Publications

Abstract An isotropic dynamical system is one that looks the same in every direction, i.e., if we imagine - standing somewhere within an isotropic system, we would not be able to differentiate between different lines of sight. Conversely, anisotropy is a measure of the extent to which a system deviates from perfect isotropy, with larger values indicating greater discrepancies between the structure of the system along its axes. Here, we derive the form of a generalised scalable (mechanically similar) discretized field theoretic Lagrangian that allows for levels of anisotropy to be directly estimated via timeseries of arbitrary dimensionality. We generate synthetic data for both isotropic and anisotropic systems and, by using Bayesian model inversion and reduction, show that we can discriminate between the two datasets – thereby demonstrating proof of principle. We then apply this methodology to murine calcium imaging data collected in rest and task states, showing that anisotropy can be estimated directly from different brain states and cortical regions in an empirical in vivo biological setting. We hope that this theoretical foundation, together with the methodology and publicly available MATLAB code, will provide an accessible way for researchers to obtain new insight into the structural organization of neural systems in terms of how scalable neural regions grow – both ontogenetically during the development of an individual organism, as well as phylogenetically across species.

Current deep reinforcement learning (DRL) approaches achieve state-of-the-art performance in various domains, but struggle with data efficiency compared to human learning, which leverages core priors about objects and their interactions. Active inference offers a principled framework for integrating sensory information with prior knowledge to learn a world model and quantify the uncertainty of its own beliefs and predictions. However, active inference models are usually crafted for a single task with bespoke knowledge, so they lack the domain flexibility typical of DRL approaches. To bridge this gap, we propose a novel architecture that integrates a minimal yet expressive set of core priors about object-centric dynamics and interactions to accelerate learning in low-data regimes. The resulting approach, which we call AXIOM, combines the usual data efficiency and interpretability of Bayesian approaches with the across-task generalization usually associated with DRL. AXIOM represents scenes as compositions of objects, whose dynamics are modeled as piecewise linear trajectories that capture sparse object-object interactions. The structure of the generative model is expanded online by growing and learning mixture models from single events and periodically refined through Bayesian model reduction to induce generalization. AXIOM masters various games within only 10,000 interaction steps, with both a small number of parameters compared to DRL, and without the computational expense of gradient-based optimization.

Abstract Background Following stringent social distancing measures, some European countries are beginning to report a slowed or negative rate of growth of daily case numbers testing positive for the novel coronavirus. The notion that the first wave of infection is close to its peak begs the question of whether future peaks or ‘second waves’ are likely. We sought to determine the current size of the effective (i.e. susceptible) population for seven European countries—to estimate immunity levels following this first wave. We compare these numbers to the total population sizes of these countries, in order to investigate the potential for future peaks. Methods We used Bayesian model inversion to estimate epidemic parameters from the reported case and death rates from seven countries using data from late January 2020 to April 5 th 2020. Two distinct generative model types were employed: first a continuous time dynamical-systems implementation of a Susceptible-Exposed-Infectious-Recovered (SEIR) model and second: a partially observable Markov Decision Process (MDP) or hidden Markov model (HMM) implementation of an SEIR model. Both models parameterise the size of the initial susceptible population (‘S0’), as well as epidemic parameters. Parameter estimation (‘data fitting’) was performed using a standard Bayesian scheme (variational Laplace) designed to allow for latent unobservable states and uncertainty in model parameters. Results Both models recapitulated the dynamics of transmissions and disease as given by case and death rates. The peaks of the current waves were predicted to be in the past for four countries (Italy, Spain, Germany and Switzerland) and to emerge in 0.5 – 2 weeks in Ireland and 1-3 weeks in the UK. For France one model estimated the peak within the past week and the other in the future in two weeks. Crucially, Maximum a posteriori (MAP) estimates of S0 for each country indicated effective population sizes of below 20% (of total population size), under both the continuous time and HMM models. Using for all countries—with a Bayesian weighted average across all seven countries and both models, we estimated that 6.4% of the total population would be immune. From the two models the maximum percentage of the effective population was estimated at 19.6% of the total population for the UK, 16.7% for Ireland, 11.4% for Italy, 12.8% for Spain, 18.8% for France, 4.7% for Germany and 12.9% for Switzerland. Conclusion Our results indicate that after the current wave, a large proportion of the total population will remain without immunity. This suggests that in the absence of strong seasonal effects, new medications or more comprehensive contact tracing, a further set of epidemic waves in different geographic centres are likely. These findings may have implications for ‘exit strategies’ from any lockdown stage.

In this paper, we introduce an active inference model of ant colony foraging behavior, and implement the model in a series of in silico experiments. Active inference is a multiscale approach to behavioral modeling that is being applied across settings in theoretical biology and ethology. The ant colony is a classic case system in the function of distributed systems in terms of stigmergic decision-making and information sharing. Here we specify and simulate a Markov decision process (MDP) model for ant colony foraging. We investigate a well-known paradigm from laboratory ant colony behavioral experiments, the alternating T-maze paradigm, to illustrate the ability of the model to recover basic colony phenomena such as trail formation after food location discovery. We conclude by outlining how the active inference ant colony foraging behavioral model can be extended and situated within a nested multiscale framework and systems approaches to biology more generally.

The main question that Firestone & Scholl (F&S) pose is whether "what and how we see is functionally independent from what and how we think, know, desire, act, and so forth" (sect. 2, para. 1). We synthesize a collection of concerns from an interdisciplinary set of coauthors regarding F&S's assumptions and appeals to intuition, resulting in their treatment of visual perception as context-free.

The aim of this paper is to illustrate a method for identifying macroscopic anatomical differences among the brains of different populations of subjects. The method involves spatially normalizing the structural MR images of a number of subjects so that they all conform to the same stereotactic space. Multivariate statistics are then applied to the parameters describing the estimated nonlinear deformations that ensue. To illustrate the method, we compared the gross morphometry of male and female subjects. We also assessed brain asymmetry, the effect of handedness, and interactions among these effects. Hum. Brain Mapping 6:348–357, 1998. © 1998 Wiley-Liss, Inc.

Abstract Apathy is common in neurological disease, associated with poor prognosis and limited treatments. Current models posit that goal-directed actions are reduced because costs or effort outweigh the expected reward. We highlight an alternative account of apathy, based on the reduction in precision of prior beliefs about action outcomes. In this preregistered study, we test the hypothesis that precision is encoded in the GABAergic gain of prefrontal superficial pyramidal neurons. Fifty healthy adults undertook a goal-directed task during magnetoencephalography. Estimates of synaptic efficacy or gain were obtained by dynamic causal modelling of induced responses. There was strong evidence of a negative correlation between prior precision and apathy (Bayes Factor=12, p<0.01), and that prior precision was associated with gain in prefrontal and premotor neuronal populations (Posterior probability>0.99). The importance of prior precision and GABAergic gain for goal-directed actions opens new avenues to advance the understanding and treatment of apathy.

The characteristics and determinants of health and disease are often organised in space, reflecting our spatially extended nature. Understanding the influence of such factors requires models capable of capturing spatial relations. Though a mature discipline, spatial analysis is comparatively rare in medicine, arguably a consequence of the complexity of the domain and the inclemency of the data regimes that govern it. Drawing on statistical parametric mapping, a framework for topological inference well-established in the realm of neuroimaging, we propose and validate a novel approach to the spatial analysis of diverse clinical data - GeoSPM - based on differential geometry and random field theory. We evaluate GeoSPM across an extensive array of synthetic simulations encompassing diverse spatial relationships, sampling, and corruption by noise, and demonstrate its application on large-scale data from UK Biobank. GeoSPM is transparently interpretable, can be implemented with ease by non-specialists, enables flexible modelling of complex spatial relations, exhibits robustness to noise and under-sampling, offers well-founded criteria of statistical significance, and is through computational efficiency readily scalable to large datasets. We provide a complete, open-source software implementation of GeoSPM, and suggest that its adoption could catalyse the wider use of spatial analysis across the many aspects of medicine that urgently demand it.

Statistical Parametric Mapping (SPM) is an integrated set of methods for testing hypotheses about the brain's structure and function, using data from imaging devices. These methods are implemented in an open source software package, SPM, which has been in continuous development for more than 30 years by an international community of developers. This paper reports the release of SPM 25.01, a major new version of the software that incorporates novel analysis methods, optimisations of existing methods, as well as improved practices for open science and software development.