This text is written from a personal perspective and I'm not sure how well it applies to other scientists. If you agree or disagree please let me know.

A standard tenet of experimental science is that the number of parameters that one varies in an experimental set-up should be kept to a minimum. This makes is possible to disentangle the effects of different variables on the outcome of the experiment. It has been claimed that the pace at which physics has moved forward in the last century (and molecular biology in the last half century) is due to possibility of physicists to isolate phenomena in strict experimental set-ups. In such a setting each variable can be varied individually, while all others are kept constant. This is in stark contrast to e.g. sociology, where controlled experiments are much harder to perform.

In a sense the process of doing science is similar to an experiment with a number of parameters. The 'experiment' corresponds to a specific scientific question and the 'parameters' correspond to different approaches to solving the problem. However, we do not know which approach will be successful. If not, it would not classify as research.

Most approaches or methods are in fact aggregates of many submethods. To give an example, say that I would like to describe some biological system using ordinary differential equations. Then the equations I write down might be novel, but I rely on established methods for solving these equations. I try to describe the system by trying (varying) the equations that describe the dynamics until I find the ones I'm happy with. In this sense we use both existing and new methods when trying to solve some scientific question. However, in order to actually make progress we often minimise the number of novel methods in our approach. If possible we only vary one method and keep all others fixed.

The problem with interdisciplinary research is that it often calls for novelty on the part of all the involved disciplines. In the case of mathematical biology for example we are asked to invent new mathematics at the same time as we discover new biology. Maybe this is not always the case, but to a certain extent these expectations are always present. A mathematician is expected to develop new mathematical tools, while a biologist is expected to discover new things about biology.

If both parts enter a project with the ambition of advancing their own discipline this might introduce too much uncertainty in the scientific work (we are now varying two "parameters" in the experiment), which could lead to little or no progress. If the mathematician stands back then new biology can be discovered using existing mathematical tools, while existing biological knowledge and data could serve as a testing ground for novel mathematics.

So what is the solution to this problem? I'm not sure. But being clear about your intentions in an interdisciplinary project is a good starting point. And maybe taking turns when it comes to novelty with an established collaborator.

## Thursday, 1 September 2016

### Back from parental leave

As of the 15th Aug I'm back to science and teaching. It's been some great 9 months, but now it's time to get serious about work again. This autumn I'm looking forward to lecturing on mathematical modelling and learning more about cell migration and the extra-cellular matrix.

### Scientific Models

In 2009 when I was a postdoc at Center for Models of Life at the Niels Bohr Institute my former MSc-supervisor Torbjörn Lundh came to visit me. As usual we had a great time together, but what I remember most from that visit was that we started talking about scientific models, and in particular how little is actually written (outside philosophy of science) about modelling. Then and there we wrote down an outline of a book that now 7 years on is published. A Swedish edition was in fact published in 2012, but now there's an English edition out on Springer.

Read more here and get your copy!

Read more here and get your copy!

## Thursday, 10 March 2016

### Travelling wave analysis of a mathematical model of glioblastoma growth

This paper has been on arxiv for a while (and the work dates back to 2011), but it was at last accepted for publication in Mathematical Biosciences after 1.5 years of review. The paper contains an analysis of a PDE-model of brain tumour growth that takes into account phenotypic switching between migratory and proliferative cell types. We derive an approximate analytic expression of the rate of spread of the tumour, and also show (and this is in my view the most intruiging result) that

Accepted version: http://arxiv.org/abs/1305.5036

**the inverse relationship between wave front steepness and its speed observed for the Fisher equation no longer holds when phenotypic switching is considered. By tuning the switching rates we can obtain steep fronts that move fast and vice versa.**Accepted version: http://arxiv.org/abs/1305.5036

## Wednesday, 30 September 2015

### Creative force fields

Yesterday (29th september) I made an appearance as an opponent at a seminar on the topic of mathematical modelling for predicting the spread of culture (Swedish title: "Kan algoritmer ge oss bättre förståelse för kultur och regional utveckling?").

The work that I was reviewing was that of Massimo Buscema at the Semeion Institute in Rome, who has been collaborating with several counties in Sweden in order to make predictions of how culture in the region will grow in the future.

The central tool for this analysis is the 'topological weighted centroid' (TWC) which can be viewed as a generalisation of centre of mass of set of points representing cultural activities.

I am highly critical of the validity and utility of these tools, since it is unclear what the TWC actually represents.

If you want to know more please have a look at the video:

http://bambuser.com/v/5820575

(I make my appearance around 2:20 into the video)

The work that I was reviewing was that of Massimo Buscema at the Semeion Institute in Rome, who has been collaborating with several counties in Sweden in order to make predictions of how culture in the region will grow in the future.

The central tool for this analysis is the 'topological weighted centroid' (TWC) which can be viewed as a generalisation of centre of mass of set of points representing cultural activities.

I am highly critical of the validity and utility of these tools, since it is unclear what the TWC actually represents.

If you want to know more please have a look at the video:

http://bambuser.com/v/5820575

(I make my appearance around 2:20 into the video)

## Tuesday, 18 August 2015

### Photos of nature

This summer I spent almost two months in a cottage in the Swedish countryside with my family. The cottage is fairly isolated with the closest neighbours a kilometer or so away. This meant living closer to nature than I have ever done, and resulted in me taking an interest in the flora and fauna of the surrounding meadow and forest. The below photos document some of my findings. I will in future post (with the tentative title 'The doubts of a mathematical biologist') write more about my impressions of living close to nature.

Crab spider that has caught a hover fly. |

Mini forest |

Dragon fly trying to hide |

Lady bug |

Cloud berry that is slowly ripening |

Pine sap (Monotropa hypopitys) is plant without clorophyll that parasitises on fungi |

Common self-heal (Prunella vulgaris) |

Cross spider (Araneus diadematus) |

Poppies |

Unknown spider taking a walk on the clothes line |

## Monday, 17 August 2015

### The evolution of carrying capacity in constrained and expanding tumour cell populations

My position at Moffitt Cancer Center certainly payed off in terms of research output. Recently my second paper based on work done at the Integrated Mathematical Oncology group was published. The paper investigates the dynamics of carrying capacity evolution in tumours and was written together with Sandy Anderson. The paper is published in Physical Biology, and was chosen as a "featured article" and is therefore open access for a limited time.

A copy can be found here, and the arxiv-version here (which will remain open access forever).

A copy can be found here, and the arxiv-version here (which will remain open access forever).

Illustrating the evolution of carrying capacity (A) and growth rate (B) in a constrained population of tumour cells. |

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