On the Maximum Crossing Number

Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure

Geometric Multicut: Shortest Fences for Separating Groups of Objects in the Plane

We study the following separation problem: Given a collection of pairwise disjoint coloured objects in the plane with k different colours, compute a shortest “fence” F, i.e., a union of curves of minimum total length, that separates every pair of objects of different colours. Two objects are separated if F contains a simple closed curve that has one object in the interior and the other in the exterior. We refer to the problem as GEOMETRIC k-CUT, as it is a geometric analog to the well-studied multicut problem on graphs. We first give an O(n4log3n)-time algorithm that computes an optimal fence for the case where the input consists of polygons of two colours with n corners in total. We then show that the problem is NP-hard for the case of three colours. Finally, we give a randomised 4/3⋅1.2965-approximation algorithm for polygons and any number of colours

Recognizing and Drawing IC-planar Graphs

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$ vertices, we present an $O(n)$-time algorithm that computes a straight-line drawing of $G$ in quadratic area, and an $O(n^3)$-time algorithm that computes a straight-line drawing of $G$ with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is NP-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar

On Arrangements of Orthogonal Circles

In this paper, we study arrangements of orthogonal circles, that is, arrangements of circles where every pair of circles must either be disjoint or intersect at a right angle. Using geometric arguments, we show that such arrangements have only a linear number of faces. This implies that orthogonal circle intersection graphs have only a linear number of edges. When we restrict ourselves to orthogonal unit circles, the resulting class of intersection graphs is a subclass of penny graphs (that is, contact graphs of unit circles). We show that, similarly to penny graphs, it is NP-hard to recognize orthogonal unit circle intersection graphs.Comment: Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019

"A calorie is a calorie" violates the second law of thermodynamics

The principle of "a calorie is a calorie," that weight change in hypocaloric diets is independent of macronutrient composition, is widely held in the popular and technical literature, and is frequently justified by appeal to the laws of thermodynamics. We review here some aspects of thermodynamics that bear on weight loss and the effect of macronutrient composition. The focus is the so-called metabolic advantage in low-carbohydrate diets – greater weight loss compared to isocaloric diets of different composition. Two laws of thermodynamics are relevant to the systems considered in nutrition and, whereas the first law is a conservation (of energy) law, the second is a dissipation law: something (negative entropy) is lost and therefore balance is not to be expected in diet interventions. Here, we propose that a misunderstanding of the second law accounts for the controversy about the role of macronutrient effect on weight loss and we review some aspects of elementary thermodynamics. We use data in the literature to show that thermogenesis is sufficient to predict metabolic advantage. Whereas homeostasis ensures balance under many conditions, as a general principle, "a calorie is a calorie" violates the second law of thermodynamics

Ideal and actual involvement of community pharmacists in health promotion and prevention: a cross-sectional study in Quebec, Canada

<p>Abstract</p> <p>Background</p> <p>An increased interest is observed in broadening community pharmacists' role in public health. To date, little information has been gathered in Canada on community pharmacists' perceptions of their role in health promotion and prevention; however, such data are essential to the development of public-health programs in community pharmacy. A cross-sectional study was therefore conducted to explore the perceptions of community pharmacists in urban and semi-urban areas regarding their ideal and actual levels of involvement in providing health-promotion and prevention services and the barriers to such involvement.</p> <p>Methods</p> <p>Using a five-step modified Dillman's tailored design method, a questionnaire with 28 multiple-choice or open-ended questions (11 pages plus a cover letter) was mailed to a random sample of 1,250 pharmacists out of 1,887 community pharmacists practicing in Montreal (Quebec, Canada) and surrounding areas. It included questions on pharmacists' ideal level of involvement in providing health-promotion and preventive services; which services were actually offered in their pharmacy, the employees involved, the frequency, and duration of the services; the barriers to the provision of these services in community pharmacy; their opinion regarding the most appropriate health professionals to provide them; and the characteristics of pharmacists, pharmacies and their clientele.</p> <p>Results</p> <p>In all, 571 out of 1,234 (46.3%) eligible community pharmacists completed and returned the questionnaire. Most believed they should be very involved in health promotion and prevention, particularly in smoking cessation (84.3%); screening for hypertension (81.8%), diabetes (76.0%) and dyslipidemia (56.9%); and sexual health (61.7% to 89.1%); however, fewer respondents reported actually being very involved in providing such services (5.7% [lifestyle, including smoking cessation], 44.5%, 34.8%, 6.5% and 19.3%, respectively). The main barriers to the provision of these services in current practice were lack of: time (86.1%), coordination with other health care professionals (61.1%), staff or resources (57.2%), financial compensation (50.8%), and clinical tools (45.5%).</p> <p>Conclusions</p> <p>Although community pharmacists think they should play a significant role in health promotion and prevention, they recognize a wide gap between their ideal and actual levels of involvement. The efficient integration of primary-care pharmacists and pharmacies into public health cannot be envisioned without addressing important organizational barriers.</p

Genetic and neurological foundations of customer orientation: field and experimental evidence

We explore genetic and neurological bases for customer orientation (CO) and contrast them with sales orientation (SO). Study 1 is a field study that establishes that CO, but not SO, leads to greater opportunity recognition. Study 2 examines genetic bases for CO and finds that salespeople with CO are more likely to have the 7R variant of the DRD4 gene. This is consistent with basic research on dopamine receptor activity in the brain that underlies novelty seeking, the reward function, and risk taking. Study 3 examines the neural basis of CO and finds that salespeople with CO, but not SO, experience greater activation of their mirror neuron systems and neural processes associated with empathy. Managerial and research implications are discussed

Nonequilibrium thermodynamics and energy efficiency in weight loss diets

Carbohydrate restriction as a strategy for control of obesity is based on two effects: a behavioral effect, spontaneous reduction in caloric intake and a metabolic effect, an apparent reduction in energy efficiency, greater weight loss per calorie consumed. Variable energy efficiency is established in many contexts (hormonal imbalance, weight regain and knock-out experiments in animal models), but in the area of the effect of macronutrient composition on weight loss, controversy remains. Resistance to the idea comes from a perception that variable weight loss on isocaloric diets would somehow violate the laws of thermodynamics, that is, only caloric intake is important ("a calorie is a calorie"). Previous explanations of how the phenomenon occurs, based on equilibrium thermodynamics, emphasized the inefficiencies introduced by substrate cycling and requirements for increased gluconeogenesis. Living systems, however, are maintained far from equilibrium, and metabolism is controlled by the regulation of the rates of enzymatic reactions. The principles of nonequilibrium thermodynamics which emphasize kinetic fluxes as well as thermodynamic forces should therefore also be considered

Therapeutic Management of Primary Immunodeficiency in Older Patients

Primary immunodeficiency disease (PID) has traditionally been viewed as a group of illnesses seen in the paediatric age group. New advances in diagnosis and treatment have led to an increase in the number of elderly PID patients. However, there is lack of research evidence on which to base clinical management in this group of patients. Management decisions often have to be based therefore on extrapolations from other patient cohorts or from younger patients. Data from the European Society for Immunodeficiencies demonstrates that the vast majority of elderly patients suffer from predominantly antibody deficiency syndromes. We review the management of PID disease in the elderly, with a focus on antibody deficiency disease