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.
To limit energy costs and environmental impacts related to road lighting, luminance-based designing is the best solution to provide the right amount of light on the surfaces to be lit. However, this exercise requires knowledge of the reflection properties of the road surface, which are generally unknown. Therefore, the design is often done in terms of illuminance, and luminance is estimated using the standard r -tables provided by the CIE 50 years ago. This review article presents the state of knowledge on the reflection properties of road surfaces and the internal factors (family and nature of road surface, composition, type of aggregates, binders used, surface treatments) that may influence them for road lighting applications. Although some trends emerge based on the family of road surface, the wide variety of these factors, their interactions, or the extent to which they have been studied make it difficult to establish generalisable rules. The main international consensus is the need to revise the CIE standard r -tables. This article also identifies the need for further research, and the descriptive summary of the characteristics of road surfaces and their field of use that we propose is a solid basis for carrying this out in a unified manner.
National track access charge (TAC) regimes create persistent pricing inconsistency that undermines cross-border rail competitiveness, a challenge acute along Rail Baltica (RB)—the developing corridor spanning Estonia, Latvia, and Lithuania. This study examines under what conditions TAC harmonisation is achievable along this corridor and what framework would best support phased alignment. A comparative case analysis of the three Baltic states is conducted using regulatory filings, EU policy documentation, and infrastructure manager data, with descriptive analysis mapping structural divergences across national TAC regimes. The analysis identifies quantifiable differences in charging structures and delineates metrics where harmonisation is already viable. A forward agenda specifies the regulatory and governance preconditions required for deeper alignment. The findings indicate that full TAC unification remains premature, constrained primarily by divergent interpretations of the common EU legal framework and deeply embedded national accounting methodologies, while structured harmonisation through a shared methodological framework can meaningfully improve pricing transparency and regulatory comparability without undermining national financial autonomy. The decision-support framework developed here offers a transferable instrument for infrastructure managers, regulators, and EU-level bodies pursuing TAC reform across cross-border corridors.
Optimizing functionals over the space of probability measures is now ubiquitous in machine learning. A widely used approach is to perform the optimization directly over the Wasserstein space, but many objective functionals of practical interest are non-convex along Wasserstein geodesics, making the analysis of standard first-order methods challenging. In this work, we study a class of objectives over the Wasserstein space that admit a difference-of-convex (DC) decomposition and we lift the classical convex-concave procedure (CCCP) to this setting. Under smoothness and strong convexity assumptions on the convex components of the decomposition, we prove almost stationarity along the iterates of the resulting algorithm. Our main focus is on the Maximum Mean Discrepancy (MMD) and the Energy Distance (ED) functionals, for which we develop explicit Wasserstein DC decompositions, and establish local convergence of the scheme under mild assumptions. Empirically, we show that well-chosen DC decompositions yield faster and more stable convergence than Wasserstein gradient descent on these MMD objectives.
