Mathematical research at Norwegian University of Life Sciences

In the Western world, ischemic heart disease is one of the most widespread, and possibly fatal, illnesses killing millions of people every year. In many cases, the traditional man-based interpretation procedure of ECG recordings fails to detect the ischemic region. Moreover, ECG recordings provide only a rather crude picture of the position and size of the damaged tissue. Thus, there is a need to improve this technology. In this project we will develop novel mathematical models, and suitable solution strategies, for improving the classical ECG interpretation method. The recent couple of years have also witnessed a considerable interest in waves in neural tissue since they apparently underlie both natural and pathological phenomena in the brain. An understanding of such phenomena will hopefully contribute to new medical therapies for different types of neurobiological disorders, like epilepsy. In the present project we will therefore also develop and analyze new mathematical models for waves in neural tissues. In 2015-2017 we showed that some classical point-neuron models are mathematically ill-posed, which implies that they cannot be solved with finite precision arithmetic (i.e. the arithmetic used by computers). The last two years we have therefore investigated whether these ill-posed point-neuron models can be approximated by well-posed equations. Unfortunately, it turned out that the standard regularization technique for these problems does not provide a consistent framework. Consequently, it is questionable whether published simulation results employing these models can be trusted. We are currently exploring the well-posedness of other models used in computational neuroscience, but it is unlikely that we will be able to finish these studies within the timeframe of the present NFR project. We also analyze generalized eigenvalues for elliptic differential operators. This is of importance for the efficient numerical solution of a number of equations appearing in many applications. kjashdckjszdxbkjshd.

Alt gikk etter planen, bortsett fra at vi ikke fikk brukt opp pengene. Mange flotte publikasjoner og ny matematisk innsikt. Les artiklene som har blitt publisert i løpet av prosjektperioden!

The main purpose of this project is to implement the evaluation committee's recommendations. Hence, we will expand our collaboration with Simula Research Laboratory (Simula) and initiate cooperation with Norwegian University of Science and Technology (NTNU). In order to accomplish this, we ask for funding for one adjunct professor and a post doc. These two positions will aid the practical implementation of the collaboration and secure the knowledge transfer from Simula and NTNU to Norwegian University of Life Sciences (NMBU). Modern applications of mathematics almost always involve the use of numerical methods and simulation software. And, since our group is hosted by a technology department, it is expected that our research and educational efforts are targeted toward applications in technology. Unfortunately, only the two younger mathematicians at NMBU have a formal background covering these topics, whereas our older staff members have a more traditional mathematical training targeted at solving problems of more theoretical nature. Simula and NTNU are the leading Norwegian research units for the use of complex mathematical models and simulation technology. Collaborating with these two institutions will therefore be very important for implementing the shift from theoretical studies to applied mathematics and simulation technology. As expressed by the evaluation committee, our group needs to improve our international relations in order to conduct research at an international level. This will be accomplished by strengthening cooperation with research units outside Norway. We hence ask for funding for sabbaticals, for attending international meetings and for inviting guest researchers. We also intend to introduce the guideline that our faculty members should present their work at minimum two international conferences every year. At the end of the project period, we hope to have sufficiently good international connections to participate in an ERC grant application