AbstractThe structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces such as plasma pressure gradients and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relationship between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently a large area of research, as accurate measurements of the photospheric field are available from ground-based observatories such as the Synoptic Optical Long-term Investigations of the Sun and the Daniel K. Inouye Solar Telescope (DKIST) and space-born, e.g., from Hinode and the Solar Dynamics Observatory. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma.
In this note, we propose polynomial-time algorithms solving the Monge and Kantorovich formulations of the $\infty$-optimal transport problem in the discrete and finite setting. It is the first time, to the best of our knowledge, that efficient numerical methods for these problems have been proposed.
In this note we apply a lemma due to Sabach and Shtern to compute linear rates of asymptotic regularity for Halpern-type nonlinear iterations studied in optimization and nonlinear analysis.
We show that every two-player stochastic game with finite state and action sets and bounded, Borel-measurable, and shift-invariant payoffs, admits an $\ep$-equilibrium for all $\varepsilon>0$.
In this paper, we connect some recent papers on smoothing of energy landscapes and scored-based generative models of machine learning to classical work in stochastic control. We clarify these connections providing rigorous statements and representations which may serve as guidelines for further learning models.
In this paper, we consider a problem in calculus of variations motivated by a quantitative isoperimetric inequality in the plane. More precisely, the aim of this article is the computation of the minimum of the variational problem $$\inf_{u\in\mathcal{W}}\frac{\displaystyle\int_{-π}^π[(u')^2-u^2]dθ}{\displaystyle\left[\int_{-π}^π|u| dθ\right]^2}$$where $u\in \mathcal{W}$ is a $H^1(-π,π)$ periodic function, with zero average on $(-π,π)$ and orthogonal to sine and cosine.
The minimization of a multiobjective Lagrangian with non-constant discount is studied. The problem is embedded into a set-valued framework and a corresponding definition of the value function is given. Bellman's optimality principle and Hopf-Lax formula are derived. The value function is shown to be a solution of a set-valued Hamilton-Jacobi equation.
Background: Malaria remains a global challenge with approximately 228 million cases and 405,000 malaria-related deaths reported in 2018 alone; 93% of which were in sub-Saharan Africa. Aware of the critical role than environmental factors play in malaria transmission, this study aimed at assessing the relationship between precipitation, temperature, and clinical malaria cases in East Africa and how the relationship may change under 1.5 o C and 2.0 o C global warming levels (hereinafter GWL1.5 and GWL2.0, respectively). Methods: A correlation analysis was done to establish the current relationship between annual precipitation, mean temperature, and clinical malaria cases. Differences between annual precipitation and mean temperature value projections for periods 2008-2037 and 2023-2052 (corresponding to GWL1.5 and GWL2.0, respectively), relative to the control period (1977-2005), were computed to determine how malaria transmission may change under the two global warming scenarios. Results : A predominantly positive/negative correlation between clinical malaria cases and temperature/precipitation was observed. Relative to the control period, no major significant changes in precipitation were shown in both warming scenarios. However, an increase in temperature of between 0.5 o C and 1.5 o C and 1.0 o C to 2.0 o C under GWL1.5 and GWL2.0, respectively, was recorded. Hence, more areas in East Africa are likely to be exposed to temperature thresholds favourable for increased malaria vector abundance and, hence, potentially intensify malaria transmission in the region. Conclusions : GWL1.5 and GWL2.0 scenarios are likely to intensify malaria transmission in East Africa. Ongoing interventions should, therefore, be intensified to sustain the gains made towards malaria elimination in East Africa in a warming climate.
We provide comparison principles for convex functions through its proximal mappings. Consequently, we prove that the norm of the proximal operator determines a convex the function up to a constant. A new characterization of Lipschitzianity in terms of the proximal operator is given.
We obtain universal affine type estimates for the location of the geometric medians of triangle perimeters and for the location of the geometric medians of triangular domains. At the end, some alternative implementations of the triangle space are discussed.
Background: Malaria remains a global challenge with approximately 228 million cases and 405,000 malaria-related deaths reported in 2018 alone; 93% of which were in sub-Saharan Africa. Aware of the critical role than environmental factors play in malaria transmission, this study aimed at assessing the relationship between precipitation, temperature, and clinical malaria cases in E. Africa and how the relationship may change under 1.5 o C and 2.0 o C global warming levels (hereinafter GWL1.5 and GWL2.0, respectively). Methods: A correlation analysis was done to establish the current relationship between annual precipitation, mean temperature, and clinical malaria cases. Differences between annual precipitation and mean temperature value projections for periods 2008-2037 and 2023-2052 (corresponding to GWL1.5 and GWL2.0, respectively), relative to the control period (1977-2005), were computed to determine how malaria transmission may change under the two global warming scenarios. Results : A predominantly positive/negative correlation between clinical malaria cases and temperature/precipitation was observed. Relative to the control period, no major significant changes in precipitation were shown in both warming scenarios. However, an increase in temperature of between 0.5 o C and 1.5 o C and 1.0 o C to 2.0 o C under GWL1.5 and GWL2.0, respectively, was recorded. Hence, more areas in E. Africa are likely to be exposed to temperature thresholds favourable for increased malaria vector abundance and, hence, potentially intensify malaria transmission in the region. Conclusions : GWL1.5 and GWL2.0 scenarios are likely to intensify malaria transmission in E. Africa. Ongoing interventions should, therefore, be intensified to sustain the gains made towards malaria elimination in E. Africa in a warming climate.
The problem of scheduling the (time) resource allocation of a base station (cell tower) that interacts with clients (users of wireless mobile devices with Internet access) and servers from which they download web pages (files in general) is studied.
In this paper, we prove an approximate controllability result for the linearized Boussinesq system around a fluid at rest, in a two dimensional channel, when the control acts only on the temperature, through the upper boundary.
This article develops sufficient conditions of local optimality for the scalar and vectorial cases of the calculus of variations. The results are established through the construction of stationary fields which keep invariant what we define as the generalized Hilbert integral.
It is known that the solvability of a Sylvester equation over max-plus algebra can be determined in polynomial time by verifying its principal solution. A succinct representation of the principal solution is presented, with a more accurate computational complexity, for a Sylvester equation over max-plus algebra.
In this paper we will establish necessary and sufficient conditions for a Laplace-Carleson embedding to be bounded for certain spaces of functions on the positive half-line. We will use these results to characterise weighted (infinite-time) admissibility of control and observation operators.
Given a linear system, we consider the expected energy to move from the origin to a uniformly random point on the unit sphere as a function of the set of actuated variables. We show this function is not necessarily supermodular, correcting some claims in the existing literature.
We define two new constants associated with real eigenvalues of a P-tensor. With the help of these two constants, in the case of P-tensors, we establish upper bounds of two important quantities, whose positivity is a necessary and sufficient condition for a general tensor to be a P-tensor.