Strong generators in tensor triangulated categories

We show that in an essentially small rigid tensor triangulated category with connected Balmer spectrum there are no proper non-zero thick tensor ideals admitting strong generators. This proves, for instance, that the category of perfect complexes over a commutative ring without non-trivial idempotents has no proper non-zero thick subcategories that are strongly generated.Comment: 9 pages, comments welcom

Graphical models for mediation analysis

Mediation analysis seeks to infer how much of the effect of an exposure on an outcome can be attributed to specific pathways via intermediate variables or mediators. This requires identification of so-called path-specific effects. These express how a change in exposure affects those intermediate variables (along certain pathways), and how the resulting changes in those variables in turn affect the outcome (along subsequent pathways). However, unlike identification of total effects, adjustment for confounding is insufficient for identification of path-specific effects because their magnitude is also determined by the extent to which individuals who experience large exposure effects on the mediator, tend to experience relatively small or large mediator effects on the outcome. This chapter therefore provides an accessible review of identification strategies under general nonparametric structural equation models (with possibly unmeasured variables), which rule out certain such dependencies. In particular, it is shown which path-specific effects can be identified under such models, and how this can be done

Measuring the 3D shape of X-ray clusters

Observations and numerical simulations of galaxy clusters strongly indicate that the hot intracluster x-ray emitting gas is not spherically symmetric. In many earlier studies spherical symmetry has been assumed partly because of limited data quality, however new deep observations and instrumental designs will make it possible to go beyond that assumption. Measuring the temperature and density profiles are of interest when observing the x-ray gas, however the spatial shape of the gas itself also carries very useful information. For example, it is believed that the x-ray gas shape in the inner parts of galaxy clusters is greatly affected by feedback mechanisms, cooling and rotation, and measuring this shape can therefore indirectly provide information on these mechanisms. In this paper we present a novel method to measure the three-dimensional shape of the intracluster x-ray emitting gas. We can measure the shape from the x-ray observations only, i.e. the method does not require combination with independent measurements of e.g. the cluster mass or density profile. This is possible when one uses the full spectral information contained in the observed spectra. We demonstrate the method by measuring radial dependent shapes along the line of sight for CHANDRA mock data. We find that at least 10^6 photons are required to get a 5-{\sigma} detection of shape for an x-ray gas having realistic features such as a cool core and a double powerlaw for the density profile. We illustrate how Bayes' theorem is used to find the best fitting model of the x-ray gas, an analysis that is very important in a real observational scenario where the true spatial shape is unknown. Not including a shape in the fit may propagate to a mass bias if the x-ray is used to estimate the total cluster mass. We discuss this mass bias for a class of spacial shapes.Comment: 29 pages, 16 figure

Cotorsion torsion triples and the representation theory of filtered hierarchical clustering

We give a full classification of representation types of the subcategories of representations of an $m \times n$ rectangular grid with monomorphisms (dually, epimorphisms) in one or both directions, which appear naturally in the context of clustering as two-parameter persistent homology in degree zero. We show that these subcategories are equivalent to the category of all representations of a smaller grid, modulo a finite number of indecomposables. This equivalence is constructed from a certain cotorsion torsion triple, which is obtained from a tilting subcategory generated by said indecomposables.Comment: 39 pages; corrected the lists appearing in Cor. 1.6 and minor changes throughou

The obesity paradox in critically ill patients : a causal learning approach to a casual finding

Background While obesity confers an increased risk of death in the general population, numerous studies have reported an association between obesity and improved survival among critically ill patients. This contrary finding has been referred to as the obesity paradox. In this retrospective study, two causal inference approaches were used to address whether the survival of non-obese critically ill patients would have been improved if they had been obese. Methods The study cohort comprised 6557 adult critically ill patients hospitalized at the Intensive Care Unit of the Ghent University Hospital between 2015 and 2017. Obesity was defined as a body mass index of >= 30 kg/m(2). Two causal inference approaches were used to estimate the average effect of obesity in the non-obese (AON): a traditional approach that used regression adjustment for confounding and that assumed missingness completely at random and a robust approach that used machine learning within the targeted maximum likelihood estimation framework along with multiple imputation of missing values under the assumption of missingness at random. 1754 (26.8%) patients were discarded in the traditional approach because of at least one missing value for obesity status or confounders. Results Obesity was present in 18.9% of patients. The in-hospital mortality was 14.6% in non-obese patients and 13.5% in obese patients. The raw marginal risk difference for in-hospital mortality between obese and non-obese patients was - 1.06% (95% confidence interval (CI) - 3.23 to 1.11%,P = 0.337). The traditional approach resulted in an AON of - 2.48% (95% CI - 4.80 to - 0.15%,P = 0.037), whereas the robust approach yielded an AON of - 0.59% (95% CI - 2.77 to 1.60%,P = 0.599). Conclusions A causal inference approach that is robust to residual confounding bias due to model misspecification and selection bias due to missing (at random) data mitigates the obesity paradox observed in critically ill patients, whereas a traditional approach results in even more paradoxical findings. The robust approach does not provide evidence that the survival of non-obese critically ill patients would have been improved if they had been obese

Imputation strategies for natural effect models probing mediation

Natural effect models parameterize the natural direct and indirect effects of an exposure on an outcome in function of baseline covariates. Vansteelandt and colleagues introduced a regression mean imputation strategy for fitting these models. Compared to direct application of the mediation formula, this framework allows for (i) more easily interpretable effect estimates and (ii) more convenient hypothesis testing. So far, the statistical properties (robustness to model misspecification, and efficiency) of the considered imputation strategy are not well understood. For instance, in non-linear settings where traditional product-of-coefficients estimators for the indirect effect are applicable for assessing mediation under the null of no effect of exposure on mediator, these estimators outperform the imputation estimators in terms of efficiency when the imputation model is fitted using MLE. In this talk, we will discuss advanced imputation strategies to improve efficiency and robustness. We will discuss their implementation using the R package flexmed