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A recent measure of 'integrated information', Φ(DM), quantifies the extent to which a system generates more information than the sum of its parts as it transitions between states, possibly reflecting levels of consciousness generated by neural systems. However, Φ(DM) is defined only for discrete Markov systems, which are unusual in biology; as a result, Φ(DM) can rarely be measured in practice. Here, we describe two new measures, Φ(E) and Φ(AR), that overcome these limitations and are easy to apply to time-series data. We use simulations to demonstrate the in-practice applicability of our measures, and to explore their properties. Our results provide new opportunities for examining information integration in real and model systems and carry implications for relations between integrated information, consciousness, and other neurocognitive processes. However, our findings pose challenges for theories that ascribe physical meaning to the measured quantities.

The broad concept of emergence is instrumental in various of the most challenging open scientific questions—yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory of causal emergence in multivariate systems, which studies the relationship between the dynamics of parts of a system and macroscopic features of interest. Our theory provides a quantitative definition of downward causation , and introduces a complementary modality of emergent behaviour—which we refer to as causal decoupling . Moreover, the theory allows practical criteria that can be efficiently calculated in large systems, making our framework applicable in a range of scenarios of practical interest. We illustrate our findings in a number of case studies, including Conway’s Game of Life, Reynolds’ flocking model, and neural activity as measured by electrocorticography.

Integrated Information Theory (IIT) is a prominent theory of consciousness that has at its centre measures that quantify the extent to which a system generates more information than the sum of its parts. While several candidate measures of integrated information (“ Φ ”) now exist, little is known about how they compare, especially in terms of their behaviour on non-trivial network models. In this article, we provide clear and intuitive descriptions of six distinct candidate measures. We then explore the properties of each of these measures in simulation on networks consisting of eight interacting nodes, animated with Gaussian linear autoregressive dynamics. We find a striking diversity in the behaviour of these measures—no two measures show consistent agreement across all analyses. A subset of the measures appears to reflect some form of dynamical complexity, in the sense of simultaneous segregation and integration between system components. Our results help guide the operationalisation of IIT and advance the development of measures of integrated information and dynamical complexity that may have more general applicability.

Neuroimaging studies commonly associate dorsolateral prefrontal cortex (DLPFC) and posterior parietal cortex with conscious perception. However, such studies only investigate correlation, rather than causation. In addition, many studies conflate objective performance with subjective awareness. In an influential recent paper, Rounis and colleagues addressed these issues by showing that continuous theta burst transcranial magnetic stimulation (cTBS) applied to the DLPFC impaired metacognitive (subjective) awareness for a perceptual task, while objective performance was kept constant. We attempted to replicate this finding, with minor modifications, including an active cTBS control site. Using a between-subjects design for both DLPFC and posterior parietal cortices, we found no evidence of a cTBS-induced metacognitive impairment. In a second experiment, we devised a highly rigorous within-subjects cTBS design for DLPFC, but again failed to find any evidence of metacognitive impairment. One crucial difference between our results and the Rounis study is our strict exclusion of data deemed unsuitable for a signal detection theory analysis. Indeed, when we included this unstable data, a significant, though invalid, metacognitive impairment was found. These results cast doubt on previous findings relating metacognitive awareness to DLPFC, and inform the current debate concerning whether or not prefrontal regions are preferentially implicated in conscious perception.

Changes in conscious level have been associated with changes in dynamical integration and segregation among distributed brain regions. Recent theoretical developments emphasize changes in directed functional (i.e., causal) connectivity as reflected in quantities such as 'integrated information' and 'causal density'. Here we develop and illustrate a rigorous methodology for assessing causal connectivity from electroencephalographic (EEG) signals using Granger causality (GC). Our method addresses the challenges of non-stationarity and bias by dividing data into short segments and applying permutation analysis. We apply the method to EEG data obtained from subjects undergoing propofol-induced anaesthesia, with signals source-localized to the anterior and posterior cingulate cortices. We found significant increases in bidirectional GC in most subjects during loss-of-consciousness, especially in the beta and gamma frequency ranges. Corroborating a previous analysis we also found increases in synchrony in these ranges; importantly, the Granger causality analysis showed higher inter-subject consistency than the synchrony analysis. Finally, we validate our method using simulated data generated from a model for which GC values can be analytically derived. In summary, our findings advance the methodology of Granger causality analysis of EEG data and carry implications for integrated information and causal density theories of consciousness.

An outstanding challenge in neuroscience is to develop theoretically grounded and practically applicable quantitative measures that are sensitive to conscious level. Such measures should be high for vivid alert conscious wakefulness, and low for unconscious states such as dreamless sleep, coma and general anaesthesia. Here, we describe recent progress in the development of measures of dynamical complexity, in particular causal density and integrated information. These and similar measures capture in different ways the extent to which a system's dynamics are simultaneously differentiated and integrated. Because conscious scenes are distinguished by the same dynamical features, these measures are therefore good candidates for reflecting conscious level. After reviewing the theoretical background, we present new simulation results demonstrating similarities and differences between the measures, and we discuss remaining challenges in the practical application of the measures to empirically obtained data.

A commentary on Causality analysis of neural connectivity: critical examination of existing methods and advances of new methods

The capacity to attend to multiple objects in the visual field is limited. However, introspectively, people feel that they see the whole visual world at once. Some scholars suggest that this introspective feeling is based on short-lived sensory memory representations, whereas others argue that the feeling of seeing more than can be attended to is illusory. Here, we investigated this phenomenon by combining objective memory performance with subjective confidence ratings during a change-detection task. This allowed us to compute a measure of metacognition—the degree of knowledge that subjects have about the correctness of their decisions—for different stages of memory. We show that subjects store more objects in sensory memory than they can attend to but, at the same time, have similar metacognition for sensory memory and working memory representations. This suggests that these subjective impressions are not an illusion but accurate reflections of the richness of visual perception.

Accurate models of synaptic plasticity are essential to understand the adaptive properties of the nervous system and for realistic models of learning and memory. Experiments have shown that synaptic plasticity depends not only on pre- and post-synaptic activity patterns, but also on the strength of the connection itself. Namely, weaker synapses are more easily strengthened than already strong ones. This so called soft-bound plasticity automatically constrains the synaptic strengths. It is known that this has important consequences for the dynamics of plasticity and the synaptic weight distribution, but its impact on information storage is unknown. In this modeling study we introduce an information theoretic framework to analyse memory storage in an online learning setting. We show that soft-bound plasticity increases a variety of performance criteria by about 18% over hard-bound plasticity, and likely maximizes the storage capacity of synapses.

Recent data indicate that plasticity protocols have not only synapse-specific but also more widespread effects. In particular, in synaptic tagging and capture (STC), tagged synapses can capture plasticity-related proteins, synthesized in response to strong stimulation of other synapses. This leads to long-lasting modification of only weakly stimulated synapses. Here we present a biophysical model of synaptic plasticity in the hippocampus that incorporates several key results from experiments on STC. The model specifies a set of physical states in which a synapse can exist, together with transition rates that are affected by high- and low-frequency stimulation protocols. In contrast to most standard plasticity models, the model exhibits both early- and late-phase LTP/D, de-potentiation, and STC. As such, it provides a useful starting point for further theoretical work on the role of STC in learning and memory.