A variational principle for cyclic polygons with prescribed edge lengths

We provide a new proof of the elementary geometric theorem on the existence and uniqueness of cyclic polygons with prescribed side lengths. The proof is based on a variational principle involving the central angles of the polygon as variables. The uniqueness follows from the concavity of the target function. The existence proof relies on a fundamental inequality of information theory. We also provide proofs for the corresponding theorems of spherical and hyperbolic geometry (and, as a byproduct, in $1+1$ spacetime). The spherical theorem is reduced to the euclidean one. The proof of the hyperbolic theorem treats three cases separately: Only the case of polygons inscribed in compact circles can be reduced to the euclidean theorem. For the other two cases, polygons inscribed in horocycles and hypercycles, we provide separate arguments. The hypercycle case also proves the theorem for "cyclic" polygons in $1+1$ spacetime.Comment: 18 pages, 6 figures. v2: typos corrected, final versio

Decontextualizing contextual inversion

Contextual inversion, introduced as an analytical tool by David Lewin, is a concept of wide reach and value in music theory and analysis, at the root of neo-Riemannian theory as well as serial theory, and useful for a range of analytical applications. A shortcoming of contextual inversion as it is currently understood, however, is, as implied by the name, that the transformation has to be defined anew for each application. This is potentially a virtue, requiring the analyst to invest the transformational system with meaning in order to construct it in the first place. However, there are certainly instances where new transformational systems are continually redefined for essentially the same purposes. This paper explores some of the most common theoretical bases for contextual inversion groups and considers possible definitions of inversion operators that can apply across set class types, effectively decontextualizing contextual inversions.Accepted manuscrip

Groupoids and Wreath Products of Musical Transformations: a Categorical Approach from poly-Klumpenhouwer Networks

Transformational music theory, pioneered by the work of Lewin, shifts the music-theoretical and analytical focus from the "object-oriented" musical content to an operational musical process, in which transformations between musical elements are emphasized. In the original framework of Lewin, the set of transformations often form a group, with a corresponding group action on a given set of musical objects. Klumpenhouwer networks have been introduced based on this framework: they are informally labelled graphs, the labels of the vertices being pitch classes, and the labels of the arrows being transformations that maps the corresponding pitch classes. Klumpenhouwer networks have been recently formalized and generalized in a categorical setting, called poly-Klumpenhouwer networks. This work proposes a new groupoid-based approach to transformational music theory, in which transformations of PK-nets are considered rather than ordinary sets of musical objects. We show how groupoids of musical transformations can be constructed, and an application of their use in post-tonal music analysis with Berg's Four pieces for clarinet and piano, Op. 5/2. In a second part, we show how groupoids are linked to wreath products (which feature prominently in transformational music analysis) through the notion of groupoid bisectionsComment: 16 pages, 9 figures; comments welcom

Bias in trials comparing paired continuous tests can cause researchers to choose the wrong screening modality

<p>Abstract</p> <p>Background</p> <p>To compare the diagnostic accuracy of two continuous screening tests, a common approach is to test the difference between the areas under the receiver operating characteristic (ROC) curves. After study participants are screened with both screening tests, the disease status is determined as accurately as possible, either by an invasive, sensitive and specific secondary test, or by a less invasive, but less sensitive approach. For most participants, disease status is approximated through the less sensitive approach. The invasive test must be limited to the fraction of the participants whose results on either or both screening tests exceed a threshold of suspicion, or who develop signs and symptoms of the disease after the initial screening tests.</p> <p>The limitations of this study design lead to a bias in the ROC curves we call <it>paired screening trial bias</it>. This bias reflects the synergistic effects of inappropriate reference standard bias, differential verification bias, and partial verification bias. The absence of a gold reference standard leads to inappropriate reference standard bias. When different reference standards are used to ascertain disease status, it creates differential verification bias. When only suspicious screening test scores trigger a sensitive and specific secondary test, the result is a form of partial verification bias.</p> <p>Methods</p> <p>For paired screening tests with bivariate normally distributed scores, we give formulae and programs to quantify the effect of <it>paired screening trial bias </it>on a paired comparison of area under the curves. We fix the prevalence of disease, and the chance a diseased subject manifests signs and symptoms. We derive the formulas for true sensitivity and specificity, and those for the sensitivity and specificity observed by the study investigator.</p> <p>Results</p> <p>The observed area under the ROC curves is quite different from the true area under the ROC curves. The typical direction of the bias is a strong inflation in sensitivity, paired with a concomitant slight deflation of specificity.</p> <p>Conclusion</p> <p>In paired trials of screening tests, when area under the ROC curve is used as the metric, bias may lead researchers to make the wrong decision as to which screening test is better.</p

Correlates of comorbid anxiety and externalizing disorders in childhood obsessive compulsive disorder

The present study examines the influence of diagnostic comorbidity on the demographic, psychiatric, and functional status of youth with a primary diagnosis of obsessive compulsive disorder (OCD). Two hundred and fifteen children (ages 5–17) referred to a university-based OCD specialty clinic were compared based on DSM-IV diagnostic profile: OCD without comorbid anxiety or externalizing disorder, OCD plus anxiety disorder, and OCD plus externalizing disorder. No age or gender differences were found across groups. Higher OCD severity was found for the OCD + ANX group, while the OCD + EXT group reported greater functional impairment than the other two groups. Lower family cohesion was reported by the OCD + EXT group compared to the OCD group and the OCD + ANX group reported higher family conflict compared to the OCD + EXT group. The OCD + ANX group had significantly lower rates of tic disorders while rates of depressive disorders did not differ among the three groups. The presence of comorbid anxiety and externalizing psychopathology are associated with greater symptom severity and functional and family impairment and underscores the importance of a better understanding of the relationship of OCD characteristics and associated disorders. Results and clinical implications are further discussed

A mobile telehealth intervention for adults with insulin-requiring diabetes: early results of a mixed-methods randomized controlled trial

BACKGROUND: The role of technology in health care delivery has grown rapidly in the last decade. The potential of mobile telehealth (MTH) to support patient self-management is a key area of research. Providing patients with technological tools that allow for the recording and transmission of health parameters to health care professionals (HCPs) may promote behavior changes that result in improved health outcomes. Although for some conditions the evidence of the effectiveness of MTH is clear, to date the findings on the effects of MTH on diabetes management remain inconsistent. OBJECTIVE: This study aims to evaluate an MTH intervention among insulin-requiring adults with diabetes to establish whether supplementing standard care with MTH results in improved health outcomes-glycated hemoglobin (HbA1c), blood pressure (BP), health-related quality of life (HRQoL), diabetes self-management behaviors, diabetes health care utilization, and diabetes self-efficacy and illness beliefs. An additional objective was to explore the acceptability of MTH and patients' perceptions of, and experience, using it. METHODS: A mixed-method design consisting of a 9-month, two-arm, parallel randomized controlled trial (RCT) was used in combination with exit qualitative interviews. Quantitative data was collected at baseline, 3 months, and 9 months. Additional intervention fidelity data, such as participants' MTH transmissions and contacts with the MTH nurse during the study, were also recorded. RESULTS: Data collection for both the quantitative and qualitative components of this study has ended and data analysis is ongoing. A total of 86 participants were enrolled into the study. Out of 86 participants, 45 (52%) were randomized to the intervention group and 36 (42%) to the control group. Preliminary data on MTH training sessions and MTH usage by intervention participants are presented in this paper. We expect to publish complete study results in 2015. CONCLUSIONS: The range of data collected in this study will allow for a comprehensive evaluation of processes and outcomes. The early results presented suggest that MTH usage decreases over time and that MTH participants would benefit from attending more than one training session. TRIAL REGISTRATION: ClinicalTrials.gov NCT00922376; http://clinicaltrials.gov/ct2/show/NCT00922376 (Archived by WebCite at http://www.webcitation.org/6Vu4nhLI6)

Evidence-Based Assessment of Child Obsessive Compulsive Disorder: Recommendations for Clinical Practice and Treatment Research

Obsessive-compulsive disorder (OCD) presents heterogeneously and can be difficult to assess in youth. This review focuses on research-supported assessment approaches for OCD in childhood. Content areas include pre-visit screening, diagnostic establishment, differential diagnosis, assessment of comorbid psychiatric conditions, tracking symptom severity, determining psychosocial functioning, and evaluating clinical improvement. Throughout this review, similarities and differences between assessment approaches geared towards clinical and research settings are discussed

Pharmacokinetics of Teriparatide (rhPTH[1–34]) and Calcium Pharmacodynamics in Postmenopausal Women with Osteoporosis

Teriparatide (rhPTH[1–34]) affects calcium metabolism in a pattern consistent with the known actions of endogenous parathyroid hormone (PTH). This report describes the pharmacokinetics and resulting serum calcium response to teriparatide in postmenopausal women with osteoporosis. Pharmacokinetic samples for this analysis were obtained from 360 women who participated in the Fracture Prevention Trial. Postmenopausal women with osteoporosis received daily subcutaneous injections of either teriparatide 20 μg (4.86 μmol) or placebo, median 21 months’ treatment. Serum teriparatide and calcium concentrations were measured throughout the study. An indirect-response model was developed to describe the pharmacokinetic–pharmacodynamic relationship between teriparatide concentrations and serum calcium response. The pharmacokinetics of teriparatide were characterized by rapid absorption (maximum concentration achieved within 30 min) and rapid elimination (half-life of 1 h), resulting in a total duration of exposure to the peptide of approximately 4 h. Teriparatide transiently increased serum calcium, with the maximum effect observed at approximately 4.25 h (median increase 0.4 mg/dl [0.1 mmol/l]). Calcium concentrations returned to predose levels by 16–24 h after each dose. Persistent hypercalcemia was not observed; one teriparatide 20 μg-treated patient had a predose serum calcium value above the normal range but <11.0 mg/dl (2.75 mmol/l). Following once-daily subcutaneous administration, teriparatide produces a modest but transient increase in serum calcium, consistent with the known effects of endogenous PTH on mineral metabolism. The excursion in serum calcium is brief, due to the short length of time that teriparatide concentrations are elevated