Children’s Experiences of Family Disruption in Sweden

This paper examines the living arrangements of Swedish children from 1970 through 1999 using the Level of Living Survey. Sweden, with low levels of economic inequality and a generous welfare state, provides an important context for studying socioeconomic differentials in family structure. We find that, although differences by parent education in non-marital childbearing are substantial and persistent, cohabiting childbearing is common even among highly educated Swedish parents. Educational differences in family instability were small during the 1970s, but increased over time as a result of rising union disruption among less-educated parents (secondary graduates or less). Children in more advantaged families experienced substantially less change in family structure and instability over the study period. Although cohabiting parents were more likely to separate than parents married at the child’s birth, differences were greater for the less-educated. Data limitations precluded investigating these differences across time. We conclude that educational differences in children’s living arrangements in Sweden have grown, but remain small in international comparisons.children, cohabitation, family dynamics, family structure

A Geometric Perspective on Sparse Filtrations

We present a geometric perspective on sparse filtrations used in topological data analysis. This new perspective leads to much simpler proofs, while also being more general, applying equally to Rips filtrations and Cech filtrations for any convex metric. We also give an algorithm for finding the simplices in such a filtration and prove that the vertex removal can be implemented as a sequence of elementary edge collapses

Optimal rates of convergence for persistence diagrams in Topological Data Analysis

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results