Model validation of spatiotemporal systems using correlation function tests

Model validation is an important and essential final step in system identification. Although model validation for nonlinear temporal systems has been extensively studied, model validation for spatiotemporal systems is still an open question. In this paper, correlation based methods, which have been successfully applied in nonlinear temporal systems are extended and enhanced to validate models of spatiotemporal systems. Examples are included to demonstrate the application of the tests

The identification of complex spatiotemporal patterns using Coupled map lattice model

Many complex and interesting spatiotemporal patterns have been observed in a wide range of scienti¯c areas. In this paper, two kinds of spatiotemporal patterns including spot replication and Turing systems are investigated and new identi¯cation methods are proposed to obtain Coupled Map Lattice (CML) models for this class of systems. Initially, a new correlation analysis method is introduced to determine an appropriate temporal and spatial data sampling step procedure for the identification of spatiotemporal systems. A new combined Orthogonal Forward Regression and Bayesian Learning algorithm with Laplace priors is introduced to identify sparse and robust CML models for complex spatiotemporal patterns. The final identified CML models are validated using correlation based model validation tests for spatiotemporal systems. Numerical re-sults illustrate the identification procedure and demonstrate the validity of the identified models

Online estimation of rollator user condition using spatiotemporal gait parameters

Assistance to people during rehabilitation has to be adapted to their needs. Too little help can lead to frustration and stress in the user; an excess of help may lead to low participation and loss of residual skills. Robotic rollators may adapt assistance. The main challenge to cope with this issue is to estimate how much help is needed on the fly, because it depends not only on the person condition, but also on the specific situation that they are negotiating. Clinical scales provide a global condition based estimation, but no local estimator based on punctual needs. Condition also changes in time, so clinical scales need to be recalculated again and again. In this paper we propose a novel approach to estimate users’ condition in a continuous way via a robotic rollator. Our work focuses on predicting the value of the well known Tinetti Mobility test from spatiotemporal gait parameters obtained from our platform while users walk. This prediction provides continuous insight on the condition of the user and could be used to modify the amount of help provided. The proposed method has been validated with 19 volunteers at a local hospital that use a rollator for rehabilitation. All volunteers presented some physical or mental disabilities. Our results sucessfully show a high correlation of spatiotemporal gait parameters with Tinetti Mobility test gait (R2 = 0.7) and Tinetti Mobility test balance (R2 = 0.6).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Using skewness and the first-digit phenomenon to identify dynamical transitions in cardiac models

Disruptions in the normal rhythmic functioning of the heart, termed as arrhythmia, often result from qualitative changes in the excitation dynamics of the organ. The transitions between different types of arrhythmia are accompanied by alterations in the spatiotemporal pattern of electrical activity that can be measured by observing the time-intervals between successive excitations of different regions of the cardiac tissue. Using biophysically detailed models of cardiac activity we show that the distribution of these time-intervals exhibit a systematic change in their skewness during such dynamical transitions. Further, the leading digits of the normalized intervals appear to fit Benford's law better at these transition points. This raises the possibility of using these observations to design a clinical indicator for identifying changes in the nature of arrhythmia. More importantly, our results reveal an intriguing relation between the changing skewness of a distribution and its agreement with Benford's law, both of which have been independently proposed earlier as indicators of regime shift in dynamical systems.Comment: 11 pages, 6 figures; incorporating changes as in the published versio

A Spatial and Temporal Autoregressive Local Estimation for the Paris Housing Market

This original study examines the potential of a spatiotemporal autoregressive Local (LSTAR) approach in modelling transaction prices for the housing market in inner Paris. We use a data set from the Paris Region notary office (“Chambre des notaires d’Île-de-France”) which consists of approximately 250,000 transactions units between the first quarter of 1990 and the end of 2005. We use the exact X -- Y coordinates and transaction date to spatially and temporally sort each transaction. We first choose to use the spatiotemporal autoregressive (STAR) approach proposed by Pace, Barry, Clapp and Rodriguez (1998). This method incorporates a spatiotemporal filtering process into the conventional hedonic function and attempts to correct for spatial and temporal correlative effects. We find significant estimates of spatial dependence effects. Moreover, using an original methodology, we find evidence of a strong presence of both spatial and temporal heterogeneity in the model. It suggests that spatial and temporal drifts in households socio-economic profiles and local housing market structure effects are certainly major determinants of the price level for the Paris Housing Market.Hedonic Prices; Heterogeneity; Paris Housing Market; STAR Model

Detecting multineuronal temporal patterns in parallel spike trains

We present a non-parametric and computationally efficient method that detects spatiotemporal firing patterns and pattern sequences in parallel spike trains and tests whether the observed numbers of repeating patterns and sequences on a given timescale are significantly different from those expected by chance. The method is generally applicable and uncovers coordinated activity with arbitrary precision by comparing it to appropriate surrogate data. The analysis of coherent patterns of spatially and temporally distributed spiking activity on various timescales enables the immediate tracking of diverse qualities of coordinated firing related to neuronal state changes and information processing. We apply the method to simulated data and multineuronal recordings from rat visual cortex and show that it reliably discriminates between data sets with random pattern occurrences and with additional exactly repeating spatiotemporal patterns and pattern sequences. Multineuronal cortical spiking activity appears to be precisely coordinated and exhibits a sequential organization beyond the cell assembly concept

Flexible regression models over river networks

Many statistical models are available for spatial data but the vast majority of these assume that spatial separation can be measured by Euclidean distance. Data which are collected over river networks constitute a notable and commonly occurring exception, where distance must be measured along complex paths and, in addition, account must be taken of the relative flows of water into and out of confluences. Suitable models for this type of data have been constructed based on covariance functions. The aim of the paper is to place the focus on underlying spatial trends by adopting a regression formulation and using methods which allow smooth but flexible patterns. Specifically, kernel methods and penalized splines are investigated, with the latter proving more suitable from both computational and modelling perspectives. In addition to their use in a purely spatial setting, penalized splines also offer a convenient route to the construction of spatiotemporal models, where data are available over time as well as over space. Models which include main effects and spatiotemporal interactions, as well as seasonal terms and interactions, are constructed for data on nitrate pollution in the River Tweed. The results give valuable insight into the changes in water quality in both space and time

Spatiotemporal Calibration of Atmospheric Nitrogen Dioxide Concentration Estimates From an Air Quality Model for Connecticut

A spatiotemporal calibration and resolution refinement model was fitted to calibrate nitrogen dioxide (NO$_2$) concentration estimates from the Community Multiscale Air Quality (CMAQ) model, using two sources of observed data on NO$_2$ that differed in their spatial and temporal resolutions. To refine the spatial resolution of the CMAQ model estimates, we leveraged information using additional local covariates including total traffic volume within 2 km, population density, elevation, and land use characteristics. Predictions from this model greatly improved the bias in the CMAQ estimates, as observed by the much lower mean squared error (MSE) at the NO$_2$ monitor sites. The final model was used to predict the daily concentration of ambient NO$_2$ over the entire state of Connecticut on a grid with pixels of size 300 x 300 m. A comparison of the prediction map with a similar map for the CMAQ estimates showed marked improvement in the spatial resolution. The effect of local covariates was evident in the finer spatial resolution map, where the contribution of traffic on major highways to ambient NO$_2$ concentration stands out. An animation was also provided to show the change in the concentration of ambient NO$_2$ over space and time for 1994 and 1995.Comment: 23 pages, 8 figures, supplementary materia