Escape rate and Hausdorff measure for entire functions

The escaping set of an entire function is the set of points that tend to infinity under iteration. We consider subsets of the escaping set defined in terms of escape rates and obtain upper and lower bounds for the Hausdorff measure of these sets with respect to certain gauge functions.Comment: 24 pages; some errors corrected, proof of Theorem 2 shortene

Socioeconomic risk, parenting during the preschool years and child health age 6 years

Parent–child relationships and parenting processes are emerging as potential life course determinants of health. Parenting is socially patterned and could be one of the factors responsible for the negative effects of social inequalities on health, both in childhood and adulthood. This study tests the hypothesis that some of the effect of socioeconomic risk on health in mid childhood is transmitted via early parenting. Methods: Prospective cohort study in 10 USA communities involving 1041 mother/ child pairs, selected at birth at random with conditional sampling. Exposures: income, maternal education, maternal age, lone parenthood, ethnic status and objective assessments of mother child interaction in the first 4 years of life covering warmth, negativity and positive control. Outcomes: mother’s report of child’s health in general at 6 years. Modelling: multiple regression analyses with statistical testing of mediational processes. Results: All five indicators of socioeconomic status (SES) were correlated with all three measures of parenting, such that low SES was associated with poor parenting. Among the measures of parenting maternal warmth was independently predictive of future health, and among the socioeconomic variables maternal education, partner presence and ‘other ethnic group’ proved predictive. Measures of parenting significantly mediated the impact of measures of SES on child health. Conclusions: Parenting mediates some, but not all of the detectable effects of socioeconomic risk on health in childhood. As part of a package of measures that address other determinants, interventions to support parenting are likely to make a useful contribution to reducing childhood inequalities in health

Entire functions with Julia sets of positive measure

Let f be a transcendental entire function for which the set of critical and asymptotic values is bounded. The Denjoy-Carleman-Ahlfors theorem implies that if the set of all z for which |f(z)|>R has N components for some R>0, then the order of f is at least N/2. More precisely, we have log log M(r,f) > (N/2) log r - O(1), where M(r,f) denotes the maximum modulus of f. We show that if f does not grow much faster than this, then the escaping set and the Julia set of f have positive Lebesgue measure. However, as soon as the order of f exceeds N/2, this need not be true. The proof requires a sharpened form of an estimate of Tsuji related to the Denjoy-Carleman-Ahlfors theorem.Comment: 17 page

Parent and child agreement for acute stress disorder, post-traumatic stress disorder and other psychopathology in a prospective study of children and adolescents exposed to single-event trauma

Examining parent-child agreement for Acute Stress Disorder (ASD) and Post-Traumatic Stress Disorder (PTSD) in children and adolescents is essential for informing the assessment of trauma-exposed children, yet no studies have examined this relationship using appropriate statistical techniques. Parent-child agreement for these disorders was examined by structured interview in a prospective study of assault and motor vehicle accident (MVA) child survivors, assessed at 2-4 weeks and 6 months post-trauma. Children were significantly more likely to meet criteria for ASD, as well as other ASD and PTSD symptom clusters, based on their own report than on their parent's report. Parent-child agreement for ASD was poor (Cohen's κ = -.04), but fair for PTSD (Cohen's κ = .21). Agreement ranged widely for other emotional disorders (Cohen's κ = -.07-.64), with generalised anxiety disorder found to have superior parent-child agreement (when assessed by phi coefficients) relative to ASD and PTSD. The findings support the need to directly interview children and adolescents, particularly for the early screening of posttraumatic stress, and suggest that other anxiety disorders may have a clearer presentation post-trauma

Three-Dimensional Human iPSC-Derived Artificial Skeletal Muscles Model Muscular Dystrophies and Enable Multilineage Tissue Engineering

Summary: Generating human skeletal muscle models is instrumental for investigating muscle pathology and therapy. Here, we report the generation of three-dimensional (3D) artificial skeletal muscle tissue from human pluripotent stem cells, including induced pluripotent stem cells (iPSCs) from patients with Duchenne, limb-girdle, and congenital muscular dystrophies. 3D skeletal myogenic differentiation of pluripotent cells was induced within hydrogels under tension to provide myofiber alignment. Artificial muscles recapitulated characteristics of human skeletal muscle tissue and could be implanted into immunodeficient mice. Pathological cellular hallmarks of incurable forms of severe muscular dystrophy could be modeled with high fidelity using this 3D platform. Finally, we show generation of fully human iPSC-derived, complex, multilineage muscle models containing key isogenic cellular constituents of skeletal muscle, including vascular endothelial cells, pericytes, and motor neurons. These results lay the foundation for a human skeletal muscle organoid-like platform for disease modeling, regenerative medicine, and therapy development. : Maffioletti et al. generate human 3D artificial skeletal muscles from healthy donors and patient-specific pluripotent stem cells. These human artificial muscles accurately model severe genetic muscle diseases. They can be engineered to include other cell types present in skeletal muscle, such as vascular cells and motor neurons. Keywords: skeletal muscle, pluripotent stem cells, iPS cells, myogenic differentiation, tissue engineering, disease modeling, muscular dystrophy, organoid

Are Devaney hairs fast escaping?

Beginning with Devaney, several authors have studied transcendental entire functions for which every point in the escaping set can be connected to infinity by a curve in the escaping set. Such curves are often called Devaney hairs. We show that, in many cases, every point in such a curve, apart from possibly a finite endpoint of the curve, belongs to the fast escaping set. We also give an example of a Devaney hair which lies in a logarithmic tract of a transcendental entire function and contains no fast escaping points.Comment: 22 pages, 1 figur

A detailed clinical and molecular survey of subjects with nonsyndromic USH2A retinopathy reveals an allelic hierarchy of disease-causing variants.

Defects in USH2A cause both isolated retinal disease and Usher syndrome (ie, retinal disease and deafness). To gain insights into isolated/nonsyndromic USH2A retinopathy, we screened USH2A in 186 probands with recessive retinal disease and no hearing complaint in childhood (discovery cohort) and in 84 probands with recessive retinal disease (replication cohort). Detailed phenotyping, including retinal imaging and audiological assessment, was performed in individuals with two likely disease-causing USH2A variants. Further genetic testing, including screening for a deep-intronic disease-causing variant and large deletions/duplications, was performed in those with one likely disease-causing change. Overall, 23 of 186 probands (discovery cohort) were found to harbour two likely disease-causing variants in USH2A. Some of these variants were predominantly associated with nonsyndromic retinal degeneration ('retinal disease-specific'); these included the common c.2276 G>T, p.(Cys759Phe) mutation and five additional variants: c.2802 T>G, p.(Cys934Trp); c.10073 G>A, p.(Cys3358Tyr); c.11156 G>A, p.(Arg3719His); c.12295-3 T>A; and c.12575 G>A, p.(Arg4192His). An allelic hierarchy was observed in the discovery cohort and confirmed in the replication cohort. In nonsyndromic USH2A disease, retinopathy was consistent with retinitis pigmentosa and the audiological phenotype was variable. USH2A retinopathy is a common cause of nonsyndromic recessive retinal degeneration and has a different mutational spectrum to that observed in Usher syndrome. The following model is proposed: the presence of at least one 'retinal disease-specific' USH2A allele in a patient with USH2A-related disease results in the preservation of normal hearing. Careful genotype-phenotype studies such as this will become increasingly important, especially now that high-throughput sequencing is widely used in the clinical setting.European Journal of Human Genetics advance online publication, 4 February 2015; doi:10.1038/ejhg.2014.283

A Novel Adaptation of a Parent-Child Observational Assessment Tool for Appraisals and Coping in Children Exposed to Acute Trauma

Background: Millions of children worldwide are exposed to acute potentially traumatic events (PTEs) annually. Many children and their families experience significant emotional distress and/or functional impairment following PTEs. While current research has begun to highlight a role for early appraisals and coping in promoting or preventing full recovery from PTEs, the exact nature of the relationships among appraisals, coping, and traumatic stress reactions as well as how appraisals and coping behaviors are influenced by the child\u27s environment (e.g., parents) remains unclear; assessment tools that reach beyond self-report are needed to improve this understanding. Objective: The objective of the current study is to describe the newly created Trauma Ambiguous Situations Tool (TAST; i.e., an observational child–parent interview and discussion task that allows assessment of appraisals, coping, and parent–child processes) and to report on initial feasibility and validation of TAST implemented with child–parent dyads in which children were exposed to a PTE. Method: As part of a larger study on the role of biopsychosocial factors in posttraumatic stress reactions, children (aged 8–13) and parents (n=25 child–parent dyads) completed the TAST during the child\u27s hospitalization for injury. Results: Children and parents engaged well with the TAST. The time to administer the TAST was feasible, even in a peri-trauma context. The TAST solicited a wide array of appraisals (threat and neutral) and coping solutions (proactive and avoidant). Forced-choice and open-ended appraisal assessments provided unique information. The parent–child discussion portion of the TAST allowed for direct observation of parent–child processes and demonstrated parental influence on children\u27s appraisals and coping solutions. Conclusions: The TAST is a promising new research tool, which may help to explicate how parents influence their child\u27s developing appraisals and coping solutions following a PTE. More research should examine the relationships of appraisals, coping, and parent–child processes assessed by the TAST with traumatic stress outcomes