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Register a new userLong-Range Correlations and Memory in the Dynamics of Internet Interdomain Routing
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Data transfer is one of the main functions of the Internet. The Internet consists of a large number of interconnected subnetworks or domains, known as Autonomous Systems. Due to privacy and other reasons the information about what route to use to reach devices within other Autonomous Systems is not readily available to any given Autonomous System. The Border Gateway Protocol is responsible for discovering and distributing this reachability information to all Autonomous Systems. Since the topology of the Internet is highly dynamic, all Autonomous Systems constantly exchange and update this reachability information in small chunks, known as routing control packets or Border Gateway Protocol updates. Motivated by scalability and predictability issues with the dynamics of these updates in the quickly growing Internet, we conduct a systematic time series analysis of Border Gateway Protocol update rates. We find that Border Gateway Protocol update time series are extremely volatile, exhibit long-term correlations and memory effects, similar to seismic time series, or temperature and stock market price fluctuations. The presented statistical characterization of Border Gateway Protocol update dynamics could serve as a ground truth for validation of existing and developing better models of Internet interdomain routing.
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We perform an analytical analysis of the long-range degree correlation of the giant component in an uncorrelated random network by employing generating functions. By introducing a characteristic length, we find that a pair of nodes in the giant component is negatively degree-correlated within the characteristic length and uncorrelated otherwise. At the critical point, where the giant component becomes fractal, the characteristic length diverges and the negative long-range degree correlation emerges. We further propose a correlation function for degrees of the $l$-distant node pairs, which behaves as an exponentially decreasing function of distance in the off-critical region. The correlation function obeys a power-law with an exponential cutoff near the critical point. The ErdH{o}s-R{e}nyi random graph is employed to confirm this critical behavior.
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Whether long-range interactions allow for a form of causality in non-relativistic quantum models remains an open question with far-reaching implications for the propagation of information and thermalization processes. Here, we study the out-of-equilibrium dynamics of the one-dimensional transverse Ising model with algebraic long-range exchange coupling. Using a state of the art tensor-network approach, complemented by analytic calculations and considering various observables, we show that a weak form of causality emerges, characterized by non-universal dynamical exponents. While the local spin and spin correlation causal edges are sub-ballistic, the causal region has a rich internal structure, which, depending on the observable, displays ballistic or super-ballistic features. In contrast, the causal region of entanglement entropy is featureless and its edge is always ballistic, irrespective of the interaction range. Our results shed light on the propagation of information in long-range interacting lattice models and pave the way to future experiments, which are discussed.
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