Scaling Analysis and Evolution Equation of the North Atlantic Oscillation Index Fluctuations

The North Atlantic Oscillation (NAO) monthly index is studied from 1825 till 2002 in order to identify the scaling ranges of its fluctuations upon different delay times and to find out whether or not it can be regarded as a Markov process. A Hurst rescaled range analysis and a detrended fluctuation analysis both indicate the existence of weakly persistent long range time correlations for the whole scaling range and time span hereby studied. Such correlations are similar to Brownian fluctuations. The Fokker-Planck equation is derived and Kramers-Moyal coefficients estimated from the data. They are interpreted in terms of a drift and a diffusion coefficient as in fluid mechanics. All partial distribution functions of the NAO monthly index fluctuations have a form close to a Gaussian, for all time lags, in agreement with the findings of the scaling analyses. This indicates the lack of predictive power of the present NAO monthly index. Yet there are some deviations for large (and thus rare) events. Whence suggestions for other measurements are made if some improved predictability of the weather/climate in the North Atlantic is of interest. The subsequent Langevin equation of the NAO signal fluctuations is explicitly written in terms of the diffusion and drift parameters, and a characteristic time scale for these is given in appendix.Comment: 6 figures, 54 refs., 16 pages; submitted to Int. J. Mod. Phys. C: Comput. Phy

On human motion prediction using recurrent neural networks

Human motion modelling is a classical problem at the intersection of graphics and computer vision, with applications spanning human-computer interaction, motion synthesis, and motion prediction for virtual and augmented reality. Following the success of deep learning methods in several computer vision tasks, recent work has focused on using deep recurrent neural networks (RNNs) to model human motion, with the goal of learning time-dependent representations that perform tasks such as short-term motion prediction and long-term human motion synthesis. We examine recent work, with a focus on the evaluation methodologies commonly used in the literature, and show that, surprisingly, state-of-the-art performance can be achieved by a simple baseline that does not attempt to model motion at all. We investigate this result, and analyze recent RNN methods by looking at the architectures, loss functions, and training procedures used in state-of-the-art approaches. We propose three changes to the standard RNN models typically used for human motion, which result in a simple and scalable RNN architecture that obtains state-of-the-art performance on human motion prediction.Comment: Accepted at CVPR 1

On the Projective Geometry of Kalman Filter

Convergence of the Kalman filter is best analyzed by studying the contraction of the Riccati map in the space of positive definite (covariance) matrices. In this paper, we explore how this contraction property relates to a more fundamental non-expansiveness property of filtering maps in the space of probability distributions endowed with the Hilbert metric. This is viewed as a preliminary step towards improving the convergence analysis of filtering algorithms over general graphical models.Comment: 6 page

Statistical Derivation of the Evolution Equation of Liquid Water Path Fluctuations in Clouds

How to distinguish and quantify deterministic and random influences on the statistics of turbulence data in meteorology cases is discussed from first principles. Liquid water path (LWP) changes in clouds, as retrieved from radio signals, upon different delay times, can be regarded as a stochastic Markov process. A detrended fluctuation analysis method indicates the existence of long range time correlations. The Fokker-Planck equation which models very precisely the LWP $fluctuation$ empirical probability distributions, in particular, their non-Gaussian heavy tails is explicitly derived and written in terms of a drift and a diffusion coefficient. Furthermore, Kramers-Moyal coefficients, as estimated from the empirical data, are found to be in good agreement with their first principle derivation. Finally, the equivalent Langevin equation is written for the LWP increments themselves. Thus rather than the existence of hierarchical structures, like an energy cascade process, {\it strong correlations} on different $time$ $scales$, from small to large ones, are considered to be proven as intrinsic ingredients of such cloud evolutions.Comment: 17 pages, 6 figures; to be published in Journal of Geophysical Research - Atmosphere

Maximum Likelihood Estimation of ARMA Model with Error Processes for Replicated Observations

In this paper we analyse the repeated time series model where the fundamental component follows a ARMA process. In the model, the error variance as well as the number of repetition are allowed to change over time. It is shown that the model is identified. The maximum likelihood estimator is derived using the Kalman filter technique. The model considered in this paper can be considered as extension of the models considered by Anderson (1978), Azzalini (1981) and Wong and Miller (1990)ARMA model, Kalman filter, maximum likelihood estimation