Bayesian brain computing and the free-energy principle: an interview with Karl Friston.

The free-energy principle entails the Bayesian brain hypothesis that can be implemented by many schemes considered in this field. The combination of multimodal brain imaging and free-energy minimization has shown promise in unraveling complex brain dynamics and understanding the interactions among distinct brain regions. The Bayesian mechanics of brain computing gives a unique route to understanding authentic (neuromimetic) intelligence and, more importantly, points towards the development of brain-inspired intelligence. NSR spoke to a leading theoretical neuroscientist and authority on brain imaging-Karl Friston, the inventor of statistical parametric mapping, voxel-based morphometry and dynamic causal modeling. Friston is also known for his contributions to theoretical biology in the form of the free-energy principle and applications such as active inference. Friston is currently the Scientific Director of the Wellcome Trust Centre for Neuroimaging, Professor of Neuroscience at Queen Square Institute of Neurology, University College London and Honorary Consultant at The National Hospital for Neurology and Neurosurgery, UK.

Imitating and exploring the human brain's resting and task-performing states via brain computing: scaling and architecture.

A computational human brain model with the voxel-wise assimilation method was established based on individual structural and functional imaging data. We found that the more similar the brain model is to the biological counterpart in both scale and architecture, the more similarity was found between the assimilated model and the biological brain both in resting states and during tasks by quantitative metrics. The hypothesis that resting state activity reflects internal body states was validated by the interoceptive circuit's capability to enhance the similarity between the simulation model and the biological brain. We identified that the removal of connections from the primary visual cortex (V1) to downstream visual pathways significantly decreased the similarity at the hippocampus between the model and its biological counterpart, despite a slight influence on the whole brain. In conclusion, the model and methodology present a solid quantitative framework for a digital twin brain for discovering the relationship between brain architecture and functions, and for digitally trying and testing diverse cognitive, medical and lesioning approaches that would otherwise be unfeasible in real subjects.

A general description of criticality in neural network models.

Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A comprehensive study of how criticality emerges and how to reproduce it is still lacking. In this study, we investigate coupled networks with conductance-based neurons and illustrate the co-existence of different spiking patterns, including asynchronous irregular (AI) firing and synchronous regular (SR) state, along with a scale-invariant neuronal avalanche phenomenon (criticality). We show that fast-acting synaptic coupling can evoke neuronal avalanches in the mean-dominated regime but has little effect in the fluctuation-dominated regime. In a narrow region of parameter space, the network exhibits avalanche dynamics with power-law avalanche size and duration distributions. We conclude that three stages which may be responsible for reproducing the synchronized bursting: mean-dominated subthreshold dynamics, fast-initiating a spike event, and time-delayed inhibitory cancellation. Remarkably, we illustrate the mechanisms underlying critical avalanches in the presence of noise, which can be explained as a stochastic crossing state around the Hopf bifurcation under the mean-dominated regime. Moreover, we apply the ensemble Kalman filter to determine and track effective connections for the neuronal network. The method is validated on noisy synthetic BOLD signals and could exactly reproduce the corresponding critical network activity. Our results provide a special perspective to understand and model the criticality, which can be useful for large-scale modeling and computation of brain dynamics.

On a framework of data assimilation for hyperparameter estimation of spiking neuronal networks.

When handling real-world data modeled by a complex network dynamical system, the number of the parameters is often much more than the size of the data. Therefore, in many cases, it is impossible to estimate these parameters and the exact value of each parameter is frequently less interesting than the distribution of the parameters. In this paper, we aim to estimate the distribution of the parameters in the mesoscopic neuronal network model from the macroscopic experimental data, for example, the BOLD (blood oxygen level dependent) signal. Herein, we assume that the parameters of the neurons and synapses are inhomogeneous but independently and identically distributed from certain distributions with unknown hyperparameters. Thus, we estimate these hyperparameters of the distributions of the parameters, instead of estimating the parameters themselves. We formulate this problem under the framework of data assimilation and hierarchical Bayesian method and present an efficient method named Hierarchical Data Assimilation (HDA) to conduct the statistical inference on the neuronal network model with the BOLD signal data simulated by the hemodynamic model. We consider the Leaky Integral-Fire (LIF) neuronal networks with four synapses and show that the proposed algorithm can estimate the BOLD signals and the hyperparameters with high preciseness. In addition, we discuss the influence on the performance of the algorithm configuration and the LIF network model setup.

Intralayer Synchronization and Interlayer Quasisynchronization in Multiplex Networks of Nonidentical Layers.

In this article, we discuss synchronization in multiplex networks of different layers. Both the topologies and the uncoupled node dynamics in different layers are different. Novel sufficient criteria are derived for intralayer synchronization and interlayer quasisynchronization, in terms of the coupling matrices, the coupling strengths, and the intrinsic function of the uncoupled systems. We also investigate interlayer synchronization of multiplex networks with identical uncoupled node dynamics. Finally, we give some numerical examples to validate the effectiveness of these theoretical results.

Self-Organization of Nonlinearly Coupled Neural Fluctuations Into Synergistic Population Codes.

Neural activity in the brain exhibits correlated fluctuations that may strongly influence the properties of neural population coding. However, how such correlated neural fluctuations may arise from the intrinsic neural circuit dynamics and subsequently affect the computational properties of neural population activity remains poorly understood. The main difficulty lies in resolving the nonlinear coupling between correlated fluctuations with the overall dynamics of the system. In this study, we investigate the emergence of synergistic neural population codes from the intrinsic dynamics of correlated neural fluctuations in a neural circuit model capturing realistic nonlinear noise coupling of spiking neurons. We show that a rich repertoire of spatial correlation patterns naturally emerges in a bump attractor network and further reveals the dynamical regime under which the interplay between differential and noise correlations leads to synergistic codes. Moreover, we find that negative correlations may induce stable bound states between two bumps, a phenomenon previously unobserved in firing rate models. These noise-induced effects of bump attractors lead to a number of computational advantages including enhanced working memory capacity and efficient spatiotemporal multiplexing and can account for a range of cognitive and behavioral phenomena related to working memory. This study offers a dynamical approach to investigating realistic correlated neural fluctuations and insights to their roles in cortical computations.

Basis operator network: A neural network-based model for learning nonlinear operators via neural basis.

It is widely acknowledged that neural networks can approximate any continuous (even measurable) functions between finite-dimensional Euclidean spaces to arbitrary accuracy. Recently, the use of neural networks has started emerging in infinite-dimensional settings. Universal approximation theorems of operators guarantee that neural networks can learn mappings between infinite-dimensional spaces. In this paper, we propose a neural network-based method (BasisONet) capable of approximating mappings between function spaces. To reduce the dimension of an infinite-dimensional space, we propose a novel function autoencoder that can compress the function data. Our model can predict the output function at any resolution using the corresponding input data at any resolution once trained. Numerical experiments demonstrate that the performance of our model is competitive with existing methods on the benchmarks, and our model can address the data on a complex geometry with high precision. We further analyze some notable characteristics of our model based on the numerical results.

SEPRES: Intensive Care Unit Clinical Data Integration System to Predict Sepsis.

BACKGROUND: The lack of information interoperability between different devices and systems in the intensive care unit (ICU) hinders further utilization of data, especially for early warning of specific diseases in the ICU. OBJECTIVES: We aimed to establish a data integration system. Based on this system, the sepsis prediction module was added to compose the Sepsis PREdiction System (SEPRES), where real-time early warning of sepsis can be implemented at the bedside in the ICU. METHODS: Data are collected from bedside devices through the integration hub and uploaded to the integration system through the local area network. The data integration system was designed to integrate vital signs data, laboratory data, ventilator data, demographic data, pharmacy data, nursing data, etc. from multiple medical devices and systems. It integrates, standardizes, and stores information, making the real-time inference of the early warning module possible. The built-in sepsis early warning module can detect the onset of sepsis within 5 hours preceding at most. RESULTS: Our data integration system has already been deployed in Ruijin Hospital, confirming the feasibility of our system. CONCLUSION: We highlight that SEPRES has the potential to improve ICU management by helping medical practitioners identify at-sepsis-risk patients and prepare for timely diagnosis and intervention.

Transferability and interpretability of the sepsis prediction models in the intensive care unit.

BACKGROUND: We aimed to develop an early warning system for real-time sepsis prediction in the ICU by machine learning methods, with tools for interpretative analysis of the predictions. In particular, we focus on the deployment of the system in a target medical center with small historical samples. METHODS: Light Gradient Boosting Machine (LightGBM) and multilayer perceptron (MLP) were trained on Medical Information Mart for Intensive Care (MIMIC-III) dataset and then finetuned on the private Historical Database of local Ruijin Hospital (HDRJH) using transfer learning technique. The Shapley Additive Explanations (SHAP) analysis was employed to characterize the feature importance in the prediction inference. Ultimately, the performance of the sepsis prediction system was further evaluated in the real-world study in the ICU of the target Ruijin Hospital. RESULTS: The datasets comprised 6891 patients from MIMIC-III, 453 from HDRJH, and 67 from Ruijin real-world data. The area under the receiver operating characteristic curves (AUCs) for LightGBM and MLP models derived from MIMIC-III were 0.98 - 0.98 and 0.95 - 0.96 respectively on MIMIC-III dataset, and, in comparison, 0.82 - 0.86 and 0.84 - 0.87 respectively on HDRJH, from 1 to 5 h preceding. After transfer learning and ensemble learning, the AUCs of the final ensemble model were enhanced to 0.94 - 0.94 on HDRJH and to 0.86 - 0.9 in the real-world study in the ICU of the target Ruijin Hospital. In addition, the SHAP analysis illustrated the importance of age, antibiotics, net balance, and ventilation for sepsis prediction, making the model interpretable. CONCLUSIONS: Our machine learning model allows accurate real-time prediction of sepsis within 5-h preceding. Transfer learning can effectively improve the feasibility to deploy the prediction model in the target cohort, and ameliorate the model performance for external validation. SHAP analysis indicates that the role of antibiotic usage and fluid management needs further investigation. We argue that our system and methodology have the potential to improve ICU management by helping medical practitioners identify at-sepsis-risk patients and prepare for timely diagnosis and intervention. TRIAL REGISTRATION: NCT05088850 (retrospectively registered).

Fully Distributed Synchronization of Complex Networks With Adaptive Coupling Strengths.

This article considers the fully distributed leaderless synchronization in a complex network by only utilizing local neighboring information to design and tune the coupling strength of each node such that the synchronization problem can be solved without involving any global information of the network. For an undirected network, a fully distributed synchronization algorithm is presented to adjust the coupling strength of each node based on a simple adaptive law. When the topology of a network is directed, two different types of adaptive algorithms are developed to achieve synchronization in a fully distributed manner, where the coupling strength of each node is designed to be either the sum or product of two non-negative scalar functions. The fully distributed leaderless synchronization of a directed network is investigated in a leader-follower framework, where the leader subnetwork is analyzed by using the techniques from constrained Rayleigh quotients and the follower subnetwork is addressed by employing the properties of nonsingular M -matrices. Simulations are given to illustrate the theoretical results.

Contraction criteria for incremental stability of differential systems with discontinuous right-hand sides.

Incremental stability analysis, which plays a crucial role in dynamical systems, especially nonlinear systems, has attracted more and more concern for its applications in real world control systems nowadays. This paper presents a constructive approach to derive sufficient conditions for incremental exponential stability of the Filippov solutions of a class of differential systems with discontinuous right-hand sides, by introducing a sequence of continuous dynamical systems which is uniformly contracting and approximating the Filippov systems in terms of the evolution map graphs. Afterwards, several applications of the derived theoretical results are explored. Some specific classes of control dynamical systems with discontinuous right-hand sides are studied and relative detailed conditions are presented to show the power of the present approach to investigate the stability of switched dynamical systems, Hopfield neural network with discontinuous activations and sliding mode control.

Finite time convergence of pinning synchronization with a single nonlinear controller.

In this paper, we discuss distributive synchronization of complex networks in finite time, with a single nonlinear pinning controller. The results apply to heterogeneous dynamic networks, too. Different from many models, which assume the coupling matrix being symmetric (or the connecting graph is undirected), here, the coupling matrix is asymmetric (or the connecting graph is directed).

Sensory, somatomotor and internal mentation networks emerge dynamically in the resting brain with internal mentation predominating in older age.

Age-related changes in the brain are associated with a decline in functional flexibility. Intrinsic functional flexibility is evident in the brain's dynamic ability to switch between alternative spatiotemporal states during resting state. However, the relationship between brain connectivity states, associated psychological functions during resting state, and the changes in normal aging remain poorly understood. In this study, we analyzed resting-state functional magnetic resonance imaging (rsfMRI) data from the Human Connectome Project (HCP; N = 812) and the UK Biobank (UKB; N = 6,716). Using signed community clustering to identify distinct states of dynamic functional connectivity, and text-mining of a large existing literature for functional annotation of each state, our findings from the HCP dataset indicated that the resting brain spontaneously transitions between three functionally specialized states: sensory, somatomotor, and internal mentation networks. The occurrence, transition-rate, and persistence-time parameters for each state were correlated with behavioural scores using canonical correlation analysis. We estimated the same brain states and parameters in the UKB dataset, subdivided into three distinct age ranges: 50-55, 56-67, and 68-78 years. We found that the internal mentation network was more frequently expressed in people aged 71 and older, whereas people younger than 55 more frequently expressed sensory and somatomotor networks. Furthermore, analysis of the functional entropy - a measure of uncertainty of functional connectivity - also supported this finding across the three age ranges. Our study demonstrates that dynamic functional connectivity analysis can expose the time-varying patterns of transition between functionally specialized brain states, which are strongly tied to increasing age.

QUAD-Condition, Synchronization, Consensus of Multiagents, and Anti-Synchronization of Complex Networks.

In this article, we discuss quadratic condition (QUAD-condition) for general models of synchronization of complex networks and consensus of multiagents with or without pinning controller in detail. Synchronization analysis consists of two parts. One is connection structure, which is described with coupling matrix. The other one is the intrinsic property of the uncoupled system. QUAD-conditions play a key role in describing the intrinsic property of the uncoupled system. With QUAD-conditions, we unify synchronization and consensus of multiagents in a framework. It is interesting that anti-synchronization can be easily transformed to synchronization by introducing suitable QUAD-condition.

Products of Generalized Stochastic Matrices With Applications to Consensus Analysis in Networks of Multiagents With Delays.

Product theory of stochastic matrices provides a powerful tool in the consensus analysis of discrete-time multiagent systems. However, the classic theory cannot deal with networks with general coupling coefficients involving negative ones, which have been discussed only in very few papers due to the technicalities involved. Motivated by these works, here we developed some new results for the products of matrices which generalize that of the classical stochastic matrices by admitting negative entries. Particularly, we obtained a generalized version of the classic Hajnal inequality on this generalized matrix class. Based on these results, we proved some convergence results for a class of discrete-time consensus algorithms with time-varying delays and general coupling coefficients. At last, these results were applied to the analysis of a class of continuous-time consensus algorithms with discrete-time controller updates in the existence of communication/actuation delays.

Topographic diversity of structural connectivity in schizophrenia.

The neurobiological heterogeneity of schizophrenia is widely accepted, but it is unclear how mechanistic differences converge to produce the observed phenotype. Establishing a pathophysiological model that accounts for both neurobiological heterogeneity and phenotypic similarity is essential to inform stratified treatment approaches. In this cross-sectional diffusion tensor imaging study, we recruited 77 healthy controls, and 70 patients with DSM-IV diagnosis of schizophrenia. We first confirmed the heterogeneity in structural connectivity by showing a reduced between-individual similarity of the structural connectivity in patients compared to healthy controls. Second, at a system level, we found the diversity of the topographic distribution of the strength of structural connectivity was significantly reduced in patients (P = 7.21 × 10-7, T142 = 5.19 [95% CI: 3.37-7.52], Cohen's d = 0.91), and this affected 65 of the 90 brain regions examined (False Discovery Rate <5%). Third, when topographic diversity was used as a discriminant feature to train a model for classifying patients from controls, it significantly improved the accuracy on an independent sample (T99 = 5.54; P < 0.001). These findings suggest a highly individualized pattern of structural dysconnectivity underlies the heterogeneity of schizophrenia, but these disruptions likely converge on an emergent common pathway to generate the clinical phenotype of the disorder.

An asymptotic theory for cross-correlation between auto-correlated sequences and its application on neuroimaging data.

BACKGROUND: Functional connectivity is among the most important tools to study brain. The correlation coefficient, between time series of different brain areas, is the most popular method to quantify functional connectivity. Correlation coefficient in practical use assumes the data to be temporally independent. However, the time series data of brain can manifest significant temporal auto-correlation. NEW METHOD: A widely applicable method is proposed for correcting temporal auto-correlation. We considered two types of time series models: (1) auto-regressive-moving-average model, (2) nonlinear dynamical system model with noisy fluctuations, and derived their respective asymptotic distributions of correlation coefficient. These two types of models are most commonly used in neuroscience studies. We show the respective asymptotic distributions share a unified expression. RESULT: We have verified the validity of our method, and shown our method exhibited sufficient statistical power for detecting true correlation on numerical experiments. Employing our method on real dataset yields more robust functional network and higher classification accuracy than conventional methods. COMPARISON WITH EXISTING METHODS: Our method robustly controls the type I error while maintaining sufficient statistical power for detecting true correlation in numerical experiments, where existing methods measuring association (linear and nonlinear) fail. CONCLUSIONS: In this work, we proposed a widely applicable approach for correcting the effect of temporal auto-correlation on functional connectivity. Empirical results favor the use of our method in functional network analysis.

Statistical testing and power analysis for brain-wide association study.

The identification of connexel-wise associations, which involves examining functional connectivities between pairwise voxels across the whole brain, is both statistically and computationally challenging. Although such a connexel-wise methodology has recently been adopted by brain-wide association studies (BWAS) to identify connectivity changes in several mental disorders, such as schizophrenia, autism and depression, the multiple correction and power analysis methods designed specifically for connexel-wise analysis are still lacking. Therefore, we herein report the development of a rigorous statistical framework for connexel-wise significance testing based on the Gaussian random field theory. It includes controlling the family-wise error rate (FWER) of multiple hypothesis testings using topological inference methods, and calculating power and sample size for a connexel-wise study. Our theoretical framework can control the false-positive rate accurately, as validated empirically using two resting-state fMRI datasets. Compared with Bonferroni correction and false discovery rate (FDR), it can reduce false-positive rate and increase statistical power by appropriately utilizing the spatial information of fMRI data. Importantly, our method bypasses the need of non-parametric permutation to correct for multiple comparison, thus, it can efficiently tackle large datasets with high resolution fMRI images. The utility of our method is shown in a case-control study. Our approach can identify altered functional connectivities in a major depression disorder dataset, whereas existing methods fail. A software package is available at https://github.com/weikanggong/BWAS.

Individual differences in schizophrenia.

BACKGROUND: Whether there are distinct subtypes of schizophrenia is an important issue to advance understanding and treatment of schizophrenia. AIMS: To understand and treat individuals with schizophrenia, the aim was to advance understanding of differences between individuals, whether there are discrete subtypes, and how first-episode patients (FEP) may differ from multiple episode patients (MEP). METHOD: These issues were analysed in 687 FEP and 1880 MEP with schizophrenia using the Positive and Negative Syndrome Scale for (PANSS) schizophrenia before and after antipsychotic medication for 6 weeks. RESULTS: The seven Negative Symptoms were correlated with each other and with P2 (conceptual disorganisation), G13 (disturbance of volition), and G7 (motor retardation). The main difference between individuals was in the cluster of seven negative symptoms, which had a continuous unimodal distribution. Medication decreased the PANSS scores for all the symptoms, which were similar in the FEP and MEP groups. CONCLUSIONS: The negative symptoms are a major source of individual differences, and there are potential implications for treatment. DECLARATION OF INTERESTS: L.P. received speaker fees from Otsuka Canada and educational grant from Janssen Canada in 2017. COPYRIGHT AND USAGE: © The Royal College of Psychiatrists 2017. This is an open access article distributed under the terms of the Creative Commons Non-Commercial, No Derivatives (CC BY-NC-ND) license.