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We introduce a method that can be used to evolve the topology of a network in a way that preserves both the network's spectral as well as local structure. This method is quite versatile in the sense that it can be used to evolve a network's…
One of the central problems in the study of deep learning theory is to understand how the structure properties, such as depth, width and the number of nodes, affect the expressivity of deep neural networks. In this work, we show a new…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…
We consider a finite structured population of mobile individuals that strategically explore a network using a Markov movement model and interact with each other via a public goods game. We extend the model of Erovenko et al. (2019) from…
The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
The entropy of a hierarchical network topology in an ensemble of sparse random networks with "hidden variables" associated to its nodes, is the log-likelihood that a given network topology is present in the chosen ensemble.We obtain a…
We propose a modeling framework for growing multiplexes where a node can belong to different networks. We define new measures for multiplexes and we identify a number of relevant ingredients for modeling their evolution such as the coupling…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
It is widely appreciated that well-balanced excitation and inhibition are necessary for proper function in neural networks. However, in principle, such balance could be achieved by many possible configurations of excitatory and inhibitory…
Food web topology and energy flow rates across food web linkages can influence ecosystem properties such as stability. Stability predictions from current models of energy flow are often sensitive to details in their formulation, and their…
Networks grow and evolve by local events, such as the addition of new nodes and links, or rewiring of links from one node to another. We show that depending on the frequency of these processes two topologically different networks can…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
If each node of an idealized network has an equal capacity to efficiently exchange benefits, then the network's capacity to use energy is scaled by the average amount of energy required to connect any two of its nodes. The scaling factor…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…