Related papers: Google matrix analysis of C.elegans neural network
Control is essential to the functioning of any neural system. Indeed, under healthy conditions the brain must be able to continuously maintain a tight functional control between the system's inputs and outputs. One may therefore hypothesise…
With the success of deep learning, recent efforts have been focused on analyzing how learned networks make their classifications. We are interested in analyzing the network output based on the network structure and information flow through…
Within one decade, Deep Learning overtook the dominating solution methods of countless problems of artificial intelligence. ``Deep'' refers to the deep architectures with operations in manifolds of which there are no immediate observations.…
Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional…
We study the typical behavior of a generalized version of Google's PageRank algorithm on a large family of inhomogeneous random digraphs. This family includes as special cases directed versions of classical models such as the…
In recent years, several studies have provided insight on the functioning of the brain which consists of neurons and form networks via interconnection among them by synapses. Neural networks are formed by interconnected systems of neurons,…
The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter $\alpha \in ]0,1[$. Using extensive numerical simulations of large web networks, with a special…
In neural networks with identical neurons, the matrix of connection weights completely describes the network structure and thereby determines how it is processing information. However, due to the non-linearity of these systems, it is not…
This study establishes a benchmark for Caenorhabditis elegans neuron classification, comparing four graph methods (GCN, GraphSAGE, GAT, GraphTransformer) against four non-graph methods (Logistic Regression, MLP, LOLCAT, NeuPRINT). Using the…
While statistical analysis of a single network has received a lot of attention in recent years, with a focus on social networks, analysis of a sample of networks presents its own challenges which require a different set of analytic tools.…
Many complex networks are described by directed links; in such networks, a link represents, for example, the control of one node over the other node or unidirectional information flows. Some centrality measures are used to determine the…
Network structure or topology is the basis for understanding complex systems. Recently, higher-order structures have been considered as a new research direction that can provide new perspectives and phenomena. However, most existing studies…
Functional connectivity (FC) studies have demonstrated the overarching value of studying the brain and its disorders through the undirected weighted graph of fMRI correlation matrix. Most of the work with the FC, however, depends on the way…
The impressive performance of Convolutional Neural Networks (CNNs) when solving different vision problems is shadowed by their black-box nature and our consequent lack of understanding of the representations they build and how these…
We investigate the adaptation and performance of modularity-based algorithms, designed in the scope of complex networks, to analyze the mesoscopic structure of correlation matrices. Using a multi-resolution analysis we are able to describe…
Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial Threshold-Linear Networks (CTLNs) in order to…
Understanding the architectural subtleties of ecological networks, believed to confer them enhanced stability and robustness, is a subject of outmost relevance. Mutualistic interactions have been profusely studied and their corresponding…
{\it Caenorhabditis elegans} nematode worms are the only animals with the known detailed neural connectivity diagram, well characterized genomics, and relatively simple quantifiable behavioral output. With this in mind, many researchers…
The PageRank is a widely used scoring function of networks in general and of the World Wide Web graph in particular. The PageRank is defined for directed graphs, but in some special cases applications for undirected graphs occur. In the…
We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite size matrix approximant of this operator is constructed by the Ulam method. This…