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The accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz’s 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier–Stokes (N-S) equations suggest that one can skillfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz’s theory. Aided by numerical simulations, the present work reexamines Lorenz’s model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found that when this slope is shallower than −3, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real system is resolved—which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, the spectral slope is steeper than −3, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz’s theory is reconciled.
Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms encoded in the data and thus to better understand the probed systems. We here augment recently proposed machine-learning techniques for decoding anomalous-diffusion data to include an uncertainty estimate in addition to the predicted output. To avoid the Black-Box-Problem a Bayesian-Deep-Learning technique named Stochastic-Weight-Averaging-Gaussian is used to train models for both the classification of the diffusionmodel and the regression of the anomalous diffusion exponent of single-particle-trajectories. Evaluating their performance, we find that these models can achieve a wellcalibrated error estimate while maintaining high prediction accuracies. In the analysis of the output uncertainty predictions we relate these to properties of the underlying diffusion models, thus providing insights into the learning process of the machine and the relevance of the output.
Sprache
Englisch
Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms encoded in the data and thus to better understand the probed systems. We here augment recently proposed machine-learning techniques for decoding anomalous-diffusion data to include an uncertainty estimate in addition to the predicted output. To avoid the Black-Box-Problem a Bayesian-Deep-Learning technique named Stochastic-Weight-Averaging-Gaussian is used to train models for both the classification of the diffusionmodel and the regression of the anomalous diffusion exponent of single-particle-trajectories. Evaluating their performance, we find that these models can achieve a wellcalibrated error estimate while maintaining high prediction accuracies. In the analysis of the output uncertainty predictions we relate these to properties of the underlying diffusion models, thus providing insights into the learning process of the machine and the relevance of the output.
Observations of rift and rifted margin architecture suggest that significant spatial and temporal structural heterogeneity develops during the multiphase evolution of continental rifting. Inheritance is often invoked to explain this heterogeneity, such as preexisting anisotropies in rock composition, rheology, and deformation. Here, we use high-resolution 3-D thermal-mechanical numerical models of continental extension to demonstrate that rift-parallel heterogeneity may develop solely through fault network evolution during the transition from distributed to localized deformation. In our models, the initial phase of distributed normal faulting is seeded through randomized initial strength perturbations in an otherwise laterally homogeneous lithosphere extending at a constant rate. Continued extension localizes deformation onto lithosphere-scale faults, which are laterally offset by tens of km and discontinuous along-strike. These results demonstrate that rift- and margin-parallel heterogeneity of large-scale fault patterns may in-part be a natural byproduct of fault network coalescence.
Observations of rift and rifted margin architecture suggest that significant spatial and temporal structural heterogeneity develops during the multiphase evolution of continental rifting. Inheritance is often invoked to explain this heterogeneity, such as preexisting anisotropies in rock composition, rheology, and deformation. Here, we use high-resolution 3-D thermal-mechanical numerical models of continental extension to demonstrate that rift-parallel heterogeneity may develop solely through fault network evolution during the transition from distributed to localized deformation. In our models, the initial phase of distributed normal faulting is seeded through randomized initial strength perturbations in an otherwise laterally homogeneous lithosphere extending at a constant rate. Continued extension localizes deformation onto lithosphere-scale faults, which are laterally offset by tens of km and discontinuous along-strike. These results demonstrate that rift- and margin-parallel heterogeneity of large-scale fault patterns may in-part be a natural byproduct of fault network coalescence.
F2C2
(2012)
Background: Flux coupling analysis (FCA) has become a useful tool in the constraint-based analysis of genome-scale metabolic networks. FCA allows detecting dependencies between reaction fluxes of metabolic networks at steady-state. On the one hand, this can help in the curation of reconstructed metabolic networks by verifying whether the coupling between reactions is in agreement with the experimental findings. On the other hand, FCA can aid in defining intervention strategies to knock out target reactions.
Results: We present a new method F2C2 for FCA, which is orders of magnitude faster than previous approaches. As a consequence, FCA of genome-scale metabolic networks can now be performed in a routine manner.
Conclusions: We propose F2C2 as a fast tool for the computation of flux coupling in genome-scale metabolic networks. F2C2 is freely available for non-commercial use at https://sourceforge.net/projects/f2c2/files/.
We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T−h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
We evaluate the spatial and temporal evolution of Earth's long-wavelength surface dynamic topography since the Jurassic using a series of high-resolution global mantle convection models. These models are Earth-like in terms of convective vigour, thermal structure, surface heat-flux and the geographic distribution of heterogeneity. The models generate a degree-2-dominated spectrum of dynamic topography with negative amplitudes above subducted slabs (i.e. circum-Pacific regions and southern Eurasia) and positive amplitudes elsewhere (i.e. Africa, north-western Eurasia and the central Pacific). Model predictions are compared with published observations and subsidence patterns from well data, both globally and for the Australian and southern African regions. We find that our models reproduce the long-wavelength component of these observations, although observed smaller-scale variations are not reproduced. We subsequently define "geodynamic rules" for how different surface tectonic settings are affected by mantle processes: (i) locations in the vicinity of a subduction zone show large negative dynamic topography amplitudes; (ii) regions far away from convergent margins feature long-term positive dynamic topography; and (iii) rapid variations in dynamic support occur along the margins of overriding plates (e.g. the western US) and at points located on a plate that rapidly approaches a subduction zone (e.g. India and the Arabia Peninsula). Our models provide a predictive quantitative framework linking mantle convection with plate tectonics and sedimentary basin evolution, thus improving our understanding of how subduction and mantle convection affect the spatio-temporal evolution of basin architecture.
This study identified key somatic and demographic characteristics that benefit all swimmers and, at the same time, identified further characteristics that benefit only specific swimming strokes. Three hundred sixty-three competitive-level swimmers (male [n = 202]; female [n = 161]) participated in the study. We adopted a multiplicative, allometric regression model to identify the key characteristics associated with 100 m swimming speeds (controlling for age). The model was refined using backward elimination. Characteristics that benefited some but not all strokes were identified by introducing stroke-by-predictor variable interactions. The regression analysis revealed 7 "common" characteristics that benefited all swimmers suggesting that all swimmers benefit from having less body fat, broad shoulders and hips, a greater arm span (but shorter lower arms) and greater forearm girths with smaller relaxed arm girths. The 4 stroke-specific characteristics reveal that backstroke swimmers benefit from longer backs, a finding that can be likened to boats with longer hulls also travel faster through the water. Other stroke-by-predictor variable interactions (taken together) identified that butterfly swimmers are characterized by greater muscularity in the lower legs. These results highlight the importance of considering somatic and demographic characteristics of young swimmers for talent identification purposes (i.e., to ensure that swimmers realize their most appropriate strokes).
Proposing relevant perturbations to biological signaling networks is central to many problems in biology and medicine because it allows for enabling or disabling certain biological outcomes. In contrast to quantitative methods that permit fine-grained (kinetic) analysis, qualitative approaches allow for addressing large-scale networks. This is accomplished by more abstract representations such as logical networks. We elaborate upon such a qualitative approach aiming at the computation of minimal interventions in logical signaling networks relying on Kleene's three-valued logic and fixpoint semantics. We address this problem within answer set programming and show that it greatly outperforms previous work using dedicated algorithms.