Towards a Unified Theory of Neocortex: Laminar Cortical Circuits for Vision and Cognition

A key goal of computational neuroscience is to link brain mechanisms to behavioral functions. The present article describes recent progress towards explaining how laminar neocortical circuits give rise to biological intelligence. These circuits embody two new and revolutionary computational paradigms: Complementary Computing and Laminar Computing. Circuit properties include a novel synthesis of feedforward and feedback processing, of digital and analog processing, and of pre-attentive and attentive processing. This synthesis clarifies the appeal of Bayesian approaches but has a far greater predictive range that naturally extends to self-organizing processes. Examples from vision and cognition are summarized. A LAMINART architecture unifies properties of visual development, learning, perceptual grouping, attention, and 3D vision. A key modeling theme is that the mechanisms which enable development and learning to occur in a stable way imply properties of adult behavior. It is noted how higher-order attentional constraints can influence multiple cortical regions, and how spatial and object attention work together to learn view-invariant object categories. In particular, a form-fitting spatial attentional shroud can allow an emerging view-invariant object category to remain active while multiple view categories are associated with it during sequences of saccadic eye movements. Finally, the chapter summarizes recent work on the LIST PARSE model of cognitive information processing by the laminar circuits of prefrontal cortex. LIST PARSE models the short-term storage of event sequences in working memory, their unitization through learning into sequence, or list, chunks, and their read-out in planned sequential performance that is under volitional control. LIST PARSE provides a laminar embodiment of Item and Order working memories, also called Competitive Queuing models, that have been supported by both psychophysical and neurobiological data. These examples show how variations of a common laminar cortical design can embody properties of visual and cognitive intelligence that seem, at least on the surface, to be mechanistically unrelated.

Working Memory Networks for Learning Multiple Groupings of Temporarily Ordered Events: Applications to 3-D Visual Object Recognition

Working memory neural networks are characterized which encode the invariant temporal order of sequential events that may be presented at widely differing speeds, durations, and interstimulus intervals. This temporal order code is designed to enable all possible groupings of sequential events to be stably learned and remembered in real time, even as new events perturb the system. Such a competence is needed in neural architectures which self-organize learned codes for variable-rate speech perception, sensory-motor planning, or 3-D visual object recognition. Using such a working memory, a self-organizing architecture for invariant 3-D visual object recognition is described that is based on the model of Seibert and Waxman [1].

Working Memory Networks for Learning Temporal Order, with Application to 3-D Visual Object Recognition

Working memory neural networks are characterized which encode the invariant temporal order of sequential events. Inputs to the networks, called Sustained Temporal Order REcurrent (STORE) models, may be presented at widely differing speeds, durations, and interstimulus intervals. The STORE temporal order code is designed to enable all emergent groupings of sequential events to be stably learned and remembered in real time, even as new events perturb the system. Such a competence is needed in neural architectures which self-organize learned codes for variable-rate speech perception, sensory-motor planning, or 3-D visual object recognition. Using such a working memory, a self-organizing architecture for invariant 3-D visual object recognition is described. The new model is based on the model of Seibert and Waxman (1990a), which builds a 3-D representation of an object from a temporally ordered sequence of its 2-D aspect graphs. The new model, called an ARTSTORE model, consists of the following cascade of processing modules: Invariant Preprocessor --> ART 2 --> STORE Model --> ART 2 --> Outstar Network.

How Spinal Neural Networks Reduce Discrepancies between Motor Intention and Motor Realization

This paper attempts a rational, step-by-step reconstruction of many aspects of the mammalian neural circuitry known to be involved in the spinal cord's regulation of opposing muscles acting on skeletal segments. Mathematical analyses and local circuit simulations based on neural membrane equations are used to clarify the behavioral function of five fundamental cell types, their complex connectivities, and their physiological actions. These cell types are: α-MNs, γ-MNs, IaINs, IbINs, and Renshaw cells. It is shown that many of the complexities of spinal circuitry are necessary to ensure near invariant realization of motor intentions when descending signals of two basic types independently vary over large ranges of magnitude and rate of change. Because these two types of signal afford independent control, or Factorization, of muscle LEngth and muscle TEnsion, our construction was named the FLETE model (Bullock and Grossberg, 1988b, 1989). The present paper significantly extends the range of experimental data encompassed by this evolving model.

Working Memories for Storage and Recall of Arbitrary Temporal Sequences

A working memory model is described that is capable of storing and recalling arbitrary temporal sequences of events, including repeated items. These memories encode the invariant temporal order of sequential events that may be presented at widely differing speeds, durations, and interstimulus intervals. This temporal order code is designed to enable all possible groupings of sequential events to be stably learned and remembered in real time, even as new events perturb the system.

Neural Representations for Sensory-Motor Control I: Head-Centered 3-D Target Positions from Opponent Eye Commands

This article describes how corollary discharges from outflow eye movement commands can be transformed by two stages of opponent neural processing into a head-centered representation of 3-D target position. This representation implicitly defines a cyclopean coordinate system whose variables approximate the binocular vergence and spherical horizontal and vertical angles with respect to the observer's head. Various psychophysical data concerning binocular distance perception and reaching behavior are clarified by this representation. The representation provides a foundation for learning head-centered and body-centered invariant representations of both foveated and non-foveated 3-D target positions. It also enables a solution to be developed of the classical motor equivalence problem, whereby many different joint configurations of a redundant manipulator can all be used to realize a desired trajectory in 3-D space.

Store Working Memory Networks for Storage and Recall of Arbitrary Temporal Sequences

Neural network models of working memory, called Sustained Temporal Order REcurrent (STORE) models, are described. They encode the invariant temporal order of sequential events in short term memory (STM) in a way that mimics cognitive data about working memory, including primacy, recency, and bowed order and error gradients. As new items are presented, the pattern of previously stored items is invariant in the sense that, relative activations remain constant through time. This invariant temporal order code enables all possible groupings of sequential events to be stably learned and remembered in real time, even as new events perturb the system. Such a competence is needed to design self-organizing temporal recognition and planning systems in which any subsequence of events may need to be categorized in order to to control and predict future behavior or external events. STORE models show how arbitrary event sequences may be invariantly stored, including repeated events. A preprocessor interacts with the working memory to represent event repeats in spatially separate locations. It is shown why at least two processing levels are needed to invariantly store events presented with variable durations and interstimulus intervals. It is also shown how network parameters control the type and shape of primacy, recency, or bowed temporal order gradients that will be stored.

A Neural Network Model for Cursive Script Production

This article describes a neural network model, called the VITEWRITE model, for generating handwriting movements. The model consists of a sequential controller, or motor program, that interacts with a trajectory generator to move a. hand with redundant degrees of freedom. The neural trajectory generator is the Vector Integration to Endpoint (VITE) model for synchronous variable-speed control of multijoint movements. VITE properties enable a simple control strategy to generate complex handwritten script if the hand model contains redundant degrees of freedom. The proposed controller launches transient directional commands to independent hand synergies at times when the hand begins to move, or when a velocity peak in a given synergy is achieved. The VITE model translates these temporally disjoint synergy commands into smooth curvilinear trajectories among temporally overlapping synergetic movements. The separate "score" of onset times used in most prior models is hereby replaced by a self-scaling activity-released "motor program" that uses few memory resources, enables each synergy to exhibit a unimodal velocity profile during any stroke, generates letters that are invariant under speed and size rescaling, and enables effortless. connection of letter shapes into words. Speed and size rescaling are achieved by scalar GO and GRO signals that express computationally simple volitional commands. Psychophysical data concerning band movements, such as the isochrony principle, asymmetric velocity profiles, and the two-thirds power law relating movement curvature and velocity arise as emergent properties of model interactions.

Accommodating curvature in a highly ordered functionalized metal oxide nanofiber: synthesis, characterization and multi-scale modeling of layered nanosheets

A key element in the rational design of hybrid organic-inorganic nanostructures, is control of surfactant packing and adsorption onto the inorganic phase in crystal growth and assembly. In layered single crystal nanofibers and bilayered 2D nanosheets of vanadium oxide, we show how the chemisorption of preferred densities of surfactant molecules can direct formation of ordered, curved layers. The atom-scale features of the structures are described using molecular dynamics simulations that quantify surfactant packing effects and confirm the preference for a density of 5 dodecanethiol molecules per 8 vanadium attachment sites in the synthesised structures. This assembly maintains a remarkably well ordered interlayer spacing, even when curved. The assemblies of interdigitated organic bilayers on V2O5 are shown to be sufficiently flexible to tolerate curvature while maintaining a constant interlayer distance without rupture, delamination or cleavage. The accommodation of curvature and invariant structural integrity points to a beneficial role for oxide-directed organic film packing effects in layered architectures such as stacked nanofibers and hybrid 2D nanosheet systems.

Morphologically cryptic biological species within the liverwort Frullania asagrayana.

UNLABELLED: PREMISE OF THE STUDY: The Frullania tamarisci complex includes eight Holarctic liverwort species. One of these, F. asagrayana, is distributed broadly throughout eastern North America from Canada to the Gulf Coast. Preliminary genetic data suggested that the species includes two groups of populations. This study was designed to test whether the two groups are reproductively isolated biological species. • METHODS: Eighty-eight samples from across the range of F. asagrayana, plus 73 samples from one population, were genotyped for 13 microsatellite loci. Sequences for two plastid loci and nrITS were obtained from 13 accessions. Genetic data were analyzed using coalescent models and Bayesian inference. • KEY RESULTS: Frullania asagrayana is sequence-invariant at the two plastid loci and ITS2, but two clear groups were resolved by microsatellites. The two groups are largely reproductively isolated, but there is a low level of gene flow from the southern to the northern group. No gene flow was detected in the other direction. A local population was heterogeneous but displayed strong genetic structure. • CONCLUSIONS: The genetic structure of F. asagrayana in eastern North America reflects morphologically cryptic differentiation between reproductively isolated groups of populations, near-panmixis within groups, and clonal propagation at local scales. Reproductive isolation between groups that are invariant at the level of nucleotide sequences shows that caution must be exercised in making taxonomic and evolutionary inferences from reciprocal monophyly (or lack thereof) between putative species.

Spike avalanches exhibit universal dynamics across the sleep-wake cycle.

BACKGROUND: Scale-invariant neuronal avalanches have been observed in cell cultures and slices as well as anesthetized and awake brains, suggesting that the brain operates near criticality, i.e. within a narrow margin between avalanche propagation and extinction. In theory, criticality provides many desirable features for the behaving brain, optimizing computational capabilities, information transmission, sensitivity to sensory stimuli and size of memory repertoires. However, a thorough characterization of neuronal avalanches in freely-behaving (FB) animals is still missing, thus raising doubts about their relevance for brain function. METHODOLOGY/PRINCIPAL FINDINGS: To address this issue, we employed chronically implanted multielectrode arrays (MEA) to record avalanches of action potentials (spikes) from the cerebral cortex and hippocampus of 14 rats, as they spontaneously traversed the wake-sleep cycle, explored novel objects or were subjected to anesthesia (AN). We then modeled spike avalanches to evaluate the impact of sparse MEA sampling on their statistics. We found that the size distribution of spike avalanches are well fit by lognormal distributions in FB animals, and by truncated power laws in the AN group. FB data surrogation markedly decreases the tail of the distribution, i.e. spike shuffling destroys the largest avalanches. The FB data are also characterized by multiple key features compatible with criticality in the temporal domain, such as 1/f spectra and long-term correlations as measured by detrended fluctuation analysis. These signatures are very stable across waking, slow-wave sleep and rapid-eye-movement sleep, but collapse during anesthesia. Likewise, waiting time distributions obey a single scaling function during all natural behavioral states, but not during anesthesia. Results are equivalent for neuronal ensembles recorded from visual and tactile areas of the cerebral cortex, as well as the hippocampus. CONCLUSIONS/SIGNIFICANCE: Altogether, the data provide a comprehensive link between behavior and brain criticality, revealing a unique scale-invariant regime of spike avalanches across all major behaviors.

Emotion-attention network interactions during a visual oddball task.

Emotional and attentional functions are known to be distributed along ventral and dorsal networks in the brain, respectively. However, the interactions between these systems remain to be specified. The present study used event-related functional magnetic resonance imaging (fMRI) to investigate how attentional focus can modulate the neural activity elicited by scenes that vary in emotional content. In a visual oddball task, aversive and neutral scenes were presented intermittently among circles and squares. The squares were frequent standard events, whereas the other novel stimulus categories occurred rarely. One experimental group [N=10] was instructed to count the circles, whereas another group [N=12] counted the emotional scenes. A main effect of emotion was found in the amygdala (AMG) and ventral frontotemporal cortices. In these regions, activation was significantly greater for emotional than neutral stimuli but was invariant to attentional focus. A main effect of attentional focus was found in dorsal frontoparietal cortices, whose activity signaled task-relevant target events irrespective of emotional content. The only brain region that was sensitive to both emotion and attentional focus was the anterior cingulate gyrus (ACG). When circles were task-relevant, the ACG responded equally to circle targets and distracting emotional scenes. The ACG response to emotional scenes increased when they were task-relevant, and the response to circles concomitantly decreased. These findings support and extend prominent network theories of emotion-attention interactions that highlight the integrative role played by the anterior cingulate.

The abelianization of the Johnson kernel

We prove that the first complex homology of the Johnson subgroup of the Torelli group Tg is a non-trivial, unipotent Tg-module for all g ≥ 4 and give an explicit presentation of it as a Sym H 1(Tg,C)-module when g ≥ 6. We do this by proving that, for a finitely generated group G satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the infinitesimal Alexander invariant of the associated graded Lie algebra of G. In this setup, we also obtain a precise nilpotence test. © European Mathematical Society 2014.

Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

Automatic verification of linear controller software

© 2015 IEEE.We consider the problem of verification of software implementations of linear time-invariant controllers. Commonly, different implementations use different representations of the controller's state, for example due to optimizations in a third-party code generator. To accommodate this variation, we exploit input-output controller specification captured by the controller's transfer function and show how to automatically verify correctness of C code controller implementations using a Frama-C/Why3/Z3 toolchain. Scalability of the approach is evaluated using randomly generated controller specifications of realistic size.