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Hallin and Ley [Bernoulli 18 (2012) 747-763] investigate and fully characterize the Fisher singularity phenomenon in univariate and multivariate families of skew-symmetric distributions. This paper proposes a refined analysis of the (univariate) problem, showing that singularity can be more or less severe, inducing n1/4 (\"simple singularity\") n⅙ (\"double singularity\"), or n1/8 (\"triple singularity\") consistency rates for the skewness parameter. We show, however, that simple singularity (yielding n⅙ consistency rates), if any singularity at all, is the rule, in the sense that double and triple singularities are possible for generalized skew-normal families only. We also show that higher-order singularities, leading to worse-than-n⅛ rates, cannot occur. Depending on the degree of the singularity, our analysis also suggests a simple reparametrization that offers an alternative to the so-called centred parametrization proposed, in the particular case of skew-normal and skew-f families, by Azzalini [Scand. J. Stat. 12 (1985) 171-178], Arei lano-Val le and Azzalini [J. Multivariate Anal. 113 (2013) 73-90], and DiCiccio and Monti [Quaderni di Statistica 13 (2011) 1-21], respectively.

This paper investigates the surprisingly wide and practicable class of continuous distributions that have densities of the form 2g{t(x)} where g is the density of a symmetric distribution and t is a suitable invertible transformation of scale function which introduces skewness. Note the simplicity of the normalising constant and its lack of dependence on the transformation function. It turns out that the key requirement is that Π = t−1 satisfies Π(y)−Π(−y) = y for all y; Π thus belongs to a class of functions that includes first iterated symmetric distribution functions but is also much wider than that. Transformation of scale distributions have a link with 'skew-g' densities of the form 2π(x)g(x), where π = Π′ is a skewing function, by using Π to transform random variables. A particular case of the general construction is the Cauchy-Schlömilch transformation recently introduced into statistics by Baker (2008); another is the long extant family of 'two-piece' distributions. Transformation of scale distributions have a number of further attractive tractabilities, modality properties, explicit density-based asymmetry functions, a beautiful Khintchine-type theorem and invariant entropy being chief amongst them. Inferential questions are considered briefly.

Skew-symmetric densities recently received much attention in the literature, giving rise to increasingly general families of univariate and multivariate skewed densities. Most of those families, however, suffer from the inferential drawback of a potentially singular Fisher information in the vicinity of symmetry. All existing results indicate that Gaussian densities (possibly after restriction to some linear subspace) play a special and somewhat intriguing role in that context. We dispel that widespread opinion by providing a full characterization, in a general multivariate context, of the information singularity phenomenon, highlighting its relation to a possible link between symmetric kernels and skewing functions - a link that can be interpreted as the mismatch of two densities.

Yin and Yang 1 gene ( YY1 ; MIM#600,013) is recognized as a dual transcriptional activating and repressing factor, RNA-binding protein, and 3D chromatin regulator, with multi roles in neurodevelopmental and maintenance pathways. YY1 haploinsufficiency caused either by heterozygous sequence variants or deletions involving the whole gene has been recently associated with Gabriele-de Vries syndrome (GADEVS), a rare congenital autosomal dominant condition, leading to intellectual disability (ID) and multiple physical/behavioural abnormalities. Herein, we describe clinical and molecular findings from a Brazilian female harbouring a de novo missense pathogenic variant in YY1 gene (NM_003403.5:c.1106A > G; p.Asn369Ser) found by whole exome sequencing with potential implications for protein structure and function. Undescribed or uncommon clinical features in this patient included non-febrile seizures, severe scoliosis, hearing impairment, and chorioretinitis. Further bioinformatics analyses using YY1-other protein interaction networks reinforced the involvement of YY1 interactors in such phenotypes, in exception of chorioretinitis. Moreover, X-chromosome inactivation (XCI) skewing was evidenced in the patient and attributed to the haploinsufficiency of YY1, which direct and indirectly interacts with numerous XCI key regulators. Besides expanding the mutational and phenotype spectrum of GADEVS, our results highlight the role of YY1 as an essential autosomal regulator of XCI epigenetic process.

Background We describe a female infant with Fragile-X syndrome, with a fully expanded FMR1 allele and preferential inactivation of the homologous X-chromosome carrying a de novo deletion. This unusual and rare case demonstrates the importance of a detailed genomic approach, the absence of which could be misguiding, and calls for reflection on the current clinical and diagnostic workup for developmental disabilities. Case presentation We present a female infant, referred for genetic testing due to psychomotor developmental delay without specific dysmorphic features or relevant family history. FMR1 mutation screening revealed a methylated full mutation and a normal but inactive FMR1 allele, which led to further investigation. Complete skewing of X-chromosome inactivation towards the paternally-inherited normal-sized FMR1 allele was found. No pathogenic variants were identified in the XIST promoter. Microarray analysis revealed a 439 kb deletion at Xq28, in a region known to be associated with extreme skewing of X-chromosome inactivation. Conclusions Overall results enable us to conclude that the developmental delay is the cumulative result of a methylated FMR1 full mutation on the active X-chromosome and the inactivation of the other homologue carrying the de novo 439 kb deletion. Our findings should be taken into consideration in future guidelines for the diagnostic workup on the diagnosis of intellectual disabilities, particularly in female infant cases.

This paper analyses the impact of the number of stator slots to rotor bars, i.e. the slot combination, in a cage rotor induction motor (IM) on its electromagnetic torque ripple during steady-state conditions. The study is focused on a conventional low voltage, eight-pole, three-phase, mains-fed IM design. To adequately evaluate the torque ripple magnitude, a ‘torque ripple factor’ is introduced and numerically calculated. To this end, IM behaviour in two common eight-pole stator slot number geometries is examined using numerical models, where, for each examined stator geometry, operation with a range of different rotor bar numbers used in practical IM designs is evaluated. For the sake of completeness and cross-validation, two different modelling approaches are used: a recently reported low-computational intensity winding function-based model and a commercial finite element analysis electromagnetic modelling software package. The paper findings deliver a detailed insight into the impact of rotor bar number, whether skewed or otherwise, on the motor steady-state torque ripple level. The presented results are indicative of the fact that the number of rotor bars only, and not the slot combination, is the dominant factor that influences the electromagnetic torque ripple in IMs with skewed rotor bars.

We introduce a general perspective on the introduction of skewness into symmetric distributions. Through inverse probability integral transformations we provide a constructive representation of skewed distributions, where the skewing mechanism and the original symmetric distributions are specified separately. We study the effects of the skewing mechanism on, e.g., modality, tail behavior and the amount of skewness generated. The representation is used to introduce novel classes of skewed distributions, where we induce certain prespecified characteristics through particular choices of the skewing mechanism. Finally, we use a Bayesian linear regression framework to compare the new classes with some existing distributions in the context of two empirical examples.

The paper investigates the effect of pole arc skewing in synchronous reluctance machine on its torque ripple. To do this, the machine’s reluctances are calculated by using winding function approach (WFA). A numerical-based method is proposed for modeling the machine’s dynamic equations. The effect of rotor skewing and the winding type (single-layer or double layer) on the machine’s behavior and torque ripple are investigated. The results show that skewing the rotor is significantly effective in double-layer winding case and it is not a proper idea for machine with single-layer winding. The proposed method is capable of studying the voltage-fed machine’s behavior which is common in reality in comparison with current source-fed machine. Also, shorter calculation time and capability of studying parameter sensitivity are other advantages of the proposed method in comparison with finite element method (FEM).

Background X chromosome inactivation (XCI) is an important gene regulation mechanism in females to equalize the expression levels of X chromosome between two sexes. Generally, one of two X chromosomes in females is randomly chosen to be inactivated. Nonrandom XCI (XCI skewing) is also observed in females, which has been reported to play an important role in many X-linked diseases. However, there is no statistical measure available for the degree of the XCI skewing based on family data in population genetics. Results In this article, we propose a statistical approach to measure the degree of the XCI skewing based on family trios, which is represented by a ratio of two genotypic relative risks in females. The point estimate of the ratio is obtained from the maximum likelihood estimates of two genotypic relative risks. When parental genotypes are missing in some family trios, the expectation-conditional-maximization algorithm is adopted to obtain the corresponding maximum likelihood estimates. Further, the confidence interval of the ratio is derived based on the likelihood ratio test. Simulation results show that the likelihood-based confidence interval has an accurate coverage probability under the situations considered. Also, we apply our proposed method to the rheumatoid arthritis data from USA for its practical use, and find out that a locus, rs2238907, may undergo the XCI skewing against the at-risk allele. But this needs to be further confirmed by molecular genetics. Conclusions The proposed statistical measure for the skewness of XCI is applicable to complete family trio data or family trio data with some paternal genotypes missing. The likelihood-based confidence interval has an accurate coverage probability under the situations considered. Therefore, our proposed statistical measure is generally recommended in practice for discovering the potential loci which undergo the XCI skewing.

To investigate X-chromosome inactivation (XCI) in human trophoblasts during early pregnancy, tropho-blast genomic DNA was extracted and analyzed for a Bst XI restriction endonuclease site polymorphism in the X-linked phosphoglycerate kinase gene, after digestion with methylation-sensitive Hpa II (control samples were digested instead with Afa I ). Six villous trophoblast DNA samples were informative for the polymorphism (ie, heterozygous) and were derived from women homozygous for the polymorphism. These samples were then evaluated for XCI. In five of the six samples with Hpa II predigestion, the sizes of the two heterozygous band peaks differed; maternal X-chromosome (X M )-derived alleles showed smaller peak sizes than paternal X-chromosome (X P )-derived alleles, but the differences varied in degree. In samples obtained by microdissection from formalin-fixed, paraffin-embedded tissues (30 samples from different anchoring villi, and 38 samples from different branch villi), monoclonal band patterns of X P -derived alleles were observed more frequently than those of X M -derived alleles, but almost half of the samples showed polyclonal pat-terns. Our results suggest that a skewing of XCI exists in the human trophoblast; however, the degree of non-randomness due to predominant X P inactivation appears to be restricted. It is probable that transcription of the X inactivation center ( XIC ) begins earlier in mice than in humans.