Non-fixation for Biased Activated Random Walks

We prove that the model of Activated Random Walks on Z^d with biased jump distribution does not fixate for any positive density, if the sleep rate is small enough, as well as for any finite sleep rate, if the density is close enough to 1. The proof uses a new criterion for non-fixation. We provide a pathwise construction of the process, of independent interest, used in the proof of this non-fixation criterion

Reconstruction of Multidecadal Country-Aggregated Hydro Power Generation in Europe Based on a Random Forest Model

Hydro power can provide a source of dispatchable low-carbon electricity and a storage solution in a climate-dependent energy mix with high shares of wind and solar production. Therefore, understanding the effect climate has on hydro power generation is critical to ensure a stable energy supply, particularly at a continental scale. Here, we introduce a framework using climate data to model hydro power generation at the country level based on a machine learning method, the random forest model, to produce a publicly accessible hydro power dataset from 1979 to present for twelve European countries. In addition to producing a consistent European hydro power generation dataset covering the past 40 years, the specific novelty of this approach is to focus on the lagged effect of climate variability on hydro power. Specifically, multiple lagged values of temperature and precipitation are used. Overall, the model shows promising results, with the correlation values ranging between 0.85 and 0.98 for run-of-river and between 0.73 and 0.90 for reservoir-based generation. Compared to the more standard optimal lag approach the normalised mean absolute error reduces by an average of 10.23% and 5.99%, respectively. The model was also implemented over six Italian bidding zones to also test its skill at the sub-country scale. The model performance is only slightly degraded at the bidding zone level, but this also depends on the actual installed capacity, with higher capacities displaying higher performance. The framework and results presented could provide a useful reference for applications such as pan-European (continental) hydro power planning and for system adequacy and extreme events assessments

Dimensionality of Local Minimizers of the Interaction Energy

In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated to a repulsive-attractive potential. We show how the imensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.Comment: 27 page

Nonlocal interactions by repulsive-attractive potentials: radial ins/stability

In this paper, we investigate nonlocal interaction equations with repulsive-attractive radial potentials. Such equations describe the evolution of a continuum density of particles in which they repulse each other in the short range and attract each other in the long range. We prove that under some conditions on the potential, radially symmetric solutions converge exponentially fast in some transport distance toward a spherical shell stationary state. Otherwise we prove that it is not possible for a radially symmetric solution to converge weakly toward the spherical shell stationary state. We also investigate under which condition it is possible for a non-radially symmetric solution to converge toward a singular stationary state supported on a general hypersurface. Finally we provide a detailed analysis of the specific case of the repulsive-attractive power law potential as well as numerical results. We point out the the conditions of radial ins/stability are sharp.Comment: 42 pages, 7 figure

Reynolds number effect on the velocity increment skewness in isotropic turbulence

Second and third order longitudinal structure functions and wavenumber spectra of isotropic turbulence are computed using the EDQNM model and compared to results of the multifractal formalism. At the highest Reynolds number available in windtunnel experiments, $R_\lambda=2500$, both the multifractal model and EDQNM give power-law corrections to the inertial range scaling of the velocity increment skewness. For EDQNM, this correction is a finite Reynolds number effect, whereas for the multifractal formalism it is an intermittency correction that persists at any high Reynolds number. Furthermore, the two approaches yield realistic behavior of second and third order statistics of the velocity fluctuations in the dissipative and near-dissipative ranges. Similarities and differences are highlighted, in particular the Reynolds number dependence

A bottom–up model of spatial attention predicts human error patterns in rapid scene recognition

Humans demonstrate a peculiar ability to detect complex targets in rapidly presented natural scenes. Recent studies suggest that (nearly) no focal attention is required for overall performance in such tasks. Little is known, however, of how detection performance varies from trial to trial and which stages in the processing hierarchy limit performance: bottom–up visual processing (attentional selection and/or recognition) or top–down factors (e.g., decision-making, memory, or alertness fluctuations)? To investigate the relative contribution of these factors, eight human observers performed an animal detection task in natural scenes presented at 20 Hz. Trial-by-trial performance was highly consistent across observers, far exceeding the prediction of independent errors. This consistency demonstrates that performance is not primarily limited by idiosyncratic factors but by visual processing. Two statistical stimulus properties, contrast variation in the target image and the information-theoretical measure of “surprise” in adjacent images, predict performance on a trial-by-trial basis. These measures are tightly related to spatial attention, demonstrating that spatial attention and rapid target detection share common mechanisms. To isolate the causal contribution of the surprise measure, eight additional observers performed the animal detection task in sequences that were reordered versions of those all subjects had correctly recognized in the first experiment. Reordering increased surprise before and/or after the target while keeping the target and distractors themselves unchanged. Surprise enhancement impaired target detection in all observers. Consequently, and contrary to several previously published findings, our results demonstrate that attentional limitations, rather than target recognition alone, affect the detection of targets in rapidly presented visual sequences