4,705 research outputs found
Quantifying information transfer and mediation along causal pathways in complex systems
Measures of information transfer have become a popular approach to analyze interactions in complex systems such as the Earth or the human brain from measured time series. Recent work has focused on causal definitions of information transfer aimed at decompositions of predictive information about a target variable, while excluding effects of common drivers and indirect influences. While common drivers clearly constitute a spurious causality, the aim of the present article is to develop measures quantifying different notions of the strength of information transfer along indirect causal paths, based on first reconstructing the multivariate causal network. Another class of novel measures quantifies to what extent different intermediate processes on causal paths contribute to an interaction mechanism to determine pathways of causal information transfer. The proposed framework complements predictive decomposition schemes by focusing more on the interaction mechanism between multiple processes. A rigorous mathematical framework allows for a clear information-theoretic interpretation that can also be related to the underlying dynamics as proven for certain classes of processes. Generally, however, estimates of information transfer remain hard to interpret for nonlinearly intertwined complex systems. But if experiments or mathematical models are not available, then measuring pathways of information transfer within the causal dependency structure allows at least for an abstraction of the dynamics. The measures are illustrated on a climatological example to disentangle pathways of atmospheric flow over Europe
Optimal model-free prediction from multivariate time series
© 2015 American Physical Society.Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal preselection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used suboptimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Niño Southern Oscillation
Classical correlations of defects in lattices with geometrical frustration in the motion of a particle
We map certain highly correlated electron systems on lattices with
geometrical frustration in the motion of added particles or holes to the
spatial defect-defect correlations of dimer models in different geometries.
These models are studied analytically and numerically. We consider different
coverings for four different lattices: square, honeycomb, triangular, and
diamond. In the case of hard-core dimer covering, we verify the existed results
for the square and triangular lattice and obtain new ones for the honeycomb and
the diamond lattices while in the case of loop covering we obtain new numerical
results for all the lattices and use the existing analytical Liouville field
theory for the case of square lattice.The results show power-law correlations
for the square and honeycomb lattice, while exponential decay with distance is
found for the triangular and exponential decay with the inverse distance on the
diamond lattice. We relate this fact with the lack of bipartiteness of the
triangular lattice and in the latter case with the three-dimensionality of the
diamond. The connection of our findings to the problem of fractionalized charge
in such lattices is pointed out.Comment: 6 pages, 6 figures, 1 tabl
The Infati Data
The ability to perform meaningful empirical studies is of essence in research
in spatio-temporal query processing. Such studies are often necessary to gain
detailed insight into the functional and performance characteristics of
proposals for new query processing techniques.
We present a collection of spatio-temporal data, collected during an
intelligent speed adaptation project, termed INFATI, in which some two dozen
cars equipped with GPS receivers and logging equipment took part. We describe
how the data was collected and how it was "modified" to afford the drivers some
degree of anonymity.
We also present the road network in which the cars were moving during data
collection.
The GPS data is publicly available for non-commercial purposes. It is our
hope that this resource will help the spatio-temporal research community in its
efforts to develop new and better query processing techniques
Observation of soliton explosions in a passively mode-locked fiber laser
Soliton explosions are among the most exotic dissipative phenomena studied in
mode-locked lasers. In this regime, a dissipative soliton circulating in the
laser cavity experiences an abrupt structural collapse, but within a few
roundtrips returns to its original quasi-stable state. In this work we report
on the first observation of such events in a fiber laser. Specifically, we
identify clear explosion signatures in measurements of shot-to-shot spectra of
an Yb-doped mode-locked fiber laser that is operating in a transition regime
between stable and noise-like emission. The comparatively long,
all-normal-dispersion cavity used in our experiments also permits direct
time-domain measurements, and we show that the explosions manifest themselves
as abrupt temporal shifts in the output pulse train. Our experimental results
are in good agreement with realistic numerical simulations based on an
iterative cavity map.Comment: 5 pages, 5 figures, submitte
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Identifying causal gateways and mediators in complex spatio-temporal systems
Coldâpoolâdriven convective initiation: using causal graph analysis to determine what convectionâpermitting models are missing
Coldâpoolâdriven convective initiation is investigated in highâresolution, convectionâpermitting simulations with a focus on the diurnal cycle and organization of convection and the sensitivity to grid size. Simulations of four different days over Germany were performed using the ICONâLEM model with grid sizes from 156 to 625âm. In these simulations, we identify cold pools, coldâpool boundaries and initiated convection. Convection is triggered much more efficiently in the vicinity of cold pools than in other regions and can provide as much as 50% of total convective initiation, in particular in the late afternoon. By comparing different model resolutions, we find that cold pools are more frequent, smaller and less intense in lowerâresolution simulations. Furthermore, their gust fronts are weaker and less likely to trigger new convection. To identify how model resolution affects this triggering probability, we use a linear causal graph analysis. In doing so, we postulate a graph structure with potential causal pathways and then apply multiâlinear regression accordingly. We find a dominant, systematic effect: reducing grid sizes directly reduces upward mass flux at the gust front, which causes weaker triggering probabilities. These findings are expected to be even more relevant for kmâscale, numerical weather prediction models. We thus expect that a better representation of coldâpoolâdriven convective initiation will improve forecasts of convective precipitation
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