Physics

We formulate, using the discrete nonlinear Schroedinger equation (DNLS), a general approach to encode and process information based on reservoir computing. Reservoir computing is a promising avenue for realizing neuromorphic computing devices. In such computing systems, training is performed only at the output level, by adjusting the output from the reservoir with respect to a target signal. In our formulation, the reservoir can be an arbitrary physical system, driven out of thermal equilibrium by an external driving. The DNLS is a general oscillator model with broad application in physics and we argue that our approach is completely general and does not depend on the physical realisation of the reservoir. The driving, which encodes the object to be recognised, acts as a thermodynamical force, one for each node in the reservoir. Currents associated to these thermodynamical forces in turn encode the output signal from the reservoir. As an example, we consider numerically the problem of supervised learning for pattern recognition, using as reservoir a network of nonlinear oscillators.

In the context of food quality control, ultrasonics provide proven methods which are able to replace manual controls. The latter are subject to the lack of objectivity of human judgement. Automatic control increases reliability and reduces costs. This paper revisits data coming from ultrasonics through reconstituted milk powder. Two characteristics are studied using five productions of a well known manufacturer. Measured attenuation and dispersion of ultrasonics are explained through stable probability laws and random propagation times. We have proved elsewhere that this model is available in many propagation problems,in acoustics, ultrasonics and in the electromagnetic world.

It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting numbers. We show that the application of this approximation leads to skewed results not only for low-count features, such as background level estimation, but also for its estimation at double-digit count numbers. In effect, this approximation is shown to be imprecise on all levels of count. Instead, a Multinomial approach is introduced as well as a more standard Poisson method, which we compare with the Gaussian case. These two methods originate from a proper analysis of a multi-detector setup and a standard triple axis instrument.We devise a simple mathematical procedure to produce unbiased fits using the Multinomial distribution and demonstrate this method on synthetic and actual inelastic scattering data. We find that the Multinomial method provide almost unbiased results, and in some cases outperforms the Poisson statistics. Although significantly biased, the Gaussian approach is in general more robust in cases where the fitted model is not a true representation of reality. For this reason, a proper data analysis toolbox for low-count neutron scattering should therefore contain more than one model for counting statistics.

We have introduced a novel multiplex recurrence network (MRN) approach by combining recurrence networks with the multiplex network approach in order to investigate multivariate time series. The potential use of this approach is demonstrated on coupled map lattices and a typical example from palaeobotany research. In both examples, topological changes in the multiplex recurrence networks allow for the detection of regime changes in their dynamics. The method goes beyond classical interpretation of pollen records by considering the vegetation as a whole and using the intrinsic similarity in the dynamics of the different regional vegetation elements. We find that the different vegetation types behave more similar when one environmental factor acts as the dominant driving force.

When dealing with non-stationary systems, for which many time series are available, it is common to divide time in epochs, i.e. smaller time intervals and deal with short time series in the hope to have some form of approximate stationarity on that time scale. We can then study time evolution by looking at properties as a function of the epochs. This leads to singular correlation matrices and thus poor statistics. In the present paper, we propose an ensemble technique to deal with a large set of short time series without any consideration of non-stationarity. We randomly select subsets of time series and thus create an ensemble of non-singular correlation matrices. As the selection possibilities are binomially large, we will obtain good statistics for eigenvalues of correlation matrices, which are typically not independent. Once we defined the ensemble, we analyze its behavior for constant and block-diagonal correlations and compare numerics with analytic results for the corresponding correlated Wishart ensembles. We discuss differences resulting from spurious correlations due to repeatitive use of time-series. The usefulness of this technique should extend beyond the stationary case if, on the time scale of the epochs, we have quasi-stationarity at least for most epochs.

We reconcile for the first time the strict mathematical formalism of multivariate cumulants with the usage of cumulants in anisotropic flow analyses in high-energy nuclear collisions. This reconciliation yields to the next generation of observables to be used in flow analyses. We review all fundamental properties of multivariate cumulants and use them as a foundation to establish two simple necessary conditions to determine whether some multivariate observable is a multivariate cumulant in the basis they are expressed in. We argue that properties of cumulants are preserved only for the stochastic observables on which the cumulant expansion has been performed directly, and if there are no underlying symmetries due to which some terms in the cumulant expansion are identically zero. We illustrate one possibility of how new multivariate cumulants of azimuthal angles can be defined which do satisfy all fundamental properties of multivariate cumulants, by defining them event-by-event and by keeping all non-isotropic terms in the cumulant expansion. We introduce new cumulants of flow amplitudes named Asymmetric Cumulants, which generalize recently introduced Symmetric Cumulants for the case when flow amplitudes are raised to different powers. Finally, we present the new concept of Cumulants of Symmetry Plane Correlations and provide the first realisation for the lowest orders. All the presented results are supported by Monte Carlo studies using state-of-the-art models.

Structural changes in a network representation of a system (e.g.,different experimental conditions, time evolution), can provide insight on its organization, function and on how it responds to external perturbations. The deeper understanding of how gene networks cope with diseases and treatments is maybe the most incisive demonstration of the gains obtained through this differential network analysis point-of-view, which lead to an explosion of new numeric techniques in the last decade. However, {\it where} to focus ones attention, or how to navigate through the differential structures can be overwhelming even for few experimental conditions. In this paper, we propose a theory and a methodological implementation for the characterization of shared "structural roles" of nodes simultaneously within and between networks, whose outcome is a highly {\em interpretable} map. The main features and accuracy are investigated with numerical benchmarks generated by a stochastic block model. Results show that it can provide nuanced and interpretable information in scenarios with very different (i) community sizes and (ii) total number of communities, and (iii) even for a large number of 100 networks been compared (e.g., for 100 different experimental conditions). Then, we show evidence that the strength of the method is its "story-telling"-like characterization of the information encoded in a set of networks, which can be used to pinpoint unexpected differential structures, leading to further investigations and providing new insights. We provide an illustrative, exploratory analysis of four gene co-expression networks from two cell types × two treatments (interferon- β stimulated or control). The method proposed here allowed us to elaborate and test a set of very specific hypotheses related to {\em unique} and {\em subtle} nuances of the structural differences between these networks.

In inertial confinement fusion (ICF), X-ray radiography is a critical diagnostic for measuring implosion dynamics, which contains rich 3D information. Traditional methods for reconstructing 3D volumes from 2D radiographs, such as filtered backprojection, require radiographs from at least two different angles or lines of sight (LOS). In ICF experiments, space for diagnostics is limited and cameras that can operate on the fast timescales are expensive to implement, limiting the number of projections that can be acquired. To improve the imaging quality as a result of this limitation, convolutional neural networks (CNN) have recently been shown to be capable of producing 3D models from visible light images or medical X-ray images rendered by volumetric computed tomography LOS (SLOS). We propose a CNN to reconstruct 3D ICF spherical shells from single radiographs. We also examine sensitivity of the 3D reconstruction to different illumination models using preprocessing techniques such as pseudo-flat fielding. To resolve the issue of the lack of 3D supervision, we show that training the CNN utilizing synthetic radiographs produced by known simulation methods allows for reconstruction of experimental data as long as the experimental data is similar to the synthetic data. We also show that the CNN allows for 3D reconstruction of shells that possess low mode asymmetries. Further comparisons of the 3D reconstructions with direct multiple LOS measurements are justified.

The author considers a hypothesis of neutron lifetime splitting in beta-decay and shows that the beta-decay of neutrons could be described by the triad of lifetimes tau_{Left}, tau_{Mean}, tau_{Right}. The lifetime tau_{Left} is the lifetime of L-neutrons emitting electrons against the neutron spin direction (L-type neutron decay). The lifetime tau_{Right} is the lifetime of R-neutrons emitting electrons in the direction of the neutron spin (R-type neutron decay). The lifetime tau_{Mean} is the arithmetic average of tau_{Left}, tau_{Right} or the mean neutron lifetime. While using the parameters of electron-spin asymmetry of neutron decay and the results for determining the mean neutron lifetime, the performed numerical estimates gave the numerical values of the triad tau_{Left}, tau_{Mean}, tau_{Right} as 813 s, 900 s and 987 s respectively. In addition to the estimates, the lifetimes of the triad are determined from experimental data applying the decay scale tuning method proposed by the author. The experimental values of the triad coincided with the estimates with high accuracy. The weighted average neutron lifetime tau_{W} determined from the experimental neutron lifetimes tau_{Left} and tau_{Right} is equal to tau_{W}=833.33 +- 0.02 s, and is in good agreement with the values of the neutron lifetime obtained by the other methods.

Multiple types of fluctuations impact the collective dynamics of power grids and thus challenge their robust operation. Fluctuations result from processes as different as dynamically changing demands, energy trading, and an increasing share of renewable power feed-in. Here we analyze principles underlying the dynamics and statistics of power grid frequency fluctuations. Considering frequency time series for a range of power grids, including grids in North America, Japan and Europe, we find a substantial deviation from Gaussianity best described as Lévy-stable and q-Gaussian distributions. We present a coarse framework to analytically characterize the impact of arbitrary noise distributions as well as a superstatistical approach which systematically interprets heavy tails and skewed distributions. We identify energy trading as a substantial contribution to today's frequency fluctuations and effective damping of the grid as a controlling factor enabling reduction of fluctuation risks, with enhanced effects for small power grids.