Quantifying the contributions, or weights, of comparisons or single studies to the estimates in a network meta-analysis (NMA) is an active area of research. We extend this work to include the contributions of paths of evidence. We present a general framework, based on the path-design matrix, that describes the problem of finding path contributions as a linear equation. The resulting solutions may have negative coefficients. We show that two known approaches, called shortestpath and randomwalk, are special solutions of this equation, and both meet an optimization criterion, as they minimize the sum of absolute path contributions. In general, there is an infinite set of solutions, which can be identified using the generalized inverse (Moore-Penrose pseudoinverse). We consider two further special approaches. For large networks we find that shortestpath is superior with respect to run time and variability, compared to the other approaches, and is thus recommended in practice. The path-weights framework also has the potential to answer more general research questions in NMA.

In this article, we find an α-valuation for disjoint union of some bipartite graphs and the tensor product of paths and even cycles.

In this data paper, we propose an open dataset (named SROADEX) containing more than 527,000 image tiles of 256 × 256 pixels stored in the lossless PNG format, tagged at pixel level with road information. The dataset covers approximately 8650 km2 of the Spanish territory, is divided in train, validation and test sets and can be used by researchers and professionals for training other extraction solutions and benchmarking additional models. The SROADEX dataset is available under a CC-BY 4.0 licence and can be freely downloaded from the Zenodo repository.

Outdoor public recreation spaces are important settings for leisure and physical activity. Adolescents\' use of these spaces may contribute to social connectedness via social interaction with peers and the community in these settings. However, research on this topic is limited. This exploratory study examined associations of frequency of visitation and physical activity in outdoor public recreation spaces with social connectedness among adolescents in Melbourne, Australia.
Adolescents self-reported their frequency of visitation to parks, trails, beach/lake, and sports facilities; frequency of physical activity in a park, local street or path, and their street; and social connectedness. Separate analyses were conducted for visitation (n = 349, 15.4 ± 1.6 years, 58% female) and physical activity (n = 441, 15.4 ± 1.6 years, 59% female) using multilevel linear regression models.
No significant associations were observed for frequency of visitation to a park (B = 0.86, 95% CI = - 0.26, 1.99), trails (B = 0.41, 95% CI = - 0.61, 1.44), beach/lake (B = - 0.44, 95% CI = - 1.46, 0.57), or sports facilities (B = 0.64, 95% CI = - 0.43, 1.70), nor for frequency of physical activity in their street (B = - 0.07, 95% CI = - 0.46, 0.31), local street/path (B = - 0.05, 95% CI = - 0.43, 0.33) or in a park (B = 0.23, 95% CI = - 0.14, 0.60) with adolescents\' social connectedness.
The findings did not support the hypothesis that visiting and being active in outdoor public recreation spaces are associated with adolescents\' social connectedness. Future research should consider the duration and context of outdoor public recreation space use (e.g., sports, socialising, relaxing alone) and whether different types and/or a combination of public spaces are more/less conducive to social connectedness.

Based on the conceptual basis of information theory, we propose a novel mutual information measure-\'path-based mutual information\'. This information measure results from the representation of a set of random variables as a probabilistic graphical model. The edges in this graph are modeled as discrete memoryless communication channels, that is, the underlying data is ergodic, stationary, and the Markov condition is assumed to be applicable. The associated multilinear stochastic maps, tensors, transform source probability mass functions into destination probability mass functions. This allows for an exact expression of the resulting tensor of a cascade of discrete memoryless communication channels in terms of the tensors of the constituting communication channels in the paths. The resulting path-based information measure gives rise to intuitive, non-negative, and additive path-based information components-redundant, unique, and synergistic information-as proposed by Williams and Beer. The path-based redundancy satisfies the axioms postulated by Williams and Beer, the identity axiom postulated by Harder, and the left monotonicity axiom postulated Bertschinger. The ordering relations between redundancies of different joint collections of sources, as captured in the redundancy lattices of Williams and Beer, follow from the data processing inequality. Although negative information components can arise, we speculate that these either result from unobserved variables, or from adding additional sources that are statistically independent from all other sources to a system containing only non-negative information components. This path-based approach illustrates that information theory provides the concepts and measures for a partial information decomposition.

Analyses of the relationship between levels of implementation and outcomes of school-based social and emotional learning (SEL) interventions are relatively infrequent and are typically narrowly focused. Thus, our objective was to assess the relationship between variability in a range of implementation dimensions and intervention outcomes in the Promoting Alternative Thinking Strategies (PATHS) curriculum. Implementation of PATHS was examined in 69 classrooms across 23 schools in the first year of a major randomized controlled trial. Implementation data were generated via classroom-level structured observations. In addition to factual data on dosage and reach, exploratory factor analysis of observer ratings revealed two distinct implementation dimensions, namely, \"quality and participant responsiveness\" and \"procedural fidelity.\" Student social-emotional skills, pro-social behavior, internalizing symptoms, and externalizing problems were captured through child self-report and teacher informant-report surveys (N = 1721). Hierarchical linear modeling of study data revealed that higher implementation quality and participant responsiveness was associated with significantly lower ratings of students\' externalizing problems at 12-month follow-up. Conversely, and contrary to expectations, higher dosage was associated with significantly lower pro-social behavior and social-emotional skills at 12-month follow-up. No significant associations were found between variability in either procedural fidelity or reach and any intervention outcomes. The implications of these findings are discussed, and study limitations are noted.

How do animals follow demarcated paths? Different species are sensitive to optic flow and one control solution is to maintain the balance of flow symmetry across visual fields; however, it is unclear whether animals are sensitive to changes in asymmetries when steering along curved paths. Flow asymmetries can alter the global properties of flow (i.e. flow speed) which may also influence steering control. We tested humans steering curved paths in a virtual environment. The scene was manipulated so that the ground plane to either side of the demarcated path produced larger or smaller asymmetries in optic flow. Independent of asymmetries and the locomotor speed, the scene properties were altered to produce either faster or slower globally averaged flow speeds. Results showed that rather than being influenced by changes in flow asymmetry, steering responded to global flow speed. We conclude that the human brain performs global averaging of flow speed from across the scene and uses this signal as an input for steering control. This finding is surprising since the demarcated path provided sufficient information to steer, whereas global flow speed (by itself) did not. To explain these findings, existing models of steering must be modified to include a new perceptual variable: namely global optic flow speed.

A number of classroom-based interventions have been developed to improve social and behavioral outcomes for students, yet few studies have examined how these programs impact the teachers who are implementing them. Impacts on teachers may affect students and therefore also serve as an important proximal outcome to examine. The current study draws upon data from a school-based randomized controlled trial testing the impact of two prevention programs. In one intervention condition, teachers were trained in the classroom behavior management program, PAX Good Behavior Game (PAX GBG). In a second intervention condition, teachers were trained to use an integrated program, referred to as PATHS to PAX, of the PAX GBG and a social and emotional learning curriculum called Promoting Alternative Thinking Strategies (PATHS©). This study aimed to determine whether both interventions positively impacted teachers, with a particular interest in the teachers\' own beliefs and perceptions regarding self-efficacy, burnout, and social-emotional competence. The sample included 350 K-5 teachers across 27 schools (18 schools randomized to intervention, 9 to control). Multilevel latent growth curve analyses indicated that the PATHS to PAX condition generally demonstrated the most benefits to teachers, relative to both the control and PAX GBG conditions. These findings suggest that school-based preventive interventions can have a positive impact on teachers\' beliefs and perceptions, particularly when the program includes a social-emotional component. Several possible mechanisms might account for the added benefit to teachers. Additional research is needed to better understand how these programs impact teachers, as well as students.