An ideal of polynomials is symmetric if it is closed under permutations of variables. We relate general symmetric ideals to the so called Specht ideals generated by all Specht polynomials of a given shape. We show a connection between the leading monomials of polynomials in the ideal and the Specht polynomials contained in the ideal. This provides applications in several contexts. Most notably, this ...

Holomorphically homogeneous Cauchy–Riemann (CR) real hypersurfaces M³⊂C² were classified by Élie Cartan in 1932. In the next dimension, we complete the classification of simply-transitive Levi non-degenerate hypersurfaces M⁵⊂C³ using a novel Lie algebraic approach independent of any earlier classifications of abstract Lie algebras. Central to our approach ...

Given the high prevalence and associated cost of chronic pain, it has a significant impact on individuals and society. Improvements in the treatment and management of chronic pain may increase patients’ quality of life and reduce societal costs. In this paper, we evaluate state-of-the-art machine learning approaches in chronic pain research. A literature search was conducted using the PubMed, IEEE ...

Sensitive data is normally required to develop rule-based or train machine learning-based models for de-identifying electronic health record (EHR) clinical notes; and this presents important problems for patient privacy. In this study, we add non-sensitive public datasets to EHR training data; (i) scientific medical text and (ii) Wikipedia word vectors. The data, all in Swedish, is used to train a ...

We study binary linear codes C obtained from the quadric Veronese embedding of P³ in P⁹ over F₂. We show how one can find the higher weight spectra of these codes. Our method will be a study of the Stanley-Reisner rings of a series of matroids associated to each code <i>C</i>.

We consider the equivalence problem for symplectic and conformal symplectic group actions on submanifolds and functions of symplectic and contact linear spaces. This is solved by computing differential invariants via the Lie-Tresse theorem.

We realize the simple Lie superalgebra <i>G</i>(3) as supersymmetry of various geometric structures, most importantly super-versions of the Hilbert–Cartan equation (SHC) and Cartan's involutive PDE system that exhibit <i>G</i>(2) symmetry. We provide the symmetries explicitly and compute, via the first Spencer cohomology groups, the Tanaka–Weisfeiler prolongation of the negatively graded Lie ...

<p>Foraminifera are single-celled marine organisms, which may have a planktic or benthic lifestyle. During their life cycle they construct shells consisting of one or more chambers, and these shells remain as fossils in marine sediments. Classifying and counting these fossils have become an important tool in e.g. oceanography and climatology. <p>Currently the process of identifying and counting ...

In this paper, we describe a new statistical approach to estimate blood glucose concentration along time during endurance sports based on measurements of glucose concentration in subcutaneous interstitial tissue. The final goal is the monitoring of glucose concentration in blood to maximize performance in endurance sports. Blood glucose concentration control during and after aerobic physical ...

We consider the notion of a (<i>q,m)</i>-polymatroid, due to Shiromoto, and the more general notion of (<i>q,m</i>)-demi-polymatroids, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality for generalized Hamming weights of linear codes. The corresponding results of Ravagnani for Delsarte rank metric codes, and Martínez-Peñas ...