In 1960, Ghouila-Houri proved that every strongly connected directed graph G on n vertices with minimum degree at least n contains a directed Hamilton cycle. We asymptotically generalize this result by proving the following: every directed graph G on n vertices and with minimum degree at least (1+o(1))n contains every orientation of a Hamilton cycle, except for the directed Hamilton cycle in the case when G is not strongly connected. In fact, this minimum degree condition forces every orientation of a cycle in G of every possible length, other than perhaps the directed cycles.
Accurate registration of multi-stained whole-slide images (WSIs) enables the integration of complementary morphological and molecular information, improving both clinical diagnostic and prognostic analysis. It also enables efficient transfer of annotations between consecutive or re-stained slides, significantly reducing annotation time and cost, as well as three-dimensional tissue reconstruction. Despite its importance, WSI registration remains challenging due to variations in slide preparation across stains and complex tissue deformations. Existing methods are often tailored to specific staining modalities and fail to generalize across diverse settings, highlighting the need for a robust and generalizable cell-level multi-stain registration method. In this work, we introduce CORE, a novel coarse-to-fine framework for accurate cell-centric registration across six multimodal WSI datasets, encompassing 30 distinct staining types, including Hematoxylin & Eosin (H&E), periodic acid-Schiff (PAS), multiplex immunohistochemistry (mIHC), multiplex immunofluorescence (mIF) and Cyclic immunofluorescence (Cyc-IF). CORE first performs coarse global registration by extracting tissue masks through prompt-based segmentation to remove artifacts and non-tissue regions, followed by rigid alignment using tissue morphology and a pre-trained feature extractor. The resulting alignment is refined using a shape-aware point-set registration model applied to automatically detected nuclei centroids, enabling fine-grained rigid alignment. Finally, Coherent Point Drift (CPD) is used to estimate a non-linear displacement field for non-rigid cellular alignment. Using nuclei correspondences throughout the pipeline, CORE achieves accurate and robust cell-level alignment across modalities. Experimental results show that CORE consistently outperforms state-of-the-art methods in accuracy, robustness, and generalization across both bright-field and immunofluorescence WSIs.
This study conducted an intra-disciplinary review exploring how multinational enterprises (MNEs) contribute to sustainability in local markets within the fields of international business (IB) and strategy. It comprehensively examines four key themes of corporate social responsibility, economic (regional) development, social performance, and environmental sustainability of MNEs. By doing so, it seeks to consolidate fragmented findings from existing independent studies while broadening understanding through problematizing assumptions made in research. In addition, it sheds light on the complexities that MNEs face to address sustainability challenges, and how to strategically integrate economic, social, and environmental goals while adapting to global and local pressures. In turn, we propose new research directions and draw implications for MNEs in addressing grand challenges. Overall, this study contributes to deepening sustainability research in IB and strategy fields, and provides valuable insights for MNEs’ sustainable business practice.
The deployment of ammonia–natural gas combustion in clean powertrains is limited not only by combustion instability, but also by the lack of cycle-resolved tools able to connect stochastic combustion behaviour with emissions formation and control. This work addresses this gap by developing an integrated cycle‑resolved digital diagnostic framework combining engine in‑cylinder pressure analysis, a two‑zone thermodynamic model, a digital twin for residual gas estimation, and detailed chemical kinetics to predict cycle‑to‑cycle variability (CCV) of emissions in low- and zero-carbon fuels, including ammonia (NH3), natural gas (NG) and their blends.The results show that the key phenomena governing NO emissions and their variability when NH3 replaces NG are: i) slower flame kinetics, particularly during early flame development, which limit combustion stability at high NH3 fractions; and ii) a reduction in residual gas fraction driven by higher specific heat ratios (γ), which enhance blow-down. Consequently, increasing NH3 substitution reduces NO formation under the investigated conditions, as the effects of lower peak pressures and temperatures dominate over the longer residence times in the burned-gas zone, reduced residual fractions, and the contribution of fuel-bound nitrogen. NO variability is shown to be partly inherited from combustion dynamics, increasing with NH3 due to greater flame kernel instability. The kinetic analysis further identifies oxygen-sensitive burned-gas pathways controlling NO2, N2O, CO and CO2 evolution under stoichiometric operation, providing mechanistic insight into the local nitrogen-species chemistry associated with NH3–NG combustion.These findings identify combustion temperature and species residence time as key control-relevant parameters governing emissions formation within the narrow stoichiometric window required for three-way catalyst (TWC) operation. The proposed integrated diagnostic framework provides a practical predictive solution supporting the design and control of NH3–NG combustion systems in future clean powertrains.
