Transient localized wave patterns and their application to migraine

Transient dynamics is pervasive in the human brain and poses challenging problems both in mathematical tractability and clinical observability. We investigate statistical properties of transient cortical wave patterns with characteristic forms (shape, size, duration) in a canonical reaction-diffusion model with mean field inhibition. The patterns are formed by a ghost near a saddle-node bifurcation in which a stable traveling wave (node) collides with its critical nucleation mass (saddle). Similar patterns have been observed with fMRI in migraine. Our results support the controversial idea that waves of cortical spreading depression (SD) have a causal relationship with the headache phase in migraine and therefore occur not only in migraine with aura (MA) but also in migraine without aura (MO), i.e., in the two major migraine subforms. We suggest a congruence between the prevalence of MO and MA with the statistical properties of the traveling waves' forms, according to which (i) activation of nociceptive mechanisms relevant for headache is dependent upon a sufficiently large instantaneous affected cortical area anti-correlated to both SD duration and total affected cortical area such that headache would be less severe in MA than in MO (ii) the incidence of MA is reflected in the distance to the saddle-node bifurcation, and (iii) the contested notion of MO attacks with silent aura is resolved. We briefly discuss model-based control and means by which neuromodulation techniques may affect pathways of pain formation.Comment: 14 pages, 11 figure

Coarse-Graining Auto-Encoders for Molecular Dynamics

Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and spatial scales involved in thermodynamic and kinetic phenomena in materials, atomistic simulations are often computationally unfeasible. Coarse-graining methods allow simulating larger systems, by reducing the dimensionality of the simulation, and propagating longer timesteps, by averaging out fast motions. Coarse-graining involves two coupled learning problems; defining the mapping from an all-atom to a reduced representation, and the parametrization of a Hamiltonian over coarse-grained coordinates. Multiple statistical mechanics approaches have addressed the latter, but the former is generally a hand-tuned process based on chemical intuition. Here we present Autograin, an optimization framework based on auto-encoders to learn both tasks simultaneously. Autograin is trained to learn the optimal mapping between all-atom and reduced representation, using the reconstruction loss to facilitate the learning of coarse-grained variables. In addition, a force-matching method is applied to variationally determine the coarse-grained potential energy function. This procedure is tested on a number of model systems including single-molecule and bulk-phase periodic simulations.Comment: 8 pages, 6 figure

VIOLA - A multi-purpose and web-based visualization tool for neuronal-network simulation output

Neuronal network models and corresponding computer simulations are invaluable tools to aid the interpretation of the relationship between neuron properties, connectivity and measured activity in cortical tissue. Spatiotemporal patterns of activity propagating across the cortical surface as observed experimentally can for example be described by neuronal network models with layered geometry and distance-dependent connectivity. The interpretation of the resulting stream of multi-modal and multi-dimensional simulation data calls for integrating interactive visualization steps into existing simulation-analysis workflows. Here, we present a set of interactive visualization concepts called views for the visual analysis of activity data in topological network models, and a corresponding reference implementation VIOLA (VIsualization Of Layer Activity). The software is a lightweight, open-source, web-based and platform-independent application combining and adapting modern interactive visualization paradigms, such as coordinated multiple views, for massively parallel neurophysiological data. For a use-case demonstration we consider spiking activity data of a two-population, layered point-neuron network model subject to a spatially confined excitation originating from an external population. With the multiple coordinated views, an explorative and qualitative assessment of the spatiotemporal features of neuronal activity can be performed upfront of a detailed quantitative data analysis of specific aspects of the data. Furthermore, ongoing efforts including the European Human Brain Project aim at providing online user portals for integrated model development, simulation, analysis and provenance tracking, wherein interactive visual analysis tools are one component. Browser-compatible, web-technology based solutions are therefore required. Within this scope, with VIOLA we provide a first prototype.Comment: 38 pages, 10 figures, 3 table

Synchronization of electrically coupled resonate-and-fire neurons

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with strong electrical coupling have been shown to exhibit resonant properties, and the subthreshold fluctuations arising from resonance are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with linear subthreshold dynamics and discrete post-spike reset. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuity in the dynamics. We find that both spikes and resonant subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs

Network Plasticity as Bayesian Inference

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features of synaptic plasticity and spine motility enable cortical networks of neurons to carry out probabilistic inference by sampling from a posterior distribution of network configurations. This model provides a viable alternative to existing models that propose convergence of parameters to maximum likelihood values. It explains how priors on weight distributions and connection probabilities can be merged optimally with learned experience, how cortical networks can generalize learned information so well to novel experiences, and how they can compensate continuously for unforeseen disturbances of the network. The resulting new theory of network plasticity explains from a functional perspective a number of experimental data on stochastic aspects of synaptic plasticity that previously appeared to be quite puzzling.Comment: 33 pages, 5 figures, the supplement is available on the author's web page http://www.igi.tugraz.at/kappe

Sensory Motor Remapping of Space in Human-Machine Interfaces

Studies of adaptation to patterns of deterministic forces have revealed the ability of the motor control system to form and use predictive representations of the environment. These studies have also pointed out that adaptation to novel dynamics is aimed at preserving the trajectories of a controlled endpoint, either the hand of a subject or a transported object. We review some of these experiments and present more recent studies aimed at understanding how the motor system forms representations of the physical space in which actions take place. An extensive line of investigations in visual information processing has dealt with the issue of how the Euclidean properties of space are recovered from visual signals that do not appear to possess these properties. The same question is addressed here in the context of motor behavior and motor learning by observing how people remap hand gestures and body motions that control the state of an external device. We present some theoretical considerations and experimental evidence about the ability of the nervous system to create novel patterns of coordination that are consistent with the representation of extrapersonal space. We also discuss the perspective of endowing human–machine interfaces with learning algorithms that, combined with human learning, may facilitate the control of powered wheelchairs and other assistive devices