A note on dominating cycles in 2-connected graphs

Let G be a 2-connected graph on n vertices such that d(x) + d(y) + d(z) n for all triples of independent vertices x, y, z. We prove that every longest cycle in G is a dominating cycle unless G is a spanning subgraph of a graph belonging to one of four easily specified classes of graphs

Convergent and divergent trajectories of corporate governance

This Special Issue revisits the classic question of comparative corporate governance research, namely whether national corporate governance systems are converging. More specifically, it focuses on several ‘convergence vectors’ which comprise the political, legal, economic and social arrangements that influence or drive the international trajectories of governance systems towards a common denominator. Taken together, the contributors to this Special Issue invite us to think critically about the functional explanations commonly mobilized in favour of convergence and consider instead the convergence debate from a broader and more interdisciplinary point of view

A framework for randomized time-splitting in linear-quadratic optimal control

Inspired by the successes of stochastic algorithms in the training of deep neural networks and the simulation of interacting particle systems, we propose and analyze a framework for randomized time-splitting in linear-quadratic optimal control. In our proposed framework, the linear dynamics of the original problem is replaced by a randomized dynamics. To obtain the randomized dynamics, the system matrix is split into simpler submatrices and the time interval of interest is split into subintervals. The randomized dynamics is then found by selecting randomly one or more submatrices in each subinterval. We show that the dynamics, the minimal values of the cost functional, and the optimal control obtained with the proposed randomized time-splitting method converge in expectation to their analogues in the original problem when the time grid is refined. The derived convergence rates are validated in several numerical experiments. Our numerical results also indicate that the proposed method can lead to a reduction in computational cost for the simulation and optimal control of large-scale linear dynamical systemsThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No: 694126- DyCon), the Alexander von Humboldt-Professorship program, the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement No.765579-ConFlex and the Transregio 154 Project “Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks”, project C08, of the German DFG, the grant PID2020-112617GB-C22, “Kinetic equations and learning control” of the Spanish MINECO, and the COST Action grant CA18232, “Mathematical models for interacting dynamics on networks” (MAT-DYN-NET

Age-dependent modulation of motor network connectivity for skill acquisition, consolidation and interlimb transfer after motor practice

Objective: Age-related differences in neural strategies for motor learning are not fully understood. We determined the effects of age on the relationship between motor network connectivity and motor skill acquisition, consolidation, and interlimb transfer using dynamic imaging of coherent sources. Methods: Healthy younger (n = 24, 18-24 y) and older (n = 24, 65-87 y) adults unilaterally practiced a visuomotor task and resting-state electroencephalographic data was acquired before and after practice as well as at retention. Results: The results showed that right-hand skill acquisition and consolidation did not differ between age groups. However, age affected the ability to transfer the newly acquired motor skill to the non-practiced limb. Moreover, strengthened left- and right-primary motor cortex-related beta conectivity was negatively and positively associated with right-hand skill acquisition and left-hand skill consolidation in older adults, respectively. Conclusion: Age-dependent modulations of bilateral resting-state motor network connectivity indicate age-specific strategies for the acquisition, consolidation, and interlimb transfer of novel motor tasks. Significance: The present results provide insights into the mechanisms underlying motor learning that are important for the development of interventions for patients with unilateral injuries. (C) 2021 International Federation of Clinical Neurophysiology. Published by Elsevier B.V. All rights reserved

Incompressible viscous flow near the leading edge of a flat plate admitting slip

The shear stress at the leading edge, calculated on basis of the Navier-Stokes equations and the no-slip boundary condition, approaches infinity. However, taking into account the mean free path of the molecules, which implies admitting a certain slip, the shear stress becomes inversely proportional to the square root of the Knudsen number κ if κ→0. κ is defined as the ratio between the mean free path and the viscous length. The new boundary condition modifies the shear stress only within the Knudsen region of which the size is of the order of 3 to 4 times the mean free path.

Soluble PD-L1 is a promising disease biomarker but does not reflect tissue expression in classic Hodgkin lymphoma

Individually, tissue and soluble markers involved in the programmed cell death protein 1/programmed death-ligand (PD-1/PD-L) axis have been described as biomarkers with clinical value in classical Hodgkin lymphoma (cHL). In the context of the success of immune checkpoint blockade therapy in cHL, it is interesting to discover whether plasma levels of proteins in the PD-1/PD-L axis are a reflection of expression by the corresponding tissue. Paired tissue and plasma samples of cHL patients were collected and analysed for PD-1, PD-L1 and PD-L2 levels. In addition, vascular endothelial growth factor (VEGF) and CD83, molecules regarded to influence the expression of PD-1, PD-L1 and/or PD-L2, were included. PD-L1 was upregulated in the plasma of cHL patients compared to healthy controls and correlated well with several clinical parameters. Strong PD-L1 expression in the tumour microenvironment contributed to high soluble (s)PD-L1 levels, although there was no direct correlation between plasma PD-L1 levels and total expression of PD-L1 in corresponding cHL tissue. Interestingly, we observed a positive correlation between VEGF and PD-1 levels in both tissue and plasma. In conclusion, although PD-L1 is a promising soluble biomarker in cHL, its levels do not reflect the total tissue expression. Future studies focusing on PD-L1 as a predictor for immune checkpoint treatment response, should include both biopsy and plasma samples

Condition-Based Production Planning:Adjusting Production Rates to Balance Output and Failure Risk

Problem Definition: Many production systems deteriorate over time as a result of load and stress caused by production. The deterioration rate of these systems typically depends on the production rate, implying that the equipment's deterioration rate can be controlled by adjusting the production rate. We introduce the use of condition monitoring to dynamically adjust the production rate to minimize maintenance costs and maximize production revenues. We study a single-unit system for which the next maintenance action is scheduled upfront. Academic/Practical Relevance: Condition-based maintenance decisions are frequently seen in the literature. However, in many real-life systems, maintenance planning has limited flexibility and cannot be done last minute. As an alternative, we are the first to propose using condition information to optimize the production rate, which is a more flexible short-term decision. Methodology: We derive structural optimality results from the analysis of deterministic deterioration processes. A Markov decision process formulation of the problem is used to obtain numerical results for stochastic deterioration processes. Results: The structure of the optimal policy strongly depends on the (convex or concave) relation between the production rate and the corresponding deterioration rate. Condition-based production rate decisions result in significant cost savings (by up to 50%), achieved by better balancing the failure risk and production output. For several systems a win-win scenario is observed, with both reduced failure risk and increased expected total production. Furthermore, condition-based production rates increase robustness and lead to more stable profits and production output. Managerial Implications: Using condition information to dynamically adjust production rates provides opportunities to improve the operational performance of systems with production-dependent deterioration

Nutritional, immune, micronutrient and health status of HIV-infected children in care centres in Mangaung

Aim: To assess the nutritional, immune, micronutrient and health status of antiretroviral-naïve HIV-infected children.Method: A cross-sectional descriptive study was undertaken between September 2004 and March 2006 amongst HIV-infected children of which none received antiretroviral therapy, in care centres in Mangaung, Free State.Results: The study included 37 clinically stable and food-secure HIV-infected children. Their median age was 5.4 years (range 1.2–10.2 years). Fifteen children (41%) were underweight, 30 (81%) were stunted and one (3%) was wasted. The most commonly observed clinical features were lymphadenopathy (84%), skin rashes (51%), hepatomegaly (32%) and pallor (41%). Eight per cent of children had features of TB, while 19% had a lower respiratory tract infection. The median viral load of the group (n = 35) was 117 000 copies/ml, the median CD4+ cell count was 477 cells/mm3 and the median CD4 percentage was 22.5%. A significant negative correlation could be demonstrated between viral load and nutritional indicators. Children had deficient serum levels relative to normal reference values for glutathione (91% of children), albumin (78%), vitamin A (63%), vitamin D (44%), zinc (38%) and vitamin E (13%). Sixty per cent of the children were anaemic and 30% were iron deficient.Conclusion: A high prevalence of acute and chronic malnutrition and micronutrient deficiencies occurred among HIV-infected children residing in care centres. The study highlights the need to investigate early initiation of antiretroviral therapy and nutrition interventions, including aggressive supplementation, in order to improve the prognosis of these children