Transmission needs across a fully renewable European power system

The residual load and excess power generation of 27 European countries with a 100% penetration of variable renewable energy sources are explored in order to quantify the benefit of power transmission between countries. Estimates are based on extensive weather data, which allows for modelling of hourly mismatches between the demand and renewable generation from wind and solar photovoltaics. For separated countries, balancing is required to cover around 24% of the total annual energy consumption. This number can be reduced down to 15% once all countries are networked together with uncon- strained interconnectors. The reduction represents the maximum possible benefit of transmission for the countries. The total Net Transfer Capacity of the unconstrained interconnectors is roughly twelve times larger than current values. However, constrained interconnector capacities six times larger than the current values are found to provide 97% of the maximum possible benefit of cooperation. This motivates a detailed investigation of several constrained transmission capacity layouts to determine the export and import capabilities of countries participating in a fully renewable European electricity system

Coordinated optimization of visual cortical maps : 2. Numerical studies

In the juvenile brain, the synaptic architecture of the visual cortex remains in a state of flux for months after the natural onset of vision and the initial emergence of feature selectivity in visual cortical neurons. It is an attractive hypothesis that visual cortical architecture is shaped during this extended period of juvenile plasticity by the coordinated optimization of multiple visual cortical maps such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we introduced a class of analytically tractable coordinated optimization models and solved representative examples, in which a spatially complex organization of the OP map is induced by interactions between the maps. We found that these solutions near symmetry breaking threshold predict a highly ordered map layout. Here we examine the time course of the convergence towards attractor states and optima of these models. In particular, we determine the timescales on which map optimization takes place and how these timescales can be compared to those of visual cortical development and plasticity. We also assess whether our models exhibit biologically more realistic, spatially irregular solutions at a finite distance from threshold, when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. We show that, although maps typically undergo substantial rearrangement, no other solutions than pinwheel crystals and stripes dominate in the emerging layouts. Pinwheel crystallization takes place on a rather short timescale and can also occur for detuned wavelengths of different maps. Our numerical results thus support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the architecture of the visual cortex. We discuss several alternative scenarios that may improve the agreement between model solutions and biological observations

Coordinated optimization of visual cortical maps : 1. Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps

Statistische Physik von Leistungsflüssen auf Netzwerken mit einem hohen Anteil fluktuierender erneuerbarer Erzeugung

Renewable energy sources will play an important role in future generation of electrical energy. This is due to the fact that fossil fuel reserves are limited and because of the waste caused by conventional electricity generation. The most important sources of renewable energy, wind and solar irradiation, exhibit strong temporal fluctuations. This poses new problems for the security of supply. Further, the power flows become a stochastic character so that new methods are required to predict flows within an electrical grid. The main focus of this work is the description of power flows in a electrical transmission network with a high share of renewable generation of electrical energy. To define an appropriate model, it is important to understand the general set-up of a stable system with fluctuating generation. Therefore, generation time series of solar and wind power are compared to load time series for whole Europe and the required balancing or storage capacities analyzed. With these insights, a simple model is proposed to study the power flows. An approximation to the full power flow equations is used and evaluated with Monte-Carlo simulations. Further, approximations to the distributions of power flows along the links are analytically derived. Finally, the results are compared to the power flows calculated from the generation and load data.Erneuerbare Energien werden zukünftig eine große Rolle bei der Versorgung mit elektrischer Energie spielen. Zum einen entstehen keine Abgase, die mit dem Klimawandel in Verbindung gebracht werden, als auch keine radioaktiven Abfälle. Zum anderen bedeutet der Einsatz von regenerativen Energiequellen Unabhängigkeit von endlichen fossilen Energieträgern. Die wichtigsten erneuerbaren Energiequellen, Wind- und Solarenergie, zeigen starke zeitliche Fluktuationen. Dies stellt ein Problem für die Versorgungssicherheit dar. Ein anderes wichtiges Problem ist, dass die resultierenden Leistungsflüsse bei einen hohen Anteil erneuerbarer Energieerzeugung einen stochastischen Charakter bekommen. Der Hauptfokus dieser Arbeit liegt auf der Beschreibung von Leistungsflüssen, die aus fluktuierender Energieerzeugung resultiert. Für die Formulierung sinnvoller Modelle ist es wichtig die Rahmenbedingungen zukünftiger Energiesysteme zu verstehen. Daher werden Zeitreihen von Wind- und Solarerzeugung mit der Last verglichen und der Bedarf an Ausgleichskraftwerken oder Speicher ermittelt. Zur Beschreibung der Leistungsflüsse wird ein einfaches Modell formuliert. Eine Näherung der Flussgleichungen wird verwendet und mit Hilfe von Monte-Carlo Simulationen ausgewertet. Im folgenden werden Näherungen der Flussverteilungen auf den Links analytisch hergeleitet. Diese Ergebnisse werden mit den Leistungsflüssen basierend auf den Daten verglichen

Coordinated optimization of visual cortical maps (I) Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of OP columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about an hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference.Comment: 90 pages, 16 figure

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

Polarization Wavefront Lidar: Learning Large Scene Reconstruction from Polarized Wavefronts

Lidar has become a cornerstone sensing modality for 3D vision, especially for large outdoor scenarios and autonomous driving. Conventional lidar sensors are capable of providing centimeter-accurate distance information by emitting laser pulses into a scene and measuring the time-of-flight (ToF) of the reflection. However, the polarization of the received light that depends on the surface orientation and material properties is usually not considered. As such, the polarization modality has the potential to improve scene reconstruction beyond distance measurements. In this work, we introduce a novel long-range polarization wavefront lidar sensor (PolLidar) that modulates the polarization of the emitted and received light. Departing from conventional lidar sensors, PolLidar allows access to the raw time-resolved polarimetric wavefronts. We leverage polarimetric wavefronts to estimate normals, distance, and material properties in outdoor scenarios with a novel learned reconstruction method. To train and evaluate the method, we introduce a simulated and real-world long-range dataset with paired raw lidar data, ground truth distance, and normal maps. We find that the proposed method improves normal and distance reconstruction by 53\% mean angular error and 41\% mean absolute error compared to existing shape-from-polarization (SfP) and ToF methods. Code and data are open-sourced at https://light.princeton.edu/pollidar.Comment: Accepted at CVPR 2024; Project Website: https://light.princeton.edu/publication/pollida

A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio

Stimulation sites in the subthalamic nucleus projected onto a mean 3-D atlas of the thalamus and basal ganglia

Background: In patients with severe forms of Parkinson's disease (PD), deep brain stimulation (DBS) commonly targets the subthalamic nucleus (STN). Recently, the mean 3-D Morel-Atlas of the basal ganglia and the thalamus was introduced. It combines information contained in histological data from ten post-mortem brains. We were interested whether the Morel-Atlas is applicable for the visualization of stimulation sites. Methods: In a consecutive PD patient series, we documented preoperative MRI planning, intraoperative target adjustment based on electrophysiological and neurological testing, and perioperative CT target reconstruction. The localization of the DBS electrodes and the optimal stimulation sites were projected onto the Morel-Atlas. Results: We included 20 patients (median age 62 years). The active contact had mean coordinates Xlat = ±12.1mm, Yap = −1.8mm, Zvert = −3.2mm. There was a significant difference between the initially planned site and the coordinates of the postoperative active contact site (median 2.2mm). The stimulation site was, on average, more anterior and more dorsal. The electrode contact used for optimal stimulation was found within the STN of the atlas in 38/40 (95%) of implantations. Conclusions: The cluster of stimulation sites in individual patients—as deduced from preoperative MR, intraoperative electrophysiology and neurological testing—showed a high degree of congruence with the atlas. The mean 3D Morel Atlas is thus a useful tool for postoperative target visualization. This represents the first clinical evaluation of the recently created atla