1,149 research outputs found
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
- …