Pipe failure is a common occurrence in America's water distribution networks. In this paper, we propose a tri-level stochastic network interdiction formulation to model the fortification (via sensor placement), attack (i.e., failure of pipeline components), and defense (i.e., recovery from the impacts of interdiction) for a water pipeline network. We adapt column-constraint generation for our algorithmic approach to solve for the optimal solution. In the final section of our paper, we apply our model and approach to a few well-studied networks and discuss our numerical studies.
In spatial voting games, the concept of the yolk is crucial as it represents the smallest sphere intersecting all median hyperplanes and reflects the central tendency of voters' preferences. Median hyperplanes are those that split the voter ideal points into two groups, with no more than half on either side. The yolk's radius is not just a measure of central tendency but also informs on the stability of majority rule outcomes, often disrupted by strategic voting and coalitional dynamics. The research poster also presents 3D visualizations from various perspectives, illustrating a potential counterexample to an existing algorithm. This counterexample is defined by specific coordinates and binding hyperplanes with distinct normals. The ongoing research aims to ascertain whether this counterexample reveals an inherent flaw or if it necessitates a refinement of the current algorithm, thereby enhancing the precision of yolk calculation in spatial voting scenarios.
The expansion of cloud computing industries has spurred efforts to understand the behaviors of large switch networks due to the increasing scale of data we use and store. This study focuses on observable phenomena such as the total queue length and clearing times from switch networks to observe their stationary behavior in respect to 'n', the size of the switch network. The stability of switch network is assured by the max-weight algorithm that serves jobs in high-performance polynomial runtime complexity. While job scheduling relies on the current state of the queue lengths within the switch network, the state of queue lengths within the switch follows a discrete time Markov chain. In this research, we implemented a simulation of switch network using the Hungarian algorithm in Python, and this study aims to identify the stationary distributions of switch network phenomena with respect to 'n'.
Fair distribution in allocation problems is a well-studied problem where a variety of fairness criteria have been studied. In this project, we study the maximin fairness criteria that generalizes the classical cake cutting problem to the setting for indivisible goods. For two players, “you divide and I choose” strategy satisfies the fairness criteria but such a simple strategy does not exists for three players. The project aim to understand how good maximin shares exist for three and more players. The project also explores the connections to other fairness criteria including envy-freeness and average share.
This project delves into the impact of highly processed food on health, spotlighting the United States' notably low Healthy Life Expectancy (HALE) compared to other developed nations, as highlighted by WHO data from 2000 to 2018 (before Covid pandemic). HALE measures years living without assistance. The overconsumption of highly processed food is one of the major contributors to poor health performance. This research employs online resources, government survey results, and field studies to examine dietary habits, connecting overconsumption of processed foods to the U.S.'s shortened HALE and exploring broader health implications.
Following a move by California to mandate later start times for high school students, the San Francisco Unified School District (SFUSD) proposed new optimized start times for the 2022-2023 school year. School start times are a complex issue that affect families, teachers, and staff in many different ways. After the change, we conducted a survey of families and staff from SFUSD to assess their thoughts on the change. We found that families tend to prefer moving later rather than moving earlier, and that stakeholder satisfaction may depend not only on the outcome of the process but also on its perceived fairness.