Towards the quantification of the semantic information encoded in written language

Written language is a complex communication signal capable of conveying information encoded in the form of ordered sequences of words. Beyond the local order ruled by grammar, semantic and thematic structures affect long-range patterns in word usage. Here, we show that a direct application of information theory quantifies the relationship between the statistical distribution of words and the semantic content of the text. We show that there is a characteristic scale, roughly around a few thousand words, which establishes the typical size of the most informative segments in written language. Moreover, we find that the words whose contributions to the overall information is larger, are the ones more closely associated with the main subjects and topics of the text. This scenario can be explained by a model of word usage that assumes that words are distributed along the text in domains of a characteristic size where their frequency is higher than elsewhere. Our conclusions are based on the analysis of a large database of written language, diverse in subjects and styles, and thus are likely to be applicable to general language sequences encoding complex information.Comment: 19 pages, 4 figure

A hybrid tree/finite-difference approach for Heston-Hull-White type models

We study a hybrid tree-finite difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the reliability and the efficiency of the proposed method

Noise-induced breakdown of coherent collective motion in swarms

We consider swarms formed by populations of self-propelled particles with attractive long-range interactions. These swarms represent multistable dynamical systems and can be found either in coherent traveling states or in an incoherent oscillatory state where translational motion of the entire swarm is absent. Under increasing the noise intensity, the coherent traveling state of the swarms is destroyed and an abrupt transition to the oscillatory state takes place.Comment: 6 pages, 5 figures; to appear in Phys. Rev.

Entropic analysis of the role of words in literary texts

Beyond the local constraints imposed by grammar, words concatenated in long sequences carrying a complex message show statistical regularities that may reflect their linguistic role in the message. In this paper, we perform a systematic statistical analysis of the use of words in literary English corpora. We show that there is a quantitative relation between the role of content words in literary English and the Shannon information entropy defined over an appropriate probability distribution. Without assuming any previous knowledge about the syntactic structure of language, we are able to cluster certain groups of words according to their specific role in the text.Comment: 9 pages, 5 figure

Dynamical clustering in oscillator ensembles with time-dependent interactions

We consider an ensemble of coupled oscillators whose individual states, in addition to the phase, are characterized by an internal variable with autonomous evolution. The time scale of this evolution is different for each oscillator, so that the ensemble is inhomogeneous with respect to the internal variable. Interactions between oscillators depend on this variable and thus vary with time. We show that as the inhomogeneity of time scales in the internal evolution grows, the system undergoes a critical transition between ordered and incoherent states. This transition is mediated by a regime of dynamical clustering, where the ensemble recurrently splits into groups formed by varying subpopulations.Comment: 4 pages, 3 figure

Mutual synchronization in ensembles of globally coupled neural networks

The collective dynamics in globally coupled ensembles of identical neural networks with random asymmetric synaptic connections is investigated. We find that this system shows a spontaneous synchronization transition, i.e., networks with synchronous activity patterns appear in the ensemble when the coupling intensity exceeds a threshold. Under further increase of the coupling intensity, the entire ensemble breaks down into a number of coherent clusters, until complete mutual synchronization is eventually established

Intermittency in a stochastic birth-death model

A stochastic model of a population of particles that reproduce, die, and randomly walk over the lattice is numerically investigated. Simulations show that the spatial population distributions produced by this system are intermittent. The statistical cluster analysis of the data indicates similarity with the intermittency found in the hydrodynamic turbulence

Propagation of small perturbations in synchronized oscillator networks

We study the propagation of a harmonic perturbation of small amplitude on a network of coupled identical phase oscillators prepared in a state of full synchronization. The perturbation is externally applied to a single oscillator, and is transmitted to the other oscillators through coupling. Numerical results and an approximate analytical treatment, valid for random and ordered networks, show that the response of each oscillator is a rather well-defined function of its distance from the oscillator where the external perturbation is applied. For small distances, the system behaves as a dissipative linear medium: the perturbation amplitude decreases exponentially with the distance, while propagating at constant speed. We suggest that the pattern of interactions may be deduced from measurements of the response of individual oscillators to perturbations applied at different nodes of the network