Estimation of the mixing kernel and the disturbance covariance in IDE-based spatiotemporal systems

The integro-difference equation (IDE) is an increasingly popular mathematical model of spatiotemporal processes, such as brain dynamics, weather systems, and disease spread. We present an efficient approach for system identification based on correlation techniques for linear temporal systems that extended to spatiotemporal IDE-based models. The method is derived from the average (over time) spatial correlations of observations to calculate closed-form estimates of the spatial mixing kernel and the disturbance covariance function. Synthetic data are used to demonstrate the performance of the estimation algorithm

The Neutrophil's Eye-View: Inference and Visualisation of the Chemoattractant Field Driving Cell Chemotaxis In Vivo

As we begin to understand the signals that drive chemotaxis in vivo, it is becoming clear that there is a complex interplay of chemotactic factors, which changes over time as the inflammatory response evolves. New animal models such as transgenic lines of zebrafish, which are near transparent and where the neutrophils express a green fluorescent protein, have the potential to greatly increase our understanding of the chemotactic process under conditions of wounding and infection from video microscopy data. Measurement of the chemoattractants over space (and their evolution over time) is a key objective for understanding the signals driving neutrophil chemotaxis. However, it is not possible to measure and visualise the most important contributors to in vivo chemotaxis, and in fact the understanding of the main contributors at any particular time is incomplete. The key insight that we make in this investigation is that the neutrophils themselves are sensing the underlying field that is driving their action and we can use the observations of neutrophil movement to infer the hidden net chemoattractant field by use of a novel computational framework. We apply the methodology to multiple in vivo neutrophil recruitment data sets to demonstrate this new technique and find that the method provides consistent estimates of the chemoattractant field across the majority of experiments. The framework that we derive represents an important new methodology for cell biologists investigating the signalling processes driving cell chemotaxis, which we label the neutrophils eye-view of the chemoattractant field

A spatiotemporal estimation framework for real-world LIDAR wind speed measurements

Despite significant advances in the remote sensing of fluid flows, light detection and ranging (LIDAR) measurement equipment still presents the problems of having only radial (line-of-sight) wind speed measurements (Cyclops' dilemma). Substantial expanses of unmeasured flow still remain and range weighting errors have a considerable influence on LIDAR measurements. Clearly, more information needs to be extracted from LIDAR data. With this motivation in mind, this brief shows that it is possible to estimate the wind velocity, wind direction, and absolute pressure over the entire spatial region of interest. A key challenge is that most established estimation techniques cater for systems that are finite-dimensional and described by ordinary differential equations (ODEs). By contrast, many fluid flows are governed by the Navier-Stokes equations, which are partial differential-algebraic equations (PDAEs). We show how a basis function decomposition method in conjunction with a pressure Poisson equation (PPE) formulation yields a spatially continuous, strangeness-free, reduced-order dynamic model for which a modified DAE form of the unscented Kalman filter (UKF) algorithm is used to estimate unmeasured velocities and pressure using sparse measurements from wind turbine-mounted LIDAR instruments. The approach is validated for both synthetic data generated from large eddy simulations of the atmospheric boundary layer and real-world LIDAR measurement data. Results show that a reconstruction of the flow field is achievable, thus presenting a validated estimation framework for potential applications including wind gust prediction systems and the preview control of wind turbines

Spatio-temporal bivariate statistical models for atmospheric trace-gas inversion

Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal fluxes using mole-fraction measurements and atmospheric simulations obtained from computer models. Studies to date are most often of a data-assimilation flavour, which implicitly consider univariate statistical models with the flux as the variate of interest. This univariate approach typically assumes that the flux field is either a spatially correlated Gaussian process or a spatially uncorrelated non-Gaussian process with prior expectation fixed using flux inventories (e.g., NAEI or EDGAR in Europe). Here, we extend this approach in three ways. First, we develop a bivariate model for the mole-fraction field and the flux field. The bivariate approach allows optimal prediction of both the flux field and the mole-fraction field, and it leads to significant computational savings over the univariate approach. Second, we employ a lognormal spatial process for the flux field that captures both the lognormal characteristics of the flux field (when appropriate) and its spatial dependence. Third, we propose a new, geostatistical approach to incorporate the flux inventories in our updates, such that the posterior spatial distribution of the flux field is predominantly data-driven. The approach is illustrated on a case study of methane (CH$_4$) emissions in the United Kingdom and Ireland.Comment: 39 pages, 8 figure

Spatiotemporal System Identification With Continuous Spatial Maps and Sparse Estimation.

We present a framework for the identification of spatiotemporal linear dynamical systems. We use a state-space model representation that has the following attributes: 1) the number of spatial observation locations are decoupled from the model order; 2) the model allows for spatial heterogeneity; 3) the model representation is continuous over space; and 4) the model parameters can be identified in a simple and sparse estimation procedure. The model identification procedure we propose has four steps: 1) decomposition of the continuous spatial field using a finite set of basis functions where spatial frequency analysis is used to determine basis function width and spacing, such that the main spatial frequency contents of the underlying field can be captured; 2) initialization of states in closed form; 3) initialization of state-transition and input matrix model parameters using sparse regression-the least absolute shrinkage and selection operator method; and 4) joint state and parameter estimation using an iterative Kalman-filter/sparse-regression algorithm. To investigate the performance of the proposed algorithm we use data generated by the Kuramoto model of spatiotemporal cortical dynamics. The identification algorithm performs successfully, predicting the spatiotemporal field with high accuracy, whilst the sparse regression leads to a compact model

Multi-Scale Process Modelling and Distributed Computation for Spatial Data

Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that modelling and prediction using infinite-dimensional process models is not possible with large data sets, and that both approximate models and, often, approximate-inference methods, are needed. The problem of fitting simple global spatial models to large data sets has been solved through the likes of multi-resolution approximations and nearest-neighbour techniques. Here we tackle the next challenge, that of fitting complex, nonstationary, multi-scale models to large data sets. We propose doing this through the use of superpositions of spatial processes with increasing spatial scale and increasing degrees of nonstationarity. Computation is facilitated through the use of Gaussian Markov random fields and parallel Markov chain Monte Carlo based on graph colouring. The resulting model allows for both distributed computing and distributed data. Importantly, it provides opportunities for genuine model and data scaleability and yet is still able to borrow strength across large spatial scales. We illustrate a two-scale version on a data set of sea-surface temperature containing on the order of one million observations, and compare our approach to state-of-the-art spatial modelling and prediction methods.Comment: 33 pages, 10 figures, 1 tabl

Model-based estimation of intra-cortical connectivity using electrophysiological data

This paper provides a new method for model-based estimation of intra-cortical connectivity from electrophysiological measurements. A novel closed-form solution for the connectivity function of the Amari neural field equations is derived as a function of electrophysiological observations. The resultant intra-cortical connectivity estimate is driven from experimental data, but constrained by the mesoscopic neurodynamics that are encoded in the computational model. A demonstration is provided to show how the method can be used to image physiological mechanisms that govern cortical dynamics, which are normally hidden in clinical data from epilepsy patients. Accurate estimation performance is demonstrated using synthetic data. Following the computational testing, results from patient data are obtained that indicate a dominant increase in surround inhibition prior to seizure onset that subsides in the cases when the seizures spread

Estimation of temporal and spatio-temporal nonlinear descriptor systems

As advances in the remote sensing of fluid flows forge ahead at an impressive rate, we face an increasingly compelling question of how best to exploit this progress. Light detection and ranging (LIDAR) measurement equipment still presents the problems of having only radial (line-of-sight) wind speed measurements (Cyclops' dilemma). Substantial expanses of unmeasured flow still remain and range weighting errors have a considerable influence on LIDAR measurements. Clearly, more information needs to be extracted from LIDAR data and an estimation problem naturally arises. A key challenge is that most established estimation techniques, such as Kalman filters, cater for systems that are finite-dimensional and described by ordinary differential equations (ODEs). By contrast, many fluid flows are governed by the Navier-Stokes equations, which are nonlinear partial differential-algebraic equations (PDAEs). With this motivation in mind, this thesis proposes a novel statistical signal processing framework for the model-based estimation of a class of spatio-temporal nonlinear partial differential-algebraic equations (PDAEs). The method employs finite-dimensional reduction that converts this formulation to a nonlinear DAE form for which new unscented transform-based filtering and smoothing algorithms are proposed. Gaussian approximations are derived for differential state variables and more importantly, extended to algebraic state variables. A mean-square error lower bound for the nonlinear descriptor filtering problem is obtained based on the posterior Cramér-Rao inequality. The potential of adopting a descriptor systems approach to spatio-temporal estimation is shown for a wind field estimation problem. A basis function decomposition method is used in conjunction with a pressure Poisson equation (PPE) formulation to yield a spatially-continuous, strangeness-free, reduced-order descriptor flow model which is used to estimate unmeasured wind velocities and pressure over the entire spatial region of interest using sparse measurements from wind turbine-mounted LIDAR instruments. The methodology is validated for both synthetic data generated from large eddy simulations of the atmospheric boundary layer and real-world LIDAR measurement data. Results show that a reconstruction of the flow field is achievable, thus presenting a validated estimation framework for potential applications including wind gust prediction systems, the preview control of wind turbines and other spatio-temporal descriptor systems spanning several disciplines