This paper presents a framework for creating neural field models from electrophysiological data. The Wilson and Cowan or Amari style neural field equations are used to form a parametric model, where the parameters are estimated from data. To illustrate the estimation framework, data is generated using the neural field equations incorporating modeled sensors enabling a comparison between the estimated and true parameters. To facilitate state and parameter estimation, we introduce a method to reduce the continuum neural field model using a basis function decomposition to form a finite-dimensional state-space model. Spatial frequency analysis methods are introduced that systematically specify the basis function configuration required to capture the dominant characteristics of the neural field. The estimation procedure consists of a two-stage iterative algorithm incorporating the unscented Rauch–Tung–Striebel smoother for state estimation and a least squares algorithm for parameter estimation. The results show that it is theoretically possible to reconstruct the neural field and estimate intracortical connectivity structure and synaptic dynamics with the proposed framework.

A continuous-in-space, discrete-in-time dynamic spatio-temporal model known as the integro-difference equation (IDE) model is presented in the context of data-driven modeling. A novel decomposition of the IDE is derived, leading to state-space representation that does not couple the number of states with the number of observation locations or the number of parameters. Based on this state-space model, an expectation-maximization (EM) algorithm is developed in order to jointly estimate the IDE model's spatial field and spatial mixing kernel. The resulting modeling framework is demonstrated on a set of examples.

Propagation Phase Contrast Synchrotron Microtomography (PPC-SRμCT) is the gold standard for non-invasive and non-destructive access to internal structures of archaeological remains. In this analysis, the virtual specimen needs to be segmented to separate different parts or materials, a process that normally requires considerable human effort. In the Automated SEgmentation of Microtomography Imaging (ASEMI) project, we developed a tool to automatically segment these volumetric images, using manually segmented samples to tune and train a machine learning model. For a set of four specimens of ancient Egyptian animal mummies we achieve an overall accuracy of 94–98% when compared with manually segmented slices, approaching the results of off-the-shelf commercial software using deep learning (97–99%) at much lower complexity. A qualitative analysis of the segmented output shows that our results are close in terms of usability to those from deep learning, justifying the use of these techniques.

A state space model of the stochastic spatio-temporal integro-difference equation (IDE) is derived. Based on multidimensional sampling theory, the dimensions of the state space and parameter space of the model are identified from the spatial bandwidth of the system and the support of the redistribution kernel of the IDE. When both the bandwidth and the kernel support are unknown, a method to propose a number of state space and parameter space dimensions is presented. These chosen dimensions result in a number of candidate model structures. Bayesian model selection, making use of Bayes factor, the data augmentation algorithm and importance sampling, is then used to identify the model best suited to represent the data in a maximum a posteriori sense.

An online dual estimation algorithm is developed to jointly estimate in real-time traffic quantities such as queue lengths, occupancies and flows, as well as the parameters of a macroscopic model of a signalized junction. These parameters include turning ratios and saturation flows, together with model uncertainties. The proposed novel methodology is based on the Expectation-Maximization algorithm, modified for real-time estimation, with a Kalman filter implementing the expectation step and a multivariate gradient-based approach for the maximisation step. The algorithm is validated by simulating the typical signalized 3-arm and 4-arm junctions. This work is aimed to form a part of the adaptive control loops for traffic light systems that are able to autonomously adjust with changing traffic conditions, so as to ensure efficient vehicle flows.

Neural fields are spatially continuous state variables described by integro-differential equations, which are well suited to describe the spatiotemporal evolution of cortical activations on multiple scales. Here we develop a multi-resolution approximation (MRA) framework for the integro-difference equation (IDE) neural field model based on semi-orthogonal cardinal B-spline wavelets. In this way, a flexible framework is created, whereby both macroscopic and microscopic behavior of the system can be represented simultaneously. State and parameter estimation is performed using the expectation maximization (EM) algorithm. A synthetic example is provided to demonstrate the framework.