Supernova type Ia luminosities, their dependence on second parameters, and the value of H_0

A sample of 35 SNe Ia with good to excellent photometry in B and V, minimum internal absorption, and 1200 < v < \approx 30000 km/s is compiled from the literature. As far as their spectra are known they are all Branch-normal. For 29 of the SNe Ia also peak magnitudes in I are known. The SNe Ia have uniform colors at maximum, i.e. =-0.012 mag (sigma=0.051) and =-0.276 mag (sigma=0.078). In the Hubble diagram they define a Hubble line with a scatter of $\sigma_M$=0.21-0.16 mag, decreasing with wavelength. The scatter is further reduced if the SNe Ia are corrected for differences in decline rate Delta_m_15 or color (B-V). A combined correction reduces the scatter to sigma<=0.13 mag. After the correction no significant dependence remains on Hubble type or galactocentric distance. The Hubble line suggests some curvature which can be differently interpreted. A consistent solution is obtained for a cosmological model with Omega_M=0.3, Omega_Lambda=0.7, which is indicated also by much more distant SNe Ia. Absolute magnitudes are available for eight equally blue (Branch-normal) SNe Ia in spirals, whose Cepheid distances are known. If their well defined mean values of M_B, M_V, and M_I are used to fit the Hubble line to the above sample of SNe Ia one obtains H_0=58.3 km/s/Mpc, or, after adjusting all SNe Ia to the average values of Delta_m_15 and (B-V), H_0=60.9 km/s/Mpc. Various systematic errors are discussed whose elimination tends to decrease H_0. The finally adopted value at the 90-percent level, including random and systematic errors, is H_0=58.5 +/- 6.3 km/s/Mpc. Several higher values of H_0 from SNe Ia, as suggested in the literature, are found to depend on large corrections for variations of the light curve parameter and/or on an unwarranted reduction of the Cepheid distances of the calibrating SNe Ia.Comment: 42 pages, including 9 figures; submitted to Ap

FixFit: using parameter-compression to solve the inverse problem in overdetermined models

All fields of science depend on mathematical models. One of the fundamental problems with using complex nonlinear models is that data-driven parameter estimation often fails because interactions between model parameters lead to multiple parameter sets fitting the data equally well. Here, we develop a new method to address this problem, FixFit, which compresses a given mathematical model's parameters into a latent representation unique to model outputs. We acquire this representation by training a neural network with a bottleneck layer on data pairs of model parameters and model outputs. The bottleneck layer nodes correspond to the unique latent parameters, and their dimensionality indicates the information content of the model. The trained neural network can be split at the bottleneck layer into an encoder to characterize the redundancies and a decoder to uniquely infer latent parameters from measurements. We demonstrate FixFit in two use cases drawn from classical physics and neuroscience

Metabolism of ticagrelor in patients with acute coronary syndromes.

© The Author(s) 2018Ticagrelor is a state-of-the-art antiplatelet agent used for the treatment of patients with acute coronary syndromes (ACS). Unlike remaining oral P2Y12 receptor inhibitors ticagrelor does not require metabolic activation to exert its antiplatelet action. Still, ticagrelor is extensively metabolized by hepatic CYP3A enzymes, and AR-C124910XX is its only active metabolite. A post hoc analysis of patient-level (n = 117) pharmacokinetic data pooled from two prospective studies was performed to identify clinical characteristics affecting the degree of AR-C124910XX formation during the first six hours after 180 mg ticagrelor loading dose in the setting of ACS. Both linear and multiple regression analyses indicated that ACS patients presenting with ST-elevation myocardial infarction or suffering from diabetes mellitus are more likely to have decreased rate of ticagrelor metabolism during the acute phase of ACS. Administration of morphine during ACS was found to negatively influence transformation of ticagrelor into AR-C124910XX when assessed with linear regression analysis, but not with multiple regression analysis. On the other hand, smoking appears to increase the degree of ticagrelor transformation in ACS patients. Mechanisms underlying our findings and their clinical significance warrant further research.Peer reviewedFinal Published versio