Bayesian networks are a commonly used method of representing conditional probability relationships between a set of variables in the form of a directed acyclic graph (DAG). Determination of the DAG which best explains observed data is an NP-hard problem [1]. This problem can be stated as a constrained optimisation problem using Integer Linear Programming (ILP). This paper explores how the performance of ILP-based Bayesian network learning can be improved through ILP techniques and in particular through the addition of non-essential, implied constraints. There are exponentially many such constraints that can be added to the problem. This paper explores how these constraints may best be generated and added as needed. The results show that using these constraints in the best discovered configuration can lead to a significant improvement in performance and show significant improvement in speed using a state-of-the-art Bayesian network structure learner.

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The increasing awareness of climate change and human capital issues is shifting companies towards aspects other than traditional financial earnings. In particular, the changing behaviors towards sustainability issues of the global community and the availability of environmental, social and governance (ESG) indicators are attracting investors to socially responsible investment decisions. Furthermore, whereas the strategic importance of ESG metrics has been particularly studied for private enterprises, little attention have received public companies. To address this gap, the present work has three aims—1. To predict the accuracy of main financial indicators such as the expected Return of Equity (ROE) and Return of Assets (ROA) of public enterprises in Europe based on ESG indicators and other economic metrics; 2. To identify whether ESG initiatives affect the financial performance of public European enterprises; and 3. To discuss how ESG factors, based on the findings of aims #1 and #2, can contribute to the advancements of the current debate on Corporate Social Responsibility (CSR) policies and practices in public enterprises in Europe. To fulfil the above aims, we use a combined approach of machine learning (ML) techniques and inferential (i.e., ordered logistic regression) model. The former predicts the accuracy of ROE and ROA on several ESG and other economic metrics and fulfils aim #1. The latter is used to test whether any causal relationships between ESG investment decisions and ROA and ROE exist and, whether these relationships exist, to assess their magnitude. The inferential analysis fulfils aim #2. Main findings suggest that ML accurately predicts ROA and ROE and indicate, through the ordered logistic regression model, the existence of a positive relationship between ESG practices and the financial indicators. In addition, the existing relationship appears more evident when companies invest in environmental innovation, employment productivity and diversity and equal opportunity policies. As a result, to fulfil aim #3 useful policy insights are advised on these issues to strengthen CSR strategies and sustainable development practices in European public enterprises.

BackgroundPatients experiencing disuse atrophy report acute loss of skeletal muscle mass which subsequently leads to loss of strength and physical capacity. In such patients, especially the elderly, complete recovery remains a challenge even with improved nutrition and resistance exercise. This study aimed to explore the clinical potential of bimagrumab, a human monoclonal antibody targeting the activin type II receptor, for the recovery of skeletal muscle volume from disuse atrophy using an experimental model of lower extremity immobilization.MethodsIn this double‐blind, placebo‐controlled trial, healthy young men (n = 24; mean age, 24.1 years) were placed in a full‐length cast of one of the lower extremities for 2 weeks to induce disuse atrophy. After cast removal, subjects were randomized to receive a single intravenous (i.v.) dose of either bimagrumab 30 mg/kg (n = 15) or placebo (n = 9) and were followed for 12 weeks. Changes in thigh muscle volume (TMV) and inter‐muscular adipose tissue (IMAT) and subcutaneous adipose tissue (SCAT) of the thigh, maximum voluntary knee extension strength, and safety were assessed throughout the 12 week study.ResultsCasting resulted in an average TMV loss of −4.8% and comparable increases in IMAT and SCAT volumes. Bimagrumab 30 mg/kg i.v. resulted in a rapid increase in TMV at 2 weeks following cast removal and a +5.1% increase above pre‐cast levels at 12 weeks. In comparison, TMV returned to pre‐cast level at 12 weeks (−0.1%) in the placebo group. The increased adiposity of the casted leg was sustained in the placebo group and decreased substantially in the bimagrumab group at Week 12 (IMAT: −6.6%, SCAT: −3.5%). Knee extension strength decreased by ~25% in the casted leg for all subjects and returned to pre‐cast levels within 6 weeks after cast removal in both treatment arms. Bimagrumab was well tolerated with no serious or severe adverse events reported during the study.ConclusionsA single dose of bimagrumab 30 mg/kg i.v. safely accelerated the recovery of TMV and reversal of accumulated IMAT following 2 weeks in a joint‐immobilizing cast.

Average systemic exposure to fingolimod was similar after oral and intravenous administration. However, the acute decrease in lymphocyte counts was weaker after intravenous administration, likely because of lower blood levels of the active metabolite fingolimod-phosphate compared with oral administration.

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The challenging task of learning structures of probabilistic graphical models is an important problem within modern AI research. Recent years have witnessed several major algorithmic advances in structure learning for Bayesian networks-arguably the most central class of graphical models-especially in what is known as the score-based setting. A successful generic approach to optimal Bayesian network structure learning (BNSL), based on integer programming (IP), is implemented in the gobnilp system. Despite the recent algorithmic advances, current understanding of foundational aspects underlying the IP based approach to BNSL is still somewhat lacking. Understanding fundamental aspects of cutting planes and the related separation problem is important not only from a purely theoretical perspective, but also since it holds out the promise of further improving the efficiency of state-of-the-art approaches to solving BNSL exactly. In this paper, we make several theoretical contributions towards these goals: (i) we study the computational complexity of the separation problem, proving that the problem is NP-hard; (ii) we formalise and analyse the relationship between three key polytopes underlying the IP-based approach to BNSL; (iii) we study the facets of the three polytopes both from the theoretical and practical perspective, providing, via exhaustive computation, a complete enumeration of facets for low-dimensional family-variable polytopes; and, furthermore, (iv) we establish a tight connection of the BNSL problem to the acyclic subgraph problem.