Equivalence of weak formulations of the steady water waves equations

We prove the equivalence of three weak formulations of the steady water waves equations, namely: the velocity formulation, the stream function formulation and the Dubreil-Jacotin formulation, under weak Hölder regularity assumptions on their solutions.

Natural disaster accounting bias and its equivalence across genetic resource stocks

Two sources of bias arise in conventional loss predictions in the wake of natural disasters. One source of bias stems from neglect of accounting for animal genetic resource loss. A second source of bias stems from failure to identify, in addition to the direct effects of such loss, the indirect effects arising from implications impacting animal-human interactions. We argue that, in some contexts, the magnitude of bias imputed by neglecting animal genetic resource stocks is substantial. We show, in addition, and contrary to popular belief, that the biases attributable to losses in distinct genetic resource stocks are very likely to be the same. We derive the formal equivalence across the distinct resource stocks by deriving an envelope result in a model that forms the mainstay of enquiry in subsistence farming and we validate the theory, empirically, in a World-Society-for-the-Protection-of-Animals application

Strangely dual orbifold equivalence I

In this brief note we prove orbifold equivalence between two potentials described by strangely dual exceptional unimodular singularities of type K14 and Q10 in two different ways. The matrix factorizations proving the orbifold equivalence give rise to equations whose solutions are permuted by Galois groups which differ for different expressions of the same singularity.

C(0) and bi-Lipschitz K-equivalence of mappings

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. We give an algebraic criterion for bi-Lipschitz K-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings f, g : R(n) -> R(n), finitely determined with respect to K-equivalence are C(0)-K-equivalent if and only if they have the same degree in absolute value.

Equivalence between supersymmetric self-dual and Maxwell-Chern-Simons models coupled to a matter spinor superfield

We study the duality of the supersymmetric self-dual and Maxwell-Chern-Simons theories coupled to a fermionic matter superfield, using a master action. This approach evades the difficulties inherent to the quartic couplings that appear when matter is represented by a scalar superfield. The price is that the spinorial matter superfield represents a unusual supersymmetric multiplet, whose main physical properties we also discuss. (C) 2009 Elsevier B.V. All rights reserved.

Methods for Equivalence and Noninferiority Testing

Classical hypothesis testing focuses on testing whether treatments have differential effects on outcome. However, sometimes clinicians may be more interested in determining whether treatments are equivalent or whether one has noninferior outcomes. We review the hypotheses for these noninferiority and equivalence research questions, consider power and sample size issues, and discuss how to perform such a test for both binary and survival outcomes. The methods are illustrated on 2 recent studies in hematopoietic cell transplantation.

Comparison of treatment of incomplete abortion with misoprostol by physicians and midwives at district level in Uganda : a randomised controlled equivalence trial

BACKGROUND: Misoprostol is established for the treatment of incomplete abortion but has not been systematically assessed when provided by midwives at district level in a low-resource setting. We investigated the effectiveness and safety of midwives diagnosing and treating incomplete abortion with misoprostol, compared with physicians. METHODS: We did a multicentre randomised controlled equivalence trial at district level at six facilities in Uganda. Eligibility criteria were women with signs of incomplete abortion. We randomly allocated women with first-trimester incomplete abortion to clinical assessment and treatment with misoprostol either by a physician or a midwife. The randomisation (1:1) was done in blocks of 12 and was stratified for study site. Primary outcome was complete abortion not needing surgical intervention within 14-28 days after initial treatment. The study was not masked. Analysis of the primary outcome was done on the per-protocol population with a generalised linear-mixed effects model. The predefined equivalence range was -4% to 4%. The trial was registered at ClinicalTrials.gov, number NCT01844024. FINDINGS: From April 30, 2013, to July 21, 2014, 1108 women were assessed for eligibility. 1010 women were randomly assigned to each group (506 to midwife group and 504 to physician group). 955 women (472 in the midwife group and 483 in the physician group) were included in the per-protocol analysis. 452 (95·8%) of women in the midwife group had complete abortion and 467 (96·7%) in the physician group. The model-based risk difference for midwife versus physician group was -0·8% (95% CI -2·9 to 1·4), falling within the predefined equivalence range (-4% to 4%). The overall proportion of women with incomplete abortion was 3·8% (36/955), similarly distributed between the two groups (4·2% [20/472] in the midwife group, 3·3% [16/483] in the physician group). No serious adverse events were recorded. INTERPRETATION: Diagnosis and treatment of incomplete abortion with misoprostol by midwives is equally safe and effective as when provided by physicians, in a low-resource setting. Scaling up midwives' involvement in treatment of incomplete abortion with misoprostol at district level would increase access to safe post-abortion care. FUNDING: The Swedish Research Council, Karolinska Institutet, and Dalarna University.

Women's acceptability of misoprostol treatment for incomplete abortion by midwives and physicians : secondary outcome analysis from a randomized controlled equivalence trial at district level in Uganda

OBJECTIVE: This study aimed to assess women´s acceptability of diagnosis and treatment of incomplete abortion with misoprostol by midwives, compared with physicians. METHODS: This was an analysis of secondary outcomes from a multi-centre randomized controlled equivalence trial at district level in Uganda. Women with first trimester incomplete abortion were randomly allocated to clinical assessment and treatment with misoprostol by a physician or a midwife. The randomisation (1:1) was done in blocks of 12 and stratified for health care facility. Acceptability was measured in expectations and satisfaction at a follow up visit 14-28 days following treatment. Analysis of women's overall acceptability was done using a generalized linear mixed-effects model with an equivalence range of -4% to 4%. The study was not masked. The trial is registered at ClinicalTrials.org, NCT 01844024. RESULTS: From April 2013 to June 2014, 1108 women were assessed for eligibility of which 1010 were randomized (506 to midwife and 504 to physician). 953 women were successfully followed up and included in the acceptability analysis. 95% (904) of the participants found the treatment satisfactory and overall acceptability was found to be equivalent between the two study groups. Treatment failure, not feeling calm and safe following treatment, experiencing severe abdominal pain or heavy bleeding following treatment, were significantly associated with non-satisfaction. No serious adverse events were recorded. CONCLUSIONS: Treatment of incomplete abortion with misoprostol by midwives and physician was highly, and equally, acceptable to women. TRIAL REGISTRATION: ClinicalTrials.gov NCT01844024.

Non-equivalence of direct and indirect measures of unrealistic optimism

Individuals typically believe that they are less likely than the average person to experience negative events. Such “unrealistic optimism” (UO) has been assessed in two ways: directly (via a single question, requiring comparison of own risk to that of the average person) and indirectly (via separate questions about own risk and that of the average person). The study examined the equivalence of the direct and indirect measures of female students' UO for unwanted pregnancy. Participants (N = 120) answered questions about their own risk, that of the average female student, and their own risk relative to that of the average female student; responses and response times were recorded. There was only a moderate association between direct- and indirect-UO. Direct-UO was strongly associated with estimate of own risk, but only moderately associated with estimate of the average student's risk. Response times for the comparative risk and own risk questions did not differ, but participants took significantly longer to answer the question about average student's risk. The results suggest that the two measures of UO are not equivalent, but, rather, that individuals answering a comparative risk question focus mainly on their own risk, at the expense of that of the average person.