Related papers: The Bifurcation Coalescence Problem for Feedforwar…

Real-world complex systems always interact with each other, which causes these systems to collapse in an avalanche or cascading manner in the case of random failures or malicious attacks. The robustness of multilayer networks has attracted…

This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds…

Combinations of random and preferential growth for both on-growing and stationary networks are studied and a hierarchical topology is observed. Thus for real world scale-free networks which do not exhibit hierarchical features preferential…

Coalescent models of bifurcating genealogies are used to infer evolutionary parameters from molecular data. However, there are many situations where bifurcating genealogies do not accurately reflect the true underlying ancestral history of…

This paper aims to interpret the mechanism of feedforward ReLU networks by exploring their solutions for piecewise linear functions, through the deduction from basic rules. The constructed solution should be universal enough to explain some…

We introduce a principled approach for unsupervised structure learning of deep neural networks. We propose a new interpretation for depth and inter-layer connectivity where conditional independencies in the input distribution are encoded…

Various social, financial, biological and technological systems can be modeled by interdependent networks. It has been assumed that in order to remain functional, nodes in one network must receive the support from nodes belonging to…

We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced in the network in order to produce a scale-free graph with given exponent lambda for the degree distribution, but the…

We study the robustness properties of multiplex networks consisting of multiple layers of distinct types of links, focusing on the role of correlations between degrees of a node in different layers. We use generating function formalism to…

We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…

Entanglement in bipartite continuous-variable systems is investigated in the presence of partial losses, such as those introduced by a realistic quantum communication channel, e.g. by propagation in an optical fiber. We find that…

When an initial failure of nodes occurs in interdependent networks, a cascade of failure between the networks occurs. Earlier studies focused on random initial failures. Here we study the robustness of interdependent networks under targeted…

We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…

Scalability of graph neural networks remains one of the major challenges in graph machine learning. Since the representation of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes…

Processes of coalescence and fragmentation are used to understand the time-evolution of the mass distribution of various systems and may result in a steady state or in stable deterministic or stochastic cycles. Motivated by applications in…

Diffusion over a network refers to the phenomenon of a change of state of a cross-sectional unit in one period leading to a change of state of its neighbors in the network in the next period. One may estimate or test for diffusion by…

Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…

Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…

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…