167 research outputs found
Spectrum of a Rudin-Shapiro-like sequence
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
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Continuous Spectra For Substitution-Based Sequences
This thesis is chiefly concerned with the continuous spectra of substitution-based sequences. First, motivated by a question of Lafrance, Yee and Rampersad [34], we establish a connection between the ‘root-N’ property and the corresponding sequences that satisfy it having absolutely continuous spectrum. Then we use the recent advances in Bartlett [10, 11] to show that the Rudin–Shapiro-like sequence has singular continuous spectrum, hence does not satisfy the root-N property. This gives a negative answer to the question raised by the authors in [34].
Secondly, we use the connection we establish between the root-N property and absolute continuity to create more substitution-based sequences that have absolutely continuous/Lebesgue spectrum. This is done by modifying Rudin’s original construction [44]. We show that the binary sequences (±1 sequences) from our modification also satisfy the root-N property and they are mutually locally derivable to the corresponding substitution sequences. This shows that the spectral properties of the substitution-based sequences are inherited from their binary counterpart.
Finally, we generalise our construction using Fourier matrices. This leads to extending Rudin’s construction to sequences with complex coefficients. This approach allows us to generate substitution sequences of any constant length greater than or equal to two. We show explicitly in the length 3 and 4 cases that these systems exhibit Lebesgue spectrum, employing Bartlett’s algorithm from Chapter 3 and mutual local derivability
Substitution-based structures with absolutely continuous spectrum
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
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
© 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
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
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
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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