Mathematical model mimics melanoma

Mathematical model mimics melanoma. Left: melanoma cells grown in culture with normal cells form clusters that resemble proto-tumors. Right: Simulations using a modified version of the Widom-Rowlinson model replicate patterns of melanoma cell growth seen in laboratory experiments by controlling the exclusion area — the amount of space required — around two types of simulated…

New computational methodology gives unexpected answers to two Hilbert problems

A paper titled “Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems,” published in EMS Surveys in Mathematical Sciences describes a recent computational methodology related to the separation of mathematical objects from numeral systems involved in their representation. It allows mathematicians to work with infinities and infinitesimals numerically in a unique computational…

How to cut your lawn for grasshoppers

Picture a grasshopper landing randomly on a lawn of fixed area. If it then jumps a certain distance in a random direction, what shape should the lawn be to maximise the chance that the grasshopper stays on the lawn after jumping? One could be forgiven for wondering what the point of such a question might…

New paper answers causation conundrum

Red Tree #1, #3 by Piet Mondrian. The compression of information from one version to the next illustrates the concept of coarse-graining. Credit: Santa Fe Institute In a new paper published in a special issue of the Philosophical Transactions of the Royal Society A, SFI Professor Jessica Flack offers a practical answer to one of the…

Millions, billions, trillions—how to make sense of numbers in the news

Breaking down the big numbers. Credit: helen_g/Shutterstock.com National discussions of crucial importance to ordinary citizens – such as funding for scientific and medical research, bailouts of financial institutions and the current Republican tax proposals – inevitably involve dollar figures in the millions, billions and trillions. Unfortunately, math anxiety is widespread even among intelligent, highly educated…