Excitable human dynamics driven by extrinsic events in massive communities

Using empirical data from a social media site (Twitter) and on trading volumes of financial securities, we analyze the correlated human activity in massive social organizations. The activity, typically excited by real-world events and measured by the occurrence rate of international brand names and trading volumes, is characterized by intermittent fluctuations with bursts of high activity separated by quiescent periods. These fluctuations are broadly distributed with an inverse cubic tail and have long-range temporal correlations with a $1/f$ power spectrum. We describe the activity by a stochastic point process and derive the distribution of activity levels from the corresponding stochastic differential equation. The distribution and the corresponding power spectrum are fully consistent with the empirical observations.Comment: 9 pages, 3 figure

On the Anomalous Scaling Exponents in Nonlinear Models of Turbulence

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by `Statistically Preserved Structures' which are associated with exact conservation laws. The latter can be used for example to determine the value of the anomalous scaling exponent of the second order structure function. The approach is equally applicable to shell models and to the Navier-Stokes equations.Comment: revised version with new data on Navier-Stokes eq

Automatic Synonym Discovery with Knowledge Bases

Recognizing entity synonyms from text has become a crucial task in many entity-leveraging applications. However, discovering entity synonyms from domain-specific text corpora (e.g., news articles, scientific papers) is rather challenging. Current systems take an entity name string as input to find out other names that are synonymous, ignoring the fact that often times a name string can refer to multiple entities (e.g., "apple" could refer to both Apple Inc and the fruit apple). Moreover, most existing methods require training data manually created by domain experts to construct supervised-learning systems. In this paper, we study the problem of automatic synonym discovery with knowledge bases, that is, identifying synonyms for knowledge base entities in a given domain-specific corpus. The manually-curated synonyms for each entity stored in a knowledge base not only form a set of name strings to disambiguate the meaning for each other, but also can serve as "distant" supervision to help determine important features for the task. We propose a novel framework, called DPE, to integrate two kinds of mutually-complementing signals for synonym discovery, i.e., distributional features based on corpus-level statistics and textual patterns based on local contexts. In particular, DPE jointly optimizes the two kinds of signals in conjunction with distant supervision, so that they can mutually enhance each other in the training stage. At the inference stage, both signals will be utilized to discover synonyms for the given entities. Experimental results prove the effectiveness of the proposed framework

Kolmogorov scaling from random force fields

We show that the classical Kolmogorov and Richardson scaling laws in fully developed turbulence are consistent with a random Gaussian force field. Numerical simulations of a shell model approximation to the Navier-Stokes equations suggest that the fluctuations in the force (acceleration) field are scale independent throughout the inertial regime. We conjecture that Lagrangian statistics of the relative velocity in a turbulent flow is determined by the typical force field, whereas the multiscaling is associated to extreme events in the force field fluctuations.Comment: 4 pages, 4 figure

Stress-driven phase transformation and the roughening of solid-solid interfaces

The application of stress to multiphase solid-liquid systems often results in morphological instabilities. Here we propose a solid-solid phase transformation model for roughening instability in the interface between two porous materials with different porosities under normal compression stresses. This instability is triggered by a finite jump in the free energy density across the interface, and it leads to the formation of finger-like structures aligned with the principal direction of compaction. The model is proposed as an explanation for the roughening of stylolites - irregular interfaces associated with the compaction of sedimentary rocks that fluctuate about a plane perpendicular to the principal direction of compaction.Comment: (4 pages, 4 figures

Stochastic attractors for shell phenomenological models of turbulence

Recently, it has been proposed that the Navier-Stokes equations and a relevant linear advection model have the same long-time statistical properties, in particular, they have the same scaling exponents of their structure functions. This assertion has been investigate rigorously in the context of certain nonlinear deterministic phenomenological shell model, the Sabra shell model, of turbulence and its corresponding linear advection counterpart model. This relationship has been established through a "homotopy-like" coefficient $\lambda$ which bridges continuously between the two systems. That is, for $\lambda=1$ one obtains the full nonlinear model, and the corresponding linear advection model is achieved for $\lambda=0$. In this paper, we investigate the validity of this assertion for certain stochastic phenomenological shell models of turbulence driven by an additive noise. We prove the continuous dependence of the solutions with respect to the parameter $\lambda$. Moreover, we show the existence of a finite-dimensional random attractor for each value of $\lambda$ and establish the upper semicontinuity property of this random attractors, with respect to the parameter $\lambda$. This property is proved by a pathwise argument. Our study aims toward the development of basic results and techniques that may contribute to the understanding of the relation between the long-time statistical properties of the nonlinear and linear models