On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automata in two bases that do not share the same set of prime factors are exactly those that are definable in the first order additive theory of real and integer numbers. This result extends Cobham's theorem, which characterizes the sets of integer numbers that are recognizable by finite automata in multiple bases. In this article, we first generalize this result to multiplicatively independent bases, which brings it closer to the original statement of Cobham's theorem. Then, we study the sets of reals recognizable by Muller automata in two bases. We show with a counterexample that, in this setting, Cobham's theorem does not generalize to multiplicatively independent bases. Finally, we prove that the sets of reals that are recognizable by Muller automata in two bases that do not share the same set of prime factors are exactly those definable in the first order additive theory of real and integer numbers. These sets are thus also recognizable by weak deterministic automata. This result leads to a precise characterization of the sets of real numbers that are recognizable in multiple bases, and provides a theoretical justification to the use of weak automata as symbolic representations of sets.Comment: 17 page

Assessment of the response profile to hyaluronic acid plus sorbitol injection in patients with knee osteoarthritis: post hoc analysis of a 6-month randomized controlled trial

peer reviewe

Is the rate of responders to hyaluronic acid injection for patients with knee osteoarthritis stable over time? Post hoc analyses of a 6-month follow-up study

peer reviewe

Enumeration and Decidable Properties of Automatic Sequences

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

Assessment of health claims in the field of bone: a view of the Group for the Respect of Ethics and Excellence in Science (GREES)

Health claims for food products in Europe are permitted if the nutrient has been shown to have a beneficial nutritional or physiological effect. This paper defines health claims related to bone health and provides guidelines for the design and the methodology of clinical studies to support claims

Assessment of the performance of the SarQoL questionnaire in screening for sarcopenia in older people

Background: Because of its low prevalence and the need for physical tests to establish a diagnosis, recruiting sarcopenic people for clinical studies can be a resource-intensive process. Aims: We investigated whether the SarQoL®, a 55-item questionnaire designed to measure quality of life in sarcopenia, could be used to identify older people with a high likelihood of being sarcopenic, and to compare its performance to the SARC-F tool. Methods: We performed a secondary analysis of data from older, community-dwelling participants of the SarcoPhAge study, evaluated for sarcopenia according to the EWGSOP2 criteria, and who completed the SarQoL® and SARC-F questionnaires. We determined the optimal threshold to distinguish between sarcopenic and non-sarcopenic people with the Youden index. Screening performance was evaluated with the area under the curve (AUC) and by calculating sensitivity and specificity. Results: The analysis of 309 participants provided an optimal threshold value of ≤ 52.4 points for identifying people with sarcopenia with the SarQoL® questionnaire, which resulted in a sensitivity of 64.7% (41.1–84.2%), a specificity of 80.5% (75.7–84.7%) and an AUC of 0.771 (0.652–0.889). Compared to the SARC-F, the SarQoL® has greater sensitivity (64.7% vs 52.39%), but slightly lower specificity (80.5% vs. 86.6%). Discussion: The SarQoL® questionnaire showed acceptable screening accuracy, on par with the SARC-F. The optimal threshold of ≤ 52.4 points should be confirmed in other cohorts of older people. Conclusions: This exploratory study showed that the SarQoL® could potentially be applied in a screening strategy, with the added benefit of providing a measure of QoL at the same time

The role of diet and exercise and of glucosamine sulfate in the prevention of knee osteoarthritis: Further results from the PRevention of knee Osteoarthritis in Overweight Females (PROOF) study

Background and objectives: The PRevention of knee Osteoarthritis in Overweight Females (PROOF) study (ISRCTN 42823086) described a trend for a decrease in the incidence of knee osteoarthritis (OA) by a tailored diet and exercise program (DEP) or by oral glucosamine sulfate in women at risk for the disease, using a composite clinical and/or radiological outcome. The aim of this updated post-hoc analysis was to re-assess the results according to more precise techniques and take advantage of the 2×2 factorial design. Methods: A total of 407 overweight (BMI ≥ 27 kg/m2) women of 50-60 years of age with no diagnosis of knee OA were randomized to: (1) no DEP + placebo (Control, N = 102), (2) DEP + placebo (DEP, N = 101), (3) glucosamine sulfate + no DEP (GS, N = 102), and (4) DEP + glucosamine sulfate (DEP + GS, N =102) and followed for 2.5 years, with standardized postero-anterior, semiflexed (MTP) view knee radiographs at baseline and end of the study. DEP consisted of a tailored low fat and/or low caloric diet and easy to implement physical activities. Glucosamine was given as oral crystalline glucosamine sulfate 1500 mg once daily, double-blinded vs. placebo. Incident knee OA was defined as radiographic progression of ≥1 mm minimum joint space narrowing (mJSN) in the medial tibiofemoral compartment, as previously assessed by the visual (manual) technique and by a new semi-automated method. Logistic regression analysis was used to calculate the odds ratio for the effect of the interventions. Results: After 2.5 years, 11.8% of control subjects developed knee OA. This incidence was decreased with glucosamine sulfate, either alone or in combination with the DEP, but not by the DEP alone. Since there was no statistical interaction between treatments, the 2×2 factorial design allowed analysis of patients receiving glucosamine sulfate (= 204) vs. those not receiving it (= 203), similarly for those on the DEP (= 203) or not (= 204). Glucosamine sulfate significantly decreased the risk of developing knee OA: odds ratio (OR) = 0.41 (95% CI: 0.20-0.85, P = 0.02) by the manual JSN assessment method and OR = 0.42 (95% CI: 0.20-0.92, P = 0.03) by the semi-automated technique. Conversely, there was no decrease in risk with the DEP. Conclusions: Glucosamine sulfate decreased the risk of developing radiographic knee OA over 2.5 years in overweight, middle-aged women at risk, as determined by medial mJSN progression. Conversely a tailored diet and exercise program exerted no preventive effect, possibly because of the lower than expected effect on weight loss

Household Preferences to Reduce Their Greenhouse Gas Footprint: A Comparative Study from Four European Cities

This paper investigates households’ preferences to reduce their carbon footprint (CF) measured in carbon dioxide equivalents (CO₂e). It assumes that a substantial CF reduction of households is essential to reach the 1.5 °C goal under the Paris Agreement. Data was collected in four mid-size cities in France, Germany, Norway, and Sweden. Quantitative data was obtained from 308 households using a CF calculator based on a questionnaire, and a simulation game. The latter investigated households’ preferences when being confronted with the objective to reduce their CF by 50 percent by 2030 in a voluntary and forced scenario. Our results show that the greater the CO₂e-reduction potential of a mitigation action, the less willing a household was to implement that action. Households preferred actions with moderate lifestyle changes foremost in the food sector. Voluntarily, households reached a 25% footprint reduction by 2030. To reach a substantial reduction of 50 percent, households needed to choose actions that meant considerable lifestyle changes, mainly related to mobility. Given our results, the 1.5 °C goal is unlikely to be realizable currently, unless households receive major policy support. Lastly, the strikingly similar preferences of households in the four European cities investigated seem to justify strong EU and international policies