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The detection of an underlying chaotic behavior in experimental recordings is a longstanding issue in the field of nonlinear time series analysis. Conventional approaches require the assessment of a suitable dimension and lag pair to embed a given input sequence and, thereupon, the estimation of dynamical invariants to characterize the underlying source. In this work, we propose an alternative approach to the problem of identifying chaos, which is built upon an improved method for optimal embedding. The core of the new approach is the analysis of an input sequence on a lattice of embedding pairs whose results provide, if any, evidence of a finite-dimensional, chaotic source generating the sequence and, if such evidence is present, yield a set of equivalently suitable embedding pairs to embed the sequence. The application of this approach to two experimental case studies, namely, an electronic circuit and magnetoencephalographic recordings of the human brain, highlights how it can make up a powerful tool to detect chaos in complex systems.

The possibility of using microRNA (miRNA) levels as diagnostic and prognostic tools to detect different pathologies requires the implementation of reliable classifiers, whose training and use call for quality control of data corresponding to miRNA expression. In this work we present the MiRNA-QC-and-Diagnosis package. The package provides a set of functions for the R environment that implement the required quality control steps and thereupon allow to train, use and optimize a Bayesian classifier for diagnosis based on the measured miRNA expressions. The package thus makes up a complete and dedicated analytical toolbox for miRNA-based diagnosis.

The divergence rate method, which is used to determine the maximum Lyapunov exponent out of time series, is based on the evaluation of the time-dependent divergence exponent. For chaotic systems and in the small time regime, this exponent grows linearly in time. The asymptotic regime is instead characterized by a time-independent behavior due to the system eventually losing its memory of the starting conditions. The amplitude of this "plateau"-like divergence exponent depends both on the choice of the embedding dimension and lag and on the maximum distance of nearby starting trajectories in a way that is characteristic of the underlying dynamical system. In this paper, upon introducing the basic mathematical tools, we address the plateau evaluation for two classes of time series, those generated by a white noise source and those generated by a finite-dimensional chaotic system. The different behavior provides a novel tool to distinguish purely stochastic sources from deterministic ones, as well as to provide a precise estimate of the correlation dimension in the latter case. The method is also sensitive to correlated noise sources.

The identification of networks is an issue that is relevant in many research fields. Assessing links between nodes of a network by analyzing time series associated to those nodes is a crucial topic in fields as diverse as neuroscience and climate research. In this work we present NetOnZeroDXC, a package that implements a recently published method for the assessment of networks out of multivariate time series. The method relies on the computation of zero-delay cross-correlation between pairs of time series. The software implements the various stages of the algorithm in a general way, thus making up a novel tool that can be used for network analysis in different fields. Keywords: Cross correlation, Networks, Multivariate time series analysis

The central limit theorem for Markov chains is widely used, in particular in its pristine univariate form. As far as the multivariate case is concerned, a few proofs exist, which depend on different assumptions and require advanced mathematical and statistical tools. Here a novel proof is presented that, starting from the standard condition of regularity only, relies on time-independent quantum-mechanical perturbation theory. The result, which is obtained by using techniques that are typical of physics, is expected to enhance the usability of this cornerstone theorem, especially in nonlinear dynamics and physics of complex systems.

The study of many dynamical systems relies on the analysis of experimentally-recorded sequences of events for which information is encoded in the sequence of interevent intervals. A correct interpretation of the results of the application of analytical techniques to these sequences requires the assessment of statistical significance. In most cases, the corresponding null-hypothesis distribution is unknown, thus forbidding an evaluation of the significance. An alternative solution, which is efficient in the case of continuous signals, is provided by the generation of surrogate data that share statistical and spectral properties with the original dataset. However, in the case of event sequences, the available algorithms for the generation of surrogate data can become cumbersome and computationally demanding. In this work, we present a new method for the generation of surrogate event sequences that relies on the joint distribution of successive interevent intervals. Our method, which was tested on both synthetic and experimental sequences, performs equally well or even better than conventional methods in terms of interevent interval distribution and autocorrelation while abating the computational time by at least one order of magnitude.

Fractal structures pervade nature and are receiving increasing engineering attention towards the realization of broadband resonators and antennas. We show that fractal resonators can support the emergence of high-dimensional chaotic dynamics even in the context of an elementary, single-transistor oscillator circuit. Sierpi\'nski gaskets of variable depth are constructed using discrete capacitors and inductors, whose values are scaled according to a simple sequence. It is found that in regular fractals of this kind each iteration effectively adds a conjugate pole/zero pair, yielding gradually more complex and broader frequency responses, which can also be implemented as much smaller Foster equivalent networks. The resonators are instanced in the circuit as one-port devices, replacing the inductors found in the initial version of the oscillator. By means of a highly simplified numerical model, it is shown that increasing the fractal depth elevates the dimension of the chaotic dynamics, leading to high-order hyperchaos. This result is overall confirmed by SPICE simulations and experiments, which however also reveal that the non-ideal behavior of physical components hinders obtaining high-dimensional dynamics. The issue could be practically mitigated by building the Foster equivalent networks rather than the verbatim fractals. Furthermore, it is shown that considerably more complex resonances, and consequently richer dynamics, can be obtained by rendering the fractal resonators irregular through reshuffling the inductors, or even by inserting a limited number of focal imperfections. The present results draw attention to the potential usefulness of fractal resonators for generating high-dimensional chaotic dynamics, and underline the importance of irregularities and component non-idealities.

We report on the direct experimental observation of the 7pP23/2→7dD2 optical transitions in 209 and 210 francium isotopes. By continuously monitoring the fluorescence emitted by the isotopes collected in a magneto-optical trap (MOT), the electric dipole transitions 7pP23/2→7dD25/2 of Fr209, not yet experimentally observed, and 7pP23/2→7dD25/2, 7pP23/2→7dD25/2 of Fr210 were detected as sub-Doppler depletion dips of the cold atom population. This approach allowed unambiguous identification of the excited state hyperfine structures, even in the absence of a large stable vapor. Our findings demonstrate the effectiveness and the flexibility of fluorescence monitoring of trap depletion upon laser excitation, and broaden the experimental knowledge of francium isotopes and their electronic and nuclear properties. These results will have a relevant impact on ongoing researches for low-energy testing of fundamental symmetries with francium, from atomic parity non-conservation to the electron dipole moment.

Controlled atomic desorption from organic Poly-DiMethylSiloxane coating is demonstrated for improving the loading efficiency of 209,210Fr magneto-optical traps. A three times increase in the cold atoms population is obtained with contact-less pulsed light-induced desorption, applied to different isotopes, either bosonic or fermionic, of Francium. A six times increase of 210Fr population is obtained with a desorption mechanism based on direct charge transfer from a triboelectric probe to the adatom-organic coating complex. Our findings provide new insight on the microscopic mechanisms of atomic desorption from organic coatings. Our results, obtained at room temperature so as to preserve ideal vacuum conditions, represent concrete alternatives, independent from the atomic species in use, for high-efficiency laser cooling in critical conditions.

Assessing brain connectivity makes up a major issue in the field of network dynamics and neuroscience. Conventional experimental techniques are based on functional imaging and magnetoencephalography, allowing to reconstruct the activity of relatively small brain volume elements. A common approach to identify networks consists in singling out sets of elements that maintain a correlated activity over time. Despite the general consensus that these networks are detectable on a time window of 10 s, no study is presently available on the distribution and thus the reliability of this time scale. In this work, we describe a new method to assess time scales on which correlations between network elements occur and to consequently identify the underlying network structures. The analysis relies on the evaluation of quasi-zero-delay cross-correlation between power sequences associated with distinct volume elements. By changing the width of the running window used to analyze successive segments of time series, the behavior of cross-correlation at different time scales was investigated. The onset of connectivity was estimated to be observable at about 30 s. The method was applied to a set of volume elements that are supposed to belong to a known resting-state network, namely the Default Mode Network. Fully connected networks were identified, provided that a sufficiently long time scale is considered. Our method makes up a new tool for the investigation of the temporal dynamics of networks.

International audience; A combined gravitomagnetic trap was used to measure how the anharmonicity of a trapping potential affects the dynamics of a cold atomic cloud. A displacement of the effective potential minimum as a function of the ensemble temperature was observed. The effect is a direct consequence of the thermal nature of the atomic sample. The results of both a theory approach to the dynamical evolution of the atomic cloud and a numerical simulation are in very good agreement with the experimental observations. The effect can be exploited to devise a novel measurement technique for the temperature of a trapped atomic cloud, as well as to separate thermal and condensed phases in Bose-Einstein condensation experiments.

We report on a detailed measurement of the enhanced absorption Hanle effect resonances in 85 Rb. The effect was analysed with an experimental setup allowing for the control of each magnetic field component within 1 mG. The characterization deals with the dependence of resonances, observed under different magnetic field conditions, on the frequency, intensity and polarization of the exciting radiation field. An analytic model that precisely describes the resonance behaviour is discussed.