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High-throughput methods for yielding the set of connections in a neural system, the connectome, are now being developed. This tutorial describes ways to analyze the topological and spatial organization of the connectome at the macroscopic…

In the last decade, network science has shed new light both on the structural (anatomical) and on the functional (correlations in the activity) connectivity among the different areas of the human brain. The analysis of brain networks has…

At the inception of human brain mapping, two principles of functional anatomy underwrote most conceptions - and analyses - of distributed brain responses: namely functional segregation and integration. There are currently two main…

Non-invasive measurements of the human brain using magnetic resonance imaging (MRI) have significantly improved our understanding the brain's network organization by enabling measurement of anatomical connections between brain regions…

The fractal dimension provides a statistical index of object complexity by studying how the pattern changes with the measuring scale. Although useful in several classification tasks, the fractal dimension is under-explored in deep learning…

Spontaneous brain activity, as observed in functional neuroimaging, has been shown to display reproducible structure that expresses brain architecture and carries markers of brain pathologies. An important view of modern neuroscience is…

Deep, classical graph-theoretical parameters, like the size of the minimum vertex cover, the chromatic number, or the eigengap of the adjacency matrix of the graph were studied widely by mathematicians in the last century. Most researchers…

Predicting disease states from functional brain connectivity is critical for the early diagnosis of severe neurodegenerative diseases such as Alzheimer's Disease and Parkinson's Disease. Existing studies commonly employ Graph Neural…

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by…

We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications.…

Structure entails function and thus a structural description of the brain will help to understand its function and may provide insights into many properties of brain systems, from their robustness and recovery from damage, to their dynamics…

Finding the common structural brain connectivity network for a given population is an open problem, crucial for current neuro-science. Recent evidence suggests there's a tightly connected network shared between humans. Obtaining this…

We consider the problem of estimating the difference between two undirected functional graphical models with shared structures. In many applications, data are naturally regarded as a vector of random functions rather than as a vector of…

We developed a new method for analysis of fundamental brain waves as recorded by EEG. To this purpose we introduce a Fractal Variance Function that is based on the calculation of the variogram. The method is completed by using Random Matrix…

With distinct advantages in power over behavioral phenotypes, brain imaging traits have become emerging endophenotypes to dissect molecular contributions to behaviors and neuropsychiatric illnesses. Among different imaging features, brain…

Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However,…

Network science has been extensively developed to characterize structural properties of complex systems, including brain networks inferred from neuroimaging data. As a result of the inference process, networks estimated from experimentally…

In recent years, new and important perspectives were introduced in the field of neuroimaging with the emergence of the connectionist approach. In this new context, it is important to know not only which brain areas are activated by a…

The white-matter (micro-)structural architecture of the brain promotes synchrony among neuronal populations, giving rise to richly patterned functional connections. A fundamental problem for systems neuroscience is determining the best way…

In this study, we propose a neural network approach to capture the functional connectivities among anatomic brain regions. The suggested approach estimates a set of brain networks, each of which represents the connectivity patterns of a…