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We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their findings in a technical report. The students are required to produce a simple first-order differential equation and find the solution, given varying initial conditions. The students are also required to analyze a more complex, nonlinear ODE system model of the fermentation process. In dealing with the nonlinear system of equations, we provide the students a Mathematica file to reduce the time spent developing the model, but allow for more time to interpret the model. We also share some perspectives on the implementation of the project, provide alternative implementations, and possible extensions to the project.

The rental market's failure to provide housing for low-income immigrants now entering Australia has raised issues about the immigrants’ housing requirements and how these can be met. To date, only ...

Timely and appropriate diagnosis and treatment of patients with gastroentero- pancreatic neuroendocrine neoplasms is a difficult clinical endeavor. The field is particularly dynamic, not only in terms of expanding therapeutic options, but in the classifications and bio - logical principles that underpin good decision-making. Acknowledging the confusion created by past changes and the inevitability of future development, we combine our clinical experience with a review of the literature to frame the current understanding of gastroenteropancreatic neuroendocrine neoplasms in terms of a set of principles that have stabilized in the midst of this change. Firstly, we present five principles that guide classification of neuroendocrine neoplasms; specifically principles of prognostic classification, mechanisms of tumorigenesis, undiagnosed disease burden, clues regarding genetic etiology, and typical clinical presentation. Secondly, we offer five clinical principles upon which to build a therapeutic strategy. Specifically, these treatment principles include the separation of options by tumor cell differentiation, and the site of the primary lesion in well differentiated tumors. Chromogranin A is a moderately useful biomarker. Treatment should only be considered by clinicians in a multidisciplinary team, and in the face of multiple potential therapeutic options without a supporting evidence base, clinical trial enrolment remains imperative. Therefore, we provide a current synopsis of classification of gastroenteropancreatic neuroendocrine neoplasms, and their etiology, clinical presentation, and management in a novel framework of ten relatively stable principles.