In this study, we explore a robust testing procedure for the high-dimensional location parameters testing problem. Initially, we introduce a spatial-sign based max-type test statistic, which exhibits excellent performance for sparse alternatives. Subsequently, we demonstrate the asymptotic independence between this max-type test statistic and the spatial-sign based sum-type test statistic (Feng and Sun, 2016). Building on this, we propose a spatial-sign based max-sum type testing procedure, which shows remarkable performance under varying signal sparsity. Our simulation studies underscore the superior performance of the procedures we propose.
Talagrand's correlation inequality [25] provides quantitative lower bounds on the covariance of two increasing Boolean functions in terms of their coordinate influences, but, in general, a logarithmic loss is necessary. Motivated by a question of Kalai, Keller and Mossel [14, Problem 6.1], we identify a natural log-free regime. We prove that if two increasing Boolean functions on {0,1}n are either both submodular or both supermodular, thenE[fg]−E[f]E[g]≥14⋅∑i=1nInfi[f]Infi[g], where the constant 1/4 is optimal. We also prove a real-valued extension: for two functions with the same second-difference sign, the covariance is bounded below by the sum of products of their Level-1 Fourier coefficients. As a consequence, we verify the Friedgut–Kahn–Kalai–Keller spectral conjecture [11, Conjecture 5.8] in this structured setting. The proofs combine a heat-semigroup representation based on second-order discrete derivatives with an independent induction argument for the Boolean case.
We study the size of minimum feedback vertex sets in digraphs under degree constraints. Our focus is on oriented graphs and arbitrary digraphs of bounded maximum degree. A digraph D is an oriented graph if D does not have a pair of opposite arcs. The degree of a vertex v of D is the sum of the in-degree and out-degree of v. Let fvs(D) be the minimum number of vertices whose deletion from D makes it acyclic. Let D be a digraph with n vertices and maximum degree Δ. We prove the following bounds. If D is an oriented graph, then fvs(D)≤3n7 when Δ≤4 and fvs(D)≤n2 when Δ≤5. If D is a connected digraph, Δ≤4 and D is not obtained from an odd undirected cycle by replacing every edge with a pair of opposite arcs with the same endvertices, then fvs(D)≤n2. If D is an arbitrary digraph with Δ≤5 then fvs(D)≤2n3. The above bounds are all sharp. The obtained bounds refine and extend earlier results on feedback vertex sets in sparse digraphs, and contribute to a more detailed understanding of how local degree restrictions influence global acyclicity properties.
Strong orthogonal arrays (SOAs) were recently introduced and studied as a class of space-filling designs for computer experiments. To surely realize the desirable space-filling properties of SOAs compared with ordinary orthogonal arrays (OAs), it is better that they have strengths of three or higher. When the strength is more than three, the column numbers of the SOAs will be small. We consider the SOAs of strength three that enjoy almost all the space-filling properties of the ones of strength four, which were first introduced in Shi and Tang (2020). Column-orthogonality is also an important property for designs of computer experiments. We propose some methods to construct a new class of column-orthogonal SOAs of strength three with some of the space-filling properties of the ones of strength four. The constructed designs have flexible run sizes and more columns compared with some existing designs.
Precise modeling of electric vehicle (EV) energy consumption is fundamental to the efficient design and management of modern transportation systems. While physics-based models offer superior interpretability, they often struggle with limited adaptability to dynamic driving conditions and heterogeneous vehicle platforms. To bridge this gap, achieving real-time and accurate calibration of physical model parameters becomes essential. This paper proposes a novel two-stage Bayesian optimization framework that integrates Contextual Bayesian Optimization (CBO) and Transfer Bayesian Optimization (TBO). In the first stage, the CBO module learns a context-aware mapping between operating conditions and physical parameters within a source domain. In the second stage, the TBO module leverages the learned prior knowledge to achieve rapid adaptation to a target vehicle domain with minimal data requirements. We evaluate the proposed framework using real-world datasets from BMW i3 and Tesla Model 3. Experimental results demonstrate that the proposed framework achieves a per-second WMAPE of 17.27% in cross-condition scenarios. For cross-vehicle transfer, the primary out-of-sample evaluation on the held-out 70% of the Tesla trips yields a WMAPE of 24.82% and a total energy error of 12.65%. The CBO results further demonstrate rapid convergence under a limited online evaluation budget. This research provides a scalable and sample-efficient solution for high-fidelity energy modeling across diverse driving conditions and vehicle platforms.
