The number of malignant sites in the KMC model is shown to follow a mixed mathematical increasing expression containing both exponential and power law parts, characteristic of fractal growth phenomena [27].
The emission scenario A1B shows important changes in the far future, reaching a positive (>0, in mathematical terms) increase up to +60 days/year homogeneously distributed over the whole Mediterranean region, especially on the coast of the Provence (France) and on the Black Sea coast.
However, when re-entering the galactic disc as it does every 20 25 million years it comes under the influence of the far stronger "disc tides", which, according to mathematical models, increase the flux of Oort cloud comets into the inner Solar System by a factor of 4, thus leading to a massive increase in the likelihood of a devastating comet impact.
With the addition of multiple patches the complexity of the mathematical system increases dramatically.
The techniques for performing trade-off analyses have developed substantially in recent years aided by mathematical advancement, increased computing power, and emerging insights into systems behaviour.
In recent years, climate-health modelling has benefited from computational advances in fitting complex mathematical models; increasing availability of environmental, socioeconomic, and disease surveillance datasets; and improved ability to understand and model the climate system.
This combined with all kinds of other changes in the financial markets from the 1980s and 1990s - junk bonds, globalization, mathematical modeling, increases in leverage, deregulation, and large over-the-counter derivatives markets - turned the largest investment banks into something completely different.
Mathematical modeling increases the potential for using computers to describe complex molecular interactions numerically.
"This is an excellent example of the application of mathematical modeling to increase our understanding of the behavior of extinct species," says Nick Milne, a functional anatomist with the University of Western Australia in Crawley.
Finally, we used mathematical modeling to increase our understanding of the data.
