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Streamflow is a dynamical process that integrates water movement in space and time within basin boundaries. The authors characterize the dynamics associated with streamflow time series data from about seventy-one U.S. Geological Survey…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
For irreducible, time-homogeneous Markov networks, mutual linearity has recently been established for both occupation probabilities and network currents in the stationary regime as well as in the non-stationary regime in Laplace space. The…
The present work analyzes the statistics of finite scale local Lyapunov exponents of pairs of fluid particles trajectories in fully developed incompressible homogeneous isotropic turbulence. According to the hypothesis of fully developed…
We extend a recent model of temporal random hyperbolic graphs by allowing connections and disconnections to persist across network snapshots with different probabilities, $\omega_1$ and $\omega_2$. This extension, while conceptually simple,…
Network motifs are characteristic patterns which occur in the networks essentially more frequently than the other patterns. For five motifs found in S. Itzkovitz, U. Alon, Phys. Rev.~E, 2005, 71, 026117-1, hierarchical random graphs are…
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…
The absence of the efficient methods for the design of the information sources impact network does not allow defining the influence of the information sources on one another accurately and detecting the primary sources of the information…
Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…
In the companion paper [Linear rank-width of distance-hereditary graphs I. A polynomial-time algorithm, Algorithmica 78(1):342--377, 2017], we presented a characterization of the linear rank-width of distance-hereditary graphs, from which…
We study the linearization of a discrete transportation distance between probability distributions on finite weighted graphs originally due to Maas (``Gradient flows of the entropy for finite {M}arkov chains,'' J. Funct. Anal. 261(8), 2011)…
Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the degree distribution follows a power-law, capturing the…
We develop a method to calculate the persistent currents and their spatial distribution (and transport properties) on graphs made of quasi-1D diffusive wires. They are directly related to the field derivatives of the determinant of a matrix…
The present work analyzes the distribution function of the finite scale local Lyapunov exponent of a pair fluid particles trajectories in fully developed incompressible homogeneous isotropic turbulence. According to the hypothesis of fully…
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…
This work presents a review of previous articles dealing with an original turbulence theory proposed by the author, and provides new theoretical insights into some related issues. The new theoretical procedures and methodological approaches…
Traditional graph centrality measures effectively quantify node importance but fail to capture the structural uniqueness of multi-scale connectivity patterns -- critical for understanding network resilience and function. This paper…
Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. In particular, these models help with investigating power-law properties of degree…
We introduce a new class of countably infinite random geometric graphs, whose vertices are points in a metric space, and vertices are adjacent independently with probability p if the metric distance between the vertices is below a given…
We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume…