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Many environmental processes such as rainfall, wind or snowfall are inherently spatial and the modelling of extremes has to take into account that feature. In addition, environmental processes are often attached with an angle, e.g., wind speed and direction or extreme snowfall and time of occurrence in year. This article proposes a Bayesian hierarchical model with a conditional independence assumption that aims at modelling simultaneously spatial extremes and an angular component. The proposed model relies on the extreme value theory as well as recent developments for handling directional statistics over a continuous domain. Working within a Bayesian setting, a Gibbs sampler is introduced whose performances are analysed through a simulation study. The paper ends with an application on extreme wind speed in France. Results show that extreme wind events in France are mainly coming from West apart from the Mediterranean part of France and the Alps.

This letter investigates the problem of controlling an aerial manipulator, composed of an omnidirectional tilting drone equipped with a five-degrees-of-freedom robotic arm. The robot has to interact with the environment to inspect structures and perform non-destructive measurements. A parallel force-impedance control technique is developed to establish contact with the designed surface with a desired force profile. During the interaction, a pushing phase is required to create a vacuum between the surface and the echometer sensor mounted at the end-effector, to measure the thickness of the interaction surface. Repetitive measures are performed to show the repeatability of the algorithm.

In this paper, we investigate a nonlocal traffic flow model based on a scalar conservation law, where a stochastic velocity function is assumed. In addition to the modeling, theoretical properties of the stochastic nonlocal model are provided, also addressing the question of well-posedness. A detailed numerical analysis offers insights how the stochasticity affects the evolution of densities. Finally, numerical examples illustrate the mean behavior of solutions and the influence of parameters for a large number of realizations.

In this paper, we propose a novel shape optimization approach for the source identification of elliptic equations. This identification problem arises from two application backgrounds: actuator placement in PDE-constrained optimal controls and the regularized least-squares formulation of source identifications. The optimization problem seeks both the source strength and its support. By eliminating the variable associated with the source strength, we reduce the problem to a shape optimization problem for a coupled elliptic system, known as the first-order optimality system. As a model problem, we derive the shape derivative for the regularized least-squares formulation of the inverse source problem and propose a gradient descent shape optimization algorithm, implemented using the level-set method. Several numerical experiments are presented to demonstrate the efficiency of our proposed algorithms.

The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. This morphing is obtained by deforming a reference shape, through the resolution of a sequence of linear elasticity equations, onto the target shape. In particular, our approach does not assume any knowledge of a boundary parametrization. Furthermore, we demonstrate how constraints can be imposed on specific points, lines and surfaces in the reference domain to ensure alignment with their counterparts in the target domain after morphing. Additionally, we show how the proposed methodology can be integrated in an offline and online paradigm, which is useful in reduced-order modeling scenarii involving variable shapes. This framework facilitates the efficient computation of the morphings in various geometric configurations, thus improving the versatility and applicability of the approach. The methodology is illustrated on the regression problem of the drag and lift coefficients of airfoils of non-parameterized variable shapes.

Compared to widely used likelihood-based approaches, the minimum contrast (MC) method offers a computationally efficient method for estimation and inference of spatial point processes. These relative gains in computing time become more pronounced when analyzing complicated multivariate point process models. Despite this, there has been little exploration of the MC method for multivariate spatial point processes. Therefore, this article introduces a new MC method for parametric multivariate spatial point processes. A contrast function is computed based on the trace of the power of the difference between the conjectured $K$-function matrix and its nonparametric unbiased edge-corrected estimator. Under standard assumptions, we derive the asymptotic normality of our MC estimator. The performance of the proposed method is demonstrated through simulation studies of bivariate log-Gaussian Cox processes and five-variate product-shot-noise Cox processes.

This paper introduces a new numerical scheme for a system that includes evolution equations describing a perfect plasticity model with a time-dependent yield surface. We demonstrate that the solution to the proposed scheme is stable under suitable norms. Moreover, the stability leads to the existence of an exact solution, and we also prove that the solution to the proposed scheme converges strongly to the exact solution under suitable norms.

In shape-constrained nonparametric inference, it is often necessary to perform preliminary tests to verify whether a probability mass function (p.m.f.) satisfies qualitative constraints such as monotonicity, convexity or in general $k$-monotonicity. In this paper, we are interested in testing $k$-monotonicity of a compactly supported p.m.f. and we put our main focus on monotonicity and convexity; i.e., $k \in \{1,2\}$. We consider new testing procedures that are directly derived from the definition of $k$-monotonicity and rely exclusively on the empirical measure, as well as tests that are based on the projection of the empirical measure on the class of $k$-monotone p.m.f.s. The asymptotic behaviour of the introduced test statistics is derived and a simulation study is performed to assess the finite sample performance of all the proposed tests. Applications to real datasets are presented to illustrate the theory.

The paper analyzes how the enlarging of the sample affects to the mitigation of collinearity concluding that it may mitigate the consequences of collinearity related to statistical analysis but not necessarily the numerical instability. The problem that is addressed is of importance in the teaching of social sciences since it discusses one of the solutions proposed almost unanimously to solve the problem of multicollinearity. For a better understanding and illustration of the contribution of this paper, two empirical examples are presented and not highly technical developments are used.

In this paper, we present a rigorous proof of the convergence of first order and second order exponential time differencing (ETD) schemes for solving the nonlocal Cahn-Hilliard (NCH) equation. The spatial discretization employs the Fourier spectral collocation method, while the time discretization is implemented using ETD-based multistep schemes. The absence of a higher-order diffusion term in the NCH equation poses a significant challenge to its convergence analysis. To tackle this, we introduce new error decomposition formulas and employ the higher-order consistency analysis. These techniques enable us to establish the $\ell^\infty$ bound of numerical solutions under some natural constraints. By treating the numerical solution as a perturbation of the exact solution, we derive optimal convergence rates in $\ell^\infty(0,T;H_h^{-1})\cap \ell^2(0,T; \ell^2)$. We conduct several numerical experiments to validate the accuracy and efficiency of the proposed schemes, including convergence tests and the observation of long-term coarsening dynamics.