The 22nd Annual Computational Neuroscience Meeting (CNS 2013) was held during July 13-18, 2013 in the Latin Quarter in the heart of Paris, France at the Université Paris Descartes. The conference began just after a transition from cloudy and cool weather to sunshine and warmth that lasted for the duration of the conference. The meeting was attended by approximately 800 people (a record) with rich and diverse research backgrounds, spanning mathematics and statistics, physics, neuroscience and biology, engineering, computer science, and more. As the mission statement of the Organization for Computational Neurosciences (OCNS), which organizes the conference), reads, “Computational neuroscience is a field of research that combines mathematical analysis and computer simulation with experimental neuroscience to develop a principled understanding of the workings of the nervous system and apply it in a wide range of technologies.” Accordingly, dynamical systems theory and their simulation play a significant and integral role in this area of research, which studies the behavior of the central nervous system over a range of spatial scales, from sub-cellular structures and the single-cell level to large neuronal populations, neural tissue, and whole brain level.

The Annual CNS meeting is organized into three components: (i) tutorials, (ii) the main session and evening poster sessions, and (iii) workshops. Day 1 was composed of nine parallel tutorial sessions, each running from 9 am to 5 pm, followed by an evening keynote presentation that marked the beginning of the main section of the meeting. Days 2-4 each were composed of a single session of oral presentations from 9 am - 5 pm (including a 60-minute keynote each day in addition to many 20 - 40-minute presentations) that was then followed from 5 pm - 8 pm each evening by an extensive poster session, including 435 posters over three days. Days 5-6 were composed of focused workshops (9 am - 5:30 pm) on various subfields of research. There were 20 workshops in total, with 15 single-day workshops and 5 two-day workshops.

Neural field and neural mass models had a very strong representation this year (as compared with most years) and served as a particularly exciting feature of this conference. One tutorial and one workshop specifically devoted to this area of research enjoyed very high attendance, with the tutorial session becoming standing-room-only for much of the time. Neural mass models can be regarded as a special case of ensemble density models for describing a large population of neurons in which the dynamics of the ensemble density is replaced by the dynamics of its center of mass. Neural mass models take the form of nonlinear systems of ordinary differential equations. Conversely, neural field models are spatially-extended mean-field models that describe the average activity of local populations of neurons across layers or regions of the brain as a continuum. Neural field models are dynamical systems that take the form of either nonlinear integro-differential equations or partial differential equations.

During the first day of the conference, Axel Hutt, Victor Jirsa, John Terry, and Wolfram Erlhagen gave excellent tutorials on neural field and neural mass models, covering (i) the physiological and mathematical basis of the various families of models, (ii) pattern formation and applications to human movement, (iii) understanding transitions in electroencephalogram (EEG) recordings during normal and pathological activity associated with epilepsy, and (iv) development of a systematic way to endow robots with cognitive functions.

At the main conference, Ingo Bojak (co-organizer of the workshop on neural mass models) gave a very nice oral presentation discussing the use of a neural field model to understand spectral changes in the EEG resulting from interactions of the anesthetics ketamine and propofol which, he argued, can be explained by the anethetics’ effects on a particular potassium channel. Over the course of the three evening poster sessions, there were a large number of posters on neural field and neural mass models. A pdf of the poster abstracts is available and searchable here and here.

On the penultimate day of the conference, an excellent full-day workshop on “advances in neural mass models” and neural fields was organized by Ingo Bojak, Stephan van Gils, and Sid Visser and covered a wide range of aspects of these models, from mathematical theory to modeling and connections with experimental data. The mathematics heavily emphasized dynamical-systems approaches.

Steven Schiff gave an interesting talk on control theory, seizures and spreading depression and, as he usually does, he raised and emphasized relevant biological concerns that modelers should be aware of when developing and analyzing neural mass and neural field models.

Pascal Chossat presented recent advances on analytical techniques for studying existence and stability of solutions in neural fields with smooth (sigmoid) firing-rate functions (an important avenue in need of development). Interestingly, he revealed the origin of stationary “bump” solutions as a bifurcation from the homogeneous state as a parameter controlling the steepness of the sigmoid firing rate passes through a critical point.

To digress briefly, “stationary bump” solutions in neural fields are a common type of spatially-localized equilibrium that represents a localized population of interacting neurons that are persistently firing, either in an autonomous fashion or in response to a stimulus input. The autonomous case has served, for example, to model the neural representation of “spatial working memory,” i.e., a short-term memory of the spatial location of an object that is no longer in view. Interestingly, in a concurrent workshop at the conference organized by Albert Compte and Zachary Kilpatrick on “neural mechanisms of working memory limits,” Albert Compte presented the first experimental evidence from monkey prefrontal cortex (recently appearing in Nature Neuroscience) that supports this long-proposed idea of persistent firing in the form of a “diffusing bump” serving as a representation of working memory during spatial working memory tasks. Zachary Kilpatrick has been examining the diffusing effects of noise on stationary bumps in both neural field models and other types of network models, the latter of which he also presented in that workshop.

Returning to the workshop on neural masses and neural fields, I presented a survey of a collection of results (including some work with Paul Bressloff and some with Bard Ermentrout) on the emergence of different types of localized solutions (both stationary and oscillatory) that bifurcate from stationary bump solutions in various classes of neural field models on 1D and 2D domains. In particular, I showed how the spatial structure of synaptic interactions in each model governs the linearization about the bump and directly shapes the spatial structure of the bifurcating solutions.

Stephan van Gils discussed and raised awareness of the special issues and difficulties that arise when analyzing neural field equations with delays and described recent work developing the proper framework for analyzing the stability and bifurcation of steady-state solutions by employing the theory of dual semigroups (sun-star calculus).

Romain Veltz presented analytic methods and results for studying neural field models with two different types of delays (synaptic delays and propagation delays) and used it to explore Hopf and Hopf-Hopf bifurcations in a particular neural field model.

Nicolas Brunel illustrated a nice approach to reduce a large population of spiking neuronal models (exponential integrate-and-fire) by a small number of ODEs and subsequently demonstrated the ability of this approximation to capture the dynamics of the full network.

Victor Jirsa began by discussing the mathematical analysis of seizure dynamics to identify characteristics that are conserved across many different syndromes, brain regions, and species. This was then used to build a general phenomenological neural mass model of seizure dynamics that showed how seizure onset could be reached experimentally through very different routes, possibly indicating why seizures are difficult to treat and predict.

Michael Breakspear explored some of the implications of multiplicative noise in neural field models and discussed their role in the context of applications.

Based upon neural mass models, Thomas Knösce proposed a novel, biologically relevant model for a local cortical circuit to account for two important features: (i) more realistic interlaminar connectivity and dynamics and (ii) activity-dependent plasticity explicitly dependent on neurotransmitters. He demonstrated results of this model in the context of auditory habituation and argued that the novel features could allow one to connect the behavior of the model to macroscopic features captured in recordings of the EEG.

Dimiri Pintosis discussed recent advances for using “dynamic causal modeling” to characterize the spatial parameters of cortical connections and speed of propagation and showed how the question of interest can inform the choice of appropriate model.

Kevin Green, a doctoral student of Lennaert van Veen, presented recent work on developing scalable algorithms for simulation and dynamical analysis of a large class of neural field models that can be recast as traditional partial differential equations. He demonstrated their use for studying complex spatiotemporal dynamics and discussed a pursuit to develop a readily usable software package to aid in studying these models.

Axel Hutt presented interesting recent work on additive noise in neural field equations and showed results on developing a stochastic center manifold approach for neural field equations.

Two other workshops that were organized on the final day of the conference involved some neural field and neural mass models. In one workshop, organized by Axel Hutt on modeling general anesthesia, neural field and neural mass models were employed in some talks including presentations by Alistair Steyn-Ross on inhibitory mechanisms, Lennaert van Veen on burst suppression, and Axel Hutt on alpha band power in EEG recordings. Victor Jirsa and Gustavo Deco organized the other workshop, ambitiously titled “full brain network dynamics - modeling, analyses, experiments,” in which neural mass models had significant representation.

Contributed by Stefanos Folias