Related papers: The Optimized Model of Multiple Invasion Percolati…
Multicell joint processing has been proven to be very efficient in overcoming the interference-limited nature of the cellular paradigm. However, for reasons of practical implementation global multicell joint decoding is not feasible and…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are…
We extend our previous model, avalanche-burst invasion percolation (AIP) by introducing long-range correlations between sites described by fractional Brownian statistics. In our previous models with independent, random site strengths, we…
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
The emergence of large-scale connectivity and synchronization are crucial to the structure, function and failure of many complex socio-technical networks. Thus, there is great interest in analyzing phase transitions to large-scale…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
We develop a model in which interactions between nodes of a dynamic network are counted by non homogeneous Poisson processes. In a block modelling perspective, nodes belong to hidden clusters (whose number is unknown) and the intensity…
Cascading failures in complex systems have been studied extensively using two different models: $k$-core percolation and interdependent networks. We combine the two models into a general model, solve it analytically and validate our…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…
This work aims at optimizing injection networks, which consist in adding a set of long-range links (called bypass links) in mobile multi-hop ad hoc networks so as to improve connectivity and overcome network partitioning. To this end, we…
We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement…
We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
Most real-world complex systems can be modelled by coupled networks with multiple layers. How and to what extent the pattern of couplings between network layers may influence the interlaced structure and function of coupled networks are not…
Particle statistics plays a crucial role in a strongly interacting quantum many-body system. Here, we study the Hubbard model for distinguishable particles at unit filling. Starting from the superfluid-like state in the strong tunneling…
In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree…
Recently we have introduced a simplified model of ecosystem assembly (Capitan et al., 2009) for which we are able to map out all assembly pathways generated by external invasions in an exact manner. In this paper we provide a deeper…