Related papers: Analysing degeneracies in networks spectra
Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very…
Let $A$ be a gentle algebra. For every collection of string and band diagrammes, we consider the constructible subset of the variety of representations containing all modules with this underlying diagramme. We study degenerations of such…
Most cellular phenotypes are genetically complex. Identifying the set of genes that are most closely associated with a specific cellular state is still an open question in many cases. Here we study the transcriptional profile of cellular…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
"Every object that biology studies is a system of systems." (Fran\c{c}ois Jacob, 1974). Most networks feature intricate architectures originating from tinkering, a repetitive use of existing components where structures are not invented but…
Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…
In this review we summarize our recent efforts in trying to understand the role of heterogeneity in cancer progression by using neural networks to characterise different aspects of the mapping from a cancer cells genotype and environment to…
We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different value of correlation among their entries. Spectra of…
Many large, real-world complex networks have rich community structure that a network scientist seeks to understand. These communities may overlap or have intricate internal structure. Extracting communities with particular topological…
Triangles are an important building block and distinguishing feature of real-world networks, but their structure is still poorly understood. Despite numerous reports on the abundance of triangles, there is very little information on what…
The largest eigenvalue of the adjacency matrix of a network plays an important role in several network processes (e.g., synchronization of oscillators, percolation on directed networks, linear stability of equilibria of network coupled…
Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…
We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the…
We study networks constructed from gene expression data obtained from many types of cancers. The networks are constructed by connecting vertices that belong to each others' list of K-nearest-neighbors, with K being an a priori selected…
We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…
It is common knowledge that a key dynamical characteristic of a network is its spectrum (the collection of all eigenvalues of the network's weighted adjacency matrix). In \cite{BW10} we demonstrated that it is possible to reduce a network,…
The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better…
Finding hidden layers in complex networks is an important and a non-trivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multi-layer system exist and if so then what is…
Mechanistic Interpretability aims to reverse engineer the algorithms implemented by neural networks by studying their weights and activations. An obstacle to reverse engineering neural networks is that many of the parameters inside a…
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine…