Pathologies in functional connectivity, feedback control and robustness: a global workspace perspective on autism spectrum disorders.

Cogn Process (2015) 16:1–16 DOI 10.1007/s10339-014-0636-y

REVIEW

Pathologies in functional connectivity, feedback control and robustness: a global workspace perspective on autism spectrum disorders James F. Glazebrook • Rodrick Wallace

Received: 22 April 2014 / Accepted: 18 September 2014 / Published online: 18 October 2014 Ó Marta Olivetti Belardinelli and Springer-Verlag Berlin Heidelberg 2014

Abstract We study the background to problems of functional connectivity in autism spectrum disorders within the neurocognitive framework of the global workspace model. This we proceed to do by observing network irregularities detracting from that of a well-formed small world network architecture. This is discussed in terms of pathologies in functional connectivity and lack of central coherence disrupting inter-network communication thus impairing effective cognitive action. A typical coherenceconnectivity measure as a by-product of various neuroimaging results is considered. This is related to a model of feedback control in which a coherence function in the frequency domain is modified by an environmentally determined interaction parameter. With respect to the latter, we discuss the stability question that in theory may counterbalance inessential metabolic costs and incoherence of processing. We suggest that factors such as local overconnectivity and global underconnectivity, along with acute over-expenditure of metabolic costs give rise to instability within the connective core of the workspace.

J. F. Glazebrook (&) Department of Mathematics and Computer Science, Eastern Illinois University, 600 Lincoln Avenue, Charleston, IL 61920-3099, USA e-mail: [email protected] R. Wallace Division of Epidemiology, The New York State Psychiatric Institute, Box 47, 1051 Riverside Drive, New York, NY 10032, USA e-mail: [email protected]

Keywords Global workspace Functional connectivity Autism spectrum disorder Fragile X syndrome Oxidative stress Metabolic free energy Rate distortion Channel capacity Small world network Coherence measure Feedback control

Introduction Continuing research into the cognitive-neurodevelopmental disorder known as autism, perhaps opens up as many questions as it appears to answer. Autism spectrum disorders (ASD) are realized in individuals exhibiting one or more of a variety of behavioral and cognitive ailments such as, for instance, impairment in verbal/non-verbal communication, learning disabilities, poor social interaction, stereotyped behavioral patterns, and obsession with systematization (Baron-Cohen and Belmonte 2005; Belmonte et al. 2004; Belmonte and Baron-Cohen 2004; Courchesne and Pierce 2005; Courchesne 2007; Frith 1989; Frith and Happe 1994; Just et al. 2012; Peters et al. 2013; Rippon et al. 2007). On the other hand, high functioning ASD (Asperger’s Syndrome) subjects can nevertheless display exceptional skills, such as in visual thinking, and in performing certain mental tasks (BaronCohen and Belmonte 2005; Frith and Happe 1994; Grandin 1992). At present, there is no definitive explanation of this cognitive/sensory disorder of neuronal processing. Current research points to pathologies in connectivity and modular disorganization within the cortex that can be directly, or indirectly related to mitochondrial disease and/or oxidative stress. The origins are considered as mainly hereditary, but they may also be the result of early exposure to stress and/ or to toxic agents. Whereas much remains to be understood

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about the causes, a currently accepted range of factors also points toward inter-related metabolic dysfunction, genetic and environmental factors which are implicitly functions of these pathologies, and conversely. In approaching the general problem from a neurocognitive perspective, our development of ideas follows to some extent the functional mechanisms of global workspace theory (GWT) (Baars 1998; Baars and Franklin 2003; Baars et al. 2013; Shanahan 2010; Wallace 2005a). Thanks to significant developments in recent years, there is increasing recognition of this theory as a principal forerunner in the modeling of cognition and consciousness. Strongly supporting evidence for this model arises from a number of experimental studies such as those of Dehaene and Naccache (2001), Dehaene and Changeux (2005), Dehaene (2009), Gaillard et al. (2009) that furthermore bring GWT into consonance with other leading theories embracing the neural correlates of consciousness (cf Edelman et al. 2011; Freeman et al. 2009; Kozma et al. 2004). One aspect of the theory concerns how conscious perception is broadcasted widely across the human brain cortex to unconscious specialized processors (or ‘unconscious cognitive modules’) that continually undergo phase transitions, while breaking symmetry patterns within the network in question. The massively parallel information processing suggests that cognitive processes are distributed and embodied within an environmental framework and can be perturbed by the latter (Clark 1997; Shanahan 2010; Varela et al. 1991). The other part of the story is that together with human (animal) cognition, processes that are cognitively structured (such as the immune function, embryogenesis, epidemics, HPA-axis, tumor control, socio-cultural networks, and human-computerized control systems, for instance) also arise from patterns of diffuse broadcasting and feedback as underlying mechanisms through which their complexity emerges (see e.g., Wallace 2005a, b, 2012; Wallace and Fullilove 2008). One aim of this review is to address how the possible optimizing procedures as represented in this model, are either absent, or they collapse into failure modes. In relationship to the distributed mechanism of the workspace, we will pay particular attention to problems of functional connectivity and demise of central coherence as these are professed for autism. A particular question involves that of highly localized connectivity in comparison to a paucity of sprays of global corticocortical connections in a functional network (see e.g., Courchesne and Pierce 2005; Courchesne 2007). The nature of this aberration is considered to be a central issue for research into ASD with already an extensive amount of literature on the

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subject. For this broader perspective, we refer to Baron-Cohen and Belmonte (2005), Belmonte et al. (2004), Belmonte and Baron-Cohen (2004), Courchesne and Pierce (2005), Courchesne (2007), Frith (1989), Frith and Happe (1994), Just et al. (2012), Peters et al. (2013), Rippon et al. (2007) and likewise to David et al. (2004), Friston (2011), Mu¨ller et al. (2011), Rubenstein and Merzenich (2003), Sakkalis (2011), Tyszka et al. (2014), Welchew et al. (2005) that provide specialized accounts dealing with the connectivity issues in both theory and practice. One may also include related findings in the case of fragile X syndrome with respect to genetic stimulation/inhibitory systems and how this is linked to orders of synaptic plasticity frequently observed to be lacking in autism (Belmonte and Bourgeron 2006; Huber 2007). Besides looking at the general problem in light of the small world network property of brain connectivity, and the modular structure of the workspace, we will introduce a novel feature; namely an ‘environmentally determined’ feedback-control function H. In principle, this can be Fourier analyzed in a frequency domain, and then tied to an observable coherence-connectivity parameter. Decrease in coherence may then be tempered by the possible contextual enrichment afforded by the control-stability criteria for H. A key issue addressed, as far as autism is concerned, is how functional network irregularities may entail an unnecessary squandering of metabolic free energy. It is suggested that such abnormal functioning, falling way short of optimality regards efficiency and resilience/ robustness, can be obstructions to the development of a well-formed SWN structure. This also begs the question of the criteria for comparing ‘stable’ versus ‘unstable’ phenomena relative to connectivity-coherence and to flow of information as it applies to autism. Given the collective observations of this paper, it is suggested that pertaining to ASD, the ‘unstable’ case reflects upon the abnormality of localized over-connectivity that may incur an over-expenditure of metabolic free energy, at the cost of global underconnectivity, thus thwarting the formation of essential transnetwork connections. Such instability could be anticipated by this very reasoning, but it is not at all obvious why this should be the case. Thus, we intend to elucidate several features underlying the typical traits of unselective processing and over-adaptive mechanisms toward providing explanations. In doing so, there is some reflection upon descriptors of complexity in relationship to the connectivity problem, neurometabolism, and other factors to be discussed. Because of this, one is inevitably drawn toward more general considerations applicable to the broader framework of cognition, including its possible disorders such as autism.


ASD as syndrome of connectedness pathology An overview of the global workspace model In the Baars’ model, the brain is viewed as a collection of distributed, specialized processors through which consciousness is associated to a global workspace (GW) which maps brain activity, via a massively parallel distributed system, in the form of a fleeting memory capacity whose focal contents are then broadcasted in a punctuated fashion to unconscious specialized networks; equivalently, to ‘unconscious cognitive modules,’ as we will explain in Sect. 4. In neurocognitive terms, this means that owing to the immense orders of interconnectivity, the coherent assembly of workspace neurons is broadly distributed across a range of processors to enable a global acquisition of signaled information. A workspace is postulated to integrate a stream of competing, as well as cooperating, input networks in a modular structure having distinguished connector hubs which pattern functional processes. In turn, these connector hubs are mapped to a communications infrastructure, which through ‘broadcasting,’ determines the dynamics in which localized clusters exert a widespread influence. The image of this mapping constitutes the connective core which consists of the connector hubs along with their dense interconnections (see Fig. 1). Interacting sensorymotor and memory processes are then partitioned into competing coalitions, several of which may at any time form a joint alliance. In Shanahan (2010), it is proposed that the human brain structure can be mapped to such a connective core that effectively traces out the functional connectivity of the human brain cortex into a modular structure in which unconscious networks representing ‘contexts’ collaborate to shape and maintain conscious contents/events. In this picture, motives and emotions can be seen as both supportive of, and leading to, executive functions within a hierarchically modular formation.1 In this respect, we consider the workspace theory as an important theoretical framework for representing the various neurophysiological disorders exhibited by autism. The small world structure of the global workspace In terms of connectivity, the modular structure of the GW comprises a small world network (SWN) as seen in Fig. 1. 1 Recent findings Edelman et al. (2011) reveal that a mechanism for GW can be provided by the ‘Dynamic Core’ hypothesis in terms of re-entrantly projecting neural signals throughout the brain cortex, such that a mental image, for instance, instantaneously activates a large number of cortical regions. Likewise, the spatio-temporal features of intra-cortical phase transitions is homologous to that of the broadcasting process in the GW (Freeman et al. 2012; Shanahan 2010).

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As argued in Shanahan (2010, 2012), this structure is consistent with much of the research into the architecture of the brain’s functional network (Achard et al. 2006; Bassett and Bullmore 2006; Sporns and Honey 2006; Sporns et al. 2002; cf. Delbeuck et al. 2003; Hagmann et al. 2007, 2008; ItturiaMedina et al. 2008; Peters et al. 2013; Stam et al. 2007). Rather than enter into a detailed graph-theoretic discussion of the SWN characteristics, we will here just recall the basic features and refer to, e.g., Barrat and Barthe´lemy (2008), Latora and Marchiori (2001), Watts and Strogatz (1998) for specific details. Basically, SWNs are networks that admit an abundance of local connections usually tied to a widespread distribution of (semi) random global, transnetwork connections, with the following properties: (1) the average shortest path length is low, and (2) high clustering coefficient (a measure of the network’s segregation by the clustering of nodes). Related are measures of efficient information exchange across all nodes that indicate the overall network resilience, in terms of local and global efficiency and the network’s vulnerability. These are computable in terms of network-specific data in which local and global efficiencies are observed to be high for SWNs (Barrat and Barthe´lemy 2008; Latora and Marchiori 2001). Likewise are the orders of robustness in dealing with random failures, as observed for control subjects in Hagmann et al. (2007, 2008), and deviations from such structural patterns in the case of autism as revealed by Diffusion MRI techniques (Peters et al. 2013). The relevance to the GW is that workable efficiency in neural coding permits distributed, massively parallel computing where only an ample degree of local and intense computation needs to be relayed to the more distant regions of the graph, as proposed to be sufficient for synchronous brain activity (Hagmann et al. 2007, 2008; Itturia-Medina et al. 2008; cf. Stam et al. 2007; Shanahan 2010). Thus, SWN characteristics represent high degrees of neuronal complexity, and this architecture represents a fine-tuning for the purpose of coordinating parallel distributed with serial processing toward sensorimotor coupling with the environment. This particular instantiation affords one way of understanding ASD in the larger picture when for instance, abnormalities in connectivity effect the functioning of distributed networks to the extent that desired measures of efficiency and resilience are lacking (cf. Casanova 2007; Peters et al. 2013), along with reduced cortical response reliability in relationship to certain behavioral patterns (Dinstein et al. 2012). Collective resilience may be realized in networks that are assortatative; namely, when nodes of a certain degree level have an affinity to link up with those having that same topological type (Barrat and Barthe´lemy 2008; Rubinov and Sporns 2010). This type of network behavior reflects upon the ‘biased competition’ which is a notable factor

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determining how coalitions may form and how giant components emerge from within (cf. Glazebrook and Wallace 2009a; Wallace 2005a; Shanahan 2010).2 Positive assortative coefficients often represent a resilient core of mutually connected hubs of high degrees, in contrast to negative coefficients representing those hubs that are highly segregated, and possibly vulnerable which may be characteristic of cognitive disorders, autism included Hagmann et al. (2007, 2008), Peters et al. (2013). Further, we propose that within the workspace, biased competition reflects upon a high degree of intrinsic selectivity. The relevance to autism can be seen in the case of the auditory cortex where ASD subjects can be significantly influenced, or disturbed, by specific tonal ranges and/or frequencies leading to over-sensitized responsiveness in the corresponding cognitive modules (Rubenstein and Merzenich 2003). On the other hand, studies such as Peters et al. (2013) reveal that ASD subjects showed markedly increased network resilience to targeted attack, as attributed to the redundant connectivity patterns resulting from an irregular severance of connections and synaptic pruning. Consequently, the factor of vulnerability may be widely distributed, and the network falls short of being uniformly resilient. In less than optimal circumstances, modular disorganization within the cortex is disrupted by signal distortion, and in the GW context of cognitive disorders, it may be proposed that communication between separate broadcasts may occasionally be incongruous owing to lack of sequential coherence. This observation is supported by behavior at levels of cross-frequency coupling and selective communication, in which biased competition may amount to degrees of selectivity with resonating oscillations between preferred agents (Axmacher 2010; Fries 2005, 2009; Shin and Cho 2013). A connectionist interpretation (Maia and Cleeremans 2005), further relevant, proposes feedforward/feedbackward projections as implementing selected attraction to the most favored sites in the workspace, optimally by way of minimizing metabolic free energy costs under evolutionary demands. These are important observations as far as ASD is concerned, since such haphazard and extensively biased competition represent orders of mis-selection: attention may be inadvertently directed to less effective cognitive sites while neglecting the costs entailed. Such unselective processing reflects upon an altered developmental emphasis, contributing to adaptive mechanisms that reveal typical 2

Mathematical details pertaining to how giant components form in a semi-random graph can be found in Erd} os and Reńyi (1960), Watts and Strogatz (1998). Here they can be reasonably thought of as the network representations of the dominant coalitions that enter into the connective core while overcoming their competitors.

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Fig. 1 A SWN constructed by the methods of Watts and Strogatz (1998) is shown in (a). On creating modularity, we have in (b) a SWN that more closely represents the large-scale connectivity of a human/ animal brain. On attaching connector hubs, we have in (c) a modular SWN in which the former are the nodes that are operatively the significant junctions in the communication network between modules. The connective core in (d) arises as the network of connector hubs along with their dense interconnections [adapted from Shanahan (2012, Fig. 2)]

autistic traits such as (1) repetitive behavior, and (2) preoccupation with systems and/or over-systematizing, as professed in Baron-Cohen and Belmonte (2005), Belmonte and Baron-Cohen (2004). The connectivity problem: local versus global Here, we look closer at the connectivity problem in terms of how higher than normal levels of activity within regions subserving lower-level cognitive/perceptual processing is claimed to be an excessive strengthening of local connectivity that is out of balance and out of synchronization with respect to long-range corticocortical reciprocity and coupling, thus causing some signals to be indistinguishable from noise (Baron-Cohen and Belmonte 2005). This aberration, one of the foremost in autism, is considered as impairing the basic frontal cortex formation of integrating widespread, and contextually enriching information to lower-level modules owing to the reduced fibrous intensity caused by an acute overload of information that is highly localized, with decreased functional coupling between brain regions, as supported by studies such as Baron-Cohen and Belmonte (2005), Belmonte et al. (2004), Courchesne and Pierce (2005), Frith (1989), Frith and Happe (1994), Just et al. (2012), Rippon et al. (2007). Whereas local overconnectivity may be the culprit here, we do not necessarily regard ASD as exclusively a localized brain order,


but on the basis of evidence to date, regard this generally as a disorder of the association cortex involving multiple functional networks impairing inter-network communication. On the other hand, malfunctioning of microcircuitry caused by neuroinflammation, for instance, has already been observed in regard to increased local overconnectivity with a greater number of segments with short distance connectivity which may forsake the formation of global connections, and so lead to defects in essential selective processing (Courchesne and Pierce 2005; Courchesne 2007; Minshew and Williams 2007). In such cases, we cannot rule out the possibility of disordered or reduced connectivity globally, as inducing an adverse situation for information processing incurring levels of noisy crosstalk, and therefore a hazard in distinguishing potentially useful information from that of noise. Increased noise levels are already claimed in autistic psychological abnormalities such as high visual motion coherence thresholds (Baron-Cohen and Belmonte 2005; Belmonte et al. 2004; Belmonte and Baron-Cohen 2004; Courchesne and Pierce 2005; Courchesne 2007; Peters et al. 2013; Rippon et al. 2007). In many of these studies, there are common factors to be addressed: (1) to distinguish local connectivity between neuronal assemblies from long-range functional brain zones, and (2) to distinguish between the actual physical (neuronal) connectivity and the computational connectivity associated with information processing, where both cases involve a running up of metabolic free energy costs due to higher demands on integration of information and coordination of neural assemblies (cf. Friston 2011). In this respect, autism may seem to involve less a surfeit of computational connectivity, but rather a patent deficit of this connectivity globally, which is an observation ubiquitous to much of the research into the connectivity problem. For instance, in reference to non-uniform growth patterns in the autistic brain, Minshew and Williams (2007) report ‘. . . evidence of overgrowth of short-and-mediumrange intrahemispheric connections or connections between cortex and subcortical structures. The onset of brain overgrowth coincided with the onset of the signs and symptoms of autism, indicating that the overgrowth was part of a pathologic process that disrupted the development of normal brain structure and function in autism.’ Comparison with fragile X syndrome The existence of strong ties between genetic morphology and pathologies of connectivity in neural networks is suggested within the pathophysiology of fragile X

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syndrome (FXS) in Belmonte and Bourgeron (2006), Huber (2007). FXS, although seen as different from ASD, shares a number of common symptoms and may be comorbid with certain forms of ASD. Characteristic of FXS are localized regional clusters of neuronal dendritic spines within which are observed exuberant sprays of excessively lengthy and abnormally thin dendrites whose formation is considered to be linked to irregularities in synaptic plasticity, so impairing effective cognitive action (cf. Belmonte and Bourgeron 2006; Courchesne and Pierce 2005; Courchesne 2007; Minshew and Williams 2007). These are considered to arise from possible genetic factors responsible for premature enlargement of brain size (Casanova 2007; Courchesne and Pierce 2005), and protracted long-term synaptic depression as a result of a protein folding disorder which can impose higher than normal demands on neural circuitry (Huber 2007). Inevitably, this will involve increased metabolic costs, a matter to be addressed in a later section (cf. Lennie 2003). Likewise, the occurrence of massive neuronal surges avalanches, that despite such awesome description, could indeed enhance formation of connections toward transnetwork communication (cf. Beggs 2008; Courchesne and Pierce 2005). It is an important observation for ASD, since if such avalanches be irregularly over-localized, it is difficult to envisage complete functional integration with a manageable distribution of ‘costs,’ as failure in one or more network regions compels a re-distribution of effort elsewhere. The fact that abnormal avalanches of neurons are an important factor is supported by autism studies into early brain overgrowth. An extreme excess of neurons in frontal and temporal cortices may profoundly disrupt circuit formation in these regions, so inducing sporadic connectivity patterns. This is often claimed to be the case resulting from an over-exuberant, and a highly protracted expansion of dendritic sites (as observed in FXS, for instance) leading to abnormal cortical interactions partially responsible for disrupting functional global connections (Courchesne and Pierce 2005; Courchesne 2007; Huber 2007). Connectivity and coherence measures As for many cognitive disorders, including ASD, one is confronted with irregularities in the trade-off between wiring costs and topological efficiency which are interrelated issues responsible for a possible demise of a wellformed SWN structure. How this is related to autism is studied in (cf. Belmonte and Baron-Cohen 2004; Peters et al. 2013; Rippon et al. 2007; Sakkalis 2011; cf. Delbeuck et al. 2003; Stam et al. 2007). For instance, in studying comparisons between ASD, and Tuberous Scelrosis

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Complex (TSC), Peters at al. (2013) provided evidence supporting the above claims of abnormal (local) connectivity, by exhibiting reduced signal-to-noise ratios due to the excess of crosstalk-induced noise that can drown out a signal and disorganize the output (see Fig. 2). More specifically, we may view ‘coherence’ as a measure of stability of phase correlation over some time interval: a measure that is sensitive to varying power and phase relationships. As shown in Peters et al. (2013), this measure can be calculated over individual segments based on continuous EEG recordings, with the weighted segment length representing an average coherence. If Si ðtÞ denotes the signal in the i-th segment having length Li , with n the number of segments, CohðS; fÞ the coherence of the signal S at frequency f ,3 and u the frequency band of interest. The (coherence) connectivity measure is defined to be Z Pn i¼1 Li CohðSi ; fÞ Pn c¼ df : ð2:1Þ u i¼1 Li This measure in (2.1) estimates the consistency of relative amplitude and phase within a given bandwidth, where high coherence between two signals accounts for a measure of strong connectivity between corresponding brain regions. In contrast, a lower-valued CohðSi ; fÞ results from a diminishing signal-to-noise ratio within that particular segment, so the information channel capacity therein is not sufficiently high to bound the rate distortion of information. The EEG data computed from (2.1) reveals diminished values of the coherence c resulting from decreased longrange and increased short-range connectivities for ASD subjects (both with and without inclusion of TSC) (Peters et al. 2013). For these subjects, the absence of possible SWN characteristics corresponds to decreased long-overshort-range values of c with a marked increase in network resilience (this is depicted in Fig. 2). Supporting this hypothesis, coherence studies by fMRI reported in Marco et al. (2011) revealed high local interconnectivity with impairment in global corticocortical connections as causing an overload on the left primary cortex disrupting auditory and visual processing networks. We should mention that the scope of investigations into the functional connectivity problem is not without inconsistencies and differences in opinion. Whereas decreased functional coupling between particular brain regions appears to be ubiquitous (see e.g., Just et al. 2012), other studies have sought to reduce the problem to one principally at the microstructural synaptic level (Belmonte et al. 2004; Belmonte and Bourgeron 2006). In particular, 3

The criteria for defining functions such as CohðS; fÞ in relationship to discrete time series methods providing statistical measures of causality, is surveyed in Sakkalis (2011).

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Fig. 2 Illustrations of the functional networks of a control subject, a TSC patient, a non-syndromic autistic patient, and a TSC patient diagnosed with autism [as adapted from Peters et al. (2013, Fig. 1)]. The ASD/TSC patterns show gradual detachments from the apparently well-patterned SWN structure in the control case where the progressively lower ratio of long-to short-range coherence is seen to be a function of overdeveloped local interconnectivity, in contrast to the relatively sparse global connectivity patterns

‘underconnectivity’ has been questioned, with strictures based upon variations in fMRI methodology (Mu¨ller et al. 2011). In other situations, minor environmental perturbations, such as slight head movements and eye blinking, may significantly alter connectivity measures (Tyszka et al. 2014).

The network of cognitive dual languages Pattern recognition and response According to Atlan and Cohen (1998), the complex regulatory activities of the immune system are cognitive, and that the cognitive function itself involves the comparison of a perceived signal with an internal, learned or inherited picture of the world, and then the choice of one or more responses from a much larger repertoire of possible responses. In this fundamental model of cognition, pattern recognition and response proceeds by an algorithmic combination of an incoming external—and broadly ‘sensory’ signal—with an internal ongoing activity—incorporating the internalized picture of the world—and triggering an appropriate action based on a decision that the sensory pattern requires to implement a response. This broadly


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describes how the immune system, when viewed as a multi-agent distributed system via inter-cellular coordination, proceeds to deal with a pathogen attack. This is carried through by means of a feedback protocol within signal transduction pathways in order to increase responseeffectiveness; typically, by implementing the system’s sovereign mechanisms of grammar and syntax (for specifics in this regard see, e.g., Cohen 2000; Segel and BarOr 1999). As described in Wallace (2005a, 2012), a basic way of seeing this in the context of the GW is as follows. Consider incoming sensory input which is mixed in an unspecified but systematic manner with internal signals to create a combined path x ¼ ða0 ; a1 ; . . .; an ; . . .Þ. Each ak thus represents some functional composition of internal and the external signals. This path is fed into a highly nonlinear, but otherwise similarly unspecified, decision function, h, so as to generate an output hðxÞ that is an element of one of two disjoint sets B0 and B1 of possible system responses. Let B0 fb0 ; . . .; bk g; B1 fbkþ1 ; . . .; bm g;

ð3:1Þ

and assume a graded response, supposing that if hðxÞ 2 B0 , the pattern is not recognized, and if hðxÞ 2 B1 , the pattern is recognized, and consequently some action bj ; k þ 1 j m occurs. Identifying the alphabet of states aj ; bk may depend on the system’s coarse graining as enumerated by the tools of symbolic dynamics. Accordingly, attention is paid to those paths x which, in the course of information flow, trigger processes of pattern recognition and response. That is, given a fixed initial state a0 , we examine all possible subsequent paths x beginning with a0 and leading to the event hðxÞ 2 B1 . Thus hða0 ; . . .; aj Þ 2 B0 for all 0\j\m, whereas hða0 ; . . .; am Þ 2 B1 . This leads to criteria for ‘meaningful paths’ which we will explain next. Meaningful paths For each positive integer n, let NðnÞ denote the number of high probability grammatical/syntactical paths of length n which begin with some particular a0 , and further leading to the condition hðxÞ 2 B1 . These are paths of combined signals of the above type that are structured to some language. Let us call such paths meaningful, granted that NðnÞ will be considerably less than the number of all possible paths of length n leading from a0 to the condition hðxÞ 2 B1 . Next, there is an assumption which permits an inference on the necessary conditions constrained by the asymptotic limit theorems of information theory, namely

for a given information source X, the finite limit representing entropy, HðXÞ lim

n!1

log½NðnÞ ; n

ð3:2Þ

both exists and is independent of the path x (Yeung 2008). A guiding principle is that restriction to meaningful sequences of symbols increases the rate at which information can be transmitted with arbitrary small error, and that the grammar/syntax of the path can be associated with a dual information source. Here, X is taken to be adiabatic, piece-wise stationary, and ergodic, and that a system engaging in a cognitive process is describable as such.4 One can then reason, as in Wallace (2005a, 2012), that the information source X is defined as dual to the underlying ergodic cognitive process. In this case, an equivalence class algebra can be constructed by choosing different origin points, a0 , and defining the equivalence of two states, am ; an , by the existence of high probability meaningful paths connecting them to the same origin point. Then, the disjoint partition by equivalence classes, analogous to orbit equivalence classes for dynamical systems, defines the vertices of a modular network of cognitive dual languages (Wallace 2005a, 2012) where each vertex represents a different information source dual to a cognitive process. These are linked via mutual information that represents the probabilistic dependencies between the two and leads to a scheme mappable to the connector hubs of the workspace. It is also worth noting that the ‘ergodic’ characterization of the information source, in the context of the Atlan-Cohen model, lends a close association with the Bayesian inference principle of (cf. Friston 2010, 2012), about which more can be said in the next section. Signal-to-noise ratio A fundamental principle in information theory basically says that the channel capacity C of a communicating system arises from the maximum of mutual information over a probability distribution. In terms of a level of distortion D in transmission, the Shannon Rate Distortion Theorem asserts that a communicating system can be 4

‘Adiabatic’ means that the changes are slow enough to allow the necessary limit theorems to function. ‘Stationary’ means that, between pieces the probabilities hardly change, and ‘piecewise’ means that these properties hold between phase transitions which are described using renormalization methods (Wallace 2005a). ‘Ergodic’ means that in the long term, correlated sequences of symbols are generated at an average rate equal to their joint probabilities. Consequently, the Shannon entropy then becomes the long-term average of the ‘surprise’ element.

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designed to attain to the appropriate level of fidelity once RðDÞ C, where RðDÞ denotes the rate-distortion function of D (we refer to, e.g., Cover and Thomas 1991; Yeung 2008 for details of the underlying probabilistic formulation of these concepts). A key observation is that the channel capacity C can be related to a frequency f dependent signal-to-noise ratio Sðf Þ=Nðf Þ over some bandwidth, by means of an integral formula showing, in theory, that C generally increases as Sðf Þ=Nðf Þ increases (see, e.g., Bracewell 2000; Yeung 2008 for the explicit relationship). Autism studies such as Baron-Cohen and Belmonte (2005), Belmonte et al. (2004), Peters et al. (2013), broadly basing orders of connectivity in relationship to sensory signals, reveal over-connectivity in part due to a low signal-to-noise ratio, and hence a reduced measure of channel capacity. One may conclude that an impairment of information processing, in which there is a high surplus of connectivity, causes a significantly indiscriminate response to certain stimuli by the subsequent difficulty in bounding rate distortion. Related are the fMRI studies of Dinstein et al. (2012) revealing low signal-to-noise ratios with respect to reduced integrity in anatomical connections with poor response reliability, thus preventing an essential balance between modes of excitation and inhibition in the cognitive process. These factors can be compared with increased cortical excitation/inhibition ratios resulting from sensorimotor impairment, as observed in Rubenstein and Merzenich (2003). Thus, the excessive amount of noisy crosstalk between sensors suggests that for ASD subjects, information is inappropriately assimilated in a dispersive kind of way, lacking orders of integration, in contrast with the control case that on average exhibits higher orders of selectivity, spatial complexity, and contextual awareness, as observed in, e.g., Dominguez et al. (2013), Frith and Happe (1994), Peters et al. (2013).

Unconscious cognitive modules and tunable parameters Unconscious cognitive modules Once presented with a set of cognitive regulatory modules geared to solving a problem, we are confronted with the ‘no free lunch’ predicament (see, e.g., English 1996). This basically says that a functional optimizer has to pay for superiority on one subset of functions with inferiority on the complementary subset. It is a relevant observation in cases of ASD, in view of oxidative stress and disrupted functional connectivity, since a prospective optimizer may pay dearly for

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certain regional attention while impoverishing the global interactions.5 Squaring up to these issues, the challenges facing any cognitive regulatory, interactive system involves coordination between cooperating low-level cognitive modules of the workspace. This phenomenon may be patterned upon the network of connections between information sources dual to basic neurophysiological and conditioned unconscious cognitive modules (UCM). The latter network is of an oscillatory type that functions at a level above a neural learning network and can be viewed as a type of representation space for the remapped network of lower-level dual cognitive modules (Wallace 2005a, 2012). Once presented with two distinct problem classes, there must be two different ‘wirings’ of the latter sources with the network graph edges measured by the amount of information crosstalk between sets of nodes representing the dual information sources (see Fig. 3). The latter are then representable in terms of a language structured in a similar way to how the immunology grammar/syntax functions respond to some specified biomolecular interaction. Accordingly, a pattern of recognition and response entails the convolution of an incoming external sensory signal with an internal ongoing operation via the hypothesized system of oscillators. The network of UCM, out of which a regime of giant components emerges, can be viewed as a functional workspace in its own right. Although not strictly identifiable with the connective core, it is an oscillatory network instrumental for sensorimotor blending that is mappable to the former in relationship to mutual information (see Fig. 4). Tunable parameters and giant components The topology of the above network is linked directly to an interaction parameter x [ 0 determining the giant component that will initiate a cognitive response. Conversely, there will be a critical value xC defined by the topology induced by this component such that network components interacting by mutual information less than xC will be unable to participate (for further details, see Wallace 2005a, 2012). The workspace interpretation is that these non participating components are simply the faltering 5

We recall the striking duality, as proposed by Shannon (1959) between the properties of an information source with distortion measure, and those of a communication channel. This duality is further enhanced if channels can be assigned ‘message’ costs, so that the problem becomes one of finding a source that is suited to the channel at a tolerable level. This is the essence of the ‘tuning’ version of the Shannon Coding Theorem (see Wallace 2005a) which professes the channel as formally ‘transmitted’ by the signal. A dual channel capacity is thus definable in terms of a channel probability distribution that maximizes information transmission, once given a fixed message probability distribution.


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continually listening in to the crosstalk. These genuinely functional modes, in the former case, thus run the risk of overloading, since cascading failures of this type will generally exceed channel capacity. In this way, a possible optimizer is having to cope with high local expenditure while neurally blind-sighted to creating the essential global (corticocortical) connections. It is, to quote Courchesne and Pierce (2005), ‘... why the frontal cortex in autism might be talking only to itself.’ Phase-locking and selectivity

Fig. 3 By the ‘no free lunch’ theorem, two markedly different problems will be optimally solved by two different linkages of available lower-level cognitive modules—characterized now by their dual information sources Xj —into different temporary networks of working structures, here represented by crosstalk among those structures rather than by the physiological UCM themselves. The embedding information source Z represents the influence of external signals whose effect can be, at least formally, accounted for by network information theory

rivals to the dominant coalition. They will eventually be shifted off-stage and hence not consciously perceived by the remaining assembly of crosstalking regulatory submodules (Glazebrook and Wallace 2009a; Wallace 2005a). More generally, multiple broadcasts can be indexed by a vector X ¼ ðx1 ; . . .; xn Þ of such parameters (for some n), representing a vector of crosstalk information measures between the underlying cognitive/physiological submodules, each associated with its own tunable giant component corresponding to its own special topology. As such, it represents a crosstalk between global broadcasts in which individual submodules are multitasking within the presence of simultaneous broadcasting. Limitations on the magnitude of x (in relationship to bandwidth) will likely contribute to a disturbance of integration; thus, consequently, a lesser enrichment of contextual fluidity, and/or a reduced sense of global meaning. In the context of ASD, we view this lapse of cognitive performance as contributing to the demise of ‘central coherence’ as in Frith (1989), Frith and Happe (1994), to which we may add degrees of unselective processing and lowered spatial complexity which may form the basis for a number of traits (cf. Belmonte and Baron-Cohen 2004; Dominguez et al. 2013; Just et al. 2012). Thinking back to the ‘no free lunch’ principle, there is again the trade-off between wiring costs and topological efficiency, as when the cost of maintaining useful information at select functional components exceeds that for

The GW model professes communicating neuronal groups as doing so in rhythmic phases of competition. The close connection of the connective core with the UCM, thus suggests that the interaction parameter x corresponds to the patterns of coherence as they are modulated by firing rates, an optimal synchronization of which facilitates communication, where a selected group’s oscillatory synchronization is all the more stronger when it is distributed coherently. It is effectively a two-way function of biased competition from which cortical computations unfold when inputs converge in a patterned form toward selectivity. In essence, this is how the critical interaction parameter xC comes about, since selective attention is a choice of all possible interactions toward an integrative network, and a giant component representing the dominant coalition results from one or more selective subsets while stalling the remaining ones. On the other hand, coherence in oscillations is not in itself sufficient for communication if the resonant frequencies of the transmitting group are out of phase with those of its target. Thus, the ensuing disruption of coordinated timing with reduced brain synchronization is a particular instantiation relevant to understanding autism (as supported by, e.g., Dominguez et al. 2013 and references therein). Likewise, the observation that precisely timed reciprocal oscillatory signaling influences long-distance corticocortical coupling is impaired with loss of, or irregular patterns in connectivity (Courchesne and Pierce 2005; Courchesne 2007). Excitatory phases Capturing excitatory phases for oscillating neuronal groups based on exchange of mutual information during phaselocking is studied in Fries (2005, 2009), Shin and Cho (2013) and a workspace interpretation is given in Shanahan (2010). Unsynchronized resonant frequencies inducing unusual phase shifts are pointers toward less flexible patterns of coherence in the connective core, so disrupting essential cognitive fluidity (such as the admittance of an inadequately structured dominant coalition). Self-

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Fig. 4 The relationship between a UCM and a connector hub where maps from nodes of dual information sources to corresponding nodes in the connector hub are prescribed in terms of mutual information. Inadequately bounded rate distortion in one network will thus be reproduced as the same in the corresponding connector hub

sustaining, reverberating patterns that settle in some basin of attractor will lodge there until the initial stimulus producing them dissipates. Eventually, a competing rival that recognizes the patterned structure within the core, will shift this pattern out of its attractor niche into a neighboring one. This sequence of events continues to generate episodes of punctuated broadcasting, with the upshot of inducing a chaotic run-around between different attractors; a scenario suggested by the dynamical system depicted in Fig. 5. This suggests, along with the discussion of the theoretical framework so far, that ASD may also include pathologies in the dynamics of the attractor landscape (cf. unselective processing and over-adaptive mechanisms). Metabolic free energy. Counting the costs in autism? Following Bennett’s (1988) pioneering exploration into the thermodynamic nature of computing, Feynman in (1996) described a number of examples supporting an analogy between free energy density and the Shannon entropy HðXÞ of an information source X. This startling observation establishes a ‘fundamental homology,’ or a ‘duality’ between the two processes and can be explained by the fact that for most computational systems, the information contained in a message can be viewed as the work saved by not needing to recompute whatever has been transmitted. Otherwise said: the information contained in a message is proportional to the amount of free energy density needed to erase it. It amounts to the fact that biological computing involves a significant amount of work and a highly complex cognitive or physiological process measurable by its information source uncertainty, and tolerable levels of rate distortion will involve higher levels of metabolic free energy consumption along with the inevitable costs entailed. Specific studies highlighting these factors as

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related to neuronal processing through inference methods, can be seen in (cf. Sengupta et al. 2013; Sengupta and Stemmler 2014; Friston 2010; Lennie 2003). Minimizing these factors is a task the brain undertakes by adjusting sensory input toward optimal predictability in order to attain to equilibrium with its environment in the course of minimizing free energy while optimizing the content of mutual information. In this way, it configures in accordance with the probabilistic representation of sensory nature and response, through the task of simultaneously minimizing errors in a predictive coding scheme via ‘recognition densities’ (cf. Friston 2010; Sengupta et al. 2013; Wallace 2012). This suggests that the functional mechanisms can be based on principles of inference, and this latter property is not incompatible with the Atlan-Cohen perspective on cognition. As applied to a broad range of cognitive disorders, such an optimizing mechanism may nevertheless malfunction to the extent that the brain does not adequately assimilate the probabilistic irregularities that are latent within the sensory input and are necessary for local-to-global processing. Besides which, the ability to provide energy to the brain is limited: typically, a unit of brain tissue consumes an order of magnitude of more metabolic free energy by a tenfold factor than any other unit of tissue. The subsequent neurocognitive/physiological processes thus involve phase transitional states representing continuous changes in both uncertainty and communication. Hence, the cost of optimizing sensory input by whatever statistical methods, while simultaneously tolerating environmental perturbations exceeding that of available metabolic free energy, may drive the processing system into inevitable instability, a factor that is relevant to ASD since an impairment of inference capabilities is suggested (cf. Glazebrook and Wallace 2009a, b; Wallace 2005b, 2012; Wallace and


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Wallace 2013; Wallace and Glazebrook 2013 where details of the necessary information theory and the relevant stochastic models are exhibited). There are other approaches that study the thermodynamics of brain metabolism that are closely related, and are consistent with the information/free energy duality as explained above (see Freeman et al. 2012; Friston 2010; Kozma et al. 2004). In Freeman et al. (2012), for instance, it is postulated that the cortex while tolerating degrees of thermal noise, employs sensory information induced by conditioned stimuli, the resulting knowledge of which is later stored within a landscape of basins, each with its own attractor to which the cortex is directed via a phase transition. Positive feedback here may shift a state away from its current attractor, or possibly transform it into a new state (as, e.g., depicted in Fig. 5). Either way, a significant amount of metabolic free energy is being dissipated in the process, which in biological terms, is the ‘oxygen debt’ liability which can reasonably be tied to the ‘no free lunch’ argument: excessive squandering of free energy paid for in terms of oxidative metabolism. How this can be related to autism may been seen in the particular cases oxidative stress and mitochondrial disease which are often detected in this disorder. These influential factors we will deal with next.

What appears to be a common factor is that the structural modularity of metabolism consists of metabolic pathways that are susceptible to feedback inhibition. In the presence of such disorders, this too becomes a fragmented network in which the pruned components may be the metabolic pathways themselves. This would tie in with how the pathologies in connectivity previously discussed result in a less than optimal transport of metabolic free energy that can efficiently support integrative information and sustain optimizing representations with regards to sensory input. In other words, we have the neurobiological manifestation of excessive ‘wiring costs’ resulting from such a misappropriation of metabolic free energy that exceeds a functional upper bound, such as the protracted exuberance of dendritic formation increasing further taxation upon the nervous system that is already having to deal with significant metabolic energy consumption for the purpose of regulating action potentials and synaptic efficacy, as suggested in, e.g., Belmonte and Bourgeron (2006).

Oxidative stress

From the GW perspective, any set of external perturbations will interfere with the stability of the system accommodated by the connective core. We have discussed the interplay between excitatory and inhibitory connections that form positive and negative feedback loops, respectively. These could be malfunctioning, or out of balance due to poorly synchronized oscillations caused by corruption in functional connectivity, and/or an abnormal imbalance in the metabolic processes. Thus, the hypothesized ASD symptom of abnormal functional connectivity, and the subsequent disorganization in assimilating information due to the paucity of adequate corticocortical connections, suggest the likely characteristics of an unstable, as opposed to a stable system. This is motivated by how pathologies in connectivity create an imbalance of flux between metabolic pathways which ultimately interferes with the adjustment to environmental perturbations as when certain neuronal assemblies fail to provide effective feedback and stability into the interactive neural circuitry, but instead direct trajectories toward a less favorable basin of attraction which may result in unselective processing (as suggested by Fig. 5). This may be hypothesized to be the case for certain ASD subjects when integration of information is abnormally distributed due to impediments in certain metabolic pathways, so preventing the essential near-instantaneous relay of information between cortical zones, and hindrance in

The instantiation of thermodynamic/metabolic energy of the previous section is significant for the following reasons. In ASD, there are multifarious causes, not all of which are due to specific neurometabolic disorders, although the latter have been observed to exhibit ASD phenotype in many cases (Frye et al. 2013; Zecavati and Spence 2009). On the other hand, metabolic abnormalities are known to be related to mitochondrial dysfunction triggered by epigenetic and toxic (environmental) effects, leading to increased vulnerability to oxidative stress, so disrupting cellular communication and lowering levels of antioxidant defenses. The brain is vulnerable to oxidative stress due to its limitations on a capacity for antioxidants, while simultaneously consuming about 20 % of all metabolic oxygen. Damaged mitochondria while producing an excess of oxidants, are increasingly prone to oxidative stress (see Chauhan and Chauhan 2006 for neurobiological details pertaining to autism). We perceive such aberrant metabolic dysfunction and impairment of the immune response as contributing toward disruption of the functional networks leading to impede overall phase synchrony. In particular, mitochondrial dysfunction has been claimed to be a root cause for adverse neural morphology, neurite overgrowth and impairment in synaptic plasticity (cf. Belmonte and Bourgeron 2006).

Environmental feedback parameter and robustness Feedback data rate

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managing sensory feedback to the demise of selective processing (Belmonte et al. 2004; Belmonte and BaronCohen 2004; Courchesne and Pierce 2005). Environmental parameter On the other hand, if one looks for necessary conditions toward ‘stabilization,’ then recent advances in linear control systems provide some guidance in terms of another striking analogy, in this case, between data-rate limited control, and the source-coding, rate-distortion theorems of the Shannon theory. The basic aim is to determine a suitable environmental parameter H which will effectively be a function of rate distortion, where a fairly broad interpretation of ‘environmental’ can be assumed. The purpose here will be to relate H to the connectivity-coherence measures described previously. Consider a noise-free data link between a discrete linear controlled site (the ‘plant’) and a presumed controller. Such a system will have assigned a feedback data rate H that will determine the rate of instability (of the plant) in terms of information transmission rate over the communicating ˚ stro¨m channel in the presence of stabilizing feedback (see A and Murray 2008; Nair et al. 2007 for details). One can reasonably assume that a lowering of H will thus induce, through a sequence of phase transitions, a reduction of contextual enrichment. In this process, unstable nodes can be stabilized if the feedback data rate H exceeds the rate of the (network) topological information, as if the latter were to be generated by an unstable system. More specifically, there is a critical positive data rate below which there is no quantization and control scheme capable of stabilizing an unstable feedback-control system, suggesting that a significant imbalance arises from such an unstable system, which for the best part, will dominate the parameter H (Elia 2004; Martins and Dahleh 2008; Nair et al. 2007). In this respect, stability in the feedback system accounts for the balancing out of disturbances at some frequencies by suitable amplification at others. Such principles have been applied in a cognitive context to an ‘aging model’ as in Wallace (2014), and likewise to the connectivity-coherence measures as we will deal with next.6


H ¼ Ht ðDÞ :¼ HðRt ðDÞ; tÞ:

ð5:1Þ

This models a time-dependent function of feedback due to the prospective fidelity of information content attributed to that level D. Returning to connectivity measures, consider a signal Si in the i-th segment, and a corresponding time interval ½ti1 ; ti , such that on applying a finite Fourier transform (see, e.g., Bracewell 2000), we obtain the following function in the frequency domain Z ti Hðf ; ti1 ; ti Þ ¼ HðtÞe2pift dt: ð5:2Þ ti1

Next, we return to the setting of the coherence-connectivity measure and define KðSi ; f Þ :¼ CohðSi ; fÞ þ Hðf; ti ; ti1 Þ:

ð5:3Þ

Then, we proceed to define a connectivity-coherencefeedback control measure as modifying (2.1), given by Z Pn i¼1 Li KðSi ; f Þ Pn cH ¼ df : ð5:4Þ u i¼1 Li To see how (5.4) can be interpreted in the theoretical framework of autism, recall that diminishing values of the connectivity c in (2.1) represent a lesser ratio of long-range to short-range coherence due to the pathophysiology of connectivity. This is representable on a typical i-th segment, where apparent decrease in coherence as specified by the term CohðSi ; fÞ, is for the best part noise-influenced and can be associated to the estimate for bounding rate distortion by channel capacity. A working hypothesis is to assume that KðSi ; f Þ in (5.3) may be considered as ‘preferable’ (i.e. conducive to stability), provided H is sufficiently positive as an entropy bound in the segment in question, once a signal is amplified by means of feedback which may destabilize equilibria. This creates amplification in order to ramify switching patterns that will manifestly break symmetry in certain network components. Intermittently giant components will thus emerge, and these in turn will induce their corresponding dominant coalitions within the workspace. Connectivity-coherence and robustness

The connectivity-coherence-feedback measure Given a level of data flow D, the feedback data-rate H is a function of rate distortion Rt ðDÞ of the data channel connecting intent and response at time t: 6

Heuristically, the estimates for stability can be taken as those derived from analysis of the Bode integral formula that further determines orders of ‘fragility’ as they are relevant for robustness ˚ stro¨m and Murray 2008; Csete and Doyle 2002). (A

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To further see the relevance of the coherence measure in (5.4) in the context of ASD, we expect that newly created patterns of anatomical connectivity are maintainable through certain excitatory/inhibitory mechanisms (cf. Rubenstein and Merzenich 2003). At the same time, implementing negative feedback assists maintaining passages along essential biochemical gradients (Csete and Doyle 2002; Segel and Bar-Or 1999). The order of low coherence c is measurable not just by weak coherence, but also by the


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via feedback to inhibition of long-term synaptic depression (LTD) as reported in Huber (2007), suggesting that incongruous feedback (via excitation/inhibition) induces malfunctioning in the homologous complex of neurons.

Discussion and conclusions

Fig. 5 Adapted from Kitano (2004, Fig. 1). This shows how states may return to original attractors by adapting to perturbations in terms of negative feedback loops within a stochastic process. Positive feedback, on the other hand, may shift the system’s state away from a current attractor or propel it into a new state

magnitude of both Li and n [see (2.1)]. It is expected that effective feedback, as is generally the case, will assist in fine-tuning the system. Thus, on taking the ‘environmental’ parameter H as exceeding the entropy rate, so justifies viewing the latter as a positive increasing function. Although different environments may dictate otherwise, therefor causing fluctuating behavior on the part of H in general. A measure of how the network architecture deals with relaying essential information while simultaneously tolerating levels of noise can be considered as its robustness. Relating to the feedback mechanisms, this property can be characterized by ‘fragility’ estimates as we mentioned previously. Thus, an effective use of feedback control in molecular signaling such as used in the syndrome for autoimmune injury, and tumor control, for instance, is to locate a point of fragility, and then regain control by implementing a new feedback protocol in order to re-tune the system toward a preferred pattern of gradient flow in the corresponding biochemical process (Csete and Doyle 2002; Segel and Bar-Or 1999). An optimizing protocol of this type thus will provide the necessary robustness and evolvability into the system. This, however, will not be cost-free on account of the reasons we had discussed earlier. Further relevance to ASD of the interaction between data rate and feedback control may be realized at the level of genetic structures underlying FXS. Via protein synthesis, the FXS mental retardation protein (FMRP) operates

Throughout this review, we have discussed a number of theoretical concepts pertaining to how effective cognitive processing is disrupted in the presence of ASD. We have surveyed with supporting references, how connectivity issues of increased local, but reduced corticocortical reciprocity, significantly detract from a well-formed SWN structure in the brain’s architecture. To understand how this particular instantiation applies to deficits in the workspace and how such deficits represent unselective processing, as is often characteristic of ASD, we have considered a number of inter-related factors, several of which may be common to a variety of cognitive disorders. These include crosstalk between sensors, synchrony failures in neuronal assemblies, and irregular expenditure of metabolic free energy. We have also underscored the important role played by the corresponding coherence-connectivity measures. Relevant here are specific patterns observed in ASD toward showing how unstable and noisy cortical networks can arise from irregular and volatile sequences of spiking activity that impair sensory processing. As a result, the abnormally high ratios of excitation-to-inhibition are claimed to disrupt the mediation of language and social behavior (Marco et al. 2011; Rubenstein and Merzenich 2003).7 Using concepts of information theory we have discussed the relevance of lowered signal-to-noise ratio and how, via mutual information, this can be related to a information channel capacity with the expectancy of distortion between the inter-communicating connector hubs of the workspace. One may regard these as factors as the cause of significant deficiencies in how information is processed in the workspace; specifically, in terms of creating extraordinary giant components and congestion within the connective core. Further relevant is the role of environmental feedback, along with a suitable data rate that, in principle, will statistically select and specify channel inputs, while the overall system may be perturbed by excessive noise and crosstalk. In this case, interconnectivity and feedback control provide operative mechanisms that are interwoven

7

The neurobiological explanation for such disproportionality mainly points toward increased glutamatergic signaling (excitation), on the one hand, and reduction in GABAergic signaling (inhibition) on the other (Rubenstein and Merzenich 2003).

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within networks that are mappable to the connector hubs of the workspace. It may be supposed that evolution has created neurophysiological systems that thanks to their intrinsic robustness, possess degrees of resilience toward environmental perturbations. As a result of metabolic dysfunction, and the inevitable costs entailed, the malfunctioning components of the workspace may be subjected to mis-construed feedback protocols toward delivering effective cognitive responses. This is related to very specific causes, such as the nature of oxidative stress, mitochondrial disease, exuberant dendritic over-growth, and abnormal synaptic connectivity—disorders that impose an unnecessary toll upon those cognitive modules whose principal function is to serve memory and sensory integration. Some specific conclusions that can be made from the theoretical framework of this review, as supported by the many references cited: (1)

(2)

(3)

(4)

A high and potentially unnecessary expenditure in metabolic costs due to over-localized integration of information resulting in a paucity of essential global corticocortical connections detracting from stable functional coherence. The connectivity-coherence measures that had been discussed are proposed as relevant in this respect. Functional network fragmentation and unregulated pruning of overgrowth causing metabolic free energy imbalances, that, for instance, can be seen by network patterning that lacks sufficient global connections (as seen in Fig. 2). This has been surveyed from the point of view of the ‘no free lunch’ and ‘oxygen debt’ liabilities, together with the ensuing higher than tolerable costs in functional circuitry. With the above factors taken into account, we suggest there is instability in environmental feedback control in both the context of information processing and metabolic free energy distribution as they are instrumental for neurocognitive functions. Even if higher levels of crosstalk can be tolerated, the global broadcasts are prevented from tunable stability due to the interplay between mutual information and sensations in the presence of varying degrees of noise. Accordingly, an otherwise effective pattern of inference may be less than optimal, or become manifestly irregular in certain respects. At the same time, incongruity in mutual information, caused by noise, and imbalance in phase-locking between neuronal groups, may induce a competition between coalitions that is excessively biased, at the cost of blocking out communication toward a more effective cognitive response [compare with (3) above].

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The above observations outline what is essentially a workspace interpretation of unselective, and more generally, aberrant and inefficient processing, contextual uncertainty, over-systematization, and other closely related factors that are characteristic of ASD. To some extent, these points also represent how over-adaptive mechanisms arise in autism: the connective core may fail to adequately sustain cohesion, thus selling short the necessary degrees of wholesome embodiment of the individual’s mental state with his/her environment, as is the case for most cognitive disorders. In summary, we have placed within the context of the GW, a number of important theoretical observations enhancing the current conjecture (see, e.g., Belmonte and Bourgeron 2006) that autistic brain development may be a perturbation of neural connectivity and metabolic mismanagement. Specifically, in which irregularities of information processing at local scales, in the absence of suitable environmental feedback parameters, may interfere with transnetwork global connections between regions as envisaged in the SWN architecture, while extravagantly running up a gamut of inessential metabolic costs. Although there remain unanswered questions concerning the significant abnormality in connectivity (locally and globally), there is sufficient evidence that the pathologies we have surveyed are among the principal causes responsible for irregularities in modular communication within the workspace environment. Acknowledgments We wish to thank the reviewers and the Action Editor for their constructive criticism and suggestions. Our gratitude is extended to Ryan Boske-Cox for some production assistance.

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