Adaptive, locally-linear models of complex dynamics

The dynamics of complex systems generally include high-dimensional, non-stationary and non-linear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties we detail a new approach based on local linear models within windows determined adaptively from the data. While the dynamics within each window are simple, consisting of exponential decay, growth and oscillations, the collection of local parameters across all windows provides a principled characterization of the full time series. To explore the resulting model space, we develop a novel likelihood-based hierarchical clustering and we examine the eigenvalues of the linear dynamics. We demonstrate our analysis with the Lorenz system undergoing stable spiral dynamics and in the standard chaotic regime. Applied to the posture dynamics of the nematode $C. elegans$ our approach identifies fine-grained behavioral states and model dynamics which fluctuate close to an instability boundary, and we detail a bifurcation in a transition from forward to backward crawling. Finally, we analyze whole-brain imaging in $C. elegans$ and show that the stability of global brain states changes with oxygen concentration.Comment: 25 pages, 16 figure

Evidence for chaotic behaviour in pulsar spin-down rates

We present evidence for chaotic dynamics within the spin-down rates of 17 pulsars originally presented by Lyne et al. Using techniques that allow us to re-sample the original measurements without losing structural information, we have searched for evidence of a strange attractor in the time series of frequency derivatives for each of the 17 pulsars. We demonstrate the effectiveness of our methods by applying them to a component of the Lorenz and R\"ossler attractors that were sampled with similar cadence to the pulsar time series. Our measurements of correlation dimension and Lyapunov exponent show that the underlying behaviour appears to be driven by a strange attractor with approximately three governing non-linear differential equations. This is particularly apparent in the case of PSR B1828$-$11 where a correlation dimension of 2.06\pm0.03 and a Lyapunov exponent of $(4.0\pm0.3)\times10^{-4}$ inverse days were measured. These results provide an additional diagnostic for testing future models of this behaviour.Comment: 15 pages, 18 figures, 2 tables, Accepted to MNRA

Foam: Multi-Dimensional General Purpose Monte Carlo Generator With Self-Adapting Simplical Grid

A new general purpose Monte Carlo event generator with self-adapting grid consisting of simplices is described. In the process of initialization, the simplex-shaped cells divide into daughter subcells in such a way that: (a) cell density is biggest in areas where integrand is peaked, (b) cells elongate themselves along hyperspaces where integrand is enhanced/singular. The grid is anisotropic, i.e. memory of the axes directions of the primary reference frame is lost. In particular, the algorithm is capable of dealing with distributions featuring strong correlation among variables (like ridge along diagonal). The presented algorithm is complementary to others known and commonly used in the Monte Carlo event generators. It is, in principle, more effective then any other one for distributions with very complicated patterns of singularities - the price to pay is that it is memory-hungry. It is therefore aimed at a small number of integration dimensions (<10). It should be combined with other methods for higher dimension. The source code in Fortran77 is available from http://home.cern.ch/~jadac

Surface profile prediction and analysis applied to turning process

An approach for the prediction of surface profile in turning process using Radial Basis Function (RBF) neural networks is presented. The input parameters of the RBF networks are cutting speed, depth of cut and feed rate. The output parameters are Fast Fourier Transform (FFT) vector of surface profile for the prediction of surface profile. The RBF networks are trained with adaptive optimal training parameters related to cutting parameters and predict surface profile using the corresponding optimal network topology for each new cutting condition. A very good performance of surface profile prediction, in terms of agreement with experimental data, was achieved with high accuracy, low cost and high speed. It is found that the RBF networks have the advantage over Back Propagation (BP) neural networks. Furthermore, a new group of training and testing data were also used to analyse the influence of tool wear and chip formation on prediction accuracy using RBF neural networks

Feature Representation for Online Signature Verification

Biometrics systems have been used in a wide range of applications and have improved people authentication. Signature verification is one of the most common biometric methods with techniques that employ various specifications of a signature. Recently, deep learning has achieved great success in many fields, such as image, sounds and text processing. In this paper, deep learning method has been used for feature extraction and feature selection.Comment: 10 pages, 10 figures, Submitted to IEEE Transactions on Information Forensics and Securit

Empowerment for Continuous Agent-Environment Systems

This paper develops generalizations of empowerment to continuous states. Empowerment is a recently introduced information-theoretic quantity motivated by hypotheses about the efficiency of the sensorimotor loop in biological organisms, but also from considerations stemming from curiosity-driven learning. Empowemerment measures, for agent-environment systems with stochastic transitions, how much influence an agent has on its environment, but only that influence that can be sensed by the agent sensors. It is an information-theoretic generalization of joint controllability (influence on environment) and observability (measurement by sensors) of the environment by the agent, both controllability and observability being usually defined in control theory as the dimensionality of the control/observation spaces. Earlier work has shown that empowerment has various interesting and relevant properties, e.g., it allows us to identify salient states using only the dynamics, and it can act as intrinsic reward without requiring an external reward. However, in this previous work empowerment was limited to the case of small-scale and discrete domains and furthermore state transition probabilities were assumed to be known. The goal of this paper is to extend empowerment to the significantly more important and relevant case of continuous vector-valued state spaces and initially unknown state transition probabilities. The continuous state space is addressed by Monte-Carlo approximation; the unknown transitions are addressed by model learning and prediction for which we apply Gaussian processes regression with iterated forecasting. In a number of well-known continuous control tasks we examine the dynamics induced by empowerment and include an application to exploration and online model learning