A dynamical computational model of theta generation in hippocampal circuits to study theta-gamma oscillations during neurostimulation.

Neurostimulation of the hippocampal formation has shown promising results for modulating memory but the underlying mechanisms remain unclear. In particular, the effects on hippocampal theta-nested gamma oscillations and theta phase reset, which are both crucial for memory processes, are unknown. Moreover, these effects cannot be investigated using current computational models, which consider theta oscillations with a fixed amplitude and phase velocity. Here, we developed a novel computational model that includes the medial septum, represented as a set of abstract Kuramoto oscillators producing a dynamical theta rhythm with phase reset, and the hippocampal formation, composed of biophysically realistic neurons and able to generate theta-nested gamma oscillations under theta drive. We showed that, for theta inputs just below the threshold to induce self-sustained theta-nested gamma oscillations, a single stimulation pulse could switch the network behavior from non-oscillatory to a state producing sustained oscillations. Next, we demonstrated that, for a weaker theta input, pulse train stimulation at the theta frequency could transiently restore seemingly physiological oscillations. Importantly, the presence of phase reset influenced whether these two effects depended on the phase at which stimulation onset was delivered, which has practical implications for designing neurostimulation protocols that are triggered by the phase of ongoing theta oscillations. This novel model opens new avenues for studying the effects of neurostimulation on the hippocampal formation. Furthermore, our hybrid approach that combines different levels of abstraction could be extended in future work to other neural circuits that produce dynamical brain rhythms.

Computational benefits of structural plasticity, illustrated in songbirds.

The plasticity of nervous systems allows animals to quickly adapt to a changing environment. In particular, the structural plasticity of brain networks is often critical to the development of the central nervous system and the acquisition of complex behaviors. As an example, structural plasticity is central to the development of song-related brain circuits and may be critical for song acquisition in juvenile songbirds. Here, we review current evidences for structural plasticity and their significance from a computational point of view. We start by reviewing evidence for structural plasticity across species and categorizing them along the spatial axes as well as the along the time course during development. We introduce the vocal learning circuitry in zebra finches, as a useful example of structural plasticity, and use this specific case to explore the possible contributions of structural plasticity to computational models. Finally, we discuss current modeling studies incorporating structural plasticity and unexplored questions which are raised by such models.

Randomized Self-Organizing Map.

We propose a variation of the self-organizing map algorithm by considering the random placement of neurons on a two-dimensional manifold, following a blue noise distribution from which various topologies can be derived. These topologies possess random (but controllable) discontinuities that allow for a more flexible self-organization, especially with high-dimensional data. The proposed algorithm is tested on one-, two- and three-dimensional tasks, as well as on the MNIST handwritten digits data set and validated using spectral analysis and topological data analysis tools. We also demonstrate the ability of the randomized self-organizing map to gracefully reorganize itself in case of neural lesion and/or neurogenesis.

Stability analysis of a neural field self-organizing map.

We provide theoretical conditions guaranteeing that a self-organizing map efficiently develops representations of the input space. The study relies on a neural field model of spatiotemporal activity in area 3b of the primary somatosensory cortex. We rely on Lyapunov's theory for neural fields to derive theoretical conditions for stability. We verify the theoretical conditions by numerical experiments. The analysis highlights the key role played by the balance between excitation and inhibition of lateral synaptic coupling and the strength of synaptic gains in the formation and maintenance of self-organizing maps.

A Robust Model of Gated Working Memory.

Gated working memory is defined as the capacity of holding arbitrary information at any time in order to be used at a later time. Based on electrophysiological recordings, several computational models have tackled the problem using dedicated and explicit mechanisms. We propose instead to consider an implicit mechanism based on a random recurrent neural network. We introduce a robust yet simple reservoir model of gated working memory with instantaneous updates. The model is able to store an arbitrary real value at random time over an extended period of time. The dynamics of the model is a line attractor that learns to exploit reentry and a nonlinearity during the training phase using only a few representative values. A deeper study of the model shows that there is actually a large range of hyperparameters for which the results hold (e.g., number of neurons, sparsity, global weight scaling) such that any large enough population, mixing excitatory and inhibitory neurons, can quickly learn to realize such gated working memory. In a nutshell, with a minimal set of hypotheses, we show that we can have a robust model of working memory. This suggests this property could be an implicit property of any random population, that can be acquired through learning. Furthermore, considering working memory to be a physically open but functionally closed system, we give account on some counterintuitive electrophysiological recordings.

A natural history of skills.

The dorsal pallium (a.k.a. cortex in mammals) makes a loop circuit with the basal ganglia and the thalamus known to control and adapt behavior but the who's who of the functional roles of these structures is still debated. Influenced by the Triune brain theory that was proposed in the early sixties, many current theories propose a hierarchical organization on the top of which stands the cortex to which the subcortical structures are subordinated. In particular, habits formation has been proposed to reflect a switch from conscious on-line control of behavior by the cortex, to a fully automated subcortical control. In this review, we propose to revalue the function of the network in light of the current experimental evidence concerning the anatomy and physiology of the basal ganglia-cortical circuits in vertebrates. We briefly review the current theories and show that they could be encompassed in a broader framework of skill learning and performance. Then, after reminding the state of the art concerning the anatomical architecture of the network and the underlying dynamic processes, we summarize the evolution of the anatomical and physiological substrate of skill learning and performance among vertebrates. We then review experimental evidence supporting for the hypothesis that the development of automatized skills relies on the BG teaching cortical circuits and is actually a late feature linked with the development of a specialized cortex or pallium that evolved in parallel in different taxa. We finally propose a minimal computational framework where this hypothesis can be explicitly implemented and tested.

A Density-Driven Method for the Placement of Biological Cells Over Two-Dimensional Manifolds.

We introduce a graphical method originating from the computer graphics domain that is used for the arbitrary placement of cells over a two-dimensional manifold. Using a bitmap image whose luminance provides cell density, this method guarantees a discrete distribution of the positions of the cells respecting the local density. This method scales to any number of cells, allows one to specify arbitrary enclosing shapes and provides a scalable and versatile alternative to the more classical assumption of a uniform spatial distribution. The method is illustrated on a discrete homogeneous neural field, on the distribution of cones and rods in the retina and on the neural density of a flattened piece of cortex.

A Computational Model of Dual Competition between the Basal Ganglia and the Cortex.

We propose a model that includes interactions between the cortex, the basal ganglia (BG), and the thalamus based on a dual competition. We hypothesize that the striatum, the subthalamic nucleus (STN), the internal globus pallidus (GPi), the thalamus, and the cortex are involved in closed feedback loops through the hyperdirect and direct pathways. These loops support a competition process that results in the ability of BG to make a cognitive decision followed by a motor one. Considering lateral cortical interactions, another competition takes place inside the cortex allowing the latter to make a cognitive and a motor decision. We show how this dual competition endows the model with two regimes. One is driven by reinforcement learning and the other by Hebbian learning. The final decision is made according to a combination of these two mechanisms with a gradual transfer from the former to the latter. We confirmed these theoretical results on primates (Macaca mulatta) using a novel paradigm predicted by the model.

Re-run, Repeat, Reproduce, Reuse, Replicate: Transforming Code into Scientific Contributions.

Scientific code is different from production software. Scientific code, by producing results that are then analyzed and interpreted, participates in the elaboration of scientific conclusions. This imposes specific constraints on the code that are often overlooked in practice. We articulate, with a small example, five characteristics that a scientific code in computational science should possess: re-runnable, repeatable, reproducible, reusable, and replicable. The code should be executable (re-runnable) and produce the same result more than once (repeatable); it should allow an investigator to reobtain the published results (reproducible) while being easy to use, understand and modify (reusable), and it should act as an available reference for any ambiguity in the algorithmic descriptions of the article (replicable).

Sustainable computational science: the ReScience initiative.

Computer science offers a large set of tools for prototyping, writing, running, testing, validating, sharing and reproducing results; however, computational science lags behind. In the best case, authors may provide their source code as a compressed archive and they may feel confident their research is reproducible. But this is not exactly true. James Buckheit and David Donoho proposed more than two decades ago that an article about computational results is advertising, not scholarship. The actual scholarship is the full software environment, code, and data that produced the result. This implies new workflows, in particular in peer-reviews. Existing journals have been slow to adapt: source codes are rarely requested and are hardly ever actually executed to check that they produce the results advertised in the article. ReScience is a peer-reviewed journal that targets computational research and encourages the explicit replication of already published research, promoting new and open-source implementations in order to ensure that the original research can be replicated from its description. To achieve this goal, the whole publishing chain is radically different from other traditional scientific journals. ReScience resides on GitHub where each new implementation of a computational study is made available together with comments, explanations, and software tests.

A parsimonious computational model of visual target position encoding in the superior colliculus.

The superior colliculus (SC) is a brainstem structure at the crossroad of multiple functional pathways. Several neurophysiological studies suggest that the population of active neurons in the SC encodes the location of a visual target to foveate, pursue or attend to. Although extensive research has been carried out on computational modeling, most of the reported models are often based on complex mechanisms and explain a limited number of experimental results. This suggests that a key aspect may have been overlooked in the design of previous computational models. After a careful study of the literature, we hypothesized that the representation of the whole retinal stimulus (not only its center) might play an important role in the dynamics of SC activity. To test this hypothesis, we designed a model of the SC which is built upon three well-accepted principles: the log-polar representation of the visual field onto the SC, the interplay between a center excitation and a surround inhibition and a simple neuronal dynamics, like the one proposed by the dynamic neural field theory. Results show that the retinotopic organization of the collicular activity conveys an implicit computation that deeply impacts the target selection process.

Structure of receptive fields in a computational model of area 3b of primary sensory cortex.

In a previous work, we introduced a computational model of area 3b which is built upon the neural field theory and receives input from a simplified model of the index distal finger pad populated by a random set of touch receptors (Merkell cells). This model has been shown to be able to self-organize following the random stimulation of the finger pad model and to cope, to some extent, with cortical or skin lesions. The main hypothesis of the model is that learning of skin representations occurs at the thalamo-cortical level while cortico-cortical connections serve a stereotyped competition mechanism that shapes the receptive fields. To further assess this hypothesis and the validity of the model, we reproduced in this article the exact experimental protocol of DiCarlo et al. that has been used to examine the structure of receptive fields in area 3b of the primary somatosensory cortex. Using the same analysis toolset, the model yields consistent results, having most of the receptive fields to contain a single region of excitation and one to several regions of inhibition. We further proceeded our study using a dynamic competition that deeply influences the formation of the receptive fields. We hypothesized this dynamic competition to correspond to some form of somatosensory attention that may help to precisely shape the receptive fields. To test this hypothesis, we designed a protocol where an arbitrary region of interest is delineated on the index distal finger pad and we either (1) instructed explicitly the model to attend to this region (simulating an attentional signal) (2) preferentially trained the model on this region or (3) combined the two aforementioned protocols simultaneously. Results tend to confirm that dynamic competition leads to shrunken receptive fields and its joint interaction with intensive training promotes a massive receptive fields migration and shrinkage.

DANA: distributed numerical and adaptive modelling framework.

DANA is a python framework ( http://dana.loria.fr ) whose computational paradigm is grounded on the notion of a unit that is essentially a set of time dependent values varying under the influence of other units via adaptive weighted connections. The evolution of a unit's value are defined by a set of differential equations expressed in standard mathematical notation which greatly ease their definition. The units are organized into groups that form a model. Each unit can be connected to any other unit (including itself) using a weighted connection. The DANA framework offers a set of core objects needed to design and run such models. The modeler only has to define the equations of a unit as well as the equations governing the training of the connections. The simulation is completely transparent to the modeler and is handled by DANA. This allows DANA to be used for a wide range of numerical and distributed models as long as they fit the proposed framework (e.g. cellular automata, reaction-diffusion system, decentralized neural networks, recurrent neural networks, kernel-based image processing, etc.).

A neural field model of the somatosensory cortex: formation, maintenance and reorganization of ordered topographic maps.

We investigate the formation and maintenance of ordered topographic maps in the primary somatosensory cortex as well as the reorganization of representations after sensory deprivation or cortical lesion. We consider both the critical period (postnatal) where representations are shaped and the post-critical period where representations are maintained and possibly reorganized. We hypothesize that feed-forward thalamocortical connections are an adequate site of plasticity while cortico-cortical connections are believed to drive a competitive mechanism that is critical for learning. We model a small skin patch located on the distal phalangeal surface of a digit as a set of 256 Merkel ending complexes (MEC) that feed a computational model of the primary somatosensory cortex (area 3b). This model is a two-dimensional neural field where spatially localized solutions (a.k.a. bumps) drive cortical plasticity through a Hebbian-like learning rule. Simulations explain the initial formation of ordered representations following repetitive and random stimulations of the skin patch. Skin lesions as well as cortical lesions are also studied and results confirm the possibility to reorganize representations using the same learning rule and depending on the type of the lesion. For severe lesions, the model suggests that cortico-cortical connections may play an important role in complete recovery.

No clock to rule them all.

This article introduces general concepts and definitions related to the notion of asynchronous computation in the framework of artificial neural networks. Using the dynamic field theory as an illustrative example, we explain why one may want to perform such asynchronous computation and how one can implement it since this computational scheme draws several consequences on both the trajectories and the stability of the whole system. After giving an unequivocal definition of asynchronous computation, we present a few practically usable methods and quantitative bounds that can guarantee most of the mesoscopic properties of the system.

Implicit and explicit representations.

During the past decades, the symbol grounding problem, as has been identified by Harnard [Harnard, S. (1990). The symbol grounding problem. Physica D: Nonlinear Phenomena, 42, 335-346], became a prominent problem in the cognitive science society. The idea that a symbol is much more than a mere meaningless token that can be processed through some algorithm, sheds new light on higher brain functions such as language and cognition. We present in this article a computational framework that may help in our understanding of the nature of grounded representations. Two models are briefly introduced that aim at emphasizing the difference we make between implicit and explicit representations.

Emergence of attention within a neural population.

We present a dynamic model of attention based on the Continuum Neural Field Theory that explains attention as being an emergent property of a neural population. This model is experimentally proved to be very robust and able to track one static or moving target in the presence of very strong noise or in the presence of a lot of distractors, even more salient than the target. This attentional property is not restricted to the visual case and can be considered as a generic attentional process of any spatio-temporal continuous input.