Strong coprimality and strong irreducibility of Alexander polynomials

A polynomial f(t) with rational coefficients is strongly irreducible if f(t^k) is irreducible for all positive integers k. Likewise, two polynomials f and g are strongly coprime if f(t^k) and g(t^l) are relatively prime for all positive integers k and l. We provide some sufficient conditions for strong irreducibility and prove that the Alexander polynomials of twist knots are pairwise strongly coprime and that most of them are strongly irreducible. We apply these results to describe the structure of the subgroup of the rational knot concordance group generated by the twist knots and to provide an explicit set of knots which represent linearly independent elements deep in the solvable filtration of the knot concordance group.Comment: 16 pages, 6 figure

The proteostasis boundary in misfolding diseases of membrane traffic

AbstractProtein function is regulated by the proteostasis network (PN) [Balch, W.E., Morimoto, R.I., Dillin, A. and Kelly, J.W. (2008) Adapting proteostasis for disease intervention. Science 319, 916–919], an integrated biological system that generates and protects the protein fold. The composition of the PN is regulated by signaling pathways including the unfolded protein response (UPR), the heat-shock response (HSR), the ubiquitin proteasome system (UPS) and epigenetic programs. Mismanagement of protein folding and function during membrane trafficking through the exocytic and endocytic pathways of eukaryotic cells by the PN is responsible for a wide range of diseases that include, among others, lysosomal storage diseases, myelination diseases, cystic fibrosis, systemic amyloidoses such as light chain myeloma, and neurodegenerative diseases including Alzheimer’s. Toxicity from misfolding can be cell autonomous (affect the producing cell) or cell non-autonomous (affect a non-producing cell) or both, and have either a loss-of-function or gain-of-toxic function phenotype. Herein, we review the role of the PN and its regulatory transcriptional circuitry likely to be operational in managing the protein fold and function during membrane trafficking. We emphasize the enabling principle of a ‘proteostasis boundary (PB)’ [Powers, E.T., Morimoto, R.T., Dillin, A., Kelly, J.W., and Balch, W.E. (2009) Biochemical and chemical approaches to diseases of proteostasis deficiency. Annu. Rev. Biochem. 78, 959–991]. The PB is defined by the combined effects of the kinetics and thermodynamics of folding and the kinetics of misfolding, which are linked to the variable and adjustable PN capacity found different cell types. Differences in the PN account for the versatility of protein folding and function in health, and the cellular and tissue response to mutation and environmental challenges in disease. We discuss how manipulation of the folding energetics or the PB through metabolites and pharmacological intervention provides multiple routes for restoration of biological function in trafficking disease

Testing Modules for Experiments in Stellar Astrophysics (MESA)

Regular, automated testing is a foundational principle of modern software development. Numerous widely-used continuous integration systems exist, but they are often not suitable for the unique needs of scientific simulation software. Here we describe the testing infrastructure developed for and used by the Modules for Experiments in Stellar Astrophysics (MESA) project. This system allows the computationally-demanding MESA test suite to be regularly run on a heterogeneous set of computers and aggregates and displays the testing results in a form that allows for the rapid identification and diagnosis of regressions. Regularly collecting comprehensive testing data also enables longitudinal studies of the performance of the software and the properties of the models it generates.Comment: 12 page, 7 figures, Accepted to ApJ

BIOMECHANICAL ANALYSIS OF THE FASTBALL THROWN FROM THE WIND-UP AND THE STRETCH

This study assessed the biomechanics associated with the fastball thrown in two conditions. Fifteen men pitched from the wind-up and stretch beginning and landing on force platforms. Doppler radar was used to assess ball velocity. A paired samples t-test was used to determine differences in ball velocity, propulsive and landing phase kinetics, as well as time, distance, and subject velocity from the propulsive to landing phase. The stretch produced 5.55% more horizontal ground reaction force, a higher horizontal to vertical force ratio, 35.05% greater vertical rate of force development (RFD) in the propulsive phase, and 8.85% higher horizontal and 24.65% vertical RFD upon landing (p ≤ 0.05). The wind-up produced 39.49% greater horizontal RFD in the propulsive phase (p ≤ 0.05). These variations of the fastball use different mechanisms to achieve similar (p = 0.77) ball velocities

SEX-BASED ANALYSIS OF THE BIOMECHANICS OF PITCHING

This study assessed sex-based differences in the lower extremity kinetics and ball velocity during pitching. Fifteen men baseball players and fifteen women softball players threw fastballs on two force platforms, to assess propulsive and landing biomechanics. Doppler radar was used to assess ball velocity. Kinetic and kinematic data comparing men and women were analyzed with independent samples t-test. Paired samples t-test were used to assess difference between the propulsive and landing phases. Pearson’s bivariate correlations were used to assess the relationship between study variables and ball velocity. Few sex-based difference in the magnitude and rate of propulsive force development exist. Sex based differences (p \u3c 0.05) were found for all but one landing phase variable. None of the biomechanical variables assessed were related to ball velocity

Two Transiting Earth-size Planets Near Resonance Orbiting a Nearby Cool Star

Discoveries from the prime Kepler mission demonstrated that small planets (< 3 Earth-radii) are common outcomes of planet formation. While Kepler detected many such planets, all but a handful orbit faint, distant stars and are not amenable to precise follow up measurements. Here, we report the discovery of two small planets transiting K2-21, a bright (K = 9.4) M0 dwarf located 65$\pm$6 pc from Earth. We detected the transiting planets in photometry collected during Campaign 3 of NASA's K2 mission. Analysis of transit light curves reveals that the planets have small radii compared to their host star, 2.60 $\pm$ 0.14% and 3.15 $\pm$ 0.20%, respectively. We obtained follow up NIR spectroscopy of K2-21 to constrain host star properties, which imply planet sizes of 1.59 $\pm$ 0.43 Earth-radii and 1.92 $\pm$ 0.53 Earth-radii, respectively, straddling the boundary between high-density, rocky planets and low-density planets with thick gaseous envelopes. The planets have orbital periods of 9.32414 days and 15.50120 days, respectively, and have a period ratio of 1.6624, very near to the 5:3 mean motion resonance, which may be a record of the system's formation history. Transit timing variations (TTVs) due to gravitational interactions between the planets may be detectable using ground-based telescopes. Finally, this system offers a convenient laboratory for studying the bulk composition and atmospheric properties of small planets with low equilibrium temperatures.Comment: Updated to ApJ accepted version; photometry available alongside LaTeX source; 10 pages, 7 figure