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)

Image_1_Fast and Accurate Approaches for Large-Scale, Automated Mapping of Food Diaries on Food Composition Tables.PDF

<p>Aim of Study: The use of weighed food diaries in nutritional studies provides a powerful method to quantify food and nutrient intakes. Yet, mapping these records onto food composition tables (FCTs) is a challenging, time-consuming and error-prone process. Experts make this effort manually and no automation has been previously proposed. Our study aimed to assess automated approaches to map food items onto FCTs.</p><p>Methods: We used food diaries (~170,000 records pertaining to 4,200 unique food items) from the DiOGenes randomized clinical trial. We attempted to map these items onto six FCTs available from the EuroFIR resource. Two approaches were tested: the first was based solely on food name similarity (fuzzy matching). The second used a machine learning approach (C5.0 classifier) combining both fuzzy matching and food energy. We tested mapping food items using their original names and also an English-translation. Top matching pairs were reviewed manually to derive performance metrics: precision (the percentage of correctly mapped items) and recall (percentage of mapped items).</p><p>Results: The simpler approach: fuzzy matching, provided very good performance. Under a relaxed threshold (score > 50%), this approach enabled to remap 99.49% of the items with a precision of 88.75%. With a slightly more stringent threshold (score > 63%), the precision could be significantly improved to 96.81% while keeping a recall rate > 95% (i.e., only 5% of the queried items would not be mapped). The machine learning approach did not lead to any improvements compared to the fuzzy matching. However, it could increase substantially the recall rate for food items without any clear equivalent in the FCTs (+7 and +20% when mapping items using their original or English-translated names). Our approaches have been implemented as R packages and are freely available from GitHub.</p><p>Conclusion: This study is the first to provide automated approaches for large-scale food item mapping onto FCTs. We demonstrate that both high precision and recall can be achieved. Our solutions can be used with any FCT and do not require any programming background. These methodologies and findings are useful to any small or large nutritional study (observational as well as interventional).</p

Analysis of difference in weight loss between placebo and topiramate pooled (96 and 192 mg/day) from baseline to week 60 using different methods.

<p>Analysis of difference in weight loss between placebo and topiramate pooled (96 and 192 mg/day) from baseline to week 60 using different methods.</p

Analysis of weight loss over time in the placebo group using different imputation methods.

<p>Analysis of weight loss over time in the placebo group using different imputation methods.</p

Analysis of weight loss over time in topiramate pooled (96 or 192 mg/day) group using different imputation methods.

<p>Analysis of weight loss over time in topiramate pooled (96 or 192 mg/day) group using different imputation methods.</p

Percentage weight change from enrolment (- 8 week) to end of treatment (week 60).

<p>SE: standard error.</p><p>For each difference (topiramate - placebo), P<0.001 (t-test).</p><p>Percentage weight change from enrolment (- 8 week) to end of treatment (week 60).</p

Mean weight of participants attending or missing the next visit.

<p>Some patients return after a missed visit. Therefore no change in number of patients at week 28 and 32.</p

Normalized intensity for metabolites reflected by TFA intake.

<p>PC(40:7) (A) and SM(36:3) (B) at w0, w16 and w28. The values are the mean of samples in CTR and TFA groups. Each variable is normalized with the mean of the 9 recordings (at week 0, 16 and 28 with three OGTT time point recordings) for each subject.</p

Data structure and arrangement scheme.

<p>Baseline subtraction (A) concatenation of time points (applied on LC-MS and NMR profiles), and selection of lipid classes (B) (applied on LC/MS data).</p

PC1 vs. PC2 scores plot of LC-MS based lipid profiles.

<p>The LC-MS profiles with concatenated time points including only LPCs, PCs and SMs as variables. Filled circles: TFA, empty circles: CTR.</p