The Mathematica Journal


Applying the Formal and General Approach to Problems in the Biological Sciences

Jim Karagiannis
Published March 24, 2015

A formal, axiomatic conceptualization of buffering action—generally applicable to any physical, chemical, or biological process—was first presented by B. M. Schmitt in 2005 [1, 2]. This article provides a series of tools designed to aid in the application of these concepts to both classical and non-classical buffering phenomena. To illustrate the utility of the approach in the biological sciences, an abstract measure of the magnitude of “genetic” buffering associated with an allele of the gene encoding the heat shock protein Hsp90 is determined. Read More »

Todd D. Allen
Published February 21, 2015

This article describes the implementation of RIFA, a computational biology algorithm designed to identify the genes most directly responsible for creating differences in phenotype between two biological states, for example, tumorous liver tissue versus cirrhotic liver tissue. Read More »

A. T. Spathis
Published January 16, 2015

There exists a range of explicit and approximate solutions to the cubic polynomial Rayleigh equation for the speed of surface waves across an elastic half-space. This article presents an alternative approach that uses Padé approximants to estimate the Rayleigh wave speed with five different approximations derived for two expansions about different points. Maximum relative absolute errors of between 0.34% and 0.00011% occur for the full range of the Poisson ratio from to 0.5. Even smaller errors occur when the Poisson ratio is restricted within a range of 0 to 0.5. For higher-order approximants, the derived expressions for the Rayleigh wave speed are more accurate than previously published solutions, but incur a slight cost in extra arithmetic operations, depending on the desired accuracy. Read More »