Causality analysis of groundwater dynamics based on a Vector Autoregressive model in the semi-arid basin of Gundal (South India)

Causal relationships existing between observed levels of groundwater in a semi-arid sub-basin of the Kabini River basin (Karnataka state, India) are investigated in this study. A Vector Auto Regressive model is used for this purpose. Its structure is built on an upstream/downstream interaction network based on observed hydro-physical properties. Exogenous climatic forcing is used as an input based on cumulated rainfall departure. Optimal models are obtained thanks to a trial approach and are used as a proxy of the dynamics to derive causal networks. It appears to be an interesting tool for analysing the causal relationships existing inside the basin. The causal network reveals 3 main regions: the Northeastern part of the Gundal basin is closely coupled to the outlet dynamics. The Northwestern part is mainly controlled by the climatic forcing and only marginally linked to the outlet dynamic. Finally, the upper part of the basin plays as a forcing rather than a coupling with the lower part of the basin allowing for a separate analysis of this local behaviour. The analysis also reveals differential time scales at work inside the basin when comparing upstream oriented with downstream oriented causalities. In the upper part of the basin, time delays are close to 2 months in the upward direction and lower than 1 month in the downward direction. These time scales are likely to be good indicators of the hydraulic response time of the basin which is a parameter usually difficult to estimate practically. This suggests that, at the sub-basin scale, intra-annual time scales would be more relevant scales for analysing or modelling tropical basin dynamics in hard rock (granitic and gneissic) aquifers ubiquitous in south India. (c) 2012 Elsevier B.V. All rights reserved.

Velocity Fluctuations in Helical Propulsion: How Small Can a Propeller Be

Helical propulsion is at the heart of locomotion strategies utilized by various natural and artificial swimmers. We used experimental observations and a numerical model to study the various fluctuation mechanisms that determine the performance of an externally driven helical propeller as the size of the helix is reduced. From causality analysis, an overwhelming effect of orientational noise at low length scales is observed, which strongly affects the average velocity and direction of motion of a propeller. For length scales smaller than a few micrometers in aqueous media, the operational frequency for the propulsion system would have to increase as the inverse cube of the size, which can be the limiting factor for a helical propeller to achieve locomotion in the desired direction.

Analyzing multiple spike trains with nonparametric granger causality

Simultaneous recordings of spike trains from multiple single neurons are becoming commonplace. Understanding the interaction patterns among these spike trains remains a key research area. A question of interest is the evaluation of information flow between neurons through the analysis of whether one spike train exerts causal influence on another. For continuous-valued time series data, Granger causality has proven an effective method for this purpose. However, the basis for Granger causality estimation is autoregressive data modeling, which is not directly applicable to spike trains. Various filtering options distort the properties of spike trains as point processes. Here we propose a new nonparametric approach to estimate Granger causality directly from the Fourier transforms of spike train data. We validate the method on synthetic spike trains generated by model networks of neurons with known connectivity patterns and then apply it to neurons limultaneously recorded from the thalamus and the primary somatosensory cortex of a squirrel monkey undergoing tactile stimulation.

Effect of measurement noise on Granger causality

Most of the signals recorded in experiments are inevitably contaminated by measurement noise. Hence, it is important to understand the effect of such noise on estimating causal relations between such signals. A primary tool for estimating causality is Granger causality. Granger causality can be computed by modeling the signal using a bivariate autoregressive (AR) process. In this paper, we greatly extend the previous analysis of the effect of noise by considering a bivariate AR process of general order p. From this analysis, we analytically obtain the dependence of Granger causality on various noise-dependent system parameters. In particular, we show that measurement noise can lead to spurious Granger causality and can suppress true Granger causality. These results are verified numerically. Finally, we show how true causality can be recovered numerically using the Kalman expectation maximization algorithm.

A Cause and Effect Analysis of Motion Trajectories for Modeling Actions

An action is typically composed of different parts of the object moving in particular sequences. The presence of different motions (represented as a 1D histogram) has been used in the traditional bag-of-words (BoW) approach for recognizing actions. However the interactions among the motions also form a crucial part of an action. Different object-parts have varying degrees of interactions with the other parts during an action cycle. It is these interactions we want to quantify in order to bring in additional information about the actions. In this paper we propose a causality based approach for quantifying the interactions to aid action classification. Granger causality is used to compute the cause and effect relationships for pairs of motion trajectories of a video. A 2D histogram descriptor for the video is constructed using these pairwise measures. Our proposed method of obtaining pairwise measures for videos is also applicable for large datasets. We have conducted experiments on challenging action recognition databases such as HMDB51 and UCF50 and shown that our causality descriptor helps in encoding additional information regarding the actions and performs on par with the state-of-the art approaches. Due to the complementary nature, a further increase in performance can be observed by combining our approach with state-of-the-art approaches.