Third Hankel Determinant for a Subclass of Univalent Functions Associated with Lemniscate of Bernoulli

This paper deals with a new subclass of univalent function associated with the right half of the lemniscate of Bernoulli. We have find the upper bound of the Hankel determinant H3(1) for this subclass by applying the Carlson–Shaffer operator to it. The present work also deals with certain properties of this newly defined subclass, such as the upper bound of the Hankel determinant of order 3, the co-efficient estimate, etc.

Efficient Estimate of Low-Frequency Words’ Embeddings Based on the Dictionary: A Case Study on Chinese

Obtaining high-quality embeddings of out-of-vocabularies (OOVs) and low-frequency words is a challenge in natural language processing (NLP). To efficiently estimate the embeddings of OOVs and low-frequency words, we propose a new method that uses the dictionary to estimate the embeddings of OOVs and low-frequency words. More specifically, the explanatory note of an entry in dictionaries accurately describes the semantics of the corresponding word. Naturally, we adopt the sentence representation model to extract the semantics of the explanatory note and regard the semantics as the embedding of the corresponding word. We design a new sentence representation model to encode sentences to extract the semantics from the explanatory notes of entries more efficiently. Based on the assumption that the higher quality of word embeddings will lead to better performance, we design an extrinsic experiment to evaluate the quality of low-frequency words’ embeddings. The experimental results show that the embeddings of low-frequency words estimated by our proposed method have higher quality. In addition, both intrinsic and extrinsic experiments show that our proposed sentence representation model can represent the semantics of sentences well.

On numerical solution by method of V.K. Dzyadyk of Goursat problem with constant coefficients

By means of Fourier-Chebyshev operators we construct, by approximative method, the generalized polynomial that approximates the solution of Goursat problem with constant coefficients. We obtain the efficient estimate of this approximation.

A diagnostic primer pair to distinguish between wMel and wAlbB Wolbachia infections

Detection of the Wolbachia endosymbiont in Aedes aegypti mosquitoes through real-time polymerase chain reaction assays is widely used during and after Wolbachia releases in dengue reduction trials involving the wMel and wAlbB strains. Although several different primer pairs have been applied in current successful Wolbachia releases, they cannot be used in a single assay to distinguish between these strains. Here, we developed a new diagnostic primer pair, wMwA, which can detect the wMel or wAlbB infection in the same assay. We also tested current Wolbachia primers and show that there is variation in their performance when they are used to assess the relative density of Wolbachia. The new wMwA primers provide an accurate and efficient estimate of the presence and density of both Wolbachia infections, with practical implications for Wolbachia estimates in field collected Ae. aegypti where Wolbachia releases have taken place.

The Triangulation WIthin a STudy (TWIST) framework for causal inference within pharmacogenetic research

In this paper we review the methodological underpinnings of the general pharmacogenetic approach for uncovering genetically-driven treatment effect heterogeneity. This typically utilises only individuals who are treated and relies on fairly strong baseline assumptions to estimate what we term the ‘genetically moderated treatment effect’ (GMTE). When these assumptions are seriously violated, we show that a robust but less efficient estimate of the GMTE that incorporates information on the population of untreated individuals can instead be used. In cases of partial violation, we clarify when Mendelian randomization and a modified confounder adjustment method can also yield consistent estimates for the GMTE. A decision framework is then described to decide when a particular estimation strategy is most appropriate and how specific estimators can be combined to further improve efficiency. Triangulation of evidence from different data sources, each with their inherent biases and limitations, is becoming a well established principle for strengthening causal analysis. We call our framework ‘Triangulation WIthin a STudy’ (TWIST)’ in order to emphasise that an analysis in this spirit is also possible within a single data set, using causal estimates that are approximately uncorrelated, but reliant on different sets of assumptions. We illustrate these approaches by re-analysing primary-care-linked UK Biobank data relating to CYP2C19 genetic variants, Clopidogrel use and stroke risk, and data relating to APOE genetic variants, statin use and Coronary Artery Disease.

Logarithmic Ratio-Type Estimator of Population Coefficient of Variation

The estimation of population coefficient of variation is one of the challenging aspects in sampling survey techniques for the past decades and much effort has been employed to develop estimators to produce its efficient estimate. In this paper, we proposed logarithmic ratio type estimator for the estimating population coefficient of variation using logarithm transformation on the both population and sample variances of the auxiliary character. The expression for the mean squared error (MSE) of the proposed estimator has been derived using Taylor series first order approximation approach. Efficiency conditions of the proposed estimator over other estimators in the study has also been derived. The empirical study was conducted using two-sets of populations and the results showed that the proposed estimator is more efficient. This result implies that, the estimate of proposed estimator will be closer to the true parameter than the estimates of other estimators in the study.

Diagnostic primers to distinguish between wMel and wAlbB Wolbachia infection - A simplified approach for use in field-collected Aedes aegypti in dengue reduction trials

Detection of the Wolbachia endosymbiont in Aedes aegypti mosquitoes through real-time PCR assays is widely used during and after Wolbachia releases in dengue reduction trials involving the wMel and wAlbB strains. However, primers applied in current successful Wolbachia releases cannot be used in a single assay to distinguish between these strains. Here, we developed a new diagnostic primer pair wMA which can detect wMel or wAlbB infection in the same assay. We also tested current Wolbachia primers and show that there is variation in their performance when they are used to assess the relative density of Wolbachia. The new wMA primers provide an accurate and efficient estimate of the presence and density of both Wolbachia infections.

The Triangulation WIthin A STudy (TWIST) framework for causal inference within Pharmacogenetic research

In this paper we review the methodological underpinnings of the general pharmacogenetic approach for uncovering genetically-driven treatment effect heterogeneity. This typically utilises only individuals who are treated and relies on fairly strong baseline assumptions to estimate what we term the `genetically mediated treatment effect' (GMTE). When these assumptions are seriously violated, we show that a robust but less efficient estimate of the GMTE that incorporates information on the population of untreated individuals can instead be used. In cases of partial violation, we clarify when Mendelian randomization and a modified confounder adjustment method can also yield consistent estimates for the GMTE. A decision framework is then described to decide when a particular estimation strategy is most appropriate and how specific estimators can be combined to further improve efficiency. Triangulation of evidence from different data sources, each with their inherent biases and limitations, is becoming a well established principle for strengthening causal analysis. We call our framework `Triangulation WIthin a STudy' (TWIST)' in order to emphasise that an analysis in this spirit is also possible within a single data set, using causal estimators that are approximately statistically uncorrelated, but reliant on different sets of assumptions. We illustrate these approaches by re-analysing primary-care-linked UK Biobank data relating to CYP2C19 genetic variants, Clopidogrel use and stroke risk, and data relating to APOE genetic variants, statin use and Coronary Artery Disease.