A reinterpretation of set differential equations as differential equations in a Banach space

Set differential equations are usually formulated in terms of the Hukuhara differential, which implies heavy restrictions for the nature of a solution. We propose to reformulate set differential equations as ordinary differential equations in a Banach space by identifying the convex and compact subsets of $\R^d$ with their support functions. Using this representation, we demonstrate how existence and uniqueness results can be applied to set differential equations. We provide a simple example, which can be treated in support function representation, but not in the Hukuhara setting

Individual differences in children’s early strategy behavior in arithmetic tasks

As demonstrated by the Overlapping Waves Model (Siegler, 1996), children’s strategy use in arithmetic tasks is variable, adaptive, and changes gradually with age and experience. In this study, first grade elementary school children (n = 73), who scored high, middle, or low in a standardized scholastic mathematic achievement test, were confronted with different arithmetic tasks (simple addition, e.g., 3 + 2, simple subtraction, e.g., 7 – 2, and more advanced addition, e.g., 7 + 9) to evoke different calculation strategies. Video analysis and children’s self-report were used to identify individual strategy behavior. In accordance with the Overlapping Waves Model, children in all achievement groups showed variable and multiple strategy usage and adapted their behavior to the tasks of the different categories. We demonstrated that not only low achievers differed from normal achievers but also that high achievers exhibited a unique pattern of strategy behavior in early mathematics

Analyse von notfallmedizinischen Routinedaten aus Präklinik und Klinik

Background: In the 2018 advisory opinion concerning the realignment of healthcare, it is advocated that in order to relieve pressure on emergency departments (ED) prehospital medical emergency services should be given the option to directly transport suitable patients to doctors' offices. Objectives: To determine the prevalence of patients treated by prehospital emergency services that have the potential to be directly allocated to a primary care provider. Materials and methods: Preclinical and clinical data of adult patients who in a 2-month period were transported to the ED of a university hospital by an ambulance were evaluated. To determine a safe and meaningful transport directly to a doctor's office, a stepwise assessment was carried out: patients were categorized on the basis of the prehospital assessment of urgency as "urgent" (contact to doctor necessary within a maximum time of 30 min) and "less urgent" (contact to doctor not necessary within 30 min, maximum 120 min). "Less urgent" patients were further divided and those treated as outpatients were identified. This group was further restricted to cases whose administrative reception in the ED was documented Monday-Friday between 8 am and 7 pm. In addition, these cases were further differentiated with regard to medical content and compared with the triage results in the ED (Manchester Triage, MTS). Results: In all, 1260 patients were brought to the ED by ambulance within the study period (total number of patients treated in this time period n = 11,506); 894 cases had a documented prehospital level of urgency and could therefore be included. Of these n = 477 (53.4%) were categorized as "less urgent"; 317 (66.5%) of these "less urgent" cases were treated as outpatients in the ED, and n = 114 (23.9%) in a time frame potentially suitable for direct transport to doctors' offices, which is 1% of all patients treated in the ED in the time period examined. However, 70 of the cases suitable for doctors' office (63.6% of n = 110 with documented MTS) were rated more urgent in the ED. With regards to prehospital complaints and documented diagnosis we assume employment of a relevant amount of resources in the treatment of these cases. Conclusions: EDs could be relieved from every tenth patient brought in by prehospital emergency services (1% of all patients treated) during normal offices hours by direct allocation to doctors' offices. Regarding patient's safety this process however has to be seen critically as > 60% of these cases were potentially undertriaged. Necessary resources for diagnostics and treatment have to be available in the doctors' offices and known to prehospital emergency services. Primary assignment of patients to doctors' offices by prehospital emergency can only relieve urban EDs to a negligible extent, is potentially dangerous and linked to a tremendous logistic effort

Evaluation of statistical approaches for association testing in noisy drug screening data

Background Identifying associations among biological variables is a major challenge in modern quantitative biological research, particularly given the systemic and statistical noise endemic to biological systems. Drug sensitivity data has proven to be a particularly challenging field for identifying associations to inform patient treatment. Results To address this, we introduce two semi-parametric variations on the commonly used concordance index: the robust concordance index and the kernelized concordance index (rCI, kCI), which incorporate measurements about the noise distribution from the data. We demonstrate that common statistical tests applied to the concordance index and its variations fail to control for false positives, and introduce efficient implementations to compute p-values using adaptive permutation testing. We then evaluate the statistical power of these coefficients under simulation and compare with Pearson and Spearman correlation coefficients. Finally, we evaluate the various statistics in matching drugs across pharmacogenomic datasets. Conclusions We observe that the rCI and kCI are better powered than the concordance index in simulation and show some improvement on real data. Surprisingly, we observe that the Pearson correlation was the most robust to measurement noise among the different metrics.Peer reviewe

Job requirements compared to medical school education: differences between graduates from problem-based learning and conventional curricula

Background: Problem-based Learning (PBL) has been suggested as a key educational method of knowledge acquisition to improve medical education. We sought to evaluate the differences in medical school education between graduates from PBL-based and conventional curricula and to what extent these curricula fit job requirements. Methods: Graduates from all German medical schools who graduated between 1996 and 2002 were eligible for this study. Graduates self-assessed nine competencies as required at their day-to-day work and as taught in medical school on a 6-point Likert scale. Results were compared between graduates from a PBL-based curriculum (University Witten/Herdecke) and conventional curricula. Results: Three schools were excluded because of low response rates. Baseline demographics between graduates of the PBL-based curriculum (n = 101, 49% female) and the conventional curricula (n = 4720, 49% female) were similar. No major differences were observed regarding job requirements with priorities for "Independent learning/working" and "Practical medical skills". All competencies were rated to be better taught in PBL-based curriculum compared to the conventional curricula (all p < 0.001), except for "Medical knowledge" and "Research competence". Comparing competencies required at work and taught in medical school, PBL was associated with benefits in "Interdisciplinary thinking" (Δ + 0.88), "Independent learning/working" (Δ + 0.57), "Psycho-social competence" (Δ + 0.56), "Teamwork" (Δ + 0.39) and "Problem-solving skills" (Δ + 0.36), whereas "Research competence" (Δ - 1.23) and "Business competence" (Δ - 1.44) in the PBL-based curriculum needed improvement. Conclusion: Among medical graduates in Germany, PBL demonstrated benefits with regard to competencies which were highly required in the job of physicians. Research and business competence deserve closer attention in future curricular development

Optimality regions and fluctuations for Bernoulli last passage models

We study the sequence alignment problem and its independent version,the discrete Hammersley process with an exploration penalty. We obtain rigorous upper bounds for the number of optimality regions in both models near the soft edge.At zero penalty the independent model becomes an exactly solvable model and we identify cases for which the law of the last passage time converges to a Tracy-Widom law

Combining high sensitivity cardiac troponin I and cardiac troponin T in the early diagnosis of acute myocardial infarction

-Combining two signals of cardiomyocyte injury, cardiac troponin I (cTnI) and T (cTnT), might overcome some individual pathophysiological and analytical limitations and thereby increase diagnostic accuracy for acute myocardial infarction (AMI) with a single blood draw. We aimed to evaluate the diagnostic performance of combinations of high sensitivity (hs) cTnI and hs-cTnT for the early diagnosis of AMI. -The diagnostic performance of combining hs-cTnI (Architect, Abbott) and hs-cTnT (Elecsys, Roche) concentrations (sum, product, ratio and a combination algorithm) obtained at the time of presentation was evaluated in a large multicenter diagnostic study of patients with suspected AMI. The optimal rule out and rule in thresholds were externally validated in a second large multicenter diagnostic study. The proportion of patients eligible for early rule out was compared with the ESC 0/1 and 0/3 hour algorithms. -Combining hs-cTnI and hs-cTnT concentrations did not consistently increase overall diagnostic accuracy as compared with the individual isoforms. However, the combination improved the proportion of patients meeting criteria for very early rule-out. With the ESC 2015 guideline recommended algorithms and cut-offs, the proportion meeting rule out criteria after the baseline blood sampling was limited (6-24%) and assay dependent. Application of optimized cut-off values using the sum (9 ng/L) and product (18 ng2/L2) of hs-cTnI and hs-cTnT concentrations led to an increase in the proportion ruled-out after a single blood draw to 34-41% in the original (sum: negative predictive value (NPV) 100% (95%CI: 99.5-100%); product: NPV 100% (95%CI: 99.5-100%) and in the validation cohort (sum: NPV 99.6% (95%CI: 99.0-99.9%); product: NPV 99.4% (95%CI: 98.8-99.8%). The use of a combination algorithm (hs-cTn