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The human brain forms functional networks on all spatial scales. Modern fMRI scanners allow to resolve functional brain data in high resolutions, allowing to study large-scale networks that relate to cognitive processes. The analysis of…
Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure…
It is widely believed that the particular wiring observed within cortical columns boosts neural computation. We use rewiring of neural networks performing real-world cognitive tasks to study the validity of this argument. In a vast survey…
Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of…
In many real-world systems, partial synchronization is the dominant dynamical regime and, in systems such as the brain, is often accompanied by collective oscillations in which multiple overlapping modes interact to produce complex rhythmic…
Understanding the complex hierarchical topology of functional brain networks is a key aspect of functional connectivity research. Such topics are obscured by the widespread use of sparse binary network models which are fundamentally…
Abnormal cortical folding patterns may be related to neurodevelopmental disorders such as lissencephaly and polymicrogyria. In this context, computational modeling is a powerful tool to provide a better understanding of the early brain…
We examine the global organization of heterogeneous equilibrium networks consisting of a number of well distinguished interconnected parts--``communities'' or modules. We develop an analytical approach allowing us to obtain the statistics…
The interactions play one of the central roles in the brain mediating various processes and functions. They are particularly important for the brain as a complex system that has many different functions from the same structural…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
Investigating the frequency and distribution of small subgraphs with a few nodes/edges, i.e., motifs, is an effective analysis method for static networks. Motif-driven analysis is also useful for temporal networks where the spectrum of…
Investigations of the human connectome have elucidated core features of adult structural networks, particularly the crucial role of hub-regions. However, little is known regarding network organisation of the healthy elderly connectome, a…
Activity in neocortex exhibits a range of behaviors, from irregular to temporally precise, and from weakly to strongly correlated. So far there has been no single theoretical framework that could explain all these behaviors, leaving open…
In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…
Despite differences in brain sizes and cognitive niches among mammals, their cerebral cortices posses many common features and regularities. These regularities have been a subject of experimental investigation in neuroanatomy for the last…
This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…
In the past decade, the cell-type specific connectivity and activity of local cortical networks have been characterized experimentally to some detail. In parallel, modeling has been established as a tool to relate network structure to…
Neurons in the visual cortex are correlated in their variability. The presence of correlation impacts cortical processing because noise cannot be averaged out over many neurons. In an effort to understand the functional purpose of…
This report investigates the modular organisation of the Central region in the Drosophila connectome. We identify groups of neurones amongst which information circulates rapidly before spreading to the rest of the network using Infomap. We…
We study the topological properties of functional connectivity patterns among cortical areas in the frequency domain. The cortical networks were estimated from high-resolution EEG recordings in a group of spinal cord injured patients and in…