The Functional Benefits of Criticality in the Cortex
TL;DR: An introductory-level thought experiment is described to provide the reader with an intuitive understanding of criticality and quantitative evidence that three functional properties of the cortex are optimized at criticality is reviewed.
Abstract: Rapidly growing empirical evidence supports the hypothesis that the cortex operates near criticality. Although the confirmation of this hypothesis would mark a significant advance in fundamental understanding of cortical physiology, a natural question arises: What functional benefits are endowed to cortical circuits that operate at criticality? In this review, we first describe an introductory-level thought experiment to provide the reader with an intuitive understanding of criticality. Second, we discuss some practical approaches for investigating criticality. Finally, we review quantitative evidence that three functional properties of the cortex are optimized at criticality: 1) dynamic range, 2) information transmission, and 3) information capacity. We focus on recently reported experimental evidence and briefly discuss the theory and history of these ideas.
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TL;DR: Recent findings showing that the anatomical neural correlates of consciousness are primarily localized to a posterior cortical hot zone that includes sensory areas, rather than to a fronto-parietal network involved in task monitoring and reporting are described.
Abstract: Several brain regions and physiological processes have been proposed to constitute the neural correlates of consciousness. In this Review, Koch and colleagues discuss studies that distinguish the neural correlates of consciousness from other neural processes that precede, accompany or follow it, and suggest that the neural correlates of consciousness are localized to posterior cortical regions.
894 citations
TL;DR: The results suggest that neural activity in vivo shows a mélange of avalanches, and not temporally separated ones, and that their global activity propagation can be approximated by the principle that one spike on average triggers a little less than one spike in the next step.
Abstract: In self-organized critical (SOC) systems avalanche size distributions follow power-laws. Power-laws have also been observed for neural activity, and so it has been proposed that SOC underlies brain organization as well. Surprisingly, for spiking activity in vivo, evidence for SOC is still lacking. Therefore we analyzed highly parallel spike recordings from awake rats and monkeys, anaesthetized cats, and also local field potentials from humans. We compared these to spiking activity from two established critical models: the Bak-Tang-Wiesenfeld model, and a stochastic branching model. We found fundamental differences between the neural and the model activity. These differences could be overcome for both models through a combination of three modifications: (1) subsampling, (2) increasing the input to the model (this way eliminating the separation of time scales, which is fundamental to SOC and its avalanche definition), and (3) making the model slightly sub-critical. The match between the neural activity and the modified models held not only for the classical avalanche size distributions and estimated branching parameters, but also for two novel measures (mean avalanche size, and frequency of single spikes), and for the dependence of all these measures on the temporal bin size. Our results suggest that neural activity in vivo shows a melange of avalanches, and not temporally separated ones, and that their global activity propagation can be approximated by the principle that one spike on average triggers a little less than one spike in the next step. This implies that neural activity does not reflect a SOC state but a slightly sub-critical regime without a separation of time scales. Potential advantages of this regime may be faster information processing, and a safety margin from super-criticality, which has been linked to epilepsy.
552 citations
Cites background from "The Functional Benefits of Critical..."
...Thus, a slightly sub-critical regime allows the brain to avoid runaway activity, while still allowing moderate activity propagation, and maintaining most of the possible computational advantages that come with criticality (Haldeman and Beggs, 2005; Kinouchi and Copelli, 2006; Beggs, 2008; Shew et al., 2009; Shew and Plenz, 2013)....
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TL;DR: An emerging research focus on within-person brain signal variability is providing novel insights, and offering highly predictive, complementary, and even orthogonal views of brain function in relation to human lifespan development, cognitive performance, and various clinical conditions.
432 citations
Cites background from "The Functional Benefits of Critical..."
...Remarkably, dynamic range, information capacity, and information transfer optimize when brain networks are at criticality, signal variability is optimal, and network synchrony is maximally variable (Shew et al., 2009, 2011; Shew and Plenz, 2013; Yang et al., 2012)....
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TL;DR: The concepts of criticality and universality are discussed when applied to biological systems and it is suggested that in some cases these systems can extract functional advantages close to criticality.
Abstract: Close to a transition between different phases a substance can show universal behavior that is independent of the microscopic details and is characterized by power law correlations and critical exponents. In this Colloquium the concepts of criticality and universality are discussed when applied to biological systems and suggest that in some cases these systems can extract functional advantages close to criticality.
430 citations
TL;DR: It is proposed that the concept of intrinsic coupling modes can provide a unifying framework for capturing the dynamics of intrinsically generated neuronal interactions at multiple spatial and temporal scales.
418 citations
Cites background from "The Functional Benefits of Critical..."
...Indeed, in the critical state, the dynamic range of an excitable network is maximized (Kinouchi and Copelli, 2006) and brain networks optimize their response to inputs as well as their information processing ability (Shew and Plenz, 2013)....
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TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
Abstract: In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and calculating the various parameters involved on a discrete basis. As the size of the regions is decreased these parameters in general approach as limits the proper values for the continuous case. There are, however, a few new effects that appear and also a general change of emphasis in the direction of specialization of the general results to particular cases.
65,425 citations
"The Functional Benefits of Critical..." refers background in this paper
...In fact, Shannon (1948) defined the term information capacity in terms of entropy....
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TL;DR: A summary of the layout of cortical areas associated with vision and with other modalities, a computerized database for storing and representing large amounts of information on connectivity patterns, and the application of these data to the analysis of hierarchical organization of the cerebral cortex are reported on.
Abstract: In recent years, many new cortical areas have been identified in the macaque monkey. The number of identified connections between areas has increased even more dramatically. We report here on (1) a summary of the layout of cortical areas associated with vision and with other modalities, (2) a computerized database for storing and representing large amounts of information on connectivity patterns, and (3) the application of these data to the analysis of hierarchical organization of the cerebral cortex. Our analysis concentrates on the visual system, which includes 25 neocortical areas that are predominantly or exclusively visual in function, plus an additional 7 areas that we regard as visual-association areas on the basis of their extensive visual inputs. A total of 305 connections among these 32 visual and visual-association areas have been reported. This represents 31% of the possible number of pathways if each area were connected with all others. The actual degree of connectivity is likely to be closer to 40%. The great majority of pathways involve reciprocal connections between areas. There are also extensive connections with cortical areas outside the visual system proper, including the somatosensory cortex, as well as neocortical, transitional, and archicortical regions in the temporal and frontal lobes. In the somatosensory/motor system, there are 62 identified pathways linking 13 cortical areas, suggesting an overall connectivity of about 40%. Based on the laminar patterns of connections between areas, we propose a hierarchy of visual areas and of somatosensory/motor areas that is more comprehensive than those suggested in other recent studies. The current version of the visual hierarchy includes 10 levels of cortical processing. Altogether, it contains 14 levels if one includes the retina and lateral geniculate nucleus at the bottom as well as the entorhinal cortex and hippocampus at the top. Within this hierarchy, there are multiple, intertwined processing streams, which, at a low level, are related to the compartmental organization of areas V1 and V2 and, at a high level, are related to the distinction between processing centers in the temporal and parietal lobes. However, there are some pathways and relationships (about 10% of the total) whose descriptions do not fit cleanly into this hierarchical scheme for one reason or another. In most instances, though, it is unclear whether these represent genuine exceptions to a strict hierarchy rather than inaccuracies or uncertainities in the reported assignment.
7,796 citations
Book•
15 Nov 1996TL;DR: Spikes provides a self-contained review of relevant concepts in information theory and statistical decision theory about the representation of sensory signals in neural spike trains and a quantitative framework is used to pose precise questions about the structure of the neural code.
Abstract: Our perception of the world is driven by input from the sensory nerves. This input arrives encoded as sequences of identical spikes. Much of neural computation involves processing these spike trains. What does it mean to say that a certain set of spikes is the right answer to a computational problem? In what sense does a spike train convey information about the sensory world? Spikes begins by providing precise formulations of these and related questions about the representation of sensory signals in neural spike trains. The answers to these questions are then pursued in experiments on sensory neurons.The authors invite the reader to play the role of a hypothetical observer inside the brain who makes decisions based on the incoming spike trains. Rather than asking how a neuron responds to a given stimulus, the authors ask how the brain could make inferences about an unknown stimulus from a given neural response. The flavor of some problems faced by the organism is captured by analyzing the way in which the observer can make a running reconstruction of the sensory stimulus as it evolves in time. These ideas are illustrated by examples from experiments on several biological systems. Intended for neurobiologists with an interest in mathematical analysis of neural data as well as the growing number of physicists and mathematicians interested in information processing by "real" nervous systems, Spikes provides a self-contained review of relevant concepts in information theory and statistical decision theory. A quantitative framework is used to pose precise questions about the structure of the neural code. These questions in turn influence both the design and analysis of experiments on sensory neurons.
2,811 citations
TL;DR: In this paper, a model that postulates that some forms of autism are caused by an increased ratio of excitation/inhibition in sensory, mnemonic, social and emotional systems is proposed.
Abstract: Autism is a severe neurobehavioral syndrome, arising largely as an inherited disorder, which can arise from several diseases. Despite recent advances in identifying some genes that can cause autism, its underlying neurological mechanisms are uncertain. Autism is best conceptualized by considering the neural systems that may be defective in autistic individuals. Recent advances in understanding neural systems that process sensory information, various types of memories and social and emotional behaviors are reviewed and compared with known abnormalities in autism. Then, specific genetic abnormalities that are linked with autism are examined. Synthesis of this information leads to a model that postulates that some forms of autism are caused by an increased ratio of excitation/inhibition in sensory, mnemonic, social and emotional systems. The model further postulates that the increased ratio of excitation/inhibition can be caused by combinatorial effects of genetic and environmental variables that impinge upon a given neural system. Furthermore, the model suggests potential therapeutic interventions.
2,200 citations
TL;DR: This work shows that propagation of spontaneous activity in cortical networks is described by equations that govern avalanches, and suggests that “neuronal avalanches” may be a generic property of cortical networks, and represent a mode of activity that differs profoundly from oscillatory, synchronized, or wave-like network states.
Abstract: Networks of living neurons exhibit diverse patterns of activity, including oscillations, synchrony, and waves. Recent work in physics has shown yet another mode of activity in systems composed of many nonlinear units interacting locally. For example, avalanches, earthquakes, and forest fires all propagate in systems organized into a critical state in which event sizes show no characteristic scale and are described by power laws. We hypothesized that a similar mode of activity with complex emergent properties could exist in networks of cortical neurons. We investigated this issue in mature organotypic cultures and acute slices of rat cortex by recording spontaneous local field potentials continuously using a 60 channel multielectrode array. Here, we show that propagation of spontaneous activity in cortical networks is described by equations that govern avalanches. As predicted by theory for a critical branching process, the propagation obeys a power law with an exponent of -3/2 for event sizes, with a branching parameter close to the critical value of 1. Simulations show that a branching parameter at this value optimizes information transmission in feedforward networks, while preventing runaway network excitation. Our findings suggest that “neuronal avalanches” may be a generic property of cortical networks, and represent a mode of activity that differs profoundly from oscillatory, synchronized, or wave-like network states. In the critical state, the network may satisfy the competing demands of information transmission and network stability.
2,035 citations
"The Functional Benefits of Critical..." refers background or result in this paper
...So far, neuronal avalanches have been observed in MEA recordings from the cortex of awake monkeys (Petermann and others 2009; Shew and others 2011), awake and sleeping rats (Ribeiro and others 2010), anesthetized rats (Gireesh and Plenz 2008; Ribeiro and others 2010; Shew and others 2011) and cats (Hahn and others 2010), and in vitro in acute slices (Stewart and Plenz 2006) and cultures (Beggs and Plenz 2003; Gireesh and Plenz 2008; Pasquale and others 2008; Stewart and Plenz 2008; Shew and others 2009; Tetzlaff and others 2010; Shew and others 2011; Yang and others 2012)....
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...…begun to rigorously address the optimization of information-processing capabilities of neural networks at criticality (Greenfield and Lecar 2001; Beggs and Plenz 2003; Bertschinger and Natschläger 2004; Haldeman and Beggs 2005; Kinouchi and Copelli 2006; Legenstein and Maass 2007; Tanaka and…...
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...…Ribeiro and others 2010; Shew and others 2011) and cats (Hahn and others 2010), and in vitro in acute slices (Stewart and Plenz 2006) and cultures (Beggs and Plenz 2003; Gireesh and Plenz 2008; Pasquale and others 2008; Stewart and Plenz 2008; Shew and others 2009; Tetzlaff and others 2010; Shew…...
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...Nonetheless, at a general level, it has been shown in computational models that information transmission through a feed-forward network is maximized at criticality (Beggs and Plenz 2003)....
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...Beggs and Plenz (2003) later found similar results in a feed-forward neural network model....
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