For a graph G, a subset S subset of V (G) is called a resolving set of G if, for any two vertices u, v is an element of V (G), there exists a vertex w is an element of S such that d(w, u) not equal d(w, v). The METRIC DIMENSION problem takes as input a graph G on n vertices and a positive integer k, and asks whether there exists a resolving set of size at most k. In another metric-based graph problem , GEODETIC SET, the input is a graph G and an integer k, and the objective is to determine whether there exists a subset S subset of V (G) of size at most k such that, for any vertex u is an element of V (G), there are two vertices s(1), s(2) is an element of S such that u lies on a shortest path from s(1) to s(2). These two classical problems are intractable with respect to the solution size, as well as most structural parameters, including the feedback vertex set number and pathwidth. The very few existing tractable results state that they are both FPT with respect to the vertex cover number vc. Specifically, we observe that both problems admit an FPT algorithm running in 2(O(vc2)) . n(O(1)) time, and a kernelization algorithm that outputs a kernel with 2(O(vc)) vertices. For these problems, we also prove that, unless the Exponential Time Hypothesis fails, the established running time is asymptotically the best possible. (c) 2026 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Large language models (LLMs) are increasingly being used in network operations (NetOps) and artificial intelligence for IT operations (AIOps) for tasks ranging from telemetry retrieval and incident diagnosis to configuration planning and bounded remediation. As these systems acquire greater access to operational tools, a central question is whether operational assurance develops commensurately with the authority granted to them. This survey examines that question through a structured, evidence-stratified review of agentic NetOps and AIOps, spanning directly evaluated LLM systems, operational mechanisms, transferred evidence, and normative guidance. We organise the field around autonomy, tool scope, evidence traces, assurance controls, evaluation, security, and governance, and introduce an operational assurance contract that links each autonomy level to permitted tools, required evidence, independent gates, execution budgets, rollout and rollback duties, and audit requirements. The synthesis indicates a capability–assurance gap: evidence is comparatively strong for read-oriented assistance and tool-grounded diagnosis, but becomes substantially less complete as systems approach configuration change, bounded execution, and closed-loop operation. We therefore develop a workflow-level evaluation framework covering evidence quality, tool use, policy and invariant compliance, staged execution, recovery, calibration, cost, and human intervention, together with a threat model for prompt-borne attacks, compromised operational evidence, excessive agency, privilege boundaries, and auditability. The resulting view treats agentic NetOps and AIOps as constrained operational control, in which increasing autonomy requires correspondingly stronger evidence, independently enforced safeguards, and recovery mechanisms.
We propose a least-squares penalization as a means to extend the discontinuous Petrov-Galerkin (DPG) method with optimal test functions to a class of semilinear elliptic problems. The nonlinear contributions are replaced with independent unknowns so that standard DPG techniques apply to the then linear problem with non-trivial kernel. The nonlinear relations are added as least-squares constraints. Assuming solvability of the semilinear problem and an Aubin-Nitsche-type approximation property for the primal variable, we prove a Cea estimate for the approximation error in canonical norms. Numerical results with uniform and adaptively refined meshes illustrate the performance of the scheme.
The energy-efficient removal of CO2 from flue gas has become increasingly important for operators of CO2-emitting industrial facilities such as waste-to-energy plants and cement production sites. Conventional carbon capture processes have long been employed for acid gas removal (natural gas treatment) and are technologically mature. However, when applied for CO2 capture from flue gases, these methods substantially decrease net energy production of the plants, and in many regions the regulatory framework for underground CO2 storage remains uncertain. In recent years, a new process has been developed in which CO2 capture and conversion are integrated into a single step through electrochemical solvent regeneration and conversion. The integration of regeneration and conversion promises a more straightforward process design and lower energy requirements for the production of carbon based products from diluted CO2 sources. This work compares (1) interconnected state-of-the-art process chains—such as monoethanolamine (MEA) based CO2 separation with subsequent reverse water-gas shift synthesis gas production, and Fischer-Tropsch (FT) or methanol (MeOH) synthesis, and (2) emerging electrochemical CO2 conversion processes. Contrary to what current literature indicates, the findings in the carried out simulations show that conventional state-of-the-art processes require less energy to capture and convert CO2 than the electrochemical pathway at its current stage of development. However, the difference in energy requirement is small especially with FT syncrude as an end product. The results show that the carbon capture and conversion effectiveness of the electrochemical pathways exceeds the carbon capture and conversion effectiveness of the MEA and hot potassium carbonate (HPC) pathways and leads to higher product outputs. Compared to conventional pathways, the electrochemical pathway has a 4.4 percentage points higher carbon capture and conversion effectiveness for MeOH production and a 15.5 percentage points higher carbon capture and conversion effectiveness for FT syncrude production, which highlights the large potential for electrochemical pathways. It is anticipated that the electrochemical pathway will become energy-competitive in the future, provided that development continues rapidly and the technology achieves parity with the advancement of water electrolysis.
Linear settlements represent a distinctive village typology that is prevalent across numerous regions of Europe, encompassing both rural and more urban areas. In the context in and around Vienna, historical linear settlements are a defining feature of the built landscape.From historically grown structures to top-down planned settlements, these linear village types are defined by a range of factors, e.g. agricultural activities, geographical conditions or even internal colonisation processes by monarchs. Over the course of history, a canon of different village forms with distinct spatial qualities has developed. However, within the scope of this research on Vienna and against the background of the umbrellaing 15 mC project (emc2), the predominant types of Straßendorf and Angerdorf are the primary focus. In Vienna, these historic linear settlements are integrated into the urban fabric while still retaining varying degrees of permanence and persistence in the urban layout.By combining different methods - local morphogenetic analysis, urban network analysis, regional typological mapping and comparative analysis to regions in France and Italy - this study provides insights and findings on how linear settlement types in and around Vienna have developed morphologically, with a particular focus on the last two centuries. The objective of this study is to explore the influence of these linear settlements on the shaping of territories, networks and urbanisation processes, and their subsequent characterisation of contemporary urban and rural environments.
