Markov Blankets and Mirror Symmetries-Free Energy Minimization and Mesocortical Anatomy.

A theoretical account of development in mesocortical anatomy is derived from the free energy principle, operating in a neural field with both Hebbian and anti-Hebbian neural plasticity. An elementary structural unit is proposed, in which synaptic connections at mesoscale are arranged in paired patterns with mirror symmetry. Exchanges of synaptic flux in each pattern form coupled spatial eigenmodes, and the line of mirror reflection between the paired patterns operates as a Markov blanket, so that prediction errors in exchanges between the pairs are minimized. The theoretical analysis is then compared to the outcomes from a biological model of neocortical development, in which neuron precursors are selected by apoptosis for cell body and synaptic connections maximizing synchrony and also minimizing axonal length. It is shown that this model results in patterns of connection with the anticipated mirror symmetries, at micro-, meso- and inter-arial scales, among lateral connections, and in cortical depth. This explains the spatial organization and functional significance of neuron response preferences, and is compatible with the structural form of both columnar and noncolumnar cortex. Multi-way interactions of mirrored representations can provide a preliminary anatomically realistic model of cortical information processing.

The mesoanatomy of the cortex, minimization of free energy, and generative cognition.

Capacity for generativity and unlimited association is the defining characteristic of sentience, and this capacity somehow arises from neuronal self-organization in the cortex. We have previously argued that, consistent with the free energy principle, cortical development is driven by synaptic and cellular selection maximizing synchrony, with effects manifesting in a wide range of features of mesoscopic cortical anatomy. Here, we further argue that in the postnatal stage, as more structured inputs reach the cortex, the same principles of self-organization continue to operate at multitudes of local cortical sites. The unitary ultra-small world structures that emerged antenatally can represent sequences of spatiotemporal images. Local shifts of presynapses from excitatory to inhibitory cells result in the local coupling of spatial eigenmodes and the development of Markov blankets, minimizing prediction errors in each unit's interactions with surrounding neurons. In response to the superposition of inputs exchanged between cortical areas, more complicated, potentially cognitive structures are competitively selected by the merging of units and the elimination of redundant connections that result from the minimization of variational free energy and the elimination of redundant degrees of freedom. The trajectory along which free energy is minimized is shaped by interaction with sensorimotor, limbic, and brainstem mechanisms, providing a basis for creative and unlimited associative learning.

Unification of free energy minimization, spatiotemporal energy, and dimension reduction models of V1 organization: Postnatal learning on an antenatal scaffold.

Developmental selection of neurons and synapses so as to maximize pulse synchrony has recently been used to explain antenatal cortical development. Consequences of the same selection process-an application of the Free Energy Principle-are here followed into the postnatal phase in V1, and the implications for cognitive function are considered. Structured inputs transformed via lag relay in superficial patch connections lead to the generation of circumferential synaptic connectivity superimposed upon the antenatal, radial, "like-to-like" connectivity surrounding each singularity. The spatiotemporal energy and dimension reduction models of cortical feature preferences are accounted for and unified within the expanded model, and relationships of orientation preference (OP), space frequency preference (SFP), and temporal frequency preference (TFP) are resolved. The emergent anatomy provides a basis for "active inference" that includes interpolative modification of synapses so as to anticipate future inputs, as well as learn directly from present stimuli. Neurodynamic properties are those of heteroclinic networks with coupled spatial eigenmodes.

Different visual stimuli affect muscle activation at the knee during sidestepping.

Increasing knee stability via appropriate muscle activation could reduce anterior cruciate ligament (ACL) injury risk during unplanned sidestepping. High-level athletes may activate their knee muscles differently from low-level athletes when responding to quasi-game realistic versus non game-realistic stimuli. Eleven high-level and 10 low-level soccer players responded to a non game-realistic arrow-planned condition (AP), a quasi game-realistic one-defender scenario (1DS) and two-defender scenario (2DS), and an arrow-unplanned condition (AUNP), that imposed increasing time constraints to sidestep. Activation from eight knee muscles during sidestepping was measured during pre-contact and weight-acceptance. Knee flexor-extensor co-activation ratios were established. Muscle activation levels increased by approximately 27% solely in the 1DS in both sidestepping phases. In the 2DS, the shift from a flexor dominant co-activation strategy in pre-contact toward extensor dominance in weight-acceptance commenced earlier for the high-level players. Quasi game-realistic information allowed for anticipatory increases in knee muscle activation regardless of expertise levels but only when the time demands to respond were low (1DS). High-level players were better at interpreting complex game-realistic information (2DS) to activate their knee extensors earlier in preparation for single-leg landing during weight-acceptance.

Further Work on the Shaping of Cortical Development and Function by Synchrony and Metabolic Competition.

This paper furthers our attempts to resolve two major controversies-whether gamma synchrony plays a role in cognition, and whether cortical columns are functionally important. We have previously argued that the configuration of cortical cells that emerges in development is that which maximizes the magnitude of synchronous oscillation and minimizes metabolic cost. Here we analyze the separate effects in development of minimization of axonal lengths, and of early Hebbian learning and selective distribution of resources to growing synapses, by showing in simulations that these effects are partially antagonistic, but their interaction during development produces accurate anatomical and functional properties for both columnar and non-columnar cortex. The resulting embryonic anatomical order can provide a cortex-wide scaffold for postnatal learning that is dimensionally consistent with the representation of moving sensory objects, and, as learning progressively overwrites the embryonic order, further associations also occur in a dimensionally consistent framework. The role ascribed to cortical synchrony does not demand specific frequency, amplitude or phase variation of pulses to mediate "feature linking." Instead, the concerted interactions of pulse synchrony with short-term synaptic dynamics, and synaptic resource competition can further explain cortical information processing in analogy to Hopfield networks and quantum computation.

Möbius-strip-like columnar functional connections are revealed in somato-sensory receptive field centroids.

Receptive fields of neurons in the forelimb region of areas 3b and 1 of primary somatosensory cortex, in cats and monkeys, were mapped using extracellular recordings obtained sequentially from nearly radial penetrations. Locations of the field centroids indicated the presence of a functional system in which cortical homotypic representations of the limb surfaces are entwined in three-dimensional Möbius-strip-like patterns of synaptic connections. Boundaries of somatosensory receptive field in nested groups irregularly overlie the centroid order, and are interpreted as arising from the superposition of learned connections upon the embryonic order. Since the theory of embryonic synaptic self-organization used to model these results was devised and earlier used to explain findings in primary visual cortex, the present findings suggest the theory may be of general application throughout cortex and may reveal a modular functional synaptic system, which, only in some parts of the cortex, and in some species, is manifest as anatomical ordering into columns.

On the dynamics of cortical development: synchrony and synaptic self-organization.

We describe a model for cortical development that resolves long-standing difficulties of earlier models. It is proposed that, during embryonic development, synchronous firing of neurons and their competition for limited metabolic resources leads to selection of an array of neurons with ultra-small-world characteristics. Consequently, in the visual cortex, macrocolumns linked by superficial patchy connections emerge in anatomically realistic patterns, with an ante-natal arrangement which projects signals from the surrounding cortex onto each macrocolumn in a form analogous to the projection of a Euclidean plane onto a Möbius strip. This configuration reproduces typical cortical response maps, and simulations of signal flow explain cortical responses to moving lines as functions of stimulus velocity, length, and orientation. With the introduction of direct visual inputs, under the operation of Hebbian learning, development of mature selective response "tuning" to stimuli of given orientation, spatial frequency, and temporal frequency would then take place, overwriting the earlier ante-natal configuration. The model is provisionally extended to hierarchical interactions of the visual cortex with higher centers, and a general principle for cortical processing of spatio-temporal images is sketched.

Effects of different visual stimuli on postures and knee moments during sidestepping.

PURPOSE: Evasive sidestepping during sports commonly results in noncontact anterior cruciate ligament injuries. Sidestepping in response to different simple visual stimuli has been studied previously but never investigated using quasi-game-realistic visual conditions. We compared the biomechanics of high-level and low-level soccer players when sidestepping in response to projected, three-dimensional defender(s) and the traditionally used planned and unplanned arrow stimuli. METHODS: A three-dimensional motion analysis system captured the trunk and lower limb kinematics and ground reaction forces of 15 high-level and 15 low-level soccer players sidestepping in response to a one-defender scenario (1DS), two-defender scenario (2DS), arrow-planned condition (AP), and arrow-unplanned condition (AUNP). The temporal constraints imposed by the stimuli conditions resulted in increasing difficulty from AP, 1DS, 2DS, to AUNP. Selected joint kinematics and three-dimensional knee moments during the weight-acceptance phase of sidestepping were analyzed. RESULTS: Hip external rotation at initial foot contact was smaller when participants sidestepped in response to the projected defenders versus arrow conditions. Hip abduction was smallest in the AP, moderate in the defender scenarios, and largest in the AUNP. Peak knee valgus moments were 25% larger in the defender scenarios and 70% larger in the AUNP compared with the AP. High-level players exhibited decreased hip abduction and knee valgus moments in the 2DS compared with the low-level players. CONCLUSIONS: Compared with the arrow conditions, sidestepping in response to the defender(s) resulted in different postures and knee moments, which further differentiated between high-level and low-level players in the complex 2DS. These findings highlight the effects of stimuli realism and complexity on the visual-perceptual-motor skill of sidestepping, which has implications for anterior cruciate ligament injury prevention.

Visual search differs but not reaction time when intercepting a 3D versus 2D videoed opponent.

The authors aimed to identify differences in (a) visual search and (b) reaction time when athletes sidestepped to intercept 2D versus 3D videoed opponents. They hypothesized that participants would (a) fixate on different parts of the opponent's body and (b) react quicker when responding to the 3D versus 2D opponent due to the added depth cues. A customized integrated stereoscopic system projected the video stimuli and synchronously recorded the gaze and motor behaviors of 10 men when they responded to two- (2D) and three-dimensional (3D) opponents. The number and duration of gaze fixations were coded according to locations on the opponent's body (head, shoulders, arms, trunk, pelvis, legs) or otherwise (other). Mediolateral pelvic movement was used to infer reaction time. Participants spent 16% less time fixating on the trunk and 23% more time outside the 3D opponent's body compared with the 2D stimulus. No reaction time differences were found. Although participants fixated less on the 3D opponent's body and, by inference, invested less perceptual processing toward interpreting the opponent's movements compared with the 2D condition, they performed the interception task equally fast in both conditions. Three-dimensional depth cues may provide more meaningful information per fixation for successful task performance.

Intrinsic connections in tree shrew V1 imply a global to local mapping.

The local-global map hypothesis states that locally organized response properties--such as orientation preference--result from visuotopically organized local maps of non-retinotopic response properties. In the tree shrew, the lateral extent of horizontal patchy connections is as much as 80-100% of V1 and is consistent with the length summation property. We argue that neural signals can be transmitted across the entire extent of V1 and this allows the formation of maps at the local scale that are visuotopically organized. We describe mechanisms relevant to the formation of local maps and report modeling results showing the same patterns of horizontal connectivity, and relationships to orientation preference, seen in vivo. The structure of the connectivity that emerges in the simulations reveals a 'hub and spoke' organization. Singularities form the centers of local maps, and linear zones and saddle-points arise as smooth border transitions between maps. These findings are used to present the case for the local-global map hypothesis for tree shrew V1.

Spatial eigenmodes and synchronous oscillation: co-incidence detection in simulated cerebral cortex.

Zero-lag synchronisation arises between points on the cerebral cortex receiving concurrent independent inputs; an observation generally ascribed to nonlinear mechanisms. Using simulations of cerebral cortex and Principal Component Analysis (PCA) we show patterns of zero-lag synchronisation (associated with empirically realistic spectral content) can arise from both linear and nonlinear mechanisms. For low levels of activation, we show the synchronous field is described by the eigenmodes of the resultant damped wave activity. The first and second spatial eigenmodes (which capture most of the signal variance) arise from the even and odd components of the independent input signals. The pattern of zero-lag synchronisation can be accounted for by the relative dominance of the first mode over the second, in the near-field of the inputs. The simulated cortical surface can act as a few millisecond response coincidence detector for concurrent, but uncorrelated, inputs. As cortical activation levels are increased, local damped oscillations in the gamma band undergo a transition to highly nonlinear undamped activity with 40 Hz dominant frequency. This is associated with "locking" between active sites and spatially segregated phase patterns. The damped wave synchronisation and the locked nonlinear oscillations may combine to permit fast representation of multiple patterns of activity within the same field of neurons.