Some applications of deep learning require not only to provide accurate results but also to quantify the amount of confidence in their prediction. The management of an electric power grid is one of these cases: to avoid risky scenarios, decision-makers need both precise and reliable forecasts of, for example, power loads. For this reason, point forecasts are not enough hence it is necessary to adopt ...

Our understanding of the material organization of complex fluid flows has benefited recently from mathematical developments in the theory of objective coherent structures. These methods have provided a wealth of approaches that identify transport barriers in three-dimensional (3-D) turbulent flows. Specifically, theoretical advances have been incorporated into numerical algorithms that extract ...

Patients with type 1 diabetes must continually decide how much insulin to inject before each meal to maintain blood glucose levels within a healthy range. Recent research has worked on a solution for this burden, showing the potential of reinforcement learning as an emerging approach for the task of controlling blood glucose levels. In this paper, we test and evaluate several deep Q-learning algorithms ...

There is large geographical variation in the stroke incidence rate worldwide. In addition, stroke is one of the diseases with highest mortality rate. In this thesis, our main focus is to examine if there are any geographical variation in stroke incidence and mortality rates in Norway. We approach this study using models within the Bayesian framework. Before performing analysis, we first introduce ...

Specht polynomials classically realize the irreducible representations of the symmetric group. The ideals defined by these polynomials provide a strong connection with the combinatorics of Young tableaux and have been intensively studied by several authors. We initiate similar investigations for the ideals defined by the Specht polynomials associated to the hyperoctahedral group <i>B_n</i>. ...

We consider a heterotic version of six-dimensional Kodaira-Spencer gravity derived from the heterotic superpotential. We compute the one-loop partition function and fnd it can be expressed as a product of holomorphic Ray-Singer torsions. We discuss its topological properties and potential gauge and gravitational anomalies. We show these anomalies can be cancelled using Green-Schwarz-like ...

In this paper, we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on one function of one variable. We describe linearization of such systems and their integration via Laplace transformation, relating this to Lie's integration theorem and formal theory of PDEs.

We study second-order partial differential equations (PDEs) in four dimensions for which the conformal structure defined by the characteristic variety of the equation is half-flat (self-dual or anti-self-dual) on every solution. We prove that this requirement implies the Monge–Ampère property. Since half-flatness of the conformal structure is equivalent to the existence of a non-trivial dispersionless ...

Extreme space weather events are rare, and quantifying their likelihood is challenging, often relying on geomagnetic indices obtained from ground-based magnetometer observations that span multiple solar cycles. The Dst index ring-current monitor, derived from an hourly average over four low-latitude stations, is a benchmark for extreme space weather events, and has been extensively studied ...

Norway is one of the leading ocean-based food production nations. Its seafood industry comprises wild-capture fisheries and farmed fish production. Both industries play a provisional role but also contribute to economic development of the country and help sustain coastal communities, particularly, in Northern Norway. Coastal fishery has been the staple industry in Northern Norway for centuries, while ...