Parallels between the dynamics at the noise-perturbed onset of chaos in logistic maps and the dynamics of glass formation

We develop the characterization of the dynamics at the noise-perturbed edge of chaos in logistic maps in terms of the quantities normally used to describe glassy properties in structural glass formers. Following the recognition [Phys. Lett. \textbf{A 328}, 467 (2004)] that the dynamics at this critical attractor exhibits analogies with that observed in thermal systems close to vitrification, we determine the modifications that take place with decreasing noise amplitude in ensemble and time averaged correlations and in diffusivity. We corroborate explicitly the occurrence of two-step relaxation, aging with its characteristic scaling property, and subdiffusion and arrest for this system. We also discuss features that appear to be specific of the map.Comment: Revised version with substantial improvements. Revtex, 8 pages, 11 figure

Public Channel Cryptography: Chaos Synchronization and Hilbert's Tenth Problem

The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signal is concealed by two commutative private filters that are placed on each end of the communication channel. We demonstrate that when the transmitted signal is a convolution of the truncated time delayed output signals or some powers of the delayed output signals synchronization is still maintained. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-Complete problems. This bridge between two different disciplines, synchronization in nonlinear dynamical processes and the realm of the NPC problems, opens a horizon for a new type of secure public-channel protocols

Towards Interpretable Deep Learning Models for Knowledge Tracing

As an important technique for modeling the knowledge states of learners, the traditional knowledge tracing (KT) models have been widely used to support intelligent tutoring systems and MOOC platforms. Driven by the fast advancements of deep learning techniques, deep neural network has been recently adopted to design new KT models for achieving better prediction performance. However, the lack of interpretability of these models has painfully impeded their practical applications, as their outputs and working mechanisms suffer from the intransparent decision process and complex inner structures. We thus propose to adopt the post-hoc method to tackle the interpretability issue for deep learning based knowledge tracing (DLKT) models. Specifically, we focus on applying the layer-wise relevance propagation (LRP) method to interpret RNN-based DLKT model by backpropagating the relevance from the model's output layer to its input layer. The experiment results show the feasibility using the LRP method for interpreting the DLKT model's predictions, and partially validate the computed relevance scores from both question level and concept level. We believe it can be a solid step towards fully interpreting the DLKT models and promote their practical applications in the education domain

Do columnar defects produce bulk pinning?

From magneto-optical imaging performed on heavy-ion irradiated YBaCuO single crystals, it is found that at fields and temperatures where strong single vortex pinning by individual irradiation-induced amorphous columnar defects is to be expected, vortex motion is limited by the nucleation of vortex kinks at the specimen surface rather than by half-loop nucleation in the bulk. In the material bulk, vortex motion occurs through (easy) kink sliding. Depinning in the bulk determines the screening current only at fields comparable to or larger than the matching field, at which the majority of moving vortices is not trapped by an ion track.Comment: 5 pages, 5 figures, submitted to Physical Review Letter

Nonextensive Pesin identity. Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map

We show that the dynamical and entropic properties at the chaos threshold of the logistic map are naturally linked through the nonextensive expressions for the sensitivity to initial conditions and for the entropy. We corroborate analytically, with the use of the Feigenbaum renormalization group(RG) transformation, the equality between the generalized Lyapunov coefficient $\lambda_{q}$ and the rate of entropy production $K_{q}$ given by the nonextensive statistical mechanics. Our results advocate the validity of the $q$-generalized Pesin identity at critical points of one-dimensional nonlinear dissipative maps.Comment: Revtex, 5 pages, 3 figure

Sensitivity to initial conditions at bifurcations in one-dimensional nonlinear maps: rigorous nonextensive solutions

Using the Feigenbaum renormalization group (RG) transformation we work out exactly the dynamics and the sensitivity to initial conditions for unimodal maps of nonlinearity $\zeta >1$ at both their pitchfork and tangent bifurcations. These functions have the form of $q$-exponentials as proposed in Tsallis' generalization of statistical mechanics. We determine the $q$-indices that characterize these universality classes and perform for the first time the calculation of the $q$-generalized Lyapunov coefficient $\lambda_{q}$. The pitchfork and the left-hand side of the tangent bifurcations display weak insensitivity to initial conditions, while the right-hand side of the tangent bifurcations presents a `super-strong' (faster than exponential) sensitivity to initial conditions. We corroborate our analytical results with {\em a priori} numerical calculations.Comment: latex, 4 figures. Updated references and some general presentation improvements. To appear published in Europhysics Letter

The large scale dynamics of the outer heliosphere and the long-term modulation of galactic cosmic rays

The network of cosmic ray observatories reaching across the heliosphere has given new insight into the process of solar modulation, establishing that the decreases occur principally in the outer heliosphere and are produced by interplanetary flow systems; that the hysteresis effects appear to be produced by changes in the rigidity dependence of the diffusion coefficient and that the predicted effects on the cosmic ray gradients associated with the reversal of the solar magnetic field polarity are not observed

Rotational modulation of X-ray emission in Orion Nebula young stars

We investigate the spatial distribution of X-ray emitting plasma in a sample of young Orion Nebula Cluster stars by modulation of their X-ray light-curves due to stellar rotation. The study, part of the Chandra Orion Ultradeep Project (COUP), is made possible by the exceptional length of the observation: 10 days of ACIS integration during a time span of 13 days, yielding a total of 1616 detected sources in the 17x17 arcmin field of view. We here focus on a subsample of 233 X-ray-bright stars with known rotational periods. We search for X-ray modulation using the Lomb Normalized Periodogram method. X-ray modulation related to the rotation period is detected in at least 23 stars with periods between 2 and 12 days and relative amplitudes ranging from 20% to 70%. In 16 cases, the X-ray modulation period is similar to the stellar rotation period while in seven cases it is about half that value, possibly due to the presence of X-ray emitting structures at opposite stellar longitudes. These results constitute the largest sample of low mass stars in which X-ray rotational modulation has been observed. The detection of rotational modulation indicates that the X-ray emitting regions are distributed inhomogeneneously in longitude and do not extend to distances significantly larger than the stellar radius. Modulation is observed in stars with saturated activity levels (L_X/L_bol ~ 10^(-3)) showing that saturation is not due to the filling of the stellar surface with X-ray emitting regions.Comment: 41 pages, 15 figures, ApJS in press. Figure 15 (34 panels) is an on-line only figure and is not included. A pdf file which includes figure 15 as well as full resolution versions of figure 10 and 11 is available at: http://www.astropa.unipa.it/~ettoref/COUP_RotMod.pd

Caby Photometry of the Hyades: Comparisons to the Field Stars

Intermediate-band photometry of the Hyades cluster on the Caby system is presented for dwarf stars ranging from spectral type A through late K. A mean hk, b-y relation is constructed using only single stars without anomalous atmospheres and compared to the field stars of the solar neighborhood. For the F dwarfs, the Hyades relation defines an approximate LOWER bound in the two-color diagram, consistent with an [Fe/H] between +0.10 and +0.15. These index-color diagrams follow the common convention of presenting stars with highest abundance at the bottom of the plot although the index values for the metal-rich stars are numerically larger. For field F dwarfs in the range [Fe/H] between +0.4 and -1.0, [Fe/H] = -5.6 delta-hk + 0.125, with no evidence for a color dependence in the slope. For the G and K dwarfs, the Hyades mean relation crosses the field star distribution in the two-color diagram, defining an approximate UPPER bound for the local disk stars. Stars found above the Hyades stars fall in at least one of three categories: [Fe/H] below -0.7, [Fe/H] above that of the Hyades, or chromospherically active. It is concluded that, contrary to the predictions of model atmospheres, the hk index for cool dwarfs at a given color hits a maximum value for stars below solar composition and, with increasing [Fe/H] above some critical value, declines. This trend is consistent, however, with the predictions from synthetic indices based upon much narrower Ca filters where the crossover is caused by the metallicity sensitivity of b-y.Comment: 13 pages, 9 eps figures, 1 tex table, 1 ascii tabl

Anomalous diffusion in the dynamics of complex processes

Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively small time intervals. This paper proposes an interpolation expression for the identification of anomalous diffusion in complex signals for the cases when the dynamics of the system under study reaches a steady state (large time intervals). This interpolation expression uses the chaotic difference moment (transient structural function) of the second order as an average characteristic of displacements. A general procedure for identifying anomalous diffusion and calculating its parameters in real stochastic signals, which includes the removal of the regular (low-frequency) components from the source signal and the fitting of the chaotic part of the experimental difference moment of the second order to the interpolation expression, is presented. The procedure was applied to the analysis of the dynamics of magnetoencephalograms, blinking fluorescence of quantum dots, and X-ray emission from accreting objects. For all three applications, the interpolation was able to adequately describe the chaotic part of the experimental difference moment, which implies that anomalous diffusion manifests itself in these natural signals. The results of this study make it possible to broaden the range of complex natural processes in which anomalous diffusion can be identified. The relation between the interpolation expression and a diffusion model, which is derived in the paper, allows one to simulate the chaotic processes in the open complex systems with anomalous diffusion.Comment: 47 pages, 15 figures; Submitted to Physical Review