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We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.

XopJ is a Xanthomonas type III effector protein that promotes bacterial virulence on susceptible pepper plants through the inhibition of the host cell proteasome and a resultant suppression of salicylic acid (SA) - dependent defense responses. We show here that Nicotiana benthamiana leaves transiently expressing XopJ display hypersensitive response (HR) -like symptoms when exogenously treated with SA. This apparent avirulence function of XopJ was further dependent on effector myristoylation as well as on an intact catalytic triad, suggesting a requirement of its enzymatic activity for HR-like symptom elicitation. The ability of XopJ to cause a HR-like symptom development upon SA treatment was lost upon silencing of SGT1 and NDR1, respectively, but was independent of EDS1 silencing, suggesting that XopJ is recognized by an R protein of the CC-NBS-LRR class. Furthermore, silencing of NPR1 abolished the elicitation of HR-like symptoms in XopJ expressing leaves after SA application. Measurement of the proteasome activity indicated that proteasome inhibition by XopJ was alleviated in the presence of SA, an effect that was not observed in NPR1 silenced plants. Our results suggest that XopJ - triggered HR-like symptoms are closely related to the virulence function of the effector and that XopJ follows a two-signal model in order to elicit a response in the non-host plant N. benthamiana.

We develop a method of finding analytical sotutions of the Bogolyubov-de Gennes equations for the excitations of a Bose condensate in the Thomas-Fermi regime in harmonic traps of any asymmetry and introduce a classification of eigenstates. In the case of cylindrical symmetry we emphasize the presence of an accidental degeneracy in the excitation spectrum at certain values of the projection of orbital angular momentum on the symmetry axis and discuss possible consequences of the degeneracy in the context of new signatures of Bose- Einstein condensation

The application of electrospray ionization (ESI) ion mobility (IM) spectrometry on the detection end of a high-performance liquid chromatograph has been a subject of study for some time. So far, this method has been limited to low flow rates or has required splitting of the liquid flow. This work presents a novel concept of an ESI source facilitating the stable operation of the spectrometer at flow rates between 10 mu L min(-1) and 1500 mu L min(-1) without flow splitting, advancing the T-cylinder design developed by Kurnin and co-workers. Flow rates eight times faster than previously reported were achieved because of a more efficient dispersion of the liquid at increased electrospray voltages combined with nebulization by a sheath gas. Imaging revealed the spray operation to be in a rotationally symmetric multijet-mode. The novel ESI-IM spectrometer tolerates high water contents (<= 90%) and electrolyte concentrations up to 10 mM, meeting another condition required of high-performance liquid chromatography (HPLC) detectors. Limits of detection of 50 nM for promazine in the positive mode and 1 mu M for 1,3-dinitrobenzene in the negative mode were established. Three mixtures of reduced complexity (five surfactants, four neuroleptics, and two isomers) were separated in the millisecond regime in stand-alone operation of the spectrometer. Separations of two more complex mixtures (five neuroleptics and 13 pesticides) demonstrate the application of the spectrometer as an HPLC detector. The examples illustrate the advantages of the spectrometer over the established diode array detector, in terms of additional IM separation of substances not fully separated in the retention time domain as well as identification of substances based on their characteristic IMs.