3,603 research outputs found
Invariant submanifold for series arrays of Josephson junctions
We study the nonlinear dynamics of series arrays of Josephson junctions in
the large-N limit, where N is the number of junctions in the array. The
junctions are assumed to be identical, overdamped, driven by a constant bias
current and globally coupled through a common load. Previous simulations of
such arrays revealed that their dynamics are remarkably simple, hinting at the
presence of some hidden symmetry or other structure. These observations were
later explained by the discovery of (N - 3) constants of motion, each choice of
which confines the resulting flow in phase space to a low-dimensional invariant
manifold. Here we show that the dimensionality can be reduced further by
restricting attention to a special family of states recently identified by Ott
and Antonsen. In geometric terms, the Ott-Antonsen ansatz corresponds to an
invariant submanifold of dimension one less than that found earlier. We derive
and analyze the flow on this submanifold for two special cases: an array with
purely resistive loading and another with resistive-inductive-capacitive
loading. Our results recover (and in some instances improve) earlier findings
based on linearization arguments.Comment: 10 pages, 6 figure
Spreading dynamics on spatially constrained complex brain networks
The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics and has been widely undertaken. Typically, however, networks employed in theoretical studies bear little relation to the spatial embedding or connectivity of the neural networks that they attempt to replicate. Here, we employ detailed neuroimaging data to define a network whose spatial embedding represents accurately the folded structure of the cortical surface of a rat brain and investigate the propagation of activity over this network under simple spreading and connectivity rules. By comparison with standard network models with the same coarse statistics, we show that the cortical geometry influences profoundly the speed of propagation of activation through the network. Our conclusions are of high relevance to the theoretical modelling of epileptic seizure events and indicate that such studies which omit physiological network structure risk simplifying the dynamics in a potentially significant way
Signal processing with Levy information
Levy processes, which have stationary independent increments, are ideal for
modelling the various types of noise that can arise in communication channels.
If a Levy process admits exponential moments, then there exists a parametric
family of measure changes called Esscher transformations. If the parameter is
replaced with an independent random variable, the true value of which
represents a "message", then under the transformed measure the original Levy
process takes on the character of an "information process". In this paper we
develop a theory of such Levy information processes. The underlying Levy
process, which we call the fiducial process, represents the "noise type". Each
such noise type is capable of carrying a message of a certain specification. A
number of examples are worked out in detail, including information processes of
the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse
Gaussian, and normal inverse Gaussian type. Although in general there is no
additive decomposition of information into signal and noise, one is led
nevertheless for each noise type to a well-defined scheme for signal detection
and enhancement relevant to a variety of practical situations.Comment: 27 pages. Version to appear in: Proc. R. Soc. London
Schulman Replies
This is a reply to a comment of Casati, Chirikov and Zhirov (PRL 85, 896
(2000)) on PRL 83, 5419 (1999).
The suitability of the particlar two-time boundary value problem used in the
earlier PRL is argued
Wiener algebra for the quaternions
We define and study the counterpart of the Wiener algebra in the quaternionic
setting, both for the discrete and continuous case. We prove a Wiener-L\'evy
type theorem and a factorization theorem. We give applications to Toeplitz and
Wiener-Hopf operators
Transfer Entropy as a Log-likelihood Ratio
Transfer entropy, an information-theoretic measure of time-directed
information transfer between joint processes, has steadily gained popularity in
the analysis of complex stochastic dynamics in diverse fields, including the
neurosciences, ecology, climatology and econometrics. We show that for a broad
class of predictive models, the log-likelihood ratio test statistic for the
null hypothesis of zero transfer entropy is a consistent estimator for the
transfer entropy itself. For finite Markov chains, furthermore, no explicit
model is required. In the general case, an asymptotic chi-squared distribution
is established for the transfer entropy estimator. The result generalises the
equivalence in the Gaussian case of transfer entropy and Granger causality, a
statistical notion of causal influence based on prediction via vector
autoregression, and establishes a fundamental connection between directed
information transfer and causality in the Wiener-Granger sense
Redundant variables and Granger causality
We discuss the use of multivariate Granger causality in presence of redundant
variables: the application of the standard analysis, in this case, leads to
under-estimation of causalities. Using the un-normalized version of the
causality index, we quantitatively develop the notions of redundancy and
synergy in the frame of causality and propose two approaches to group redundant
variables: (i) for a given target, the remaining variables are grouped so as to
maximize the total causality and (ii) the whole set of variables is partitioned
to maximize the sum of the causalities between subsets. We show the application
to a real neurological experiment, aiming to a deeper understanding of the
physiological basis of abnormal neuronal oscillations in the migraine brain.
The outcome by our approach reveals the change in the informational pattern due
to repetitive transcranial magnetic stimulations.Comment: 4 pages, 5 figures. Accepted for publication in Physical Review
Precautionary Regulation in Europe and the United States: A Quantitative Comparison
Much attention has been addressed to the question of whether Europe or the United States adopts a more precautionary stance to the regulation of potential environmental, health, and safety risks. Some commentators suggest that Europe is more risk-averse and precautionary, whereas the US is seen as more risk-taking and optimistic about the prospects for new technology. Others suggest that the US is more precautionary because its regulatory process is more legalistic and adversarial, while Europe is more lax and corporatist in its regulations. The flip-flop hypothesis claims that the US was more precautionary than Europe in the 1970s and early 1980s, and that Europe has become more precautionary since then. We examine the levels and trends in regulation of environmental, health, and safety risks since 1970. Unlike previous research, which has studied only a small set of prominent cases selected non-randomly, we develop a comprehensive list of almost 3,000 risks and code the relative stringency of regulation in Europe and the US for each of 100 risks randomly selected from that list for each year from 1970 through 2004. Our results suggest that: (a) averaging over risks, there is no significant difference in relative precaution over the period, (b) weakly consistent with the flip-flop hypothesis, there is some evidence of a modest shift toward greater relative precaution of European regulation since about 1990, although (c) there is a diversity of trends across risks, of which the most common is no change in relative precaution (including cases where Europe and the US are equally precautionary and where Europe or the US has been consistently more precautionary). The overall finding is of a mixed and diverse pattern of relative transatlantic precaution over the period
Self consistent determination of plasmonic resonances in ternary nanocomposites
We have developed a self consistent technique to predict the behavior of
plasmon resonances in multi-component systems as a function of wavelength. This
approach, based on the tight lower bounds of the Bergman-Milton formulation, is
able to predict experimental optical data, including the positions, shifts and
shapes of plasmonic peaks in ternary nanocomposites without using any ftting
parameters. Our approach is based on viewing the mixing of 3 components as the
mixing of 2 binary mixtures, each in the same host. We obtained excellent
predictions of the experimental optical behavior for mixtures of Ag:Cu:SiO2 and
alloys of Au-Cu:SiO2 and Ag-Au:H2 O, suggesting that the essential physics of
plasmonic behavior is captured by this approach.Comment: 7 pages and 4 figure
Multiple G-It\^{o} integral in the G-expectation space
In this paper, motivated by mathematic finance we introduce the multiple
G-It\^{o} integral in the G-expectation space, then investigate how to
calculate. We get the the relationship between Hermite polynomials and multiple
G-It\^{o} integrals which is a natural extension of the classical result
obtained by It\^{o} in 1951.Comment: 9 page
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