J. Joseph Fowler

Collection and Visualization of Dietary Behavior and Reasons for Eating Using Twitter

Background Increasing an individual’s awareness and understanding of their dietary habits and reasons for eating may help facilitate positive dietary changes. Mobile technologies allow individuals to record diet-related behavior in real time from any location; however, the most popular software applications lack empirical evidence supporting their efficacy as health promotion tools. Objective The purpose of this study was to test the feasibility and acceptability of a popular social media software application (Twitter) to capture young adults’ dietary behavior and reasons for eating. A secondary aim was to visualize data from Twitter using a novel analytic tool designed to help identify relationships among dietary behaviors, reasons for eating, and contextual factors. Methods Participants were trained to record all food and beverages consumed over 3 consecutive days (2 weekdays and 1 weekend day) using their mobile device’s native Twitter application. A list of 24 hashtags (#) representing food groups and reasons for eating were provided to participants to guide reporting (eg, #protein, #mood). Participants were encouraged to annotate hashtags with contextual information using photos, text, and links. User experience was assessed through a combination of email reports of technical challenges and a 9-item exit survey. Participant data were captured from the public Twitter stream, and frequency of hashtag occurrence and co-occurrence were determined. Contextual data were further parsed and qualitatively analyzed. A frequency matrix was constructed to identify food and behavior hashtags that co-occurred. These relationships were visualized using GMap algorithmic mapping software. Results A total of 50 adults completed the study. In all, 773 tweets including 2862 hashtags (1756 foods and 1106 reasons for eating) were reported. Frequently reported food groups were #grains (n=365 tweets), #dairy (n=221), and #protein (n=307). The most frequently cited reasons for eating were #social (activity) (n=122), #taste (n=146), and #convenience (n=173). Participants used a combination of study-provided hash tags and their own hash tags to describe behavior. Most rated Twitter as easy to use for the purpose of reporting diet-related behavior. “Maps” of hash tag occurrences and co-occurrences were developed that suggested time-varying diet and behavior patterns. Conclusions Twitter combined with an analytical software tool provides a method for capturing real-time food consumption and diet-related behavior. Data visualization may provide a method to identify relationships between dietary and behavioral factors. These findings will inform the design of a study exploring the use of social media and data visualization to identify relationships between food consumption, reasons for engaging in specific food-related behaviors, relevant contextual factors, and weight and health statuses in diverse populations.

Characterization of unlabeled level planar graphs

We present the set of planar graphs that always have a simultaneous geometric embedding with a strictly monotone path on the same set of n vertices, for any of the n! possible mappings. These graphs are equivalent to the set of unlabeled level planar (ULP) graphs that are level planar over all possible labelings. Our contributions are twofold. First, we provide linear time drawing algorithms for ULP graphs. Second, we provide a complete characterization of ULP graphs by showing that any other graph must contain a subgraph homeomorphic to one of seven forbidden graphs.

An SPQR-Tree Approach to Decide Special Cases of Simultaneous Embedding with Fixed Edges

We present a linear-time algorithm for solving the simultaneous embedding problem with fixed edges (SEFE) for a planar graph and a pseudoforest (a graph with at most one cycle) by reducing it to the following embedding problem: Given a planar graph G, a cycle C of G, and a partitioning of the remaining vertices of G, does there exist a planar embedding in which the induced subgraph on each vertex partite of G ∖ C is contained entirely inside or outside C? For the latter problem, we present an algorithm that is based on SPQR-trees and has linear running time. We also show how we can employ SPQR-trees to decide SEFE for two planar graphs where one graph has at most two cycles and the intersection is a pseudoforest in linear time. These results give rise to our hope that our SPQR-tree approach might eventually lead to a polynomial-time algorithm for deciding the general SEFE problem for two planar graphs.

Characterization of unlabeled level planar trees

Consider a graph G drawn in the plane so that each vertex lies on a distinct horizontal line lj = {(x, j) | x ∈ R}. The bijection φ that maps the set of n vertices V to a set of distinct horizontal lines lj forms a labeling of the vertices. Such a graph G with the labeling φ is called an n-level graph and is said to be n-level planar if it can be drawn with straight-line edges and no crossings while keeping each vertex on its own level. In this paper, we consider the class of trees that are n-level planar regardless of their labeling. We call such trees unlabeled level planar (ULP). Our contributions are three-fold. First, we provide a complete characterization of ULP trees in terms of a pair of forbidden subtrees. Second, we show how to draw ULP trees in linear time. Third, we provide a linear time recognition algorithm for ULP trees.

Minimum level nonplanar patterns for trees

Minimum level nonplanar (MLNP) patterns play the role for level planar graphs that the forbidden Kuratowksi subdivisions K5 and K3,3 play for planar graphs. We add two MLNP patterns for trees to the previous set of tree patterns given by Healy et al. Neither of these patterns match any of the previous patterns. We show that this new set of patterns completely characterizes level planar trees.

Simultaneous graph embedding with bends and circular arcs

We consider the problem of simultaneous embedding of planar graphs. We demonstrate how to simultaneously embed a path and an n-level planar graph and how to use radial embeddings for curvilinear simultaneous embeddings of a path and an outerplanar graph. We also show how to use star-shaped levels to find 2-bends per path edge simultaneous embeddings of a path and an outerplanar graph. All embedding algorithms run in O(n) time.

Characterizations of Restricted Pairs of Planar Graphs Allowing Simultaneous Embedding with Fixed Edges

A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the Euclidean plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same simple curve in the simultaneous drawing. Determining in polynomial time which pairs of graphs share a simultaneous embedding with fixed edges (SEFE) has been open. We give a necessary and sufficient condition for whether a SEFE exists for pairs of graphs whose union is homeomorphic to K 5 or K 3,3 . This allows us to characterize the class of planar graphs that always have a SEFE with any other planar graph. We also characterize the class of biconnected outerplanar graphs that always have a SEFE with any other outerplanar graph. In both cases, we provide efficient algorithms to compute a SEFE. Finally, we provide a linear-time decision algorithm for deciding whether a pair of biconnected outerplanar graphs has a SEFE.

Colored simultaneous geometric embeddings

We introduce the concept of colored simultaneous geometric embeddings as a generalization of simultaneous graph embeddings with and without mapping. We show that there exists a universal pointset of size n for paths colored with two or three colors. We use these results to show that colored simultaneous geometric embeddings exist for: (1) a 2-colored tree together with any number of 2-colored paths and (2) a 2-colored outerplanar graph together with any number of 2-colored paths. We also show that there does not exist a universal pointset of size n for paths colored with five colors. We finally show that the following simultaneous embeddings are not possible: (1) three 6-colored cycles, (2) four 6-colored paths, and (3) three 9-colored paths.

Strongly-Connected Outerplanar Graphs with Proper Touching Triangle Representations

A proper touching triangle representation

On the characterization of level planar trees by minimal patterns

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