518 research outputs found

    Predicting collapse of adaptive networked systems without knowing the network

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    The collapse of ecosystems, the extinction of species, and the breakdown of economic and financial networks usually hinges on topological properties of the underlying networks, such as the existence of self-sustaining (or autocatalytic) feedback cycles. Such collapses can be understood as a massive change of network topology, usually accompanied by the extinction of a macroscopic fraction of nodes and links. It is often related to the breakdown of the last relevant directed catalytic cycle within a dynamical system. Without detailed structural information it seems impossible to state, whether a network is robust or if it is likely to collapse in the near future. Here we show that it is nevertheless possible to predict collapse for a large class of systems that are governed by a linear (or linearized) dynamics. To compute the corresponding early warning signal, we require only non-structural information about the nodes’ states such as species abundances in ecosystems, or company revenues in economic networks. It is shown that the existence of a single directed cycle in the network can be detected by a “quantization effect” of node states, that exists as a direct consequence of a corollary of the Perron–Frobenius theorem. The proposed early warning signal for the collapse of networked systems captures their structural instability without relying on structural information. We illustrate the validity of the approach in a transparent model of co-evolutionary ecosystems and show this quantization in systems of species evolution, epidemiology, and population dynamics

    How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions

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    Sample space reducing (SSR) processes offer a simple analytical way to understand the origin and ubiquity of power-laws in many path-dependent complex systems. SRR processes show a wide range of applications that range from fragmentation processes, language formation to search and cascading processes. Here we argue that they also offer a natural framework to understand stationary distributions of generic driven non-equilibrium systems that are composed of a driving- and a relaxing process. We show that the statistics of driven non-equilibrium systems can be derived from the understanding of the nature of the underlying driving process. For constant driving rates exact power-laws emerge with exponents that are related to the driving rate. If driving rates become state-dependent, or if they vary across the life-span of the process, the functional form of the state-dependence determines the statistics. Constant driving rates lead to exact power-laws, a linear state-dependence function yields exponential or Gamma distributions, a quadratic function produces the normal distribution. Logarithmic and power-law state dependence leads to log-normal and stretched exponential distribution functions, respectively. Also Weibull, Gompertz and Tsallis-Pareto distributions arise naturally from simple state-dependent driving rates. We discuss a simple physical example of consecutive elastic collisions that exactly represents a SSR process

    Conserved RNA secondary structures in Flaviviridae genomes

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    Presented here is a comprehensive computational survey of evolutionarily conserved secondary structure motifs in the genomic RNAs of the family Flaviviridae. This virus family consists of the three genera Flavivirus, Pestivirus and Hepacivirus and the group of GB virus C/hepatitis G virus with a currently uncertain taxonomic classification. Based on the control of replication and translation, two subgroups were considered separately: the genus Flavivirus, with its type I cap structure at the 5′ untranslated region (UTR) and a highly structured 3′ UTR, and the remaining three groups, which exhibit translation control by means of an internal ribosomal entry site (IRES) in the 5′ UTR and a much shorter less-structured 3′ UTR. The main findings of this survey are strong hints for the possibility of genome cyclization in hepatitis C virus and GB virus C/hepatitis G virus in addition to the flaviviruses; a surprisingly large number of conserved RNA motifs in the coding regions; and a lower level of detailed structural conservation in the IRES and 3′ UTR motifs than reported in the literature. An electronic atlas organizes the information on the more than 150 conserved, and therefore putatively functional, RNA secondary structure elements

    When do generalized entropies apply? How phase space volume determines entropy

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    We show how the dependence of phase space volume Ω(N)\Omega(N) of a classical system on its size NN uniquely determines its extensive entropy. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a {\em generalized} (non-additive) form. We show that generalized entropies can only exist when the dynamically (statistically) relevant fraction of degrees of freedom in the system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of freedom is frozen and is practically statistically inactive. Systems governed by generalized entropies are therefore systems whose phase space volume effectively collapses to a lower-dimensional 'surface'. We explicitly illustrate the situation for binomial processes and argue that generalized entropies could be relevant for self organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion.Comment: 5 pages, 2 figure

    Network topology near criticality in adaptive epidemics

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    We study structural changes of adaptive networks in the coevolutionary susceptible-infected-susceptible (SIS) network model along its phase transition. We clarify to what extent these changes can be used as early-warning signs for the transition at the critical infection rate λc at which the network collapses and the system disintegrates. We analyze the interplay between topology and node-state dynamics near criticality. Several network measures exhibit clear maxima or minima close to the critical threshold and could potentially serve as early-warning signs. These measures include the SI link density, triplet densities, clustering, assortativity, and the eigenvalue gap. For the SI link density and triplet densities the maximum is found to originate from the coexistence of two power laws. Other network quantities, such as the degree, the branching ratio, or the harmonic mean distance, show scaling with a singularity at λ=0 (not at λc), which means that they are incapable of detecting the transition. © 2018 American Physical Society

    Dynamics of gene expression and the regulatory inference problem

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    From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding of transcription factor molecules to regulatory DNA. Here, we construct stochastic models of gene expression dynamics and test them on experimental time-series data of messenger-RNA concentrations. The models are used to infer biophysical parameters of gene transcription, including the statistics of transcription factor-DNA binding and the target genes controlled by a given transcription factor.Comment: revised version to appear in Europhys. Lett., new titl

    Coexistence of opposite opinions in a network with communities

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    The Majority Rule is applied to a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in social networks. We calculate analytically the asymptotic behaviour of the model and derive a phase diagram that depends on the frequency of random opinion flips and on the inter-connectivity between the two communities. It is shown that three regimes may take place: a disordered regime, where no collective phenomena takes place; a symmetric regime, where the nodes in both communities reach the same average opinion; an asymmetric regime, where the nodes in each community reach an opposite average opinion. The transition from the asymmetric regime to the symmetric regime is shown to be discontinuous.Comment: 14 pages, 4 figure

    Complete diagrammatics of the single ring theorem

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    Using diagrammatic techniques, we provide explicit functional relations between the cumulant generating functions for the biunitarily invariant ensembles in the limit of large size of matrices. The formalism allows to map two distinct areas of free random variables: Hermitian positive definite operators and non-normal R-diagonal operators. We also rederive the Haagerup-Larsen theorem and show how its recent extension to the eigenvector correlation function appears naturally within this approach.Comment: 18 pages, 6 figures, version accepted for publicatio

    Vibration-based Health Monitoring of Earth Structures

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    Vibration-based health monitoring (VBHM) has successfully been used to assess the structural damage to bridges, buildings, aircraft, and rotating machinery. There is significant incentive to apply VBHM techniques to the damage detection and conditional assessment of earth structures (geostructures), e.g., foundations, dams, embankments, and tunnels, to improve design, construction, and performance. An experimental program was carried out to explore the efficacy of VBHM of earth structures. A vibratory roller compactor, instrumented with triaxial accelerometers to continuously measure drum and frame vibrations, was operated on a number of underlying material structures with varying properties. Time-domain and frequency-domain analyses of the coupled machine/earth structure response were performed to glean machine vibration features that reflect changes in underlying structural properties. Results illustrate that drum and frame acceleration amplitudes were fairly insensitive to changes in underlying media stiffness; however, drum acceleration frequency components (harmonics) were found to be sensitive to changes in underlying media and changes in soil properties during compaction. The strata underlying the soil undergoing compaction was found to strongly affect drum vibration characteristics.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

    Spectrum of Neutral Helium in Strong Magnetic Fields

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    We present extensive and accurate calculations for the excited state spectrum of spin-polarized neutral helium in a range of magnetic field strengths up to 101210^{12} G. Of considerable interest to models of magnetic white dwarf stellar atmospheres, we also present results for the dipole strengths of the low lying transitions among these states. Our methods rely on a systematically saturated basis set approach to solving the Hartree--Fock self-consistent field equations, combined with an ``exact'' stochastic method to estimate the residual basis set truncation error and electron correlation effects. We also discuss the applicability of the adiabatic approximation to strongly magnetized multi-electron atoms.Comment: 19 pages, 7 figures, 10 table
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