We consider a class of weakly interacting particle systems of mean-field type. The interactions between the particles are encoded in a graph sequence, i.e. two particles are interacting if and only if they are connected in the underlying graph. We establish a law of large numbers for the empirical measure of the system that holds whenever the graph sequence is convergent to a graphon. The limit is the solution of a non-linear Fokker–Planck equation weighted by the (possibly random) graphon limit. In contrast with the existing literature, our analysis focuses on both deterministic and random graphons: no regularity assumptions are made on the graph limit and we are able to include general graph sequences such as exchangeable random graphs. Finally, we identify the sequences of graphs, both random and deterministic, for which the associated empirical measure converges to the classical McKean–Vlasov mean-field limit.

Throughout the Progressive Era, settlement houses in the urban Northeast and Midwest operated robust summer camp programs for the children of their neighborhoods. Each summer, campers enjoyed two weeks of hiking, swimming, nature study, and relaxation. This article argues that summer camps exemplified the environmental agenda of settlement-house workers during the Progressive Era. Unlike smoke abatement, sanitation reform, or playground construction, which addressed isolated components of the urban environment, camps allowed them to articulate a deeply ecological critique of the industrial city. Settlement-house workers constructed camp landscapes and daily programming in response to problems endemic to atmosphere, city streets, and immigrants’ homes, providing children with a total environmental change while meanwhile pursuing slower and more piecemeal reforms back in the city. Settlement house leaders and other Progressive Era reformers discerned an intimate connection between landscapes and morality, which summer camps allowed them to address since they could reform individual behavior in addition to combatting structural inequities. Summer camps demonstrate that settlement-house workers’ environmental philosophy permeated their reform agendas, influencing social work and recreation in addition to politics and public health.

We generalize the notion of consequence relation standard in abstract treatments of logic to accommodate intuitions of relevance. The guiding idea follows the use criterion, according to which in order for some premises to have some conclusion(s) as consequence(s), the premises must each be used in some way to obtain the conclusion(s). This relevance intuition turns out to require not just a failure of monotonicity, but also a move to considering consequence relations as obtaining between multisets. We motivate and state basic definitions of relevant consequence relations, both in single conclusion (asymmetric) and multiple conclusion (symmetric) settings, as well as derivations and theories, guided by the use intuitions, and prove a number of results indicating that the definitions capture the desired results (at least in many cases).

Mobile robots are a key component for the automation of many tasks that either require high precision or are deemed too hazardous for human personnel. One of the typical duties for mobile robots in the industrial sector is to perform trajectory tracking, which involves pursuing a specific path through both space and time. In this paper, an iterative learning-based procedure for highly accurate tracking is proposed. This contribution shows how data-based techniques, namely Gaussian process regression, can be used to tailor a motion model to a specific reoccurring reference. The procedure is capable of explorative behavior meaning that the robot automatically explores states around the prescribed trajectory, enriching the data set for learning and increasing the robustness and practical training accuracy. The trade-off between highly accurate tracking and exploration is done automatically by an optimization-based reference generator using a suitable cost function minimizing the posterior variance of the underlying Gaussian process model. While this study focuses on omnidirectional mobile robots, the scheme can be applied to a wide range of mobile robots. The effectiveness of this approach is validated in meaningful real-world experiments on a custom-built omnidirectional mobile robot where it is shown that explorative behavior can outperform purely exploitative approaches.

We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups $\operatorname{SL}_{2}(q)$ for q even over a large enough field of odd characteristics. This article is a continuation of our article Trivial Source Character Tables of $\operatorname{SL}_{2}(q)$, where we considered, in particular, the case in which q is odd in non-defining characteristic.

Associations between fruit and vegetable (FV) consumption and mental health are suggested, largely from observational studies. This systematic review aimed to identify and summarise all published controlled intervention studies investigating the effects of FV consumption on mental health in adults. Four academic databases (Medline, PsycINFO, PubMed, Web of Science) were searched on 16 September 2022, over all years, for studies that used an intervention design; included FV consumption; included an appropriate non-FV-consumption control; used a validated measure of mental health and were conducted in healthy adults or adults with solely a depressive or anxiety-related condition. Study details were tabulated and combined using meta-analyses. Risk of bias was assessed using the domains of the Cochrane Collaboration. Six studies, enrolling 691 healthy adults and reporting on one or more mental health outcomes, were found. Meta-analyses found small and imprecise effects of FV consumption for: psychological well-being (4 studies, 289 participants) standardised mean difference (SMD) = 0·07 (95 % CI −0·17, 0·30), P = 0·58, I2 = 0 %; depressive symptomology (3 studies, 271 participants) SMD = –0·15 (95 % CI −0·40, 0·10), P = 0·23, I2 = 47 % and anxiety-related symptomology (4 studies, 298 participants) SMD = –0·15 (95 % CI −0·39, 0·08), P = 0·20, I2 = 71 %. Some benefit for psychological well-being was found in change-from-baseline data: SMD = 0·28 (95 % CI 0·05, 0·52), P = 0·02, I2 = 0 %. Risk of bias was high in many studies. Limitations include the consideration only of published studies and stem from the studies found. Given the few, limited studies available and the small size of effects, stronger evidence is needed before recommending FV consumption for mental health.

The traditional rationale of federal diversity jurisdiction is to protect out-of-state parties from the risk of an appearance of state-court bias in favor of an in-state adversary. Yet a strikingly high percentage—more than 50 percent—of original domestic-diversity cases are filed by in-state plaintiffs. Why these in-state plaintiffs invoke diversity jurisdiction is a question that has largely been ignored in the literature. Drawing on docket data and an original dataset based on responses to a survey sent to more than twelve thousand attorneys who represented in-state plaintiffs in domestic-diversity cases, I find that these plaintiffs can be grouped into roughly three categories. The first category is composed of tort cases, filed by individual plaintiffs against corporate defendants, that are eligible for consolidation with an existing federal multi-district litigation. The second category is composed of in-state corporate plaintiffs represented by attorneys who tend to represent defendants in federal court and who invoke diversity jurisdiction primarily based on perceptions of advantages of federal procedure, efficiencies and conveniences of federal practice, and superior quality of federal court. The third category is composed of in-state plaintiffs represented by attorneys who tend to represent plaintiffs in state court and who invoke diversity jurisdiction to preempt the defendant’s likely removal of the case. My findings offer grounds for reforming diversity jurisdiction in more tailored and nuanced ways than have previously been proposed.