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We introduce and study random bipartite networks with hidden variables. Nodes in these networks are characterized by hidden variables which control the appearance of links between node pairs. We derive analytic expressions for the degree distribution, degree correlations, the distribution of the number of common neighbors, and the bipartite clustering coefficient in these networks. We also establish the relationship between degrees of nodes in original bipartite networks and in their unipartite projections. We further demonstrate how hidden variable formalism can be applied to analyze topological properties of networks in certain bipartite network models, and verify our analytical results in numerical simulations.
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Many complex systems, including networks, are not static but can display strong fluctuations at various time scales. Characterizing the dynamics in complex networks is thus of the utmost importance in the understanding of these networks and of the dynamical processes taking place on them. In this article, we study the example of the US airport network in the time period 1990-2000. We show that even if the statistical distributions of most indicators are stationary, an intense activity takes place at the local (`microscopic) level, with many disappearing/appearing connections (links) between airports. We find that connections have a very broad distribution of lifetimes, and we introduce a set of metrics to characterize the links dynamics. We observe in particular that the links which disappear have essentially the same properties as the ones which appear, and that links which connect airports with very different traffic are very volatile. Motivated by this empirical study, we propose a model of dynamical networks, inspired from previous studies on firm growth, which reproduces most of the empirical observations both for the stationary statistical distributions and for the dynamical properties.
Life and language are discrete combinatorial systems (DCSs) in which the basic building blocks are finite sets of elementary units: nucleotides or codons in a DNA sequence and letters or words in a language. Different combinations of these finite units give rise to potentially infinite numbers of genes or sentences. This type of DCS can be represented as an Alphabetic Bipartite Network ($alpha$-BiN) where there are two kinds of nodes, one type represents the elementary units while the other type represents their combinations. There is an edge between a node corresponding to an elementary unit $u$ and a node corresponding to a particular combination $v$ if $u$ is present in $v$. Naturally, the partition consisting of the nodes representing elementary units is fixed, while the other partition is allowed to grow unboundedly. Here, we extend recently analytical findings for $alpha$-BiNs derived in [Peruani et al., Europhys. Lett. 79, 28001 (2007)] and empirically investigate two real world systems: the codon-gene network and the phoneme-language network. The evolution equations for $alpha$-BiNs under different growth rules are derived, and the corresponding degree distributions computed. It is shown that asymptotically the degree distribution of $alpha$-BiNs can be described as a family of beta distributions. The one-mode projections of the theoretical as well as the real world $alpha$-BiNs are also studied. We propose a comparison of the real world degree distributions and our theoretical predictions as a means for inferring the mechanisms underlying the growth of real world systems.
While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of non-equilibrium phenomena in diverse settings, from glasses to driven systems to biology. The length of a losslessly compressed data file is a direct measure of its information content: The more ordered the data is, the lower its information content and the shorter the length of its encoding can be made. Here, we describe how data compression enables the quantification of order in non-equilibrium and equilibrium many-body systems, both discrete and continuous, even when the underlying form of order is unknown. We consider absorbing state models on and off-lattice, as well as a system of active Brownian particles undergoing motility-induced phase separation. The technique reliably identifies non-equilibrium phase transitions, determines their character, quantitatively predicts certain critical exponents without prior knowledge of the order parameters, and reveals previously unknown ordering phenomena. This technique should provide a quantitative measure of organization in condensed matter and other systems exhibiting collective phase transitions in and out of equilibrium.
AtomAI is an open-source software package bridging instrument-specific Python libraries, deep learning, and simulation tools into a single ecosystem. AtomAI allows direct applications of the deep convolutional neural networks for atomic and mesoscopic image segmentation converting image and spectroscopy data into class-based local descriptors for downstream tasks such as statistical and graph analysis. For atomically-resolved imaging data, the output is types and positions of atomic species, with an option for subsequent refinement. AtomAI further allows the implementation of a broad range of image and spectrum analysis functions, including invariant variational autoencoders (VAEs). The latter consists of VAEs with rotational and (optionally) translational invariance for unsupervised and class-conditioned disentanglement of categorical and continuous data representations. In addition, AtomAI provides utilities for mapping structure-property relationships via im2spec and spec2im type of encoder-decoder models. Finally, AtomAI allows seamless connection to the first principles modeling with a Python interface, including molecular dynamics and density functional theory calculations on the inferred atomic position. While the majority of applications to date were based on atomically resolved electron microscopy, the flexibility of AtomAI allows straightforward extension towards the analysis of mesoscopic imaging data once the labels and feature identification workflows are established/available. The source code and example notebooks are available at https://github.com/pycroscopy/atomai.
Dynamical heterogeneities -- strong fluctuations near the glass transition -- are believed to be crucial to explain much of the glass transition phenomenology. One possible hypothesis for their origin is that they emerge from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. To test this hypothesis, we use numerical simulation data from four glass-forming models to construct coarse grained observables that probe the dynamical heterogeneity, and decompose the fluctuations of these observables into two transverse components associated with the postulated time-fluctuation soft modes and a longitudinal component unrelated to them. We find that as temperature is lowered and timescales are increased, the time reparametrization fluctuations become increasingly dominant, and that their correlation volumes grow together with the correlation volumes of the dynamical heterogeneities, while the correlation volumes for longitudinal fluctuations remain small.
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