Strong convergence rates of probabilistic integrators for ordinary differential equations

Probabilistic integration of a continuous dynamical system is a way of systematically introducing discretisation 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. (Stat Comput 27(4):1065–1082, 2017. https://doi.org/10.1007/s11222-016-9671-0), 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.

     

The racialized patterns of police violence: The critical importance of research as praxis

The tragic killing of George Floyd at the hands of the police resulted in hundreds of thousands of protestors marching in the streets demanding change. The call for change criticized the killing of Blacks by law enforcement and challenged White supremacy as an institution of social control and racial violence. A key component of the marches and protests was a message to the residents of the United States: “Black Lives Matter.” As society grapples with a reckoning, researchers studying police violence for the past 6 decades have been empirically and theoretically debating the reasons why use of force by law enforcement continues to have a higher proportion of Black and Brown victims compared to Whites. Although the research on fatal police killings was studied by only a small number of individuals prior to 2014, after the killing of Michael Brown in Ferguson, Missouri the research in different areas of the country increased rapidly as did the forms of analysis and research disciplines making their own contributions. The Washington Post and Guardian news agencies established that deaths at the hands of the police were occurring for at least 900 to 1100 individual deaths per year for which firearms resulted in the greatest cause of death. As US government agencies failed to produce a national data source on police involved killings, the media took a leading role in providing greater national understanding. The authors examine what role academic researchers contribute to the discussion for solutions, particularly those from marginalized backgrounds. As protestors march, lawyers sue and defend, and politicians create new forms of legislation, researchers need to play a more important role initiating critical studies, making sense of the data, and providing a theoretical framework for which police violence can be understood. This article will provide an overview of the literature on racialized police violence, point out key patterns involving racial and ethnic disparities, and emphasize how researchers can play a more important role in advocating for change.     

Self-exciting threshold models for time series of counts with a finite range

In this article, an integer-valued self-exciting threshold model with a finite range based on the binomial INARCH(1) model is proposed. Important stochastic properties are derived, and approaches for parameter estimation are discussed. A real-data example about the regional spread of public drunkenness in Pittsburgh demonstrates the applicability of the new model in comparison to existing models. Feasible modifications of the model are presented, which are designed to handle special features such as zero-inflation.     

Decomposing the increase in men’s time on childcare during the great recession

In this paper, I examine the time men spent on childcare during the recession of 2007–2009. The recession provides a sudden change in the employment opportunities of men relative to women in the United States. Using the American Time Use Survey and the linked Current Population Survey, I show that this lopsided shock to employment opportunities was accompanied by an increase in the average amount of time men spent on childcare. In particular, men’s average time on physical care for children increased during the recession; this is an element of childcare that men perform less than women. I decompose the total change in average time on childcare into behavioral, compositional, and between group change. A behavioral change among employed men accounted for the majority of the total increase in the average time spent on childcare; among men who are out of the labor force, the increase is entirely due to compositional changes.     

Social-ecological innovation: adaptive responses to urban environmental conditions

Novel approaches to natural resource management, particularly those which promote stakeholder participation, have been put forward as fundamental ingredients for establishing resilient, polycentric forms of environmental governance. This is nowhere more pertinent than in the case of the complex adaptive systems associated with urban areas. Decentralisation of urban green space management has been posited as an element thereof which, according to resilience thinking, should contribute to the adaptive capacity of cities and the ecosystem services upon which they rely. Implicit in this move towards increased adaptive capacity is the ability to manage through innovation. Although the importance of innovation towards system adaptability has been acknowledged, little work has thus far been carried out which demonstrates that innovative use of urban green space represents a form of adaptive response to environmental conditions. The current paper reports on research which maps examples of organised social-ecological innovation (OSEI) in an urban study area and evaluates them as adaptive responses to local environmental conditions which may contribute to system resilience. The results present OSEI as a coherent body of responses to local social and environmental deprivation, exhibiting diversity and adaptability according to individual contexts. The study therefore provides evidence for the importance of local stakeholder-led innovation as in the building of adaptive capacity in urban social-ecological systems.     

Optimal acceptance sampling for modules F and F1 of the European Measuring Instruments Directive

ABSTRACT

Acceptance sampling plans offered by ISO 2859-1 are far from optimal under the conditions for statistical verification in modules F and F1 as prescribed by Annex II of the Measuring Instruments Directive (MID) 2014/32/EU, resulting in sample sizes that are larger than necessary. An optimised single-sampling scheme is derived, both for large lots using the binomial distribution and for finite-sized lots using the exact hypergeometric distribution, resulting in smaller sample sizes that are economically more efficient while offering the full statistical protection required by the MID.     

Multi-neighborhood based iterated tabu search for routing and wavelength assignment problem

The routing and wavelength assignment problem (RWA) has shown to be NP-hard if the wavelength continuity constraint and the objective of minimizing the number of wavelengths are considered. This paper introduces a multi-neighborhood based iterated tabu search algorithm (MN-ITS), which consists of three neighborhoods with a unified incremental evaluation method, to solve the min-RWA problem. The proposed MN-ITS algorithm is tested on a set of widely studied real world instances as well as a set of challenging random ones in the literature. Comparison with other reference algorithms shows that the MN-ITS algorithm is able to improve five best upper bounds obtained by other competitive reference algorithms in the literature. This paper also presents an analysis to show the significance of the unified incremental evaluation technique and the combination of multiple neighborhoods.     

Obesity and sex ratios in the U.S.

This paper studies how rising male incarceration and its impact on marriage markets has affected female incentives to gain weight. Exogenous variation in marriage market conditions is obtained from differential trends in male incarceration rates across markets defined by race, location and age. We provide evidence that marriage market conditions do in fact affect the incidence of obesity. In particular, we find that increases in male imprisonment that reduced the male–female sex-ratio explain about 18 % of the increase in the female obesity rate for African-Americans in the United States over the 1990s. Results are particularly large for those in the younger age group (ages 18–23).