Workshop
"Graphs and neurosciences"
18 november 2016

Summary
Nowadays, more and more data are defined on the vertices of a graph: brain activity supported by neurons in networks, data from users of social media, 3D meshes or point clouds from real object scans. Graphs have long been used in computer science with many applications for instance in Machine Learning and Image Processing. However their use within a unified "signal processing" point of view has only recently emerged. This is leading to the emergence of a new research field called "Graph Signal Processing" at the intersection of computer science, mathematics, and signal processing. This new research field aims at developing novel approaches enlarging the scope of traditional signal processing methods and applications, so that they can be applied to arbitrary graph signals for denoising, filtering, clustering, etc.
In this talk we will first introduce some of the basic tools needed in developing new graphs signal processing operations.
We will then present how to adapt on graphs p-Laplacian regularization, multiscale hierarchical decomposition and active contours for graph signals. We will show examples on images and 3D points clouds or meshes.

Summary
Several methods are available to analyze signals on graphs. Fourier analysis requires the computation of the eigenvalues and eigenvectors of the graph Laplacian, it is also a non-local transformation. In this talk we will first have a look on some recently developed time-frequency and space-scale type methods. Then we will propose a fast multiresolution scheme based on random spanning forests and Markov chain intertwining, which provides well localized basis functions without requiring spectral computations.

Summary
Non invasive techniques such as functional magnetic resonance imaging (fMRI) or magnetoencephalographic (MEG) allow the observation of the functioning brain at rest. The acquired data consists in multivariate time series. Each time series corresponds to the recording of a specific parcel of the brain for a finite duration. The objective of my talk is to describe the crucial methodological steps needed to extract the brain networks. I will present results based on real data acquired using fMRI.
Each node of the brain network is one time series and an edge in the network is characterizing a coupling between two time series. I will show how wavelet correlation can be used to identify these networks. The networks obtained are compared using topological characteristics that highlight both hierarchical and modularity organisation of heathy brain networks. Finally, in a clinical application on coma patients, we find alterations of brain networks. We argue that global topological properties of complex brain networks may be homeostatically conserved under extremely different clinical conditions. Consciousness likely depends on the anatomical location of hub nodes in human brain networks.

Summary
As functional brain imaging probes brain mechanisms, hope is that it can capture markers of subjects' psychiatric status. However, to form a simple and objective measure of neuro-psychiatric state, it must avoid complex psychological experimental paradigms. For this purpose, studying the brain at rest is ideal.
Indeed, resting-state fMRI is a promising source of functional biomarkers as, unlike typical task-based fMRI paradigms, it can be applied to diminished populations.
I will discuss a model of brain interactions at rest, the connectome, representing these interactions as a graph between brain regions. Predicting subject phenotypes, such as neuro-psychiatric states, based on their connectome implies a complex classification pipeline to learn and compare connectome. I will ground the various analysis steps on models of the signal and present our efforts to understand the different modeling steps: How to define functional brain regions? How to capture functional interactions in a subject? How to compare it across subjects? I will detail theoretical and experimental validation of each step.
Validation of these modeling choices is very hard, as it often relies on assumptions about the data. Based on our understanding of the various steps, we have built a full pipeline that predicts Autism from rest-fMRI on unseen scanning site in the ABIDE dataset. To our knowledge, this is the first prediction of a clinically-relevant diagnosis status that carries over in inhomogeneous acquisitions settings. This full-blown experiment, on 871 subjects, also highlights what are the important choices in a population-level connectome analysis.

Summary
The aging brain undergoes alterations of its Structural Connectivity (SC), i.e inter-regional anatomical connections, but also transformations of the flexible interactions between brain regions during cognition. In particular, Functional Connectivity (FC) in the resting state (rs), describing spontaneously emergent correlations between the activities of different areas, distinctly displays age-related changes.
Graph theory has often been used to track changes of both SC and FC. If there is a subset of results about which some consensus is emerging (e.g., SC "disconnection" and FC reduced modularity) there are also discordances between different studies. Furthermore, it is not clear how strongly varying FC graphs could be compatible with a slowed-down but essentially equally performing cognition through healthy aging.
Here we analyze age-related variations of SC and FC using novel tools beyond conventional graph theory such as Topological Data Analysis (persistent homology approaches) as well as dynamic network approaches.
From the point of view of generic topological properties, we find that FC networks are certainly reorganized through aging but in a way which leaves global topological properties of the functional connectome essentially unaltered (such as the number of "holes", their length, etc.), possibly hinting to compensatory mechanisms introducing coordination between the changes of different FC links.
Moving to dynamic aspects, we then show that aging also profoundly impacts on the spontaneous evolution over time of FC networks. Analyzing time-dependent correlations between human rs BOLD time-series, we reveal a characteristic switching, markedly slowing down with age, between epochs of meta-stable FC and transients of fast functional network reconfiguration. Furthermore, we identify communities of functional links, rather than network nodes, whose temporal fluctuations become increasingly anti-correlated in elderly subjects. This effect is stronger when the performance is reduced in a standard screening for cognitive impairments (MoCA) or in a simple visuomotor coordination task.
Both novel "beyond graph" approaches here considered cast new light on aspects of aging which cannot be seen by more conventional static and essentially local network analyses, thus opening the avenue to novel biomarkers of the brain's functional reconfiguration through aging.