The Knapsack Problem with Neighbour Constraints

We study a constrained version of the knapsack problem in which dependencies between items are given by the adjacencies of a graph. In the 1-neighbour knapsack problem, an item can be selected only if at least one of its neighbours is also selected. In the all-neighbours knapsack problem, an item can be selected only if all its neighbours are also selected. We give approximation algorithms and hardness results when the nodes have both uniform and arbitrary weight and profit functions, and when the dependency graph is directed and undirected.Comment: Full version of IWOCA 2011 pape

Routing Regardless of Network Stability

We examine the effectiveness of packet routing in this model for the broad class next-hop preferences with filtering. Here each node v has a filtering list D(v) consisting of nodes it does not want its packets to route through. Acceptable paths (those that avoid nodes in the filtering list) are ranked according to the next-hop, that is, the neighbour of v that the path begins with. On the negative side, we present a strong inapproximability result. For filtering lists of cardinality at most one, given a network in which an equilibrium is guaranteed to exist, it is NP-hard to approximate the maximum number of packets that can be routed to within a factor of O(n^{1-\epsilon}), for any constant \epsilon >0. On the positive side, we give algorithms to show that in two fundamental cases every packet will eventually route with probability one. The first case is when each node's filtering list contains only itself, that is, D(v)={v}. Moreover, with positive probability every packet will be routed before the control plane reaches an equilibrium. The second case is when all the filtering lists are empty, that is, $\mathcal{D}(v)=\emptyset$. Thus, with probability one packets will route even when the nodes don't care if their packets cycle! Furthermore, with probability one every packet will route even when the control plane has em no equilibrium at all.Comment: ESA 201

TORIC VARIETIES AND COBORDISM

A long-standing problem in cobordism theory has been to find convenient manifolds to represent cobordism classes. For example, in the late 1950\u27s, Hirzebruch asked which complex cobordism classes can be represented by smooth connected algebraic varieties. This question is still open. Progress can be made on this and related problems by studying certain convenient connected algebraic varieties, namely smooth projective toric varieties. The primary focus of this dissertation is to determine which complex cobordism classes can be represented by smooth projective toric varieties. A complete answer is given up to dimension six, and a partial answer is described in dimension eight. In addition, the role of smooth projective toric varieties in the polynomial ring structure of complex cobordism is examined. More specifically, smooth projective toric varieties are constructed as polynomial ring generators in most dimensions, and evidence is presented suggesting that a smooth projective toric variety can be chosen as a polynomial generator in every dimension. Finally, toric varieties with an additional fiber bundle structure are used to study some manifolds in oriented cobordism. In particular, manifolds with certain fiber bundle structures are shown to all be cobordant to zero in the oriented cobordism ring

Fall 2022 Student Textbook Survey Results

During the Fall 2022 semester, eleven Oberlin Group institutions in association with the Open and Equitable Access to Scholarship Working Group conducted a student textbook survey adapted from the 2016 Florida Virtual Campus survey and the 2019 Gettysburg College survey. The goal of the project was to gain a better understanding of how the costs of course materials impact our own students. This presentation provides an overview of those results as well as action steps we as a campus can take to better support our students. This study was coordinated by the Oberlin Group - Open and Equitable Working Group

Assessing the affects of treatment services, financial assistance, race/ethnicity, and income on the criminal justice outcomes of women on probation.

The aim of this study is to examine the affect that treatment services have on the criminal justice outcomes of women on probation. The research to date on the treatment services provided to the criminal justice population has tended to focus on prisoners rather than probationers, with even fewer studies that include samples of women on probation. This study will investigate the impact on criminal justice outcomes of services intended to treat issues identified to increase recidivism among female probationers, such as substance use disorders, illicit drug use, mental health issues, and poverty. An additional assessment is conducted to determine the affect of race/ethnicity on the recidivism outcomes of the participants given the history of racial discrimination within the U.S. criminal justice system. The sample for this study included 247 women on probation that participated in three waves of data collection over a four-year period. Logistic regression models, chi-square tests, and t tests were performed to determine the relationship that treatment services for substance use, mental health, employment services, and financial assistance had on the recidivism outcomes of the participants over the course of the study. Information on the race/ethnicity and income of the participants were also investigated in the logistic regression models, chi-square tests, and t tests to assess their affect on recidivism outcomes. The findings of the logistic regression indicated that reception of more social security or disability throughout the study reduced the likelihood of recidivism, while receiving more substance use and mental health treatment services during the study increased occurrences of recidivism. Additionally, the findings from the chi-square and t test identified that participants recidivated significantly more often if they received more substance use and mental health treatment during the study in addition to using more types of illicit drugs in the past 12 months at the baseline interview, and were less likely to experience recidivism if they accessed more social security or disability throughout the study. The implications for policies and practices at U.S. probation departments are also discussed, which include expansion of affordable evidence-based practices for substance use and mental health, providing financial assistance to address the high instances of poverty among the population, elimination of the financial barriers placed on offenders by the criminal justice system, and eradication of policing practices that target African Americans

SCOTTS RUN MINERS' WALK: A COMMUNITY OF CURATORS OF THE COAL HISTORY IN SCOTTS RUN, WEST VIRGINIA

West Virginia's coal mining history is long and rich, with many cultures intersecting with the industry. As coal mining shrank from the industry it used to be, poor families were left in the once-prosperous coal towns, unable to afford to move to find better jobs. The natural landscape had yielded to the industry, and the remnants of mining remain, evocative relics of an earlier era. As the coal companies moved on, these towns and landscapes were left at a loss for how to move forward. This thesis investigates ways to revitalize an abandoned landscape and to engage people in their cultural history. Reading the remnants and fragments of industry, and the landscape as clearings, seams and runs, it proposes architectural interventions in six places on the site that are connected by various path types meant to encourage visitors to experience the culture and history of coal mining in West Virginia