv. vesicatoria are known to possess four YopJ-like proteins, AvrXv4, AvrBsT, AvrRxv, and XopJ. In this work, we have characterized AvrXv4 to determine if AvrXv4 functions like a SUMO protease in planta during Xanthomonas-plant interactions. We provide evidence that X. campestris pv. vesicatoria secretes and translocates the AvrXv4 protein into plant cells during infection in a type III-dependent manner. Once inside the plant cell, AvrXv4 is localized to the plant cytoplasm. By performing AvrXv4 deletion and mutational analysis, we have identified amino acids required for type III delivery and for host recognition. We show that AvrXv4 recognition by resistant plants requires a functional protease catalytic core, the domain that is conserved in all of the putative YopJ-like cysteine proteases. We also show that AvrXv4 expression in planta leads to a reduction in SUMO-modified proteins, demonstrating that AvrXv4 possesses SUMO isopeptidase activity. Overall, our studies reveal that the YopJ-like effector AvrXv4 encodes a type III SUMO protease effector that is active in the cytoplasmic compartment of plant cells.

Time series from complex systems with interacting nonlinear and stochastic subsystems and hierarchical regulations are often multiscaled. In devising measures characterizing such complex time series, it is most desirable to incorporate explicitly the concept of scale in the measures. While excellent scale-dependent measures such as ⑀ entropy and the finite size Lyapunov exponent ͑FSLE͒ have been proposed, simple algorithms have not been developed to reliably compute them from short noisy time series. To promote widespread application of these concepts, we propose an efficient algorithm to compute a variant of the FSLE, the scale-dependent Lyapunov exponent ͑SDLE͒. We show that with our algorithm, the SDLE can be accurately computed from short noisy time series and readily classify various types of motions, including truly low-dimensional chaos, noisy chaos, noise-induced chaos, random 1 / f ␣ and ␣-stable Levy processes, stochastic oscillations, and complex motions with chaotic behavior on small scales but diffusive behavior on large scales. To our knowledge, no other measures are able to accurately characterize all these different types of motions. Based on the distinctive behaviors of the SDLE for different types of motions, we propose a scheme to distinguish chaos from noise.