CNS*2019 Workshop

Phase Transitions in Brain Networks


Phase transitions occur in a variety of physical and biological systems, including brain networks. They are characterized by instabilities that generate special dynamical properties, which are associated with dynamical and functional benefits. Phase transition is also an appealing framework that has been utilised to explain pathological brain activity. Historically, the idea of phase transitions in the brain is not new and has sparked some controversy over the years. In this half-day workshop, a number of current world-class experts will revisit the possible roles of phase transitions in the brain. They will discuss the recent progress in the field and the relevance and limitations of this framework to computational neuroscience. In order to further exploit and explicitize contemporary viewpoints on the promises and pitfalls of phase transitions in the brain, we will end this workshop with a roundtable discussion in which the speakers and the audience will be invited to participate.

When: July 16.

Where: Room B2, Historical BuildingUniversitat de Barcelona (UB).


9:30-9:55        Linda Douw (Amsterdam UMC): A historical perspective on phase transitions in the brain

9:55-10:20      Anna Levina (MPI): Influence of spatial structure on data processing and phase transitions in neuronal networks

10:20-10:45    Jonathan Touboul (Brandeis University): Power-law scalings in neuronal data: proofs for criticality?

10:45-11:15    Coffee Break   

11:15-11:40    Etienne Hugues (Université Grenoble Alpes): Hallmarks of spontaneous and stimulation-induced activity are reproduced in a scale-invariant avalanche regime

11:40-12:05    Fernando Santos (UFPE): Topological phase transitions in functional brain networks

12:05-12:30    James Roberts (QIMRB): Geometry and fragility of the human connectome

12:30-13:00    Roundtable discussions


Linda Douw (Amsterdam UMC)

A historical perspective on phase transitions in the brain 

The brain has been seen as either a distributed collection of localized centers of function, or as an integrated, dynamic system. With the latter view come the concepts of criticality from physics and phase transitions from thermodynamics, which have been amply applied to the brain over the past decades. In this historical overview, some background on the investigation of phase transitions in the brain will be provided, as well as the controversies that have sparked over it.

Anna Levina (MPI)

Influence of spatial structure on data processing and phase transitions in neuronal networks

Networks are backbones of the complex brain activity. Modern methods allow extracting more and more reliable functional and structural networks on different scales. One of the major challenges is to understand the relationship between the structure of the network and the properties of its dynamics. Using simple models and data analysis I am going to discuss, on the one hand, how the features of the networks are reflected in the dynamics of single units. And on the other hand, how the system's structure changes the nature of the phase transition in its dynamics.

Jonathan Touboul (Brandeis University)

Power-law scalings in neuronal data: proofs for criticality?

A current debate in the theoretical and experimental neuroscience community consists in establishing whether or not neural networks operate at criticality. From neuronal cultures and brain slices to anesthetized and even behaving animals, criticality or quasi-criticality was reported based on the analysis of collective activation in macroscopic signals (Local Field Potentials or LFP) or spiking data. Such a remarkable universality of statistics appearing in widely distinct brain states is fascinating, and calls from a better understanding of their origin. In this talk, I will present our tentative to find predictive criteria distinctive of criticality in neuronal data. I will start by presenting how power laws naturally arise when considering avalanches from indirect measurement of brain activity by thresholding LFPs, even when this thresholding is not related to spiking activity, as it appears in surrogate datasets in which the structure of spiking was destroyed. These scalings, arising in non-critical systems, therefore cannot be used as a proof for criticality and more analysis is needed. At a finer scale, power-laws in avalanches were reported at the scale of single units, measurements therefore devoid of such possible confusing effects. In addition to power-law scalings, multi-unit recordings also showed scale invariance of neuronal avalanches and relationship between scaling exponents consistent with critical systems. I will show that such scalings also arise universally in non-critical systems, associated to Boltzmann’s molecular chaos regime. As such, they also arise in stochastic surrogate of the network, where all units are replaced by independent Poisson stochastic processes. However, while the scaling exponents are identical in critical and non-critical systems, the relationship between experimentally fitted scaling exponents should be significantly different, providing a way to distinguish critical and non-critical networks. This analysis thus suggests that power-law scaling of macroscopic variables seems to be a generic feature of high-dimensional systems, and does not constitute a proof of criticality, potentially explaining some contradictory experimental results and unifying measurements of the awake brain at different scales, as well as network models and their surrogates.

Etienne Hugues (Université Grenoble Alpes)
Hallmarks of spontaneous and stimulation-induced activity are reproduced in a scale-invariant avalanche regime
As neurons are spontaneously active, a global state emerges on the brain network. This spontaneous state is of utmost importance as sensory stimulation for example, activating a relatively small subset of all neurons, can be seen as a perturbation of this state. In other words, cognition inherits from the resting state. The resting state has been the focus of intense study in the last two decades, uncovering its spatial and temporal organization with functional connectivity (FC) and scale-invariant neuronal avalanches. Under stimulation, increased neural activity propagates on the brain network, and the firing variability across trials generally decreases. What properties should have the spontaneous state to exhibit such hallmarks is unknown.
Mesoscopic large-scale modeling, where the full neuronal network of the brain is coarse-grained at the local neural network level, has been essentially focused on reproducing resting state FC. The main proposed dynamical scenario of the spontaneous state -denoted here the fluctuation scenario, corresponds to neural activity wandering around a stable global fixed point with low firing rate, corresponding to a global asynchronous state. Despite its ability to reproduce FC, this scenario is unable to exhibit scale-invariant neuronal avalanches and stimulation-induced propagation of activity. In this talk, I will show why the fluctuation scenario fails. I will also show how known biophysics allows to introduce a new dynamical scenario, in which a regime of scale-invariant neuronal avalanches reproduces the hallmarks of the spontaneous state and during stimulation.  

Fernando Santos (UFPE)

Topological phase transitions in functional brain networks

Functional brain networks are often constructed by quantifying correlations among brain regions. Their topological structure includes nodes, edges, triangles and even higher-dimensional objects. Topological data analysis (TDA) is the emerging framework to process datasets under this perspective. Here we report the discovery of topological phase transitions in functional brain networks by merging concepts from TDA, topology, geometry, physics, and network theory. We show that topological phase transitions occur when the Euler entropy has a singularity, which remarkably coincides with the emergence of multidimensional topological holes in the brain network. Our results suggest that a major alteration in the pattern of brain correlations can modify the signature of such transitions, and may point to suboptimal brain functioning. Due to the universal character of phase transitions and noise robustness of TDA, our findings open perspectives towards establishing reliable topological and geometrical biomarkers of individual and group differences in functional brain network organization.

James Roberts (QIMRB)
Geometry and fragility of the human connectome
The human connectome is a topologically complex, spatially embedded network. While its topological properties have been richly characterized, the constraints imposed by its spatial embedding are poorly understood. In this talk I will present a recent novel resampling method that enables randomization of a network while preserving its spatial embedding. Applying this method to tractography data reveals that the brain's spatial embedding – its geometry – makes a major contribution to the topology of the human connectome. For example, geometry accounts for much of the brain's modularity. But geometry is not the sole determinant: the brain's structural hubs would be positioned closer to the geometric center of the brain if geometry was the only source of topology. Closer analysis of the brain's hubs under weaker randomization reveals that the brain sits at a local minimum in wiring cost, and that progressive randomization leads to a topologically unstable regime consistent with a phase transition. Moreover, prefrontal hubs are particularly fragile to perturbations, correlating with the pattern of acceleration of grey matter loss in schizophrenia. This suggests that fragile prefrontal hub connections and topological volatility act as evolutionary influences on complex brain networks, whose set point may be perturbed in neurological and psychiatric disorders.


Leonardo Gollo (QIMRB)

Linda Douw (Amsterdam UMC)

Past events:

CNS*2016 Workshop