Engagement With a Behavior Change App for Alcohol Reduction: Data Visualization for Longitudinal Observational Study

BACKGROUND: Behavior change apps can develop iteratively, where the app evolves into a complex, dynamic, or personalized intervention through cycles of research, development, and implementation. Understanding how existing users engage with an app (eg, frequency, amount, depth, and duration of use) can help guide further incremental improvements. We aim to explore how simple visualizations can provide a good understanding of temporal patterns of engagement, as usage data are often longitudinal and rich. OBJECTIVE: This study aims to visualize behavioral engagement with Drink Less, a behavior change app to help reduce hazardous and harmful alcohol consumption in the general adult population of the United Kingdom. METHODS: We explored behavioral engagement among 19,233 existing users of Drink Less. Users were included in the sample if they were from the United Kingdom; were 18 years or older; were interested in reducing their alcohol consumption; had a baseline Alcohol Use Disorders Identification Test score of 8 or above, indicative of excessive drinking; and had downloaded the app between May 17, 2017, and January 22, 2019 (615 days). Measures of when sessions begin, length of sessions, time to disengagement, and patterns of use were visualized with heat maps, timeline plots, k-modes clustering analyses, and Kaplan-Meier plots. RESULTS: The daily 11 AM notification is strongly associated with a change in engagement in the following hour; reduction in behavioral engagement over time, with 50.00% (9617/19,233) of users disengaging (defined as no use for 7 or more consecutive days) 22 days after download; identification of 3 distinct trajectories of use, namely engagers (4651/19,233, 24.18% of users), slow disengagers (3679/19,233, 19.13% of users), and fast disengagers (10,903/19,233, 56.68% of users); and limited depth of engagement with 85.076% (7,095,348/8,340,005) of screen views occurring within the Self-monitoring and Feedback module. In addition, a peak of both frequency and amount of time spent per session was observed in the evenings. CONCLUSIONS: Visualizations play an important role in understanding engagement with behavior change apps. Here, we discuss how simple visualizations helped identify important patterns of engagement with Drink Less. Our visualizations of behavioral engagement suggest that the daily notification substantially impacts engagement. Furthermore, the visualizations suggest that a fixed notification policy can be effective for maintaining engagement for some users but ineffective for others. We conclude that optimizing the notification policy to target both effectiveness and engagement is a worthwhile investment. Our future goal is to both understand the causal effect of the notification on engagement and further optimize the notification policy within Drink Less by tailoring to contextual circumstances of individuals over time. Such tailoring will be informed from the findings of our micro-randomized trial (MRT), and these visualizations were useful in both gaining a better understanding of engagement and designing the MRT

Ergodic Jacobi matrices and conformal maps

We study structural properties of the Lyapunov exponent $\gamma$ and the density of states $k$ for ergodic (or just invariant) Jacobi matrices in a general framework. In this analysis, a central role is played by the function $w=-\gamma+i\pi k$ as a conformal map between certain domains. This idea goes back to Marchenko and Ostrovskii, who used this device in their analysis of the periodic problem

Finding community structure in networks using the eigenvectors of matrices

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio

Fast algorithm for calculating two-photon absorption spectra

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Choosing party leaders: Anglophone democracies, British parties and the limits of comparative politics

Since 1965, Britain’s major political parties have radically, and repeatedly, changed the ways in which they choose their leaders. Building on a recent comparative study of party leadership selection in the five principal Anglophone (‘Westminster’) parliamentary democracies (Cross and Blais, 2012a), this article first outlines a theoretical framework that purports to explain why the major parties in three of those countries, including Britain, have adopted such reform. It then examines why five major British parties have done so since 1965. It argues that, while Cross and Blais’ study makes a significant contribution to our knowledge and understanding of processes of party leadership selection reform in Anglophone parliamentary democracies, it has limited explanatory power when applied to changes enacted by the major parties in modern and contemporary Britain. Instead, the adoption of such reform in the British context is ultimately best understood and explained by examining both the internal politics and external circumstances of individual parties

Quasisymmetric graphs and Zygmund functions

A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class $\Lambda_*$. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps.Comment: 21 pages, no figure

Nutrient density of beverages in relation to climate impact

The food chain contributes to a substantial part of greenhouse gas (GHG) emissions and growing evidence points to the urgent need to reduce GHGs emissions worldwide. Among suggestions were proposals to alter food consumption patterns by replacing animal foods with more plant-based foods. However, the nutritional dimensions of changing consumption patterns to lower GHG emissions still remains relatively unexplored. This study is the first to estimate the composite nutrient density, expressed as percentage of Nordic Nutrition Recommendations (NNR) for 21 essential nutrients, in relation to cost in GHG emissions of the production from a life cycle perspective, expressed in grams of CO2-equivalents, using an index called the Nutrient Density to Climate Impact (NDCI) index. The NDCI index was calculated for milk, soft drink, orange juice, beer, wine, bottled carbonated water, soy drink, and oat drink. Due to low-nutrient density, the NDCI index was 0 for carbonated water, soft drink, and beer and below 0.1 for red wine and oat drink. The NDCI index was similar for orange juice (0.28) and soy drink (0.25). Due to a very high-nutrient density, the NDCI index for milk was substantially higher (0.54) than for the other beverages. Future discussion on how changes in food consumption patterns might help avert climate change need to take both GHG emission and nutrient density of foods and beverages into account

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The paper presents numerical simulations performed on dielectric properties of two-dimensional binary composites on eleven regular space filling tessellations. First, significant contributions of different parameters, which play an important role in the electrical properties of the composite, are introduced both for designing and analyzing material mixtures. Later, influence of structural differences and intrinsic electrical properties of constituents on the composite's over all electrical properties are investigated. The structural differences are resolved by the spectral density representation approach. The numerical technique, without any {\em a-priori} assumptions, for extracting the spectral density function is also presented.Comment: 24 pages, 8 figure and 7 tables. It is submitted to IEEE Transactions on Dielectrics and Electrical Insulatio