For a tree T , let l p ( T ) be the number of different lengths of leaf to leaf paths in T . For a degree sequence s of a tree, let rad ( s ) be the minimum radius of a tree with degree sequence s . Recently, Di Braccio, Katsamaktsis, Ma, Malekshahian, and Zhao provided a lower bound on l p ( T ) in terms of the number of leaves and the maximum degree of T , answering a related question posed by Narins, Pokrovskiy, and Szabó. Here we show l p ( T ) ≥ rad ( s ) − log 2 ⁡ ( rad ( s ) ) for a tree T with no vertex of degree 2 and degree sequence s , and discuss possible improvements and variants.

Laser beam welding (LBW) of metallic components is a knowledge‑intensive manufacturing process whose quality depends on the complex multi‑physics. However, its engineering application is often hindered by the occurrence of porosity defects. Achieving a thorough understanding and reliable prediction of porosity defects remains difficult because it demands robust representation and reasoning over nonlinear and hard‑to‑observe physical information. In this study, we propose an integrated multimodal physics-informed machine learning (PIML) framework with the help of multi-physical modelling and experimental data to predict the porosity defects in laser beam welding of aluminum alloys. The whole framework contains a multimodal PIML model for predicting the porosity ratio and an ML-based estimator for relevant physical information. By utilizing the scalar welding parameters and high-dimensional physical information (probability of keyhole collapses, cumulative existing time of collapses, and molten pool geometry) as inputs, the multimodal PIML model shows great superiority in predicting the porosity ratio, with a reduction of the mean square error by 45%, compared with the ML model trained only with welding parameters. The ML-based estimator constructed with an encoder‐decoder architecture can accurately reproduce the critical physical information within a timeframe of seconds. By integrating these two ML models, the proposed framework advances engineering informatics by offering a scalable, physics-knowledge‑centric solution for fast and accurate porosity prediction in LBW manufacturing.

This study investigated the combined effects of drying method, wall material ratio and concentration, and green tea extract addition on the technological performance and simulated gastrointestinal survival of microcapsules containing Lactobacillus acidophilus . Microcapsules were produced by freeze-drying and spray-drying using different maltodextrin and gum arabic ratios and evaluated for viability, yield, encapsulation efficiency, storage stability, structural characteristics, and resistance under simulated gastrointestinal conditions. Freeze-drying preserved probiotic viability more effectively than spray-drying. Post-encapsulation counts after freeze-drying ranged from 8.23 to 8.54 log CFU/g, with encapsulation efficiencies above 93%. In contrast, spray-dried samples showed lower counts (7.59-8.30 log CFU/g) and reduced yields (42-62%), despite efficiencies exceeding 86%. Under simulated gastrointestinal conditions, free cells showed a reduction of approximately 3.7 log units, resulting in final viability of about 61%. Freeze-dried formulations with maltodextrin-gum arabic ratios (8:2 and 5:2) maintained survival rates above 90% throughout gastrointestinal stages, whereas spray-dried samples exhibited lower ileal counts (4.6–5.7 log CFU/g). The addition of green tea extract further improved probiotic survival, particularly in optimized freeze-dried systems. Fourier transform infrared spectroscopy and scanning electron microscopy supported the structural interpretation, indicating improved matrix vitrification, reduced structural defects, and enhanced oxygen barrier properties in polymer formulations. Although encapsulation efficiency remained high after processing, simulated gastrointestinal exposure significantly reduced viable counts, highlighting the importance of matrix composition in controlling protection. Overall, probiotic performance depended on the integrated interaction between drying method, polymer ratio, and antioxidant incorporation, providing practical formulation criteria for robust probiotic ingredients with enhanced gastrointestinal resistance. • Optimized maltodextrin–gum arabic ratios ensured >90% survival during digestion. • Freeze-dried capsules formed amorphous, low-aw matrices with high probiotic stability. • Encapsulation increased resistance to heat, pH, salt, and osmotic food stresses. • Integrated processing–digestion–storage assessment guides functional food design.

• Research highlight 1: Inflow inhomogeneity, due to the grid proximity, causes dominant tonal noise in the frequency band affected by ingested turbulence. • Research highlight 2: Blade-thickness blockage amplifies the effect of inflow inhomogeneity on unsteady loading and acoustics. • Research highlight 3: Upstream turbulence does not affect the mean flow over the blade and the first blade-passing frequency amplitude. • Research highlight 4: Upstream turbulence effects fade after reattachment; trailing-edge noise is unaffected. This work investigates the effect of grid-generated turbulence ingestion on noise generation in a propeller operating at a low Reynolds number using high-fidelity, scale-resolved simulations. The numerical setup reproduces experiments carried out at Delft University of Technology, where inflow turbulence is generated by a grid placed within a duct. It is found that, upstream of the propeller, the longitudinal correlation length of the streamwise velocity component increases with respect to the case without the propeller. The opposite happens for the transversal one. The turbulent inflow impinging on the propeller blades does not alter the mean flow characteristics over the propeller blades, e.g., the mean static pressure coefficient. However, it increases the root mean square of the pressure fluctuations up to the turbulent reattachment point of the laminar separation bubble, while leaving the downstream region mostly unaffected. This causes a broadband increase in the radiated noise in the low-to-mid frequency range, as confirmed by applying Amiet’s noise-prediction model with input data sampled near the propeller blades’ leading edge. The far-field noise spectra are characterized not only by an increase in the broadband noise with respect to the clean inflow case, but also by tonal components at multiples of the blade-passing frequency. It is found that these tones are caused by the footprint of the turbulence grid that introduces flow inhomogeneities at the propeller location for this specific configuration. It is recommended, when performing experiments and simulations, to verify if any footprint of the turbulence grid is present, not only by performing single-point measurements but also by measuring the time-averaged flow field before installing the propeller.

The nodal spreading of oral cavity and oropharynx squamous cell carcinoma (OCSCC/OSCC) remains a critical challenge. The pathological nature of lymph nodes adjacent to the tumor is sometimes difficult to interpret on PET/CT during the initial assessment. The primary objective of this study was to evaluate the impact of contralateral node PET/CT hyperfixation on disease-free survival (DFS) in lateralized OCSCC or OSCC. From our database, all patients who had a PET/CT during their management for a lateralized SCC were selected between 2018 and 2021. Clinical, histological and radiological data between patients with and without contralateral nodes on the initial PET/CT were compared, as well as the survival of these patients. The Inselspital, Bern University Hospital (ISB) publicly available dataset was then used, to estimate the positive predictive value (PPV) of a contralateral fixation. Of 48 patients who had a PET/CT for lateralized OCSCC or OSCC, 16 (33%) had contralateral lymph node hyperfixation on PET/CT (PET/CT CLN+). In this group, 4 had a bilateral lymph node dissection (27%), and only one had lymph node metastasis. Using the ISB dataset, we found a PPV of only 35% for these contralateral hyperfixation. There was no significant difference in a multivariate Cox model in terms of DFS between the two subgroups in the case of lateralized tumors. There was no difference in survival between patients with or without contralateral lymph nodes on the initial PET/CT.

• Meaningful Stakeholder Engagement (MSE) is increasingly institutionalized in Ghana’s mining governance, shaped by UNGPs and the EU CSDDD. • In practice, engagement remains procedural and ritualistic , limiting answerability, responsiveness, and enforceability. • Elite-mediated consultation (via chiefs/elders) systematically marginalizes women, youth, farmers, and other affected groups. • Corporate governance culture and firm origin shape openness: some firms institutionalize feedback loops; others remain closed/reactive. • Inclusive, transparent, and responsive MSE can strengthen community agency, improve accountability, and enable fairer development outcomes. Meaningful Stakeholder Engagement (MSE) has become a central pillar of accountability in the mineral industry amid growing scrutiny of corporate responsibility, environmental harms and human rights. This paper examines how engagement with host communities, state institutions, civil society organizations and investors shapes accountability outcomes in Ghana’s mining sector. Drawing on qualitative fieldwork and informed by global governance frameworks—including the UN Guiding Principles on Business and Human Rights and the European Union’s Corporate Sustainability Due Diligence Directive—the study finds that although engagement is now formally embedded in mining governance, its practice remains largely procedural, uneven and often ritualistic. Such approaches limit communities’ ability to exercise voice, demand answerability and secure equitable developmental benefits from mineral extraction. At the same time, empirical evidence from community participants highlights that when engagement is grounded in the principles of MSE—particularly inclusiveness, transparency and responsiveness—it can enhance local capacity to contest decisions and influence resource governance. The paper argues that advancing accountability requires moving beyond tokenistic consultations towards engagement processes that explicitly address power asymmetries and meaningfully incorporate community actors into decision-making. It concludes that substantive stakeholder engagement, reinforced by robust regulatory frameworks and genuine participatory commitments, is critical to achieving accountable and sustainable mineral governance in Ghana.

Aging is accompanied by progressive physiological declines in body functions. However, the molecular mechanisms of aging remain poorly understood in decapod crustaceans, a diverse group of invertebrates. We investigated age-related differences in the hemolymph proteomes of marbled crayfish using label-free protein quantification (LC-MS/MS), applying a significance threshold of p<0.05 and a fold change >2 to elucidate molecular mechanisms underpinning aging. Two groups including young (n=6) and old (n=7) crayfish were used. Results showed a downregulation of superoxide dismutase in the hemolymph of older individuals. At the same time, glutathione peroxidase and transketolase were upregulated, which may reflect age-dependent changes in oxidative stress regulation and potential compensatory responses. Aging crayfish exhibited changes in levels of the ProPO system and phagocytosis-related proteins that suggest a possible shift from melanization to phagocytosis in the aging immune system. Additionally, the lower levels of some other immune-related proteins in the old individuals may be consistent with a decline in the crayfish immune system with age. Proteins associated with wound healing and regeneration were higher in young individuals, which may suggest an age-based decline in regenerative capacity. Cytoskeletal and extracellular matrix proteins were upregulated in older crayfish, which could potentially influence immune cell functions. Age-related alterations in the quantities of vitellogenins, hemocyanins, and metabolic enzymes maybe associated with changes in reproductive investment, respiratory capacity, and energy metabolism. Together, these findings highlight the complex molecular basis by which aging reshapes the hemolymph composition and alters immune system characteristics in an invertebrate, revealing molecular signatures that may represent aging mechanisms. Data are available via ProteomeXchange with identifier PXD065434.

Although endogenous neural stem cells represent a promising target for noninvasive spinal cord injury repair, inflammatory lesion environments frequently trigger their death. Our prior work identified necroptosis as a key death pathway for endogenous neural stem cells migrating to spinal cord injury lesions. Rapamycin-insensitive companion of mTOR (Rictor; a core component of the mechanistic target of rapamycin complex 2 [mTORC2] complex) regulates neural stem cell self-renewal and differentiation, and our preliminary data implicate it in spinal cord injury repair; however, its role in promoting endogenous neural stem cell survival post-spinal cord injury remains unclear. Here, we generated conditional endogenous neural stem cell-specific Rictor knockout mice using the Cre-loxP system. Although the endogenous neural stem cell-specific Rictor knockout mice displayed normal baseline spinal cord morphology and function, they exhibited impaired functional recovery after spinal cord injury compared with wild-type controls. This deficit correlated with elevated inflammatory responses and the increased susceptibility of endogenous neural stem cells to necroptosis. Mechanistically, lentiviral-mediated Rictor knockdown in neural stem cells in vitro impaired lysosomal function, leading to heightened sensitivity to tumor necrosis factor-alpha- and lipopolysaccharide-induced necroptosis. Collectively, these findings indicate that Rictor/mTORC2 signaling protects endogenous neural stem cells against receptor-interacting protein kinase 1-mediated necroptosis following spinal cord injury. Consequently, the modulation of intrinsic Rictor activity represents a potential therapeutic strategy to enhance endogenous neural stem cell survival and functional recovery post-spinal cord injury.