Background Cardiovascular disease (CVD) annually claims more lives and costs more dollars than any other disease globally amid widening health disparities, despite the known significant reductions in this burden by low cost dietary changes. The world's first medical school-based teaching kitchen therefore launched CHOP-Medical Students as the largest known multisite cohort study of hands-on cooking and nutrition education versus traditional curriculum for medical students. Methods This analysis provides a novel integration of artificial intelligence-based machine learning (ML) with causal inference statistics. 43 ML automated algorithms were tested, with the top performer compared to triply robust propensity score-adjusted multilevel mixed effects regression panel analysis of longitudinal data. Inverse-variance weighted fixed effects meta-analysis pooled the individual estimates for competencies. Results 3,248 unique medical trainees met study criteria from 20 medical schools nationally from August 1, 2012, to June 26, 2017, generating 4,026 completed validated surveys. ML analysis produced similar results to the causal inference statistics based on root mean squared error and accuracy. Hands-on cooking and nutrition education compared to traditional medical school curriculum significantly improved student competencies (OR 2.14, 95% CI 2.00–2.28, p < 0.001) and MedDiet adherence (OR 1.40, 95% CI 1.07–1.84, p = 0.015), while reducing trainees' soft drink consumption (OR 0.56, 95% CI 0.37–0.85, p = 0.007). Overall improved competencies were demonstrated from the initial study site through the scale-up of the intervention to 10 sites nationally (p < 0.001). Discussion This study provides the first machine learning-augmented causal inference analysis of a multisite cohort showing hands-on cooking and nutrition education for medical trainees improves their competencies counseling patients on nutrition, while improving students' own diets. This study suggests that the public health and medical sectors can unite population health management and precision medicine for a sustainable model of next-generation health systems providing effective, equitable, accessible care beginning with reversing the CVD epidemic.
Abstract. The unit ball random geometric graph G = G d p (λ, n) has as its vertices n points distributed independently and uniformly in the unit ball in R d , with two vertices adjacent if and only if their p-distance is at most λ. Like its cousin the Erdős-Rényi random graph, G has a connectivity threshold : an asymptotic value for λ in terms of n, above which G is connected and below which G is disconnected. In the connected zone, we determine upper and lower bounds for the graph diameter of G. Specifically, almost always, diamp(B)is the p-diameter of the unit ball B. We employ a combination of methods from probabilistic combinatorics and stochastic geometry.
An asymmetric binary covering code of length n and radius R is a subset C of the n-cube Q n such that every vector x 2 Q n can be obtained from some vector c 2 C by changing at most R 1's of c to 0's, where R is as small as possible. K þ ðn; RÞ is defined as the smallest size of such a code. We show K þ ðn; RÞ 2 Yð2 n =n R Þ for constant R; using an asymmetric sphere-covering bound and probabilistic methods. We showThese two results are extended to near-constant R and % R R; respectively. Various bounds on K þ are given in terms of the total number of 0's or 1's in a minimal code. The dimension of a minimal asymmetric linear binary code (½n; R þ -code) is determined to be minf0; n À Rg:
We consider a variation of the chip-firing game in a induced subgraph S of a graph G. Starting from a given chip configuration, if a vertex v has at least as many chips as its degree, we can fire v by sending one chip along each edge from v to its neighbors. The game continues until no vertex can be fired. We will give an upper bound, in terms of Dirichlet eigenvalues, for the number of firings needed before a game terminates. We also examine the relations among three equinumerous families, the set of spanning forests on S with roots in the boundary of S, a set of "critical" configurations of chips, and a coset group, called the sandpile group associated with S.
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