An Unsolved Graph Theory Problem: Comparing Solutions of Grades 4, 6, & 8

2019 ◽  
pp. 428-433
Author(s):  
Jenna R. O´Dell ◽  
Todd R. Frauenholtz
Keyword(s):  
United States ◽  
Graph Theory ◽  
Grade Level ◽  
Unsolved Problem ◽  
Generalized Solutions ◽  
Theory Problem ◽  
Midwestern United States ◽  
Caterpillar Graphs

This study investigated how students in Grades 4, 6, and 8 reasoned through a non-routine, unsolved problem. The study took place at a K-8 school in the Midwestern United States. Each grade participated in two or three task-based sessions lasting between 45 and 60 minutes with the researchers. During the sessions, students engaged in the Graceful Tree Conjecture where they examined graceful labelling for Star, Path, and Caterpillar Graphs. We examined differences in students’ generalized solutions across the grades and how they were able to provide justifications and state generalizations of a graceful labelling for the graphs in the Path Class. Descriptions of students’ generalized solutions are included for each grade level.

Inequality in the Promised Land

2020 ◽  
Vol 9 (1) ◽  
pp. 177-180
Author(s):  
Muhammad Sharif Uddin
Keyword(s):  
United States ◽  
Minority Students ◽  
Doctoral Dissertation ◽  
Ethnographic Study ◽  
Suburban Area ◽  
Midwestern United States ◽  
Minority Community ◽  
Promised Land ◽  
Land Race ◽  
The Relationship

Inequality in the promised land: Race, resources, and suburban schooling is a well-written book by L’ Heureux Lewis-McCoy. The book is based on Lewis-McCoy’s doctoral dissertation, that included an ethnographic study in a suburban area named Rolling Acres in the Midwestern United States. Lewis-McCoy studied the relationship between families and those families’ relationships with schools. Through this study, the author explored how invisible inequality and racism in an affluent suburban area became the barrier for racial and economically minority students to grow up academically. Lewis-McCoy also discovered the hope of the minority community for raising their children for a better future.

A review of the Forensic Entomology literature in the midwestern United States

2021 ◽  
Vol 3 (5) ◽  
Author(s):  
Krystal R. Hans ◽  
Kelie Yoho ◽  
Hannah Robbins ◽  
Lauren M. Weidner
Keyword(s):  
United States ◽  
Forensic Entomology ◽  
Midwestern United States

Prevalence of Neonicotinoids and Sulfoxaflor in Alluvial Aquifers in a High Corn and Soybean Producing Region of the Midwestern United States

2021 ◽  
pp. 146762
Author(s):  
Darrin A. Thompson ◽  
Dana W. Kolpin ◽  
Michelle L. Hladik ◽  
Kimberlee K. Barnes ◽  
John D. Vargo ◽  
...  
Keyword(s):  
United States ◽  
Midwestern United States ◽  
Alluvial Aquifers

scholarly journals Predicting the Dynamics of the COVID-19 Pandemic in the United States Using Graph Theory-Based Neural Networks

2021 ◽  
Vol 18 (7) ◽  
pp. 3834
Author(s):  
Mohammad Reza Davahli ◽  
Krzysztof Fiok ◽  
Waldemar Karwowski ◽  
Awad M. Aljuaid ◽  
Redha Taiar
Keyword(s):  
United States ◽  
Neural Networks ◽  
Graph Theory ◽  
Predictive Model ◽  
Short Term Memory ◽  
The United States ◽  
Graphical Analysis ◽  
Economic Consequences ◽  
Current Status ◽  
The Usa

The COVID-19 pandemic has had unprecedented social and economic consequences in the United States. Therefore, accurately predicting the dynamics of the pandemic can be very beneficial. Two main elements required for developing reliable predictions include: (1) a predictive model and (2) an indicator of the current condition and status of the pandemic. As a pandemic indicator, we used the effective reproduction number (Rt), which is defined as the number of new infections transmitted by a single contagious individual in a population that may no longer be fully susceptible. To bring the pandemic under control, Rt must be less than one. To eliminate the pandemic, Rt should be close to zero. Therefore, this value may serve as a strong indicator of the current status of the pandemic. For a predictive model, we used graph neural networks (GNNs), a method that combines graphical analysis with the structure of neural networks. We developed two types of GNN models, including: (1) graph-theory-based neural networks (GTNN) and (2) neighborhood-based neural networks (NGNN). The nodes in both graphs indicated individual states in the US states. While the GTNN model’s edges document functional connectivity between states, those in the NGNN model link neighboring states to one another. We trained both models with Rt numbers collected over the previous four days and asked them to predict the following day for all states in the USA. The performance of these models was evaluated with the datasets that included Rt values reflecting conditions from 22 January through 26 November 2020 (before the start of COVID-19 vaccination in the USA). To determine the efficiency, we compared the results of two models with each other and with those generated by a baseline Long short-term memory (LSTM) model. The results indicated that the GTNN model outperformed both the NGNN and LSTM models for predicting Rt.

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