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In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational challenges that constitute known hindrances to existing nonparametric quantile regression methods when the number of predictors is much larger than the available sample size. We investigate conditions under which estimation is feasible and of good overall quality and obtain sharp approximations that we employ to devising statistical inference methodology. These include simultaneous confidence intervals and tests of hypotheses, whose asymptotics is borne by a non-trivial functional central limit theorem tailored to martingale differences. Additionally, we provide finite-sample results through various simulations which, accompanied by an illustrative application to real-worldesque data (on electricity demand), offer guarantees on the performance of the proposed methodology.

In this paper, we introduce a discretization scheme for the Yang-Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this framework, we define discrete versions of the exterior covariant derivative operator and its adjoint, which capture essential geometric features similar to their continuous counterparts. Our focus is on discrete models defined on a combinatorial torus, where the discrete Yang-Mills equations are presented in the form of both a system of difference equations and a matrix form.

In this paper, we describe and analyze the spectral properties of a symmetric positive definite inexact block preconditioner for a class of symmetric, double saddle-point linear systems. We develop a spectral analysis of the preconditioned matrix, showing that its eigenvalues can be described in terms of the roots of a cubic polynomial with real coefficients. We illustrate the efficiency of the proposed preconditioners, and verify the theoretical bounds, in solving large-scale PDE-constrained optimization problems.

In this paper, we present a logic for conditional strong historical necessity in branching time and apply it to analyze a nontheological version of Lavenham's argument for future determinism. Strong historical necessity is motivated from a linguistical perspective, and an example of it is ``If I had not gotten away, I must have been dead''. The approach of the logic is as follows. The agent accepts ontic rules concerning how the world evolves over time. She takes some rules as indefeasible, which determine acceptable timelines. When evaluating a sentence with conditional strong historical necessity, we introduce its antecedent as an indefeasible ontic rule and then check whether its consequent holds for all acceptable timelines. The argument is not sound by the logic.

In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in subdomains bounded by discontinuity lines (DLs), the latter defined from the Rankine-Hugoniot jump conditions. The proposed approach allows to efficiently consider an arbitrary number of entropic shock waves, shock wave generation, as well as wave interactions. Some numerical experiments are presented to illustrate the strengths and properties of the algorithms.

In this paper, we derive closed-form estimators for the parameters of some probability distributions belonging to the exponential family. A bootstrap bias-reduced version of these proposed closed-form estimators are also derived. A Monte Carlo simulation is performed for the assessment of the estimators. The results are seen to be quite favorable to the proposed bootstrap bias-reduce estimators.

This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large displacements of explicitly represented domain boundaries without generating body-fitted meshes and remeshing techniques. For the space discretization, we use a background mesh and an unfitted method that relies on integration on cut cells only. We perform this intersection by using clipping algorithms. To deal with the mesh movement, we pullback the equations to a reference configuration (the spatial mesh at the initial time slab times the time interval) that is constant in time. This way, the geometrical intersection algorithm is only required in 3D, another key property of the proposed scheme. At the end of the time slab, we compute the deformed mesh, intersect the deformed boundary with the background mesh, and consider an exact transfer operator between meshes to compute jump terms in the time discontinuous Galerkin integration. The transfer is also computed using geometrical intersection algorithms. We demonstrate the applicability of the method to fluid problems around rotating (2D and 3D) geometries described by oriented boundary meshes. We also provide a set of numerical experiments that show the optimal convergence of the method.

In this paper we analyze a conforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. We consider the classic velocity-pressure formulation which allows us to consider the divergence-conforming virtual element spaces employed for the Stokes equations. Under standard assumptions on the meshes we derive a priori error estimates for the proposed method with the aid of the compact operators theory. We report some numerical tests to confirm the theoretical results.

For a set of robots (or agents) moving in a graph, two properties are highly desirable: confidentiality (i.e., a message between two agents must not pass through any intermediate agent) and efficiency (i.e., messages are delivered through shortest paths). These properties can be obtained if the \textsc{Geodesic Mutual Visibility} (GMV, for short) problem is solved: oblivious robots move along the edges of the graph, without collisions, to occupy some vertices that guarantee they become pairwise geodesic mutually visible. This means there is a shortest path (i.e., a ``geodesic'') between each pair of robots along which no other robots reside. In this work, we optimally solve GMV on finite hexagonal grids $G_k$. This, in turn, requires first solving a graph combinatorial problem, i.e. determining the maximum number of mutually visible vertices in $G_k$.

In this paper, we investigate nonlinear optimization problems whose constraints are defined as fuzzy relational equations (FRE) with max-min composition. Since the feasible solution set of the FRE is often a non-convex set and the resolution of the FREs is an NP-hard problem, conventional nonlinear approaches may involve high computational complexity. Based on the theoretical aspects of the problem, an algorithm (called FRE-ACO algorithm) is presented which benefits from the structural properties of the FREs, the ability of discrete ant colony optimization algorithm (denoted by ACO) to tackle combinatorial problems, and that of continuous ant colony optimization algorithm (denoted by ACOR) to solve continuous optimization problems. In the current method, the fundamental ideas underlying ACO and ACOR are combined and form an efficient approach to solve the nonlinear optimization problems constrained with such non-convex regions. Moreover, FRE-ACO algorithm preserves the feasibility of new generated solutions without having to initially find the minimal solutions of the feasible region or check the feasibility after generating the new solutions. FRE-ACO algorithm has been compared with some related works proposed for solving nonlinear optimization problems with respect to maxmin FREs. The obtained results demonstrate that the proposed algorithm has a higher convergence rate and requires a less number of function evaluations compared to other considered algorithms.