9,596 research outputs found
A Partitioning Algorithm for Detecting Eventuality Coincidence in Temporal Double recurrence
A logical theory of regular double or multiple recurrence of eventualities,
which are regular patterns of occurrences that are repeated, in time, has been
developed within the context of temporal reasoning that enabled reasoning about
the problem of coincidence. i.e. if two complex eventualities, or eventuality
sequences consisting respectively of component eventualities x0, x1,....,xr and
y0, y1, ..,ys both recur over an interval k and all eventualities are of fixed
durations, is there a subinterval of k over which the occurrence xp and yq for
p between 1 and r and q between 1 and s coincide. We present the ideas behind a
new algorithm for detecting the coincidence of eventualities xp and yq within a
cycle of the double recurrence of x and y. The algorithm is based on the novel
concept of gcd partitions that requires the partitioning of each of the
incidences of both x and y into eventuality sequences each of which components
have a duration that is equal to the greatest common divisor of the durations
of x and y. The worst case running time of the partitioning algorithm is linear
in the maximum of the duration of x and that of y, while the worst case running
time of an algorithm exploring a complete cycle is quadratic in the durations
of x and y. Hence the partitioning algorithm works faster than the cyclical
exploration in the worst case
Recurrence networks - A novel paradigm for nonlinear time series analysis
This paper presents a new approach for analysing structural properties of
time series from complex systems. Starting from the concept of recurrences in
phase space, the recurrence matrix of a time series is interpreted as the
adjacency matrix of an associated complex network which links different points
in time if the evolution of the considered states is very similar. A critical
comparison of these recurrence networks with similar existing techniques is
presented, revealing strong conceptual benefits of the new approach which can
be considered as a unifying framework for transforming time series into complex
networks that also includes other methods as special cases.
It is demonstrated that there are fundamental relationships between the
topological properties of recurrence networks and the statistical properties of
the phase space density of the underlying dynamical system. Hence, the network
description yields new quantitative characteristics of the dynamical complexity
of a time series, which substantially complement existing measures of
recurrence quantification analysis
A Scalable Model of Cerebellar Adaptive Timing and Sequencing: The Recurrent Slide and Latch (RSL) Model
From the dawn of modern neural network theory, the mammalian cerebellum has been a favored object of mathematical modeling studies. Early studies focused on the fan-out, convergence, thresholding, and learned weighting of perceptual-motor signals within the cerebellar cortex. This led in the proposals of Albus (1971; 1975) and Marr (1969) to the still viable idea that the granule cell stage in the cerebellar cortex performs a sparse expansive recoding of the time-varying input vector. This recoding reveals and emphasizes combinations (of input state variables) in a distributed representation that serves as a basis for the learned, state-dependent control actions engendered by cerebellar outputs to movement related centers. Although well-grounded as such, this perspective seriously underestimates the intelligence of the cerebellar cortex. Context and state information arises asynchronously due to the heterogeneity of sources that contribute signals to compose the cerebellar input vector. These sources include radically different sensory systems - vision, kinesthesia, touch, balance and audition - as well as many stages of the motor output channel. To make optimal use of available signals, the cerebellum must be able to sift the evolving state representation for the most reliable predictors of the need for control actions, and to use those predictors even if they appear only transiently and well in advance of the optimal time for initiating the control action. Such a cerebellar adaptive timing competence has recently been experimentally verified (Perrett, Ruiz, & Mauk, 1993). This paper proposes a modification to prior, population, models for cerebellar adaptive timing and sequencing. Since it replaces a population with a single clement, the proposed Recurrent Slide and Latch (RSL) model is in one sense maximally efficient, and therefore optimal from the perspective of scalability.Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-92-J-1309, N00014-93-1-1364, N00014-95-1-0409)
Recurrence-based time series analysis by means of complex network methods
Complex networks are an important paradigm of modern complex systems sciences
which allows quantitatively assessing the structural properties of systems
composed of different interacting entities. During the last years, intensive
efforts have been spent on applying network-based concepts also for the
analysis of dynamically relevant higher-order statistical properties of time
series. Notably, many corresponding approaches are closely related with the
concept of recurrence in phase space. In this paper, we review recent
methodological advances in time series analysis based on complex networks, with
a special emphasis on methods founded on recurrence plots. The potentials and
limitations of the individual methods are discussed and illustrated for
paradigmatic examples of dynamical systems as well as for real-world time
series. Complex network measures are shown to provide information about
structural features of dynamical systems that are complementary to those
characterized by other methods of time series analysis and, hence,
substantially enrich the knowledge gathered from other existing (linear as well
as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos
(2011
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
Improved limits on gamma ray burst repetition
We tighten previous upper limits on gamma ray burst repetition by analyzing
the angular power spectrum of the BATSE 3B catalog of 1122 bursts. At 95%
confidence, we find that no more than 2% of all observed bursts can be labeled
as repeaters, even if no sources are observed to repeat more than once. If a
fraction f of all observed bursts can be labeled as repeaters that are observed
to burst v times each, then all models with (v-1)f>0.05 are ruled out at 99%
confidence, as compared to the best previous 99% limit (v-1)f>0.27. At 95%
confidence, our new limit is (v-1)f>0.02. Thus even a cluster of 6 events from
a single source would have caused excess power above that present in the 3B
catalog. We conclude that the current BATSE data are consistent with no
repetition of classical gamma ray bursts, and that any repeater model is
severely constrained by the near perfect isotropy of their angular
distribution.Comment: 18 pages, with 2 figures included. Postscript. Submitted to ApJL.
Latest version at http://astro.berkeley.edu/~max/repeaters.html (faster from
the US), from http://www.mpa-garching.mpg.de/~max/repeaters.html (faster from
Europe) or from [email protected]
Decentralized Exchange and Factor Payments: A Multiple-Matching Approach
The emergence of fiat money is studied in an environment in which exchange is organized around trading posts where many producers and shoppers are matched in a dynamic monopolistically competitive framework. Each household consumes a bundle of commodities and has a preference for consumption variety. Within this multiple matching structure we determine the endogenous organization of exchange between firms and shoppers and the means of factor payment (remuneration) as well as the price at which these trades occur. Although each household contacts many sellers, the specialization of tastes implies that the variety of the consumption basket under barter mediated exchange is sparser than that obtained under monetary exchange. We verify that the endogenous linkage of factor payments with the medium of exchange can lead to a monetary equilibrium outcome where only fiat money trades for goods, an ex-ante feature of cash-in-advance models. We also examine the long-run effects of money growth on the equilibrium pattern of exchange. A primary finding, consistent with documented hyperinflationary episodes, is that a sufficiently rapid expansion of money supply and inflation leads to the gradual emergence of barter. Under these circumstances sellers will accept both goods and cash payments whereas workers receive part of their remuneration in goods.Variety Preference, Search, Trading Post, Monetary vs. Barter Equilibrium
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