If E is an elliptic curve, then the Galois group of the extension generated by the n-torsion points acts on these points. We prove a quadratic reciprocity law involving this group action. This law is an extension of the usual quadratic reciprocity law.

Sea ice drift and deformation, namely sea ice dynamics, play a significant role in atmosphere–ice–ocean coupling. Deformation patterns in sea ice can be observed over a wide range of spatial and temporal scales, though high-resolution objective quantification of these features remains difficult. In an effort to better understand local deformation of sea ice, we adapt the trajectory-stretching exponents ...

Let <i><b>R</b></i> be a real closed field. We consider basic semi-algebraic sets defined by <i>n</i>-variate equations/inequalities of s symmetric polynomials and an equivariant family of polynomials, all of them of degree bounded by 2<i>d</i> &#60; <i>n</i>. Such a semi-algebraic set is invariant by the action of the symmetric group. We show that such a set is either empty or it contains a point ...

In this article, we explore the possibility of detecting polar lows in C-band synthetic aperture radar (SAR) images by means of deep learning. Specifically, we introduce a novel dataset consisting of Sentinel-1 images divided into two classes, representing the presence and absence of a maritime mesocyclone, respectively. The dataset is constructed using the ECMWF reanalysis version 5 (ERA5) dataset ...

The paper presents a case study of the regional ( ≈ 150 km) morphological and optical properties of a relatively thin, 70–90 cm modal thickness, first-year Arctic sea ice pack in an advanced stage of melt. The study combines in situ broadband albedo measurements representative of the four main surface types (bare ice, dark melt ponds, bright melt ponds and open water) and images acquired by a ...

We explicitly determine all the relative generalized Hamming weights of affine Cartesian codes using the notion of footprints and results from extremal combinatorics. This generalizes the previous works on the determination of relative generalized Hamming weights of Reed–Muller codes by Geil and Martin, as well as the determination of all the generalized Hamming weights of the affine Cartesian codes ...

We study which quadratic forms are representable as the local degree of a map f:An→An with an isolated zero at 0 , following the work of Kass and Wickelgren who established the connection to the quadratic form of Eisenbud, Khimshiashvili, and Levine. Our main observation is that over some base fields k , not all quadratic forms are representable as a local degree. Empirically the local degree ...

In the present paper we study the rigidity of 2-step Carnot groups, or equivalently, of graded 2-step nilpotent Lie algebras. We prove the alternative that depending on bi-dimensions of the algebra, the Lie algebra structure makes it either always of infinite type or generically rigid, and we specify the bi-dimensions for each of the choices. Explicit criteria for rigidity of pseudo Hand <i>J</i>-type ...

In this paper we present a new algorithm for parameter-free clustering by mode seeking. Mode seeking, especially in the form of the mean shift algorithm, is a widely used strategy for clustering data, but at the same time prone to poor performance if the parameters are not chosen correctly. We propose to form a <i>clustering ensemble</i> consisting of repeated and bootstrapped runs of the recent kNN ...

We describe how scale space methods can be used for quantitative analysis of blood glucose concentrations from type 2 diabetes patients. Blood glucose values were recorded voluntarily by the patients over one full year as part of a self-management process, where the timeand frequency of the recordings are decided by the patients. This makes a unique datasetin its extent, though with a large variation ...