A statistical approach to identify superluminous supernovae and probe their diversity

We investigate the identification of hydrogen-poor superluminous supernovae (SLSNe I) using a photometric analysis, without including an arbitrary magnitude threshold. We assemble a homogeneous sample of previously classified SLSNe I from the literature, and fit their light curves using Gaussian processes. From the fits, we identify four photometric parameters that have a high statistical significance when correlated, and combine them in a parameter space that conveys information on their luminosity and color evolution. This parameter space presents a new definition for SLSNe I, which can be used to analyse existing and future transient datasets. We find that 90% of previously classified SLSNe I meet our new definition. We also examine the evidence for two subclasses of SLSNe I, combining their photometric evolution with spectroscopic information, namely the photospheric velocity and its gradient. A cluster analysis reveals the presence of two distinct groups. `Fast' SLSNe show fast light curves and color evolution, large velocities, and a large velocity gradient. `Slow' SLSNe show slow light curve and color evolution, small expansion velocities, and an almost non-existent velocity gradient. Finally, we discuss the impact of our analyses in the understanding of the powering engine of SLSNe, and their implementation as cosmological probes in current and future surveys.Comment: 16 pages, 9 figures, accepted by ApJ on 23/01/201

The volumetric rate of calcium-rich transients in the local universe

We present a measurement of the volumetric rate of `calcium-rich' optical transients in the local universe, using a sample of three events from the Palomar Transient Factory (PTF). This measurement builds on a detailed study of the PTF transient detection efficiencies, and uses a Monte Carlo simulation of the PTF survey. We measure the volumetric rate of calcium-rich transients to be higher than previous estimates: $1.21^{+1.13}_{-0.39}\times10^{-5}$ events yr$^{-1}$ Mpc$^{-3}$. This is equivalent to 33-94% of the local volumetric type Ia supernova rate. This calcium-rich transient rate is sufficient to reproduce the observed calcium abundances in galaxy clusters, assuming an asymptotic calcium yield per calcium-rich event of ~0.05$\mathrm{M}_{\odot}$. We also study the PTF detection efficiency of these transients as a function of position within their candidate host galaxies. We confirm as a real physical effect previous results that suggest calcium-rich transients prefer large physical offsets from their host galaxies.Comment: Accepted for publication in ApJ. 9 pages, 5 figure

Strong convergence rates of probabilistic integrators for ordinary differential equations

Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\ Comput.}, 2017), to establish mean-square convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially-bounded local Lipschitz constants all have the same mean-square convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. These and similar results are proven for probabilistic integrators where the random perturbations may be state-dependent, non-Gaussian, or non-centred random variables.Comment: 25 page

The Southern Vilnius Photometric System. IV. The E Regions Standard Stars

This paper is the fourth in a series on the extension of the Vilnius photometric system to the southern hemisphere. Observations were made of 60 stars in the Harvard Standard E regions to increase a set of standard stars.Comment: 6 pages, TeX, requires 2 macros (baltic2.tex, baltic4.tex) included no figures, to be published in Baltic Astronomy, Vol 6, pp1-6 (1997

The Optimal Uncertainty Algorithm in the Mystic Framework

We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a framework for the communication and comparison of UQ results. In particular, this framework does not implicitly impose inappropriate assumptions nor does it repudiate relevant information. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that given a set of assumptions and information, there exist bounds on uncertainties obtained as values of optimization problems and that these bounds are optimal. It provides a uniform environment for the optimal solution of the problems of validation, certification, experimental design, reduced order modeling, prediction, extrapolation, all under aleatoric and epistemic uncertainties. OUQ optimization problems are extremely large, and even though under general conditions they have finite-dimensional reductions, they must often be solved numerically. This general algorithmic framework for OUQ has been implemented in the mystic optimization framework. We describe this implementation, and demonstrate its use in the context of the Caltech surrogate model for hypervelocity impact

Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as extreme values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions, they have finite-dimensional reductions. As an application, we develop Optimal Concentration Inequalities (OCI) of Hoeffding and McDiarmid type. Surprisingly, contrary to the classical sensitivity analysis paradigm, these results show that uncertainties in input parameters do not necessarily propagate to output uncertainties. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact, suggesting the feasibility of the framework for important complex systems

A note on the algebraic growth rate of Poincar\'e series for Kleinian groups

In this note we employ infinite ergodic theory to derive estimates for the algebraic growth rate of the Poincar\'e series for a Kleinian group at its critical exponent of convergence.Comment: 8 page

Theory of dopants and defects in Co-doped TiO2 anatase

We report first-principles microscopic calculations of the formation energy, electrical activity, and magnetic moment of Co dopants and a variety of native defects in TiO2 anatase. Using these results, we use equilibrium thermodynamics to predict the resulting carrier concentration, the average magnetic moment per Co, and the dominant oxidation state of Co. The predicted values are in good agreement with experiment under the assumption of O-poor growth conditions. In this regime, a substantial fraction of Co dopants occupy interstitial sites as donors. The incomplete compensation of these donors by substitutional Co acceptors then leads to n-type behavior, as observed experimentally.Comment: 8 pages, 3 figures, 1 table, revise