Inference of Time-Evolving Coupled Dynamical Systems in the Presence of Noise

A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of the coupling functions and other parameters to be followed. It is based on phase dynamics, with Bayesian inference of the time-evolving parameters achieved by shaping the prior densities to incorporate knowledge of previous samples. The method is tested numerically and applied to reveal and quantify the time-varying nature of cardiorespiratory interactions.Comment: 5 pages, 3 figures, accepted for Physical Review Letter

A Tutorial on Time-Evolving Dynamical Bayesian Inference

In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In practice many of the data-generating systems are not only time-variable, but also influenced by neighbouring systems and subject to random fluctuations (noise) from their environments. To encompass problems of this kind, we present a tutorial about the dynamical Bayesian inference of time-evolving coupled systems in the presence of noise. It includes the necessary theoretical description and the algorithms for its implementation. For general programming purposes, a pseudocode description is also given. Examples based on coupled phase and limit-cycle oscillators illustrate the salient features of phase dynamics inference. State domain inference is illustrated with an example of coupled chaotic oscillators. The applicability of the latter example to secure communications based on the modulation of coupling functions is outlined. MatLab codes for implementation of the method, as well as for the explicit examples, accompany the tutorial.Comment: Matlab codes can be found on http://py-biomedical.lancaster.ac.uk

4Ward: a Relayering Strategy for Efficient Training of Arbitrarily Complex Directed Acyclic Graphs

Thanks to their ease of implementation, multilayer perceptrons (MLPs) have become ubiquitous in deep learning applications. The graph underlying an MLP is indeed multipartite, i.e. each layer of neurons only connects to neurons belonging to the adjacent layer. In contrast, in vivo brain connectomes at the level of individual synapses suggest that biological neuronal networks are characterized by scale-free degree distributions or exponentially truncated power law strength distributions, hinting at potentially novel avenues for the exploitation of evolution-derived neuronal networks. In this paper, we present ``4Ward'', a method and Python library capable of generating flexible and efficient neural networks (NNs) from arbitrarily complex directed acyclic graphs. 4Ward is inspired by layering algorithms drawn from the graph drawing discipline to implement efficient forward passes, and provides significant time gains in computational experiments with various Erd\H{o}s-R\'enyi graphs. 4Ward not only overcomes the sequential nature of the learning matrix method, by parallelizing the computation of activations, but also addresses the scalability issues encountered in the current state-of-the-art and provides the designer with freedom to customize weight initialization and activation functions. Our algorithm can be of aid for any investigator seeking to exploit complex topologies in a NN design framework at the microscale

Beyond Multilayer Perceptrons: Investigating Complex Topologies in Neural Networks

In this study, we explore the impact of network topology on the approximation capabilities of artificial neural networks (ANNs), with a particular focus on complex topologies. We propose a novel methodology for constructing complex ANNs based on various topologies, including Barab\'asi-Albert, Erd\H{o}s-R\'enyi, Watts-Strogatz, and multilayer perceptrons (MLPs). The constructed networks are evaluated on synthetic datasets generated from manifold learning generators, with varying levels of task difficulty and noise. Our findings reveal that complex topologies lead to superior performance in high-difficulty regimes compared to traditional MLPs. This performance advantage is attributed to the ability of complex networks to exploit the compositionality of the underlying target function. However, this benefit comes at the cost of increased forward-pass computation time and reduced robustness to graph damage. Additionally, we investigate the relationship between various topological attributes and model performance. Our analysis shows that no single attribute can account for the observed performance differences, suggesting that the influence of network topology on approximation capabilities may be more intricate than a simple correlation with individual topological attributes. Our study sheds light on the potential of complex topologies for enhancing the performance of ANNs and provides a foundation for future research exploring the interplay between multiple topological attributes and their impact on model performance

Inferential framework for nonstationary dynamics. I. Theory.

A general Bayesian framework is introduced for the inference of time-varying parameters in nonstationary, nonlinear, stochastic dynamical systems. Its convergence is discussed. The performance of the method is analyzed in the context of detecting signaling in a system of neurons modeled as FitzHugh-Nagumo FHN oscillators. It is assumed that only fast action potentials for each oscillator mixed by an unknown measurement matrix can be detected. It is shown that the proposed approach is able to reconstruct unmeasured hidden variables of the FHN oscillators, to determine the model parameters, to detect stepwise changes of control parameters for each oscillator, and to follow continuous evolution of the control parameters in the adiabatic limit

Bayesian inferential framework for diagnosis of non-stationary systems

A Bayesian framework for parameter inference in non-stationary, nonlinear, stochastic, dynamical systems is introduced. It is applied to decode time variation of control parameters from time-series data modelling physiological signals. In this context a system of FitzHugh-Nagumo (FHN) oscillators is considered, for which synthetically generated signals are mixed via a measurement matrix. For each oscillator only one of the dynamical variables is assumed to be measured, while another variable remains hidden (unobservable). The control parameter for each FHN oscillator is varying in time. It is shown that the proposed approach allows one: (i) to reconstruct both unmeasured (hidden) variables of the FHN oscillators and the model parameters, (ii) to detect stepwise changes of control parameters for each oscillator, and (iii) to follow a continuous evolution of the control parameters in the quasi-adiabatic limit

Heritability of human "directed" functional connectome

IntroductionThe functional connectivity patterns in the brain are highly heritable; however, it is unclear how genetic factors influence the directionality of such "information flows." Studying the "directionality" of the brain functional connectivity and assessing how heritability modulates it can improve our understanding of the human connectome. MethodsHere, we investigated the heritability of "directed" functional connections using a state-space formulation of Granger causality (GC), in conjunction with blind deconvolution methods accounting for local variability in the hemodynamic response function. Such GC implementation is ideal to explore the directionality of functional interactions across a large number of networks. Resting-state functional magnetic resonance imaging data were drawn from the Human Connectome Project (total n = 898 participants). To add robustness to our findings, the dataset was randomly split into a "discovery" and a "replication" sample (each with n = 449 participants). The two cohorts were carefully matched in terms of demographic variables and other confounding factors (e.g., education). The effect of shared environment was also modeled. ResultsThe parieto- and prefronto-cerebellar, parieto-prefrontal, and posterior-cingulate to hippocampus connections showed the highest and most replicable heritability effects with little influence by shared environment. In contrast, shared environmental factors significantly affected the visuo-parietal and sensory-motor directed connectivity. ConclusionWe suggest a robust role of heritability in influencing the directed connectivity of some cortico-subcortical circuits implicated in cognition. Further studies, for example using task-based fMRI and GC, are warranted to confirm the asymmetric effects of genetic factors on the functional connectivity within cognitive networks and their role in supporting executive functions and learning

Multimodal and multicontrast image fusion via deep generative models

Recently, it has become progressively more evident that classic diagnostic labels are unable to reliably describe the complexity and variability of several clinical phenotypes. This is particularly true for a broad range of neuropsychiatric illnesses (e.g., depression, anxiety disorders, behavioral phenotypes). Patient heterogeneity can be better described by grouping individuals into novel categories based on empirically derived sections of intersecting continua that span across and beyond traditional categorical borders. In this context, neuroimaging data carry a wealth of spatiotemporally resolved information about each patient's brain. However, they are usually heavily collapsed a priori through procedures which are not learned as part of model training, and consequently not optimized for the downstream prediction task. This is because every individual participant usually comes with multiple whole-brain 3D imaging modalities often accompanied by a deep genotypic and phenotypic characterization, hence posing formidable computational challenges. In this paper we design a deep learning architecture based on generative models rooted in a modular approach and separable convolutional blocks to a) fuse multiple 3D neuroimaging modalities on a voxel-wise level, b) convert them into informative latent embeddings through heavy dimensionality reduction, c) maintain good generalizability and minimal information loss. As proof of concept, we test our architecture on the well characterized Human Connectome Project database demonstrating that our latent embeddings can be clustered into easily separable subject strata which, in turn, map to different phenotypical information which was not included in the embedding creation process. This may be of aid in predicting disease evolution as well as drug response, hence supporting mechanistic disease understanding and empowering clinical trials

Multivariate Granger causality unveils directed parietal to prefrontal cortex connectivity during task-free MRI.

While a large body of research has focused on the study of functional brain "connectivity", few investigators have focused on directionality of brain-brain interactions which, in spite of the mostly bidirectional anatomical substrates, cannot be assumed to be symmetrical. We employ a multivariate Granger Causality-based approach to estimating directed in-network interactions and quantify its advantages using extensive realistic synthetic BOLD data simulations to match Human Connectome Project (HCP) data specification. We then apply our framework to resting state functional MRI (rs-fMRI) data provided by the HCP to estimate the directed connectome of the human brain. We show that the functional interactions between parietal and prefrontal cortices commonly observed in rs-fMRI studies are not symmetrical, but consists of directional connectivity from parietal areas to prefrontal cortices rather than vice versa. These effects are localized within the same hemisphere and do not generalize to cross-hemispheric functional interactions. Our data are consistent with neurophysiological evidence that posterior parietal cortices involved in processing and integration of multi-sensory information modulate the function of more anterior prefrontal regions implicated in action control and goal-directed behaviour. The directionality of functional connectivity can provide an additional layer of information in interpreting rs-fMRI studies both in health and disease

A Parsimonious Granger Causality Formulation for Capturing Arbitrarily Long Multivariate Associations.

High-frequency neuroelectric signals like electroencephalography (EEG) or magnetoencephalography (MEG) provide a unique opportunity to infer causal relationships between local activity of brain areas. While causal inference is commonly performed through classical Granger causality (GC) based on multivariate autoregressive models, this method may encounter important limitations (e.g., data paucity) in the case of high dimensional data from densely connected systems like the brain. Additionally, physiological signals often present long-range dependencies which commonly require high autoregressive model orders/number of parameters. We present a generalization of autoregressive models for GC estimation based on Wiener-Volterra decompositions with Laguerre polynomials as basis functions. In this basis, the introduction of only one additional global parameter allows to capture arbitrary long dependencies without increasing model order, hence retaining model simplicity, linearity and ease of parameters estimation. We validate our method in synthetic data generated from families of complex, densely connected networks and demonstrate superior performance as compared to classical GC. Additionally, we apply our framework to studying the directed human brain connectome through MEG data from 89 subjects drawn from the Human Connectome Project (HCP) database, showing that it is able to reproduce current knowledge as well as to uncover previously unknown directed influences between cortical and limbic brain regions.MR