The objective functions used in spectral clustering are generally composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and helps avoiding degenerate solutions. This paper shows that a graph neural network, equipped with suitable message passing layers, can generate good cluster ...

Polar lows are intense mesoscale cyclones developing in marine polar air masses. This study presents a new global climatology of polar lows based on the ERA5 reanalysis for the years 1979–2020. Criteria for the detection of polar lows are derived based on a comparison of five polarlow archives with cyclones derived by a mesoscale tracking algorithm. The characteristics associated with polar lows are ...

Given a smooth family of unparameterized curves such that through every point in every direction there passes exactly one curve, does there exist a Lagrangian with extremals being precisely this family? It is known that in dimension 2 the answer is positive. In dimension 3, it follows from the work of Douglas that the answer is, in general, negative. We generalise this result to all higher dimensions ...

Studies of spatial population synchrony constitute a central approach for understanding the drivers of ecological dynamics. Recently, identifying the ecological impacts of climate change has emerged as a new important focus in population synchrony studies. However, while it is well known that climatic seasonality and sequential density dependence influences local population dynamics, the role of ...

We propose an end-to-end framework based on a Graph Neural Network (GNN) to balance the power flows in energy grids. The balancing is framed as a supervised vertex regression task, where the GNN is trained to predict the current and power injections at each grid branch that yield a power flow balance. By representing the power grid as a line graph with branches as vertices, we can train a GNN that ...

The thesis is an expansion of the work Gerald R. North did in 1975 on an energy balance climate model. By considering a similar model on an infinite line, and allowing the heat diffusion coefficient to vary on the line, more complicated behaviour arose from the model. Much of Norths work was recreated on the infinite lines, but a lot of new discoveries were made. Among what was found were spontaneous ...

Paleoclimate proxy records have non-negligible uncertainties that arise from both the proxy measurement and the dating processes. Knowledge of the dating uncertainties is important for a rigorous propagation to further analyses, for example, for identification and dating of stadial– interstadial transitions in Greenland ice core records during glacial intervals, for comparing the variability in ...

We have implemented a self-consistent feld solver for Hartree–Fock calculations, by making use of Multiwavelets and Multiresolution Analysis. We show how such a solver is inherently a preconditioned steepest descent method and therefore a good starting point for rapid convergence. A distinctive feature of our implementation is the absence of any reference to the kinetic energy operator. This is ...

<p><b>Background</b> A healthy diet can decrease the risk of several lifestyle diseases. From studying the health effects of single foods, research now focuses on examining complete diets and dietary patterns reflecting the combined intake of different foods. The main goals of the current study were to identify dietary patterns and then investigate how these differ in terms of sex, age, educational ...

We define and study a class of Reed–Muller type error-correcting codes obtained from elementary symmetric functions in finitely many variables. We determine the code parameters and higher weight spectra in the simplest cases.