Beyond Hartigan Consistency: Merge Distortion Metric for Hierarchical Clustering

Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given density can look very different than the correct limit tree. Specifically, Hartigan consistency permits two types of undesirable configurations which we term over-segmentation and improper nesting. Moreover, Hartigan consistency is a limit property and does not directly quantify difference between trees. In this paper we identify two limit properties, separation and minimality, which address both over-segmentation and improper nesting and together imply (but are not implied by) Hartigan consistency. We proceed to introduce a merge distortion metric between hierarchical clusterings and show that convergence in our distance implies both separation and minimality. We also prove that uniform separation and minimality imply convergence in the merge distortion metric. Furthermore, we show that our merge distortion metric is stable under perturbations of the density. Finally, we demonstrate applicability of these concepts by proving convergence results for two clustering algorithms. First, we show convergence (and hence separation and minimality) of the recent robust single linkage algorithm of Chaudhuri and Dasgupta (2010). Second, we provide convergence results on manifolds for topological split tree clustering

The Effects of Vascular Occlusion Training on Respiratory Exchange Ratio and Energy Expenditure When Coupled With Cardiovascular Training

International Journal of Exercise Science 8(1) : 57-64, 2015. Vascular occlusion training is a novel training modality that has received considerable attention in the exercise science literature. The current study is the first of its kind to look at the effects of vascular occlusion training on substrate utilization when combined with aerobic training. This study examined the effects of pairing a vascular occlusion training protocol with a bout of submaximal aerobic exercise on energy expenditure (EE) and fuel use during exercise. Subjects performed a 20 minute bout of sub-maximal aerobic exercise either exclusively, or after performing a body weight squat protocol either with or without vascular occlusion. Peak lactate concentrations, EE and respiratory exchange ratio (RER) were all measured. A repeated measures analysis of variance was performed to look at differences among groups and interactions among protocols. The results suggest no difference in peak lactate (7.29 mmol/dl vs. 10.17 mmol/dl; F=0.946; p\u3e0.05) or EE (92.09 Kcals vs 93.48 Kcals; F=0.898 p\u3e0.05) among protocols. However, there does appear to be a shift in substrate utilization towards fatty acid oxidation by performing either a vascular occlusion training protocol (mean RER= 0.836) or a protocol of body weight squats (mean RER= 0.823) prior to aerobic training in comparison to performing aerobic training alone (mean RER= 0.881). There were, however, no significant differences between the occlusion protocol and the body weight squat protocol prior to the aerobic training. These results suggest that while there are no differences in overall caloric expenditure between protocols, performing either a resistance training protocol or a vascular occlusion training protocol shifts substrate utilization in favor of fatty acid oxidation over the oxidation of carbohydrates

The Effects of Vascular Occlusion Training on Respiratory Quotient and Energy Expenditure When Coupled with Cardiovascular Training

Purpose: The Purpose of this study was to determine the effects of pairing a vascular occlusion training protocol with a bout of cardiovascular training on substrate utilization and caloric expenditure in healthy adults. Methods: 5 healthy adults were recruited to report to the lab one day a week for the duration of two hours for four consecutive weeks. During the first session informed consent was collected, a VO2max test was performed, and a familiarization session with vascular occlusion training was conducted. The next three sessions were randomized for each subject but consisted of the following three protocols. During Protocol A the subject performed 5 sets of body weight squats to volitional fatigue while having blood flow occluded to the quadriceps via 2 thigh sized blood pressure cuffs set at a pressure of 200mm/Hg. 30 seconds of rest was allowed between each set and during this period the cuffs were re-inflated to 200mm/Hg if any pressure was lost throughout the previous set. After completion of the final set blood lactate levels were analyzed in 1 minute intervals via a lactate plus portable analyzer until peak lactate was observed. After completion of the last set the subject then began a 20 minute segment of cardiovascular treadmill walking at an intensity that corresponded to 40-70% of predetermined VO2max. VO2 and VCO2 were collected during the 20 minute exercise bout, the 10 min EPOC, and for 50 minutes post-EPOC. Respiratory exchange ratio and total caloric expenditure as calculated by the Weir equation were computed for all three time segments. During Protocol B the subject performed 5 body weight squats without vascular occlusion and then performed the same 20 minute bout at the same intensity. Peak [lactate] after completion of the final set, respiratory exchange ratio and total caloric expenditure were collected for all three time segments again. Lastly during protocol C the subject performed the 20 minutes of cardiovascular training at the same intensity without performing any form of resistance training prior to beginning. RER and total caloric expenditure were collected again for all three time segments. Results: A repeated measures ANOVA revealed that there were significant differences between the respiratory exchange ratio during exercise and during EPOC between protocols (pDiscussion: There appears to be a shift in substrate utilization as a result of performing a vascular occlusion training protocol prior to cardiovascular training as reflected in the difference in RER. During the EPOC there were no significant differences between the vascular occlusion training and the cardiovascular training not preceded by occlusion however there appears to be a shift in substrate utilization by performing body weight squats to failure without occlusion prior to cardiovascular training as reflected in RER

Children’s and adolescents’ rising animal-source food intakes in 1990–2018 were impacted by age, region, parental education and urbanicity

Animal-source foods (ASF) provide nutrition for children and adolescents’ physical and cognitive development. Here, we use data from the Global Dietary Database and Bayesian hierarchical models to quantify global, regional and national ASF intakes between 1990 and 2018 by age group across 185 countries, representing 93% of the world’s child population. Mean ASF intake was 1.9 servings per day, representing 16% of children consuming at least three daily servings. Intake was similar between boys and girls, but higher among urban children with educated parents. Consumption varied by age from 0.6 at <1 year to 2.5 servings per day at 15–19 years. Between 1990 and 2018, mean ASF intake increased by 0.5 servings per week, with increases in all regions except sub-Saharan Africa. In 2018, total ASF consumption was highest in Russia, Brazil, Mexico and Turkey, and lowest in Uganda, India, Kenya and Bangladesh. These findings can inform policy to address malnutrition through targeted ASF consumption programmes.publishedVersio

Incident type 2 diabetes attributable to suboptimal diet in 184 countries

The global burden of diet-attributable type 2 diabetes (T2D) is not well established. This risk assessment model estimated T2D incidence among adults attributable to direct and body weight-mediated effects of 11 dietary factors in 184 countries in 1990 and 2018. In 2018, suboptimal intake of these dietary factors was estimated to be attributable to 14.1 million (95% uncertainty interval (UI), 13.8–14.4 million) incident T2D cases, representing 70.3% (68.8–71.8%) of new cases globally. Largest T2D burdens were attributable to insufficient whole-grain intake (26.1% (25.0–27.1%)), excess refined rice and wheat intake (24.6% (22.3–27.2%)) and excess processed meat intake (20.3% (18.3–23.5%)). Across regions, highest proportional burdens were in central and eastern Europe and central Asia (85.6% (83.4–87.7%)) and Latin America and the Caribbean (81.8% (80.1–83.4%)); and lowest proportional burdens were in South Asia (55.4% (52.1–60.7%)). Proportions of diet-attributable T2D were generally larger in men than in women and were inversely correlated with age. Diet-attributable T2D was generally larger among urban versus rural residents and higher versus lower educated individuals, except in high-income countries, central and eastern Europe and central Asia, where burdens were larger in rural residents and in lower educated individuals. Compared with 1990, global diet-attributable T2D increased by 2.6 absolute percentage points (8.6 million more cases) in 2018, with variation in these trends by world region and dietary factor. These findings inform nutritional priorities and clinical and public health planning to improve dietary quality and reduce T2D globally.publishedVersio