Challenging variants of the Collatz Conjecture

The Collatz Conjecture (also known as the 3N + 1 problem) is simple to explain, yet proving that all positive integers following the Collatz Mapping must converge to 1 has eluded mathematicians for over half a century. Aaronson and Heule are exploring solving the Collatz Conjecture using an approach involving string rewrite systems: Aaronson transformed the Conjecture into a string rewrite system and Heule has been applying parallel SAT solvers on instances of this system. Similar approaches have been applied successfully to other mathematical problems. We started looking into simpler variants of the conjecture. This thesis defines some of these variants and investigates easily provable as well as very hard variants. We study the hardness of unsolved variants by computing the number of rewrite steps needed up to 1 billion. Our hardness prediction method suggests that proving termination of the challenging variants should be considerably easier compared to solving the original conjecture.Computer Science

Neoliberalism’s Eschewal of Dependency: Putting the Work of Ann Ulanov in Conversation with Economic Theory

The elections of Ronald Reagan in the United States and Margaret Thatcher in England were important markers for the rise of a conceptual framework that continues to dominate economic policy today in the United States and around the world. Neoliberalism, defined by the anthropologist David Harvey as an attitude that advocates dismantling of the welfare state, deregulation, and weakening of trade unions in the name of a free market society (2005), has grown from a set of somewhat obscure economic principles into a hegemonic force. A far cry from its somewhat obscure origins, it is now incorporated into the “common-sense” of many of the world’s leaders and thinkers to the point that its basic assumptions are taken for granted and unquestioned

Penal reform in Africa: The case of prison chaplaincy

Penal reform is a challenge across the world. In Africa, those who are incarcerated are especially vulnerable and often deprived of basic human rights. Prison conditions are generally dire, resources are limited, and at times undue force is used to control inmates. The public attitude towards offenders is also not encouraging. Reform efforts include finding alternative ways of sentencing such as community service, making use of halfway houses and reducing sentences. These efforts have not yet yielded the desired results. The four principles of retribution, deterrence, incapacitation and rehabilitation guide penal practice in Africa. Retribution and rehabilitation stand in tension. Deterrence and incapacitation aim at forcing inmates to conform to the social order. The article argues that prison chaplaincy can make a valuable contribution to restoring the dignity and humanity of those who are incarcerated. Chaplaincy can contribute to improving attitudes and practices in the penal system and society. In addition to the social objective of rehabilitation, prison ministry can, on a spiritual level, also facilitate repentance, forgiveness and reconciliation. The aim is the holistic restoration of human beings

Hydrologic Events and Water Quality in the Pigeon River, Ottawa County, Michigan

The Pigeon River drains a 16,765-ha agricultural watershed in western Ottawa County, Michigan and discharges into south-central Lake Michigan. Extensive areas of wetlands in the upper watershed were drained in the 1920s, causing significantly altered hydrology characteristics by flashy discharges during storms and periods of snowmelt. We studied stream chemistry and hydrology for a four-year period between September, 1996, and October, 2000, to determine water quality status, to estimate annual nutrient exports, and to evaluate the effects of different seasonal flow types. Results of our study confirmed that the upper reaches of the Pigeon River experience chronically degraded water quality, with contributions from both nonpoint and point sources. As a result, the watershed has high annual rates of nutrient export (approximately 10.8 kg ha-1 inorganic N and 0.25 kg ha-1 PO4-P). With the influx of groundwater, change in land use to forest, and development of natural stream channel characteristics in the lower mainstream, water quality at baseflow in this section of the Pigeon River improves to the point where coldwater fish populations should persist. Inputs of degraded water during high flows, however, produce periods of environmental stress and the fish population in the lower Pigeon includes only a low number of pollution-tolerant, warmwater species. Large summer storms are biologically stressful because of increased temperatures and reduced dissolved oxygen levels, while spring storms and snowmelt contribute substantially to total nutrient suspended solids exports. Efforts to improve water quality in this and similar agricultural watersheds need to emphasize major reductions in the nonpoint source inputs through substantial improvements in land and water management practices. Wetland restoration and implementation of other stormwater retention practices in such watersheds also are required to reverse the acute impacts of high stormwater discharges caused by past drainage and steam channelization

Agricultural Water Quality Index Field Handout

The Agricultural Water Quality Index (AWQI) is an assessment tool designed for use in agroecosystems. Most existing environmental indices and assessment tools focus on the stream channel and/or riparian zone (the area between the channel and active land use). In contrast, the AWQI places an emphasis on land use and soil types that play a significant role in hydrologic cycles and water quality characteristics within the watershed. The AWQI is designed to be used by agricultural technicians with limited experience in aquatic ecology; however, it does assume a reasonable background in soil characteristics. This index is intended for use during the active growing season (approximately mid-May through September). The purpose of the index is two-fold; to describe the level of vulnerability or potential environmental impact a particular farming operation may have to the stream environment, and to provide direction in developing farm management strategies that work to stabilize or improve water quality. The following are condensed instructions that are designed to assist the farmer, field technician, or agricultural consultant that may be performing the assessment. A more technical version of the AWQI is available to individuals seeking additional background information or more detail involving individual metrics within the index

AGRICULTURAL WATER QUALITY INDEX

The primary purpose of the Agricultural Water Quality Index (AWQI) is to provide the agricultural community with a practical technical method for conducting cost-effective water quality assessments of rivers and streams in agroecosystems. The protocols presented have been derived from extensive literature review and the results of field research in agroecosystems performed during the summer of 1997 by the authors of this index. This assessment tool is not intended to replace those already in use by state agencies or to be used without regional modifications

Innovating for the Health Care Safety Net: Sources of Funding

Illustrates barriers to conventional financing mechanisms faced by medical technology innovations for underserved, low-resource environments, such as remote monitoring and intervention. Proposes low-risk strategies for foundations and social investors