For principled model fitting in mathematical biology

The mathematical models used to capture features of complex, biological systems are typically non-linear, meaning that there are no generally valid simple relationships between their outputs and the data that might be used to validate them. This invalidates the assumptions behind standard statistical methods such as linear regression, and often the methods used to parameterise biological models from data are ad hoc. In this perspective, I will argue for an approach to model fitting in mathematical biology that incorporates modern statistical methodology without losing the insights gained through non-linear dynamic models, and will call such an approach principled model fitting. Principled model fitting therefore involves defining likelihoods of observing real data on the basis of models that capture key biological mechanisms.Comment: 7 pages, 3 figures. To appear in Journal of Mathematical Biology. The final publication is available at Springer via http://dx.doi.org/10.1007/s00285-014-0787-

Algebraic moment closure for population dynamics on discrete structures

Moment closure on general discrete structures often requires one of the following: (i) an absence of short closed loops (zero clustering); (ii) existence of a spatial scale; (iii) ad hoc assumptions. Algebraic methods are presented to avoid the use of such assumptions for populations based on clumps, and are applied to both SIR and macroparasite disease dynamics. One approach involves a series of approximations that can be derived systematically, and another is exact and based on Lie algebraic methods.Comment: 12 pages, 4 figure

Non-Markovian stochastic epidemics in extremely heterogeneous populations

A feature often observed in epidemiological networks is significant heterogeneity in degree. A popular modelling approach to this has been to consider large populations with highly heterogeneous discrete contact rates. This paper defines an individual-level non-Markovian stochastic process that converges on standard ODE models of such populations in the appropriate asymptotic limit. A generalised Sellke construction is derived for this model, and this is then used to consider final outcomes in the case where heterogeneity follows a truncated Zipf distribution.Comment: 10 pages, 1 figur

The kinetics of calcite precipation and related processes

This review is concerned with the kinetics of calcium carbonate formation and related processes which are important in many hard waters

Addressing Gun Violence in the United States

When compared with other high-income countries, gun violence is clearly a problem in the United States. Although homicide appears to be a more serious issue compared with other countries, suicide causes many more deaths per year than homicide does and therefore deserves at least as much attention. Discussion of gun policy has also focused heavily on mental illness, and although this is a potential factor in gun violence, we must also recognize that most people with mental illness are not dangerous. Other factors that contribute to risk of gun fatalities include social environment and access to guns, which are important points for policy intervention. Possible effective responses include expanded background checks and waiting periods. However, policies which reduce the number of guns available will not be possible until cultural change is made

The High Cost of Wisconsin's Dropout Rate

Outlines the scope of the high school dropout problem in Wisconsin and dropouts' risk of unemployment, health problems, and incarceration. Estimates costs to the state through reduced tax revenues, increased Medicaid costs, and high incarceration rates