We prove that any planar 4-web defines a unique projective structure in the plane in such a way that the leaves of the web foliations are geodesics of this projective structure. We also find conditions for the projective structure mentioned above to contain an affine symmetric connection, and conditions for a planar 4-web to be equivalent to a geodesic 4-web on an affine symmetric surface. Similar ...

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 ...

Reproducible climate reconstructions of the Common Era (1 CE to present) are key to placing industrial-era warming into the context of natural climatic variability. Here we present a community-sourced database of temperature-sensitive proxy records from the PAGES2k initiative. The database gathers 692 records from 648 locations, including all continental regions and major ocean basins. The records ...

A simple conceptual model for the global mean surface temperature (GMST) response to CO2 emissions is presented and analysed. It consists of linear long-memory models for the GMST anomaly response ∆T to radiative forcing and atmospheric CO2 - 5 concentration response ∆C to emission rate. The responses are connected by the standard logarithmic relation between CO2 concentration and its radiative ...

To each linear code C over a finite field we associate the matroid M(C) of its parity check matrix. For any matroid M one can define its generalized Hamming weights, and if a matroid is associated to such a parity check matrix, and thus of type M(C) , these weights are the same as those of the code C . In our main result we show how the weights d1,…,dk of a matroid M are determined by the N -graded ...

In graph neural networks (GNNs), pooling operators compute local summaries of input graphs to capture their global properties, and they are fundamental for building deep GNNs that learn hierarchical representations. In this work, we propose the Node Decimation Pooling (NDP), a pooling operator for GNNs that generates coarser graphs while preserving the overall graph topology. During training, the ...

We study q-ary linear codes C obtained from Veronese surfaces over finite fields.We show how one can find the higher weight spectra of these codes, or equivalently, the weight distribution of all extension codes of C over all field extensions of the ground field. Our methods will be a study of the Stanley-Reisner rings of a series of matroids associated to each code C.

We consider Legendrian contact structures on odd-dimensional complex analytic manifolds. We are particularly interested in integrable structures, which can be encoded by compatible complete systems of second order PDEs on a scalar function of many independent variables and considered up to point transformations. Using the techniques of parabolic differential geometry, we compute the associated ...

We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in C³ with symmetry algebra of dimension ≥6.

Hyperspectral imaging (HSI) technology has demonstrated potential to provide useful information about the chemical composition of tissue and its morphological features in a single image modality. Deep learning (DL) techniques have demonstrated the ability of automatic feature extraction from data for a successful classification. In this study, we exploit HSI and DL for the automatic differentiation ...