167 research outputs found

    Spectrum of a Rudin-Shapiro-like sequence

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    We show that a recently proposed Rudin-Shapiro-like sequence, with balanced weights, has purely singular continuous diffraction spectrum, in contrast to the well-known Rudin-Shapiro sequence whose diffraction is absolutely continuous. This answers a question that had been raised about this new sequence

    Substitution-based structures with absolutely continuous spectrum

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    By generalising Rudin’s construction of an aperiodic sequence, we derive new substitution-based structures which have a purely absolutely continuous diffraction measure and a mixed dynamical spectrum, with absolutely continuous and pure point parts. We discuss several examples, including a construction based on Fourier matrices which yields constant-length substitutions for any length

    Bootstrapping multiple systems estimates to account for model selection

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    Multiple systems estimation is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. A typical modelling approach is to fit a Poisson loglinear model to the numbers of cases observed in each possible combination of the lists. It is necessary to decide which interaction parameters to include in the model, and information criterion approaches are often used for model selection. Difficulties in the context of multiple systems estimation may arise due to sparse or nil counts based on the intersection of lists, and care must be taken when information criterion approaches are used for model selection due to issues relating to the existence of estimates and identifiability of the model. Confidence intervals are often reported conditional on the model selected, providing an over-optimistic impression of the accuracy of the estimation. A bootstrap approach is a natural way to account for the model selection procedure. However, because the model selection step has to be carried out for every bootstrap replication, there may be a high or even prohibitive computational burden. We explore the merit of modifying the model selection procedure in the bootstrap to look only among a subset of models, chosen on the basis of their information criterion score on the original data. This provides large computational gains with little apparent effect on inference. Another model selection approach considered and investigated is a downhill search approach among models, possibly with multiple starting points.Comment: 21 pages, 5 figures, 6 table

    Multiple Systems Estimation for Sparse Capture Data: Inferential Challenges When There Are Nonoverlapping Lists

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    © 2020 American Statistical Association. Multiple systems estimation strategies have recently been applied to quantify hard-to-reach populations, particularly when estimating the number of victims of human trafficking and modern slavery. In such contexts, it is not uncommon to see sparse or even no overlap between some of the lists on which the estimates are based. These create difficulties in model fitting and selection, and we develop inference procedures to address these challenges. The approach is based on Poisson log-linear regression modeling. Issues investigated in detail include taking proper account of data sparsity in the estimation procedure, as well as the existence and identifiability of maximum likelihood estimates. A stepwise method for choosing the most suitable parameters is developed, together with a bootstrap approach to finding confidence intervals for the total population size. We apply the strategy to two empirical datasets of trafficking in US regions, and find that the approach results in stable, reasonable estimates. An accompanying R software implementation has been made publicly available. Supplementary materials for this article are available online

    Digital PCR methods improve detection sensitivity and measurement precision of low abundance mtDNA deletions

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    Mitochondrial DNA (mtDNA) mutations are a common cause of primary mitochondrial disorders, and have also been implicated in a broad collection of conditions, including aging, neurodegeneration, and cancer. Prevalent among these pathogenic variants are mtDNA deletions, which show a strong bias for the loss of sequence in the major arc between, but not including, the heavy and light strand origins of replication. Because individual mtDNA deletions can accumulate focally, occur with multiple mixed breakpoints, and in the presence of normal mtDNA sequences, methods that detect broad-spectrum mutations with enhanced sensitivity and limited costs have both research and clinical applications. In this study, we evaluated semi-quantitative and digital PCR-based methods of mtDNA deletion detection using double-stranded reference templates or biological samples. Our aim was to describe key experimental assay parameters that will enable the analysis of low levels or small differences in mtDNA deletion load during disease progression, with limited false-positive detection. We determined that the digital PCR method significantly improved mtDNA deletion detection sensitivity through absolute quantitation, improved precision and reduced assay standard error

    Classical Symmetries of Some Two-Dimensional Models

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    It is well-known that principal chiral models and symmetric space models in two-dimensional Minkowski space have an infinite-dimensional algebra of hidden symmetries. Because of the relevance of symmetric space models to duality symmetries in string theory, the hidden symmetries of these models are explored in some detail. The string theory application requires including coupling to gravity, supersymmetrization, and quantum effects. However, as a first step, this paper only considers classical bosonic theories in flat space-time. Even though the algebra of hidden symmetries of principal chiral models is confirmed to include a Kac--Moody algebra (or a current algebra on a circle), it is argued that a better interpretation is provided by a doubled current algebra on a semi-circle (or line segment). Neither the circle nor the semi-circle bears any apparent relationship to the physical space. For symmetric space models the line segment viewpoint is shown to be essential, and special boundary conditions need to be imposed at the ends. The algebra of hidden symmetries also includes Virasoro-like generators. For both principal chiral models and symmetric space models, the hidden symmetry stress tensor is singular at the ends of the line segment.Comment: 51 pages, minor corrections and added reference

    Nothing but the truth: Consistency and efficiency of the list experiment method for the measurement of sensitive health behaviours

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    Rationale: Social desirability bias, which is the tendency to under-report socially, undesirable health behaviours, significantly distorts information on sensitive behaviours, gained from self-reports and prevents accurate estimation of the prevalence of those, behaviours. We contribute to a growing body of literature that seeks to assess the performance of the list experiment method to improve estimation of these sensitive health behaviours. Method: We use a double-list experiment design in which respondents serve as the treatment group for one list and as the control group for the other list to estimate the prevalence of two sensitive health behaviours in different settings: condom use among 500 female sex workers in urban Senegal and physical intimate partner violence among 1700 partnered women in rural Burkina Faso. First, to assess whether the list experiment improves the accuracy of estimations of the prevalence of sensitive behaviours, we compare the prevalence rates estimated from self-reports with those elicited through the list experiment. Second, we test whether the prevalence rates of the sensitive behaviours obtained using the double-list design are similar, and we estimate the reduction in the standard errors obtained with this design. Finally, we compare the results obtained through another indirect elicitation method, the polling vote method. Results: We show that the list experiment method reduces misreporting by 17 percentage points for condom use and 16–20 percentage points for intimate partner violence. Exploiting the double-list experiment design, we also demonstrate that the prevalence estimates obtained through the use of the two lists are identical in the full sample and across sub-groups and that the double-list design reduces the standard errors by approximately 40% compared to the standard errors in the simple list design. Finally, we show that the list experiment method leads to a higher estimation of the prevalence of sensitive behaviours than the polling vote method. Conclusion: The study suggests that list experiments are an effective method to improve estimation of the prevalence of sensitive health behaviours
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