5,450 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
Implications of Public Opinion for Space Program Planning, 1980 - 2000
The effect of public opinion on future space programs is discussed in terms of direct support, apathy, or opposition, and concern about the tax burden, budgetary pressures, and national priorities. Factors considered include: the salience and visibility of NASA as compared with other issues, the sources of general pressure on the federal budget which could affect NASA, the public's opinions regarding the size and priority of NASA'S budget, the degree to which the executive can exercise leverage over NASA's budget through influencing or disregarding public opinion, the effects of linkages to other issues on space programs, and the public's general attitudes toward the progress of science
Contextual planning for NASA - A second workbook of alternative future environments for mission analysis, volume 1 Interim report
Contextural planning for selecting alternate NASA program
Synchronization of globally coupled two-state stochastic oscillators with a state dependent refractory period
We present a model of identical coupled two-state stochastic units each of
which in isolation is governed by a fixed refractory period. The nonlinear
coupling between units directly affects the refractory period, which now
depends on the global state of the system and can therefore itself become time
dependent. At weak coupling the array settles into a quiescent stationary
state. Increasing coupling strength leads to a saddle node bifurcation, beyond
which the quiescent state coexists with a stable limit cycle of nonlinear
coherent oscillations. We explicitly determine the critical coupling constant
for this transition
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
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
On inversions and Doob -transforms of linear diffusions
Let be a regular linear diffusion whose state space is an open interval
. We consider a diffusion which probability law is
obtained as a Doob -transform of the law of , where is a positive
harmonic function for the infinitesimal generator of on . This is the
dual of with respect to where is the speed measure of
. Examples include the case where is conditioned to stay above
some fixed level. We provide a construction of as a deterministic
inversion of , time changed with some random clock. The study involves the
construction of some inversions which generalize the Euclidean inversions.
Brownian motion with drift and Bessel processes are considered in details.Comment: 19 page
Granger causality and transfer entropy are equivalent for Gaussian variables
Granger causality is a statistical notion of causal influence based on
prediction via vector autoregression. Developed originally in the field of
econometrics, it has since found application in a broader arena, particularly
in neuroscience. More recently transfer entropy, an information-theoretic
measure of time-directed information transfer between jointly dependent
processes, has gained traction in a similarly wide field. While it has been
recognized that the two concepts must be related, the exact relationship has
until now not been formally described. Here we show that for Gaussian
variables, Granger causality and transfer entropy are entirely equivalent, thus
bridging autoregressive and information-theoretic approaches to data-driven
causal inference.Comment: In review, Phys. Rev. Lett., Nov. 200
Causal connectivity of evolved neural networks during behavior
To show how causal interactions in neural dynamics are modulated by behavior, it is valuable to analyze these interactions without perturbing or lesioning the neural mechanism. This paper proposes a method, based on a graph-theoretic extension of vector autoregressive modeling and 'Granger causality,' for characterizing causal interactions generated within intact neural mechanisms. This method, called 'causal connectivity analysis' is illustrated via model neural networks optimized for controlling target fixation in a simulated head-eye system, in which the structure of the environment can be experimentally varied. Causal connectivity analysis of this model yields novel insights into neural mechanisms underlying sensorimotor coordination. In contrast to networks supporting comparatively simple behavior, networks supporting rich adaptive behavior show a higher density of causal interactions, as well as a stronger causal flow from sensory inputs to motor outputs. They also show different arrangements of 'causal sources' and 'causal sinks': nodes that differentially affect, or are affected by, the remainder of the network. Finally, analysis of causal connectivity can predict the functional consequences of network lesions. These results suggest that causal connectivity analysis may have useful applications in the analysis of neural dynamics
Opposite Thermodynamic Arrows of Time
A model in which two weakly coupled systems maintain opposite running
thermodynamic arrows of time is exhibited. Each experiences its own retarded
electromagnetic interaction and can be seen by the other. The possibility of
opposite-arrow systems at stellar distances is explored and a relation to dark
matter suggested.Comment: To appear in Phys. Rev. Let
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