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In this paper we study a Dirichlet-type differential inclusion involving the Finsler-Laplace operator on a complete Finsler manifold. Depending on the positive $\lambda$ parameter of the inclusion, we establish non-existence, as well as existence and multiplicity results by applying non-smooth variational methods. The main difficulties are given by the problem's highly nonlinear nature due to the general Finslerian setting, as well as the nonsmooth context., Comment: 6 pages

We propose a train rescheduling algorithm which applies a standardized feature selection based on pairwise conflicts in order to serve as input for the reinforcement learning framework. We implement an analytical method which identifies and optimally solves every conflict arising between two trains, then we design a corresponding observation space which features the most relevant information considering these conflicts. The data obtained this way then translates to actions in the context of the reinforcement learning framework. We test our preliminary model using the evaluation metrics of the Flatland Challenge. The empirical results indicate that the suggested feature space provides meaningful observations, from which a sensible scheduling policy can be learned., Comment: 20th Jubilee World Symposium on Applied Machine Intelligence and Informatics (SAMI), Poprad, Slovakia, March 2-5, 2022

We present the isometry between the 2-dimensional Funk model and the Finsler-Poincar\'e disk. Then, we introduce the Finslerian Poincar\'e upper half plane model, which turns out to be also isometrically equivalent to the previous models. As application, we state the gapless character of the first eigenvalue for the aforementioned three spaces., Comment: IEEE 15th International Symposium on Applied Computational Intelligence and Informatics, Timisoara, Romania

Combining the sharp isoperimetric inequality established by Z. Balogh and A. Krist\'aly [Math. Ann., in press, doi:10.1007/s00208-022-02380-1] with an anisotropic symmetrization argument, we establish sharp Morrey-Sobolev inequalities on $n$-dimensional Finsler manifolds having nonnegative $n$-Ricci curvature. A byproduct of this method is a Hardy-Sobolev-type inequality in the same geometric setting. As applications, by using variational arguments, we guarantee the existence/multiplicity of solutions for certain eigenvalue problems and elliptic PDEs involving the Finsler-Laplace operator. Our results are also new in the Riemannian setting., Comment: 18 pages; to appear in Comm. Contemp. Math