相关论文: Percolation under Noise: Detecting Explosive Perco…

We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…

The vital nodes are the ones that play an important role in the organization of network structure or the dynamical behaviours of networked systems. Previous studies usually applied the node centralities to quantify the importance of nodes.…

We study asymptotic percolation as $N\to \infty$ in an infinite random graph ${\cal G}_N$ embedded in the hierarchical group of order $N$, with connection probabilities depending on an ultrametric distance between vertices. ${\cal G}_N$ is…

We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough…

Percolation in an information-theoretically secure graph is considered where both the legitimate and the eavesdropper nodes are distributed as Poisson point processes. For both the path-loss and the path-loss plus fading model, upper and…

We generalize the random graph evolution process of Bohman, Frieze, and Wormald [T. Bohman, A. Frieze, and N. C. Wormald, Random Struct. Algorithms, 25, 432 (2004)]. Potential edges, sampled uniformly at random from the complete graph, are…

Our understanding of cell division control in bacteria still relies largely on interpreting correlations between phenomenological variables, with limited connection to the underlying molecular mechanisms. Here, we analytically solve a…

Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…

Inferring unknown conic sections on the basis of noisy data is a challenging problem with applications in computer vision. A major limitation of the currently available methods for conic sections is that estimation methods rely on the…

Understanding what types of phenomena lead to discontinuous phase transitions in the connectivity of random networks is an outstanding challenge. Here we show that a simple stochastic model of graph evolution leads to a discontinuous…

The distortion on the intermittency signal, due to detection efficiency and to the presence of pre--equilibrium emitted particles, is studied in a schematic model of nuclear multi- fragmentation. The source of the intermittency signal is…

The ultimate sensitivity of optical detection is limited by the signal-to-noise ratio (SNR). The first part of the paper shows that coherence plays an important role in the noise analysis. Although interference between an auxiliary wave and…

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

Recent experiments have shown that the spontaneous activity of young dissociated neuronal cultures can be described as a process of highly inhomogeneous nucleation and front propagation due to the localization of noise activity, i.e., noise…

We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modellized by hard-core spherical particles surrounded by penetrable…

Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…

Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network…

The evolution of topology and morphology of ionized or neutral hydrogen during different stages of the Epoch of Reionization (EoR) have the potential to provide us a great amount of information about the properties of the ionizing sources…

Information processing in the brain is conducted by a concerted action of multiple neural populations. Gaining insights in the organization and dynamics of such populations can best be studied with broadband intracranial recordings of…

Neuroimaging data can be represented as networks of nodes and edges that capture the topological organization of the brain connectivity. Graph theory provides a general and powerful framework to study these networks and their structure at…