On Robin's criterion for the Riemann Hypothesis

Robin's criterion states that the Riemann Hypothesis (RH) is true if and only if Robin's inequality sum_{d|n}d=5041, where gamma denotes the Euler(-Mascheroni) constant. We show by elementary methods that if n>=37 does not satisfy Robin's criterion it must be even and is neither squarefree nor squarefull. Using a bound of Rosser and Schoenfeld we show, moreover, that n must be divisible by a fifth power >1. As a consequence we infer that RH holds true if and only if every natural number divisible by a fifth power >1 satisfies Robin's inequality.Comment: 15 pages. Corrected version. In the first version in Theorem 5 (main result) it was falsely asserted that n must be superabundant, invalidating the proof. An alternative proof is provided in this version, some typos have been corrected, and the presentation has been improve

Improved FPT algorithms for weighted independent set in bull-free graphs

Very recently, Thomass\'e, Trotignon and Vuskovic [WG 2014] have given an FPT algorithm for Weighted Independent Set in bull-free graphs parameterized by the weight of the solution, running in time $2^{O(k^5)} \cdot n^9$. In this article we improve this running time to $2^{O(k^2)} \cdot n^7$. As a byproduct, we also improve the previous Turing-kernel for this problem from $O(k^5)$ to $O(k^2)$. Furthermore, for the subclass of bull-free graphs without holes of length at most $2p-1$ for $p \geq 3$, we speed up the running time to $2^{O(k \cdot k^{\frac{1}{p-1}})} \cdot n^7$. As $p$ grows, this running time is asymptotically tight in terms of $k$, since we prove that for each integer $p \geq 3$, Weighted Independent Set cannot be solved in time $2^{o(k)} \cdot n^{O(1)}$ in the class of $\{bull,C_4,\ldots,C_{2p-1}\}$-free graphs unless the ETH fails.Comment: 15 page

International practice of corticosteroid replacement therapy in congenital adrenal hyperplasia - data from the I-CAH registry.

OBJECTIVE: Despite published guidelines no unified approach to hormone replacement in congenital adrenal hyperplasia (CAH) exists. We aimed to explore geographical and temporal variations in the treatment with glucocorticoids and mineralocorticoids in CAH. DESIGN: This retrospective multi-center study, including 31 centers (16 countries), analyzed data from the International-CAH Registry. METHODS: Data was collected from 461 patients aged 0-18 years with classic 21-hydroxylase deficiency (54.9% females) under follow-up between 1982 - 2018. Type, dose and timing of glucocorticoid and mineralocorticoid replacement was analyzed from 4174 patient visits. RESULTS: The most frequently used glucocorticoid was hydrocortisone (87.6%). Overall, there were significant differences between age groups with regards to daily hydrocortisone-equivalent dose for body surface, with the lowest dose (median with interquartile range) of 12.0 (10.0 - 14.5) mg/ m2/ day at age 1 - 8 years and the highest dose of 14.0 (11.6 - 17.4) mg/ m2/ day at age 12-18 years. Glucocorticoid doses decreased after 2010 in patients 0-8 years (p<0.001) and remained unchanged in patients aged 8-18 years. Fludrocortisone was used in 92% of patients, with relative doses decreasing with age. A wide variation was observed among countries with regards to all aspects of steroid hormone replacement. CONCLUSIONS: Data from the I-CAH Registry suggests international variations in hormone replacement therapy, with a tendency to treatment with high doses in children

Improved functionalization of oleic acid-coated iron oxide nanoparticles for biomedical applications

Superparamagnetic iron oxide nanoparticles can providemultiple benefits for biomedical applications in aqueous environments such asmagnetic separation or magnetic resonance imaging. To increase the colloidal stability and allow subsequent reactions, the introduction of hydrophilic functional groups onto the particles’ surface is essential. During this process, the original coating is exchanged by preferably covalently bonded ligands such as trialkoxysilanes. The duration of the silane exchange reaction, which commonly takes more than 24 h, is an important drawback for this approach. In this paper, we present a novel method, which introduces ultrasonication as an energy source to dramatically accelerate this process, resulting in high-quality waterdispersible nanoparticles around 10 nmin size. To prove the generic character, different functional groups were introduced on the surface including polyethylene glycol chains, carboxylic acid, amine, and thiol groups. Their colloidal stability in various aqueous buffer solutions as well as human plasma and serum was investigated to allow implementation in biomedical and sensing applications.status: publishe

Gonadectomy in conditions affecting sex development: a registry-based cohort study

Objectives To determine trends in clinical practice for individuals with DSD requiring gonadectomy. Design Retrospective cohort study. Methods Information regarding age at gonadectomy according to diagnosis; reported sex; time of presentation to specialist centre; and location of centre from cases reported to the International DSD Registry and who were over 16 years old in January 2019. Results Data regarding gonadectomy were available in 668 (88%) individuals from 44 centres. Of these, 248 (37%) (median age (range) 24 (17, 75) years) were male and 420 (63%) (median age (range) 26 (16, 86) years) were female. Gonadectomy was reported from 36 centres in 351/668 cases (53%). Females were more likely to undergo gonadectomy (n = 311, P < 0.0001). The indication for gonadectomy was reported in 268 (76%). The most common indication was mitigation of tumour risk in 172 (64%). Variations in the practice of gonadectomy were observed; of the 351 cases from 36 centres, 17 (5%) at 9 centres had undergone gonadectomy before their first presentation to the specialist centre. Median age at gonadectomy of cases from high-income countries and low-/middle-income countries (LMIC) was 13.0 years (0.1, 68) years and 16.5 years (1, 28), respectively (P < 0.0001) with the likelihood of long-term retention of gonads being higher in LMIC countries. Conclusions The likelihood of gonadectomy depends on the underlying diagnosis, sex of rearing and the geographical setting. Clinical benchmarks, which can be studied across all forms of DSD will allow a better understanding of the variation in the practice of gonadectomy

Boosting human force: A robotic enhancement of a human operator's force

For a human operator, lifting and carrying a load can be a hazardous task with significant health-related risks. The collaboration between the human operator and a robotic device can provide an effective solution. This study proposes a control design for the robot such that it merely amplifies the force the human operator applies to the load. The algorithm is of a cyclic nature, where each cycle is subdivided into two stages. The first phase is the estimation of the human force, since the only connection between the robot and the human is via the load. In the second phase, the scaled force is applied to the load. The proposed approach is illustrated by means of simulation results for a two-link robot manipulator. © 2008 IEEE

Bilateral teleoperation for force sensorless 1-dof robots

It is well known that for bilateral teleoperation, force feedback information is needed. In this paper, we propose a control approach for bilateral teleoperation with uncertainties in the model of the slave robot and which does not use force sensors for haptic feedback. The controller design is based on a cyclic switching algorithm. In the first phase of the cyclic algorithm, we estimate the environmental force and in the second phase a tracking controller ensures that the position of the slave robot is tracking the position of the master robot. A stability analysis of the overall closed-loop system is presented and the approach is illustrated by means of an example

Robust disturbance estimation for human-robotic comanipulation

External forces affect the dynamics of load-carrying robot devices. The knowledge of such disturbances is generally needed for control purposes. However, direct disturbance measurement using force sensors is not always possible. This paper introduces a force estimator for force-sensor-less robotic manipulators. The algorithm is based on the knowledge of the dynamics of the robotic device, whereas mass of the load is typically unknown. Using this algorithm, low-frequency external forces can be estimated robustly even for quasi-statically time-varying and uncertain loads. Experiments validate the proposed strategy in practice. Moreover, the applicability of the estimation algorithm is further illustrated by using it in a human–robot comanipulation setup in which the robot is providing additional coordinated forcing to alleviate human effort needed to manipulate the robot