Variation of Iwasawa invariants in Hida families

Let r : G_Q -> GL_2(Fpbar) be a p-ordinary and p-distinguished irreducible residual modular Galois representation. We show that the vanishing of the algebraic or analytic Iwasawa mu-invariant of a single modular form lifting r implies the vanishing of the corresponding mu-invariant for all such forms. Assuming that the mu-invariant vanishes, we also give explicit formulas for the difference in the algebraic or analytic lambda-invariants of modular forms lifting r. In particular, our formula shows that the lambda-invariant is constant on branches of the Hida family of r. We further show that our formulas are identical for the algebraic and analytic invariants, so that the truth of the main conjecture of Iwasawa theory for one form in the Hida family of r implies it for the entire Hida family

Development of the legitimacy threshold scale

A consensus in the literature supports the premise that legitimacy attainment facilitates favorable judgments from key stakeholders regarding the acceptability, appropriateness and worthiness of entrepreneurs and their efforts in emerging ventures. However, although legitimacy attainment is a milestone that emerging ventures strive to reach, as researchers we do not yet have a measure that examines whether a firm is operating pre- versus post-legitimacy. Accordingly, we develop the legitimacy threshold scale (LTS) that will facilitate the assessment of activities performed pre- and post-legitimacy in emerging ventures

MRI radiomic features are independently associated with overall survival in soft tissue sarcoma

Purpose: Soft tissue sarcomas (STS) represent a heterogeneous group of diseases, and selection of individualized treatments remains a challenge. The goal of this study was to determine whether radiomic features extracted from magnetic resonance (MR) images are independently associated with overall survival (OS) in STS. Methods and Materials: This study analyzed 2 independent cohorts of adult patients with stage II-III STS treated at center 1 (N = 165) and center 2 (N = 61). Thirty radiomic features were extracted from pretreatment T1-weighted contrast-enhanced MR images. Prognostic models for OS were derived on the center 1 cohort and validated on the center 2 cohort. Clinical-only (C), radiomics-only (R), and clinical and radiomics (C+R) penalized Cox models were constructed. Model performance was assessed using Harrell\u27s concordance index. Results: In the R model, tumor volume (hazard ratio [HR], 1.5) and 4 texture features (HR, 1.1-1.5) were selected. In the C+R model, both age (HR, 1.4) and grade (HR, 1.7) were selected along with 5 radiomic features. The adjusted c-indices of the 3 models ranged from 0.68 (C) to 0.74 (C+R) in the derivation cohort and 0.68 (R) to 0.78 (C+R) in the validation cohort. The radiomic features were independently associated with OS in the validation cohort after accounting for age and grade (HR, 2.4; Conclusions: This study found that radiomic features extracted from MR images are independently associated with OS when accounting for age and tumor grade. The overall predictive performance of 3-year OS using a model based on clinical and radiomic features was replicated in an independent cohort. Optimal models using clinical and radiomic features could improve personalized selection of therapy in patients with STS

The growth and hydrodynamic collapse of a protoplanet envelope

We have conducted three-dimensional self-gravitating radiation hydrodynamical models of gas accretion onto high mass cores (15-33 Earth masses) over hundreds of orbits. Of these models, one case accretes more than a third of a Jupiter mass of gas, before eventually undergoing a hydrodynamic collapse. This collapse causes the density near the core to increase by more than an order of magnitude, and the outer envelope to evolve into a circumplanetary disc. A small reduction in the mass within the Hill radius (R_H) accompanies this collapse as a shock propagates outwards. This collapse leads to a new hydrostatic equilibrium for the protoplanetary envelope, at which point 97 per cent of the mass contained within the Hill radius is within the inner 0.03 R_H which had previously contained less than 40 per cent. Following this collapse the protoplanet resumes accretion at its prior rate. The net flow of mass towards this dense protoplanet is predominantly from high latitudes, whilst at the outer edge of the circumplanetary disc there is net outflow of gas along the midplane. We also find a turnover of gas deep within the bound envelope that may be caused by the establishment of convection cells.Comment: 16 pages, 16 figures. Accepted for publication in MNRA

Exploring the conditions required to form giant planets via gravitational instability in massive protoplanetary discs

We carry out global three-dimensional radiation hydrodynamical simulations of self-gravitating accretion discs to determine if, and under what conditions, a disc may fragment to form giant planets. We explore the parameter space (in terms of the disc opacity, temperature and size) and include the effect of stellar irradiation. We find that the disc opacity plays a vital role in determining whether a disc fragments. Specifically, opacities that are smaller than interstellar Rosseland mean values promote fragmentation (even at small radii, R < 25AU) since low opacities allow a disc to cool quickly. This may occur if a disc has a low metallicity or if grain growth has occurred. With specific reference to the HR 8799 planetary system, given its star is metal-poor, our results suggest that the formation of its imaged planetary system could potentially have occurred by gravitational instability. We also find that the presence of stellar irradiation generally acts to inhibit fragmentation (since the discs can only cool to the temperature defined by stellar irradiation). However, fragmentation may occur if the irradiation is sufficiently weak that it allows the disc to attain a low Toomre stability parameter.Comment: Accepted for publication by MNRAS. 11 pages, 12 figures

Conduction‐dominated heat transport of the annual temperature signal in soil

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95182/1/jgrb13727.pd