Mathematics and Statistics

The North Pacific Ocean is highly productive, hosting many of the world’s largest groundfish populations and supporting a thriving fishing industry. Numerous regulations have been implemented to control the incidental take of non-target bycatch. Individual and Pooled Bycatch Quotas have recently been proposed as instruments that could further encourage the avoidance of such bycatch and increase enforceability of bycatch caps

The North Pacific Ocean is highly productive, hosting many of the world’s largest groundfish populations and supporting a thriving fishing industry. Numerous regulations have been implemented to control the incidental take of non-target bycatch. Individual and Pooled Bycatch Quotas have recently been proposed as instruments that could further encourage the avoidance of such bycatch and increase enforceability of bycatch caps at less -than-entire-fishery levels of operation. The recent advent of fishing cooperatives such as the Pacific Whiting Conservation Cooperative and the Pollock Conservation Cooperatives create an additional impetus for examining the characteristics of pool and vessel specific bycatch quotas. We have constructed an object-oriented, hierarchical simulation that allows us to aggregate hauls of individual fish, up to single vessels, vessel pools, fleets (pools of vessel pools), and the entire fishery. This simulator is written in the object-oriented programming lan...

Since the cost of petroleum fluctuates widely, it is advisable to optimize extraction of oil and other hydrocarbon products form existing oil reserves. Because of the costs involved in recovering oil from a reservoir, predicting reservoir performance can be a useful tool for determining whether continued extraction might be profitable. This can be done using computer simulations of the physical processes involved such as pressure/head, fluid velocities, and so forth. Fluid flow within a reservoir occurs at a very small scale relative to the size of the reservoir. This size difference makes performing simulations at the physically appropriate scale unfeasible. Homogenization is a technique used in reservoir simulation to upscale small scale dependent behavior, such as a permeability tensor, to make simulation feasible. To calculate a homogenized permeability tensor, the solution to a system of uncoupled elliptic partial differential equations must be found repeatedly throughout the r...

Integrating experimental biology laboratory exercises with mathematical modeling can be an effective tool to enhance mathematical relevance for biologists and to emphasize biological realism for mathematicians. This paper describes a lab project designed for and tested in an undergraduate biomathematics course. In the lab, students follow and track the paths of individual brine shrimp confined in shallow salt water in a Petri dish. Students investigate the question, “Is the movement well characterized as a 2-dimensional random walk?” Through open, but directed discussions, students derive the corresponding partial differential equation, gain an understanding of the solution behavior, and model brine shrimp dispersal under the experimental conditions developed in class. Students use data they collect to estimate a diffusion coefficient, and perform additional experiments of their own design tracking shrimp migration for model validation. We present our teaching philosophy, lecture notes, instructional and lab procedures, and the results of our class-tested experiments so that others can implement this exercise in their classes. Our own experience has led us to appreciate the pedagogical value of allowing students and faculty to grapple with open-ended questions, imperfect data, and the various issues of modeling biological phenomena.

OBJECTIVES: To examine the effects of caring for a spouse with dementia on the caregiver's risk for incident dementia.DESIGN: Population-based study of incident dementia in spouses of persons with dementia.SETTING: Rural county in northern Utah.PARTICIPANTS: Two thousand four hundred forty-two subjects (1,221 married couples) aged 65 and older.MEASUREMENTS: Incident dementia was diagnosed in 255 subjects, with onset defined as age when subject met Diagnostic and Statistical Manual of Mental Disorders, Third Edition, Revised, criteria for dementia. Cox proportional hazards regression tested the effect of time-dependent exposure to dementia in one's spouse, adjusted for potential confounders.RESULTS: A subject whose spouse experienced incident dementia onset had a six times greater risk for incident dementia as subjects whose spouses were dementia free (hazard rate ratio (HRR)=6.0, 95% confidence interval (CI)=2.2–16.2, P<.001). In sex-specific analyses, husbands had higher risks (HRR=11.9, 95% CI=1.7–85.5, P=.01) than wives (HRR=3.7, 95% CI=1.2–11.6, P=.03).CONCLUSION: The chronic and often severe stress associated with dementia caregiving may exert substantial risk for the development of dementia in spouse caregivers. Additional (not mutually exclusive) explanations for findings are discussed.