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 ...

We prove that the existence of a dispersionless Lax pair with spectral parameter for a nondegenerate hyperbolic second order partial differential equation (PDE) is equivalent to the canonical conformal structure defined by the symbol being Einstein–Weyl on any solution in 3D, and self-dual on any solution in 4D. The first main ingredient in the proof is a characteristic property for dispersionless ...

For a real-analytic connected CR-hypersurface M of CR-dimension n⩾1 having a point of Levi-nondegeneracy the following alternative is demonstrated for its symmetry algebra s=s(M): (i) either dims=n2+4n+3 and M is spherical everywhere; (ii) or dims⩽n2+2n+2+δ2,n and in the case of equality M is spherical and has fixed signature of the Levi form in the complement to its Levi-degeneracy locus. A version ...

<p><i>Background.</i> Since physical activity has a high impact on patients with type 1 diabetes and the risk of hypoglycemia (low blood glucose levels) is significantly higher during and after physical activities, an automatic method to provide a personalized recommendation is needed to improve the blood glucose management and harness the benefits of physical activities. This paper aims to reduce ...

In 2018, cancer was the second leading cause of death worldwide. Early detection can reduce mortality. Screening programs intended for early detection increases the workload for clinicians. To improve efficiency CAD systems would be highly beneficial. We have developed CAD systems using deep learning, for automatic tissue segmentation and prediction of diagnosis in lung and breast cancer. The ...

Reliable quantification of the global mean surface temperature (GMST) response to radiative forcing is essential for assessing the risk of dangerous anthropogenic climate change. We present the statistical foundations for an observation-based approach using a stochastic linear response model that is consistent with the long-range temporal dependence observed in global temperature variability. We ...

Classification of multivariate time series (MTS) has been tackled with a large variety of methodologies and applied to a wide range of scenarios. Reservoir computing (RC) provides efficient tools to generate a vectorial, fixed-size representation of the MTS that can be further processed by standard classifiers. Despite their unrivaled training speed, MTS classifiers based on a standard RC ...

With growing capabilities of high-intensity laser beams to generate ultra-short pulses of light, the simulation of pulse propagation in nonlinear media is expected to catch up with the front-line experimental setups. Among the challenges of nonlinear material response modeling is the ability to capture the back-scatter effect - a phenomenon inherently elusive for the well-established methods of ...

By restricting generating functions of infinitesimal symmetries of symplectic and contact vector spaces to quadratic forms, we obtain a finite-dimensional Lie subalgebra, consisting of vector fields isomorphic to the linear symplectic or conformal symplectic algebra. This allows us to look for joint invariants of the diagonal action of g on product manifolds. We find an explicit recipe for creating ...

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