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Data science tools can help elucidate trends from clickstreams and other interactions generated by students actively using interactive textbooks. Specifically, data generated when using animations, which are multi-step visuals with text captions, will be presented in this work. Each animation step divides content into appropriate chunks, and so aligns with tenets of cognitive load theory. Both the quantity and timing of students’ clicks record provide large data sets when examining students across hundreds of animations and multiple cohorts. Specifically, an interactive textbook for a chemical engineering course in Material and Energy Balances will be examined and build upon data presented previously. While most of the previous data focused on very high reading completion rates (>99% median) compared to traditional textbooks (20-50%), a deeper examination of how long students take when watching animations will be explored. With over 140 unique animations and tens of thousands of completed views over five cohorts, a spectral clustering algorithm applied to students’ animation view times distinguished several types of animation watching behavior as well as monitor changes in this animation watching behavior over the course of a semester. After examining different numbers of clusters, two or three clusters in each chapter captured the animation usage. These clusters usually correspond to a group of students who watched animations at 1x speed (longer), another group who watched at 2x speed (shorter), and a third group, when present, who watched irregularly, including skipping animations. Overall, more students belonged to the belonged to the cluster with longer view times, with 63% of students aggregated over all cohorts and chapters compared to 35% of students in the cluster with shorter view times. The remaining 2% of students belonged to the irregular cluster, which was present in less than one quarter of the chapters. Many students stayed in the same cluster between chapters, while a smaller fraction switched between the longer and shorter clusters. 

Interactive textbooks generate big data through student reading participation, including animations, question sets, and auto-graded homework. Animations are multi-step, dynamic visuals with text captions. By dividing new content into smaller chunks of information, student engagement is expected to be high, which aligns with tenets of cognitive load theory. Specifically, students’ clicks are recorded and measure usage, completion, and view time per step and for entire animations. Animation usage data from an interactive textbook for a chemical engineering course in Material and Energy Balances accounts for 60,000 animation views across 140+ unique animations. Data collected across five cohorts between 2016 and 2020 used various metrics to capture animation usage including watch and re-watch rates as well as the length of animation views. Variations in view rate and time were examined across content, parsed by book chapter, and five animation characterizations (Concept, Derivation, Figures and Plots, Physical World, and Spreadsheets). Important findings include: 1) Animation views were at or above 100% for all chapters and cohorts, 2) Median view time varies from 22 s (2-step) to 59 s (6-step) - a reasonable attention span for students and cognitive load, 3) Median view time for animations characterized as Derivation was the longest (40 s) compared to Physical World animations, which resulted in the shortest time (20 s). 

With the prevalence of interaction on social media, data compiled from these networks are perfect for analyzing social trends. One such trend that this paper aims to address is political homophily. Evidence of political homophily is well researched and indicates that people have a strong tendency to interact with others with similar political ideologies. Additionally, as links naturally form in a social network, either through recommendations or indirect interaction, new links are very likely to reinforce communities. This serves to make social media more insulated and ultimately more polarizing. We aim to address this problem by providing link recommendations that will reduce network homophily. We propose several variants of common neighbor-based link prediction algorithms that aim to recommend links to users who are similar but also would decrease homophily. We demonstrate that acceptance of these recommendations can indeed reduce the homophily of the network, whereas acceptance of link recommendations from a standard common neighbors algorithm does not. 

Networks and temporal point processes serve as fundamental building blocks for modeling complex dynamic relational data in various domains. We propose the latent space Hawkes (LSH) model, a novel generative model for continuous-time networks of relational events, using a latent space representation for nodes. We model relational events between nodes using mutually exciting Hawkes processes with baseline intensities dependent upon the distances between the nodes in the latent space and sender and receiver specific effects. We demonstrate that our proposed LSH model can replicate many features observed in real temporal networks including reciprocity and transitivity, while also achieving superior prediction accuracy and providing more interpretable fits than existing models. 

The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks. 

In many application settings involving networks, such as messages between users of an on-line social network or transactions between traders in financial markets, the observed data consist of timestamped relational events, which form a continuous-time network. We propose the Community Hawkes Independent Pairs (CHIP) generative model for such networks. We show that applying spectral clustering to an aggregated adjacency matrix constructed from the CHIP model provides consistent community detection for a growing number of nodes and time duration. We also develop consistent and computationally efficient estimators for the model parameters. We demonstrate that our proposed CHIP model and estimation procedure scales to large networks with tens of thousands of nodes and provides superior fits than existing continuous-time network models on several real networks. 

Contagious processes on networks, such as spread of disease through physical proximity or information diffusion over social media, are continuous-time processes that depend upon the pattern of interactions between the individuals in the network. Continuous-time stochastic epidemic models are a natural fit for modeling the dynamics of such processes. However, prior work on such continuous-time models doesn’t consider the dynamics of the underlying interaction network which involves addition and removal of edges over time. Instead, researchers have typically simulated these processes using discrete-time approximations, in which one has to trade off between high simulation accuracy and short computation time. In this paper, we incorporate continuous-time network dynamics (addition and removal of edges) into continuous-time epidemic simulations. We propose a rejection-sampling based approach coupled with the well-known Gillespie algorithm that enables exact simulation of the continuous-time epidemic process. Our proposed approach gives exact results, and the computation time required for simulation is reduced as compared to discrete-time approximations of comparable accuracy.