Ranking Functions for Vector Addition Systems

Vector addition systems are an important model in theoretical computer science and have been used for the analysis of systems in a variety of areas. Termination is a crucial property of vector addition systems and has received considerable interest in the literature. In this paper we give a complete method for the construction of ranking functions for vector addition systems with states. The interest in ranking functions is motivated by the fact that ranking functions provide valuable additional information in case of termination: They provide an explanation for the progress of the vector addition system, which can be reported to the user of a verification tool, and can be used as certificates for termination. Moreover, we show how ranking functions can be used for the computational complexity analysis of vector addition systems (here complexity refers to the number of steps the vector addition system under analysis can take in terms of the given initial vector)

<新刊紹介>瀧澤直七著稿本「日本金融史論」

<div><p></p><p><i>Background</i>: The relationship between metabolic disease and the non-modifiable risk factors sex, age and ethnicity in Africans is not well-established.</p><p><i>Aim</i>: This study aimed to describe sex, age and ethnicity differences in blood pressure (BP) and lipid status in rural Kenyans.</p><p><i>Subjects and methods</i>: A cross-sectional study was undertaken among rural Kenyans. BP and pulse rate (PR) were measured while sitting and fasting blood samples were taken for analysis of standard lipid profile. Standard anthropometric measurements were collected. Physical activity energy expenditure was obtained objectively and lifestyle data were obtained using questionnaires.</p><p><i>Results</i>: In total, 1139 individuals (61.0% women) participated aged 17–68 years. Age was positively associated with BP and plasma cholesterol levels. Sitting PR was negatively associated with age in women only (sex-interaction <i>p</i> < 0.001). Ethnicity did not modify any of the age-associations with haemodynamic or lipid outcomes. Differences in intercept between women and men were found in all parameters except for diastolic BP (<i>p</i> = 0.154), with men having lower HDL-C but higher values in all other cardiovascular risk factors.</p><p><i>Conclusion</i>: BP and plasma cholesterol levels increase with age at a similar gradient in men and women, but absolute levels of the majority of the risk factors were higher in men.</p></div

Additional file 1: Table S1. of Relative validity of a web-based food frequency questionnaire for Danish adolescents

Mean intake of food groups, energy and nutrients from FFQ and 3x24HR stratified by BMI categories. (DOCX 14 kb

Food groups and subgroups of foods with examples of foods included in the analysis.

<p>Food groups and subgroups of foods with examples of foods included in the analysis.</p

Dependence of price and food variety after step-wise release of the cultural acceptability constraint in the CAN.

<p>Percentages indicate the tolerated deviation from the averagely consumed weight of food categories by the Danish population [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0163411#pone.0163411.ref026" target="_blank">26</a>]. The initial CAN has 0% allowed deviation (top line).</p

Change of the deviation of DG, N, and DGN from the average relative consumption (ARD) of food categories in Denmark when subjected to diversification.

<p>Change of the deviation of DG, N, and DGN from the average relative consumption (ARD) of food categories in Denmark when subjected to diversification.</p

Changes of the numbers of food items in the different food baskets and their cost when subjected to diversification.

<p>A) Changes in the number of different foods in the FBs when lowering the maximum allowed relative share of any single food, expressed as percentage of the average consumption of foods in the corresponding food category. B) Change in price of the four food baskets when increasing the diversity through minimizing single food shares. All abbreviations as explained in legend of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0163411#pone.0163411.t002" target="_blank">Table 2</a>; “none” means no restriction.</p

Composition of the diversified FBs by food categories.

<p>To make the effects of the different sets of constraints more evident, the category “Meat & meat products” used in the Danish consumption survey [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0163411#pone.0163411.ref026" target="_blank">26</a>] was split up into “Meat(products)” and “Offal”; pulses are indicated as a separate category (part of the “Vegetable” group in the consumption survey; and “Nuts & seeds” are indicated separately from the “Fruit” group.</p

Use of Linear Programming to Develop Cost-Minimized Nutritionally Adequate Health Promoting Food Baskets

<div><p>Background</p><p>Food-Based Dietary Guidelines (FBDGs) are developed to promote healthier eating patterns, but increasing food prices may make healthy eating less affordable. The aim of this study was to design a range of cost-minimized nutritionally adequate health-promoting food baskets (FBs) that help prevent both micronutrient inadequacy and diet-related non-communicable diseases at lowest cost.</p><p>Methods</p><p>Average prices for 312 foods were collected within the Greater Copenhagen area. The cost and nutrient content of five different cost-minimized FBs for a family of four were calculated per day using linear programming. The FBs were defined using five different constraints: cultural acceptability (CA), or dietary guidelines (DG), or nutrient recommendations (N), or cultural acceptability and nutrient recommendations (CAN), or dietary guidelines and nutrient recommendations (DGN). The variety and number of foods in each of the resulting five baskets was increased through limiting the relative share of individual foods.</p><p>Results</p><p>The one-day version of N contained only 12 foods at the minimum cost of DKK 27 (€ 3.6). The CA, DG, and DGN were about twice of this and the CAN cost ~DKK 81 (€ 10.8). The baskets with the greater variety of foods contained from 70 (CAN) to 134 (DGN) foods and cost between DKK 60 (€ 8.1, N) and DKK 125 (€ 16.8, DGN). Ensuring that the food baskets cover both dietary guidelines and nutrient recommendations doubled the cost while cultural acceptability (CAN) tripled it.</p><p>Conclusion</p><p>Use of linear programming facilitates the generation of low-cost food baskets that are nutritionally adequate, health promoting, and culturally acceptable.</p></div

Cross-sectional associations between movement behaviors and cardio-metabolic risk markers in Danish children.

<p>Abbreviations: PA, physical activity; MVPA, moderate-to-vigorous physical activity; CSHQ, Children’s Sleep Habits Questionnaire; WC, waist circumference; MAP, mean arterial blood pressure; HOMA_IR, homeostatic model assessment of central insulin resistance; HDL-C, high density lipoprotein cholesterol; MetS-score, metabolic syndrome score.</p><p>Data are presented as unstandardized regression coefficients (β) with 95% confidence intervals (CI) using a linear mixed model with school and subject as random effects. The five cardio-metabolic risk markers were adjusted for baseline age, sex, pubertal status, and sex-pubertal status interaction (<b>Model 1</b>).</p><p>Coefficients represent the change in the outcome for a 100-cpm change in total PA, a 10-minute change in time spent in MVPA, a 1% change in sedentary time, a 60-minute change in screen time and sleep duration and a 1-point change in CSHQ. *, P<0.05; **, P<0.001.</p>¥<p>P<0.05 in <b>Model 2</b>: Model 1+ mutual adjustments between MVPA, sedentary time and sleep duration. Total PA was only adjusted for sleep duration.</p>£<p>P<0.05 in <b>Model 3</b>: Model 2+ fat mass index.</p>1<p>MAP was also adjusted for height.</p>2<p>HOMA_IR and triglycerides were log transformed.</p>3<p>MetS-score = (z-scores by baseline age, sex, pubertal status and sex-pubertal status interaction of) WC + MAP + HOMA_IR + triglycerides – HDL-C.</p