Explore the vast range of titles available.

Branch and Bound (B&B) algorithms in Global Optimization are used to perform an exhaustive search over the feasible area. One choice is to use simplicial partition sets. Obtaining sharp and cheap bounds of the objective function over a simplex is very important in the construction of efficient Global Optimization B&B algorithms. Although enclosing a simplex in a box implies an overestimation, boxes are more natural when dealing with individual coordinate bounds, and bounding ranges with Interval Arithmetic (IA) is computationally cheap. This paper introduces several linear relaxations using gradient information and Affine Arithmetic and experimentally studies their efficiency compared to traditional lower bounds obtained by natural and centered IA forms and their adaption to simplices. A Global Optimization B&B algorithm with monotonicity test over a simplex is used to compare their efficiency over a set of low dimensional test problems with instances that either have a box constrained search region or where the feasible set is a simplex. Numerical results show that it is possible to obtain tight lower bounds over simplicial subsets.

By the time of his death in 1280 Albert the Great was respected not only as a theologian and philosopher, but also as one of the greatest authorities on astrology in the West. Such expertise rarely gains plaudits today, but in late medieval Europe knowledge of esoteric pursuits was held in high regard. This is why Dominicans not only did nothing to challenge the growth of the “Albert Legend,” that Albert had mastered all magical and esoteric topics, but also promoted this myth. By promoting this legend, they bolstered and legitimized the reputation of the Order of Preachers.

Humans tend to prefer walking patterns that minimize energetic cost, but must also maintain stability to avoid falling over. The relative importance of these two goals in determining the preferred gait pattern is not currently clear. We investigated the relationship between energetic cost and stability during downhill walking, a context in which gravitational energy will assist propulsion but may also reduce stability. We hypothesized that humans will not minimize energetic cost when walking downhill, but will instead prefer a gait pattern that increases stability. Simulations of a dynamic walking model were used to determine whether stable downhill gaits could be achieved using a simple control strategy. Experimentally, twelve healthy subjects walked downhill at 1.25 m/s (0, 0.05, 0.10, and 0.15 gradients). For each slope, subjects performed normal and relaxed trials, in which they were instructed to reduce muscle activity and allow gravity to maximally assist their gait. We quantified energetic cost, stride timing, and leg muscle activity. In our model simulations, increase in slope reduced the required actuation but also decreased stability. Experimental subjects behaved more like the model when using the relaxed rather than the normal walking strategy; the relaxed strategy decreased energetic cost at the steeper slopes but increased stride period variability, an indicator of instability. These results indicate that subjects do not take optimal advantage of the propulsion provided by gravity to decrease energetic cost, but instead prefer a more stable and more costly gait pattern.

Over the last decades, algorithms have been developed for checking copositivity of a matrix. Methods are based on several principles, such as spatial branch and bound, transformation to Mixed Integer Programming, implicit enumeration of KKT points or face-based search. Our research question focuses on exploiting the mathematical properties of the relative interior minima of the standard quadratic program (StQP) and monotonicity. We derive several theoretical properties related to convexity and monotonicity of the standard quadratic function over faces of the standard simplex. We illustrate with numerical instances up to 28 dimensions the use of monotonicity in face-based algorithms. The question is what traversal through the face graph of the standard simplex is more appropriate for which matrix instance; top down or bottom up approaches. This depends on the level of the face graph where the minimum of StQP can be found, which is related to the density of the so-called convexity graph.

All too commonly scholars take a piecemeal approach toward the work of medieval intellectuals such as Albert the Great (d. 1280), with a view to understanding singly his contributions to the history of science, various philosophical approaches, or theology, as if his mind was somehow compartmentalized. Furthermore, in spite of great advances in studying the history of occult subjects, modern writers sometimes still lapse into writing about medieval astrology as a superstition. This study suggests that we should consider medieval intellectual thought holistically, as a product of a different rationality than that which is dominant today. In order to illustrate this approach, I examine astrological belief within Albert’s thought as rational and consider some of the theological reasons why Albert was fascinated with this topic.

A natural way to define branching in branch and bound (B&B) for blending problems is bisection. The consequence of using bisection is that partition sets are in general irregular. The question is how to use regular simplices in the refinement of the unit simplex. A regular simplex with fixed orientation can be represented by its center and size, facilitating storage of the search tree from a computational perspective. The problem is that a simplex defined in a space with dimension n > 3 cannot be subdivided into regular subsimplices without overlapping. We study the characteristics of the refinement by regular simplices. The main challenge is to find a refinement with a good convergence ratio which allows discarding simplices in an overlapped and already evaluated region. As the efficiency of the division rule in B&B algorithms is instance dependent, we focus on the worst case behaviour, i.e. none of the branches are pruned. This paper shows that for this case surprisingly an overlapping regular refinement may generate less simplices to be evaluated than longest edge bisection. On the other hand, the number of evaluated vertices may be larger.

The recent National Institute of Health (NIH) INCLUDE (INvestigation of Co-occurring conditions across the Lifespan to Understand Down syndromE) initiative has bolstered capacity for the current increase in clinical trials involving individuals with Down syndrome (DS). This new NIH funding mechanism offers new opportunities to expand and develop novel approaches in engaging and effectively enrolling a broader representation of clinical trials participants addressing current medical issues faced by individuals with DS. To address this opportunity, the NIH assembled leading clinicians, scientists, and representatives of advocacy groups to review existing methods and to identify those areas where new approaches are needed to engage and prepare DS populations for participation in clinical trial research. This paper summarizes the results of the Clinical Trial Readiness Working Group that was part of the INCLUDE Project Workshop: Planning a Virtual Down Syndrome Cohort Across the Lifespan Workshop held virtually September 23 and 24, 2019.

This paper studies the dynamic application of the minimax regret (MR) decision criterion to identify robust flood risk management strategies under climate change uncertainty and emerging information. An MR method is developed that uses multiple learning scenarios, for example about sea level rise or river peak flow development, to analyse effects of changes in information on optimal investment in flood protection. To illustrate the method, optimal dike height and floodplain development are studied in a conceptual model, and conventional and adaptive MR solutions are compared. A dynamic application of the MR decision criterion allows investments to be changed after new information on climate change impacts, which has an effect on today’s optimal investments. The results suggest that adaptive MR solutions are more robust than the solutions obtained from a conventional MR analysis of investments in flood protection. Moreover, adaptive MR analysis with multiple learning scenarios is more general and contains conventional MR analysis as a special case.

Background Fetal growth restriction is, despite advances in neonatal care and uptake of antenatal ultrasound scanning, still a major cause of perinatal morbidity. Neonates with birth weight > 10th percentile are assumed to be appropriate-for-gestational-age (AGA), although many are at increased risk of perinatal morbidity, because of undetected mild restriction of growth potential. We hypothesized that within AGA neonates, reduced fetal growth velocities are associated with adverse neonatal outcome. Methods A retrospective cohort study of singleton pregnancies, in the Maastricht University Medical Centre (MUMC) between 2010 and 2016. Women had two fetal biometry scans (18–22 weeks and 30–34 weeks of gestational age) and delivered a newborn with a birth weight between the 10th–80th percentile. Differences in growth velocities of the abdominal circumference (AC), biparietal diameter (BPD), head circumference (HC) and femur length (FL) were compared between the suboptimal AGA (sAGA) (birth weight centiles 10–50) and optimal AGA (oAGA) (birth weight centiles 50–80) group. We assessed the association between velocities and neonatal outcomes. Results We included 934 singleton pregnancies. In the suboptimal AGA group, fetal growth velocities were lower (in mm/week): AC 10.72 ± 1.00 vs 11.23 ± 1.00 ( p  < .001), HC 10.50 ± 0.80 vs 10.68 ± 0.77 ( p  = 0.001), BPD 3.01 ± 0.28 vs 3.08 ± 0.27 ( p  < .0001) and FL 2.47 ± 0.21 vs 2.50 ± 0.22 ( p  = 0.014), compared to the optimal AGA group. Neonates with an adverse neonatal outcome had significantly lower growth velocities (in mm/week) of: AC 10.57 vs 10.94 ( p  = 0.034), HC 10.28 vs 10.59 ( p  = 0.003) and BPD 2.97 vs 3.04 ( p  = 0.043) compared to those with normal outcome. An inverse association was observed between the AC velocity and a composite adverse neonatal outcome (OR) = 0.667 (95%CI 0.507–0.879, p  = 0.004), and between the AC velocity and neonates with NICU stay (OR) = 0.733 (95%CI 0.570–0.942, p  = 0.015). Neonates with a birthweight lower than expected (based on the abdominal circumference at 20 weeks) had significantly more composite adverse neonatal outcomes 8.5% vs 5.0% ( p  = 0.047), NICU stays 9.6% vs 3.8% ( p  < .0001) and hospital stays 44.4% vs 35.6% ( p  = 0.006). Conclusions Appropriate-for-gestational-age neonates are a heterogeneous group with some showing suboptimal fetal growth. Abnormal fetal growth velocities, especially abdominal circumference velocity, are associated with adverse neonatal outcome and can potentially improve the detection of mild growth restriction when used in multivariate models.

To match products of different quality with end market preferences under supply uncertainty, it is crucial to integrate product quality information in logistics decision making. We present a case of this integration in a meat processing company that faces uncertainty in delivered livestock quality. We develop a stochastic programming model that exploits historical product quality delivery data to produce slaughterhouse allocation plans with reduced levels of uncertainty in received livestock quality. The allocation plans generated by this model fulfil demand for multiple quality features at separate slaughterhouses under prescribed service levels while minimizing transportation costs. We test the model on real world problem instances generated from a data set provided by an industrial partner. Results show that historical farmer delivery data can be used to reduce uncertainty in quality of animals to be delivered to slaughterhouses.