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

No entire function with real multipliers in class S

We prove that there is no entire transcendental function in class S with real multipliers of all repelling periodic orbits.Comment: 7 page

To add or not to add a new treatment arm to a multiarm study: A decision-theoretic framework.

Multiarm clinical trials, which compare several experimental treatments against control, are frequently recommended due to their efficiency gain. In practise, all potential treatments may not be ready to be tested in a phase II/III trial at the same time. It has become appealing to allow new treatment arms to be added into on-going clinical trials using a "platform" trial approach. To the best of our knowledge, many aspects of when to add arms to an existing trial have not been explored in the literature. Most works on adding arm(s) assume that a new arm is opened whenever a new treatment becomes available. This strategy may prolong the overall duration of a study or cause reduction in marginal power for each hypothesis if the adaptation is not well accommodated. Within a two-stage trial setting, we propose a decision-theoretic framework to investigate when to add or not to add a new treatment arm based on the observed stage one treatment responses. To account for different prospect of multiarm studies, we define utility in two different ways; one for a trial that aims to maximise the number of rejected hypotheses; the other for a trial that would declare a success when at least one hypothesis is rejected from the study. Our framework shows that it is not always optimal to add a new treatment arm to an existing trial. We illustrate a case study by considering a completed trial on knee osteoarthritis

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

Cassini observations of ion and electron beams at Saturn and their relationship to infrared auroral arcs

We present Cassini Visual and Infrared Mapping Spectrometer observations of infrared auroral emissions from the noon sector of Saturn's ionosphere revealing multiple intense auroral arcs separated by dark regions poleward of the main oval. The arcs are interpreted as the ionospheric signatures of bursts of reconnection occurring at the dayside magnetopause. The auroral arcs were associated with upward field-aligned currents, the magnetic signatures of which were detected by Cassini at high planetary latitudes. Magnetic field and particle observations in the adjacent downward current regions showed upward bursts of 100–360 keV light ions in addition to energetic (hundreds of keV) electrons, which may have been scattered from upward accelerated beams carrying the downward currents. Broadband, upward propagating whistler waves were detected simultaneously with the ion beams. The acceleration of the light ions from low altitudes is attributed to wave-particle interactions in the downward current regions. Energetic (600 keV) oxygen ions were also detected, suggesting the presence of ambient oxygen at altitudes within the acceleration region. These simultaneous in situ and remote observations reveal the highly energetic magnetospheric dynamics driving some of Saturn's unusual auroral features. This is the first in situ identification of transient reconnection events at regions magnetically conjugate to Saturn's magnetopause

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