In response to climate goals, growing environmental awareness, and financial incentives, municipalities increasingly seek to electrify public transportation networks. We study the problem of locating stationary and dynamic inductive charging stations for electric vehicles (EVs), allowing detours from fixed transit routes and schedules. Dynamic charging, which enables energy transfer while driving, reduces space usage in dense urban areas and lowers vehicle idle times. We formulate a cost-minimization problem that considers both infrastructure and operational costs and propose an Iterated Local Search (ILS) algorithm to solve instances of realistic size. Each configuration requires solving a decomposed subproblem comprising multiple resource-constrained shortest-path problems. To do so, we employ a bidirectional label-setting algorithm with lazy dominance checks based on local bounds. On adapted benchmark instances, our approach outperforms a commercial solver by up to 57% in solution quality. We further apply our method to a real-world case study in Hof, Germany. Results indicate that, under current cost structures, calibrated from a test track in Bad Staffelstein, dynamic inductive charging is not yet cost-competitive with stationary alternatives. We quantify the value of allowing detours at up to 3.9% of the total system cost and show that integrating photovoltaics with decentralized energy storage can yield savings exceeding 20% by contributing more than 60% to the fleet’s charging demand during operations.
Assessing sustainability performance is crucial for ensuring industries align with sustainable development goals, contributing to society’s well-being. This paper investigates the impact of sustainable policies on supply chain design, examining how such policies drive industries to adopt greener production technologies, impose production caps, or relocate facilities. Unlike studies focused on individual companies, this research evaluates these impacts at the industry level. It introduces an optimization framework as an ex-ante sustainability assessment tool to compare industry performance in a business-as-usual scenario versus one with sustainable policy implementation. The model considers economic, environmental, and social factors, using the Time-to-Sustainability optimization approach to calculate the minimum time needed to achieve sustainability goals. This framework is instrumental in evaluating the effects of sustainability policies like the Paris Agreement and the United Nations Sustainable Development Goals on supply chains. The findings offer valuable decision support for policymakers crafting strategic sustainability pathways. A case study on Colombia’s dairy industry, using data from Nationally Appropriate Mitigation Actions for the country’s low-carbon strategy, highlights challenges in transforming the industry. The proposed framework aims to contribute to and assess sustainable agricultural production, but it is general in scope and can be adapted to other industries with appropriate sustainability goals.
In this paper, we address the existence of Fredholm backstepping transformations for self-adjoint and skew-adjoint operators A. Under suitable assumptions on the operator A and the possibly unbounded control operator B, we prove the existence of a Fredholm backstepping transformation for operators of order strictly greater than 1. This work overcomes two major limitations of the classical Fredholm backstepping framework. One of the main contributions is the explicit identification of the underlying isomorphism used in the construction of the transformation T, thereby bypassing the compactness arguments and Riesz basis mechanisms traditionally used in the literature. This explicit structure enables us to derive quantitative and sharp estimates for T_ℒ(H;H) and T^-1_ℒ(H;H) with respect to the decay rate λ. As a consequence, we obtain quantitative rapid stabilization and small-time null controllability results for a broad class of operators.
We study the rapid stabilization of general linear systems, when the differential operator A has a Riesz basis of eigenvectors. We find simple sufficient conditions for the rapid stabilization and the construction of a relatively explicit feedback operator. We use an F-equivalence approach relying on Fredholm transformation to show a stronger result: under these sufficient conditions the system is equivalent to a simple exponentially stable system, with arbitrarily large decay rate. In particular, our conditions improve the existing conditions of rapid stabilization for non-parabolic operators such as skewadjoint systems. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Modeling user purchase behavior is a critical challenge in display advertising systems, necessary for real-time bidding. The difficulty arises from the sparsity of positive user events and the stochasticity of user actions, leading to severe class imbalance and irregular event timing. Predictive systems usually rely on hand-crafted "counter" features, overlooking the fine-grained temporal evolution of user intent. Meanwhile, current sequential models extract direct sequential signal, missing useful event-counting statistics. We enhance deep sequential models with self-supervised pretraining strategies for display advertising. Especially, we introduce Abacus, a novel approach of predicting the empirical frequency distribution of user events. We further propose a hybrid objective unifying Abacus with sequential learning objectives, combining stability of aggregated statistics with the sequence modeling sensitivity. Experiments on two real-world datasets show that Abacus pretraining outperforms existing methods accelerating downstream task convergence, while hybrid approach yields up to +6.1% AUC compared to the baselines.
