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29 June 2017

# Funding for mathematical experiments

### Villum Experiment

Associate Professor Jesper Lund Pedersen and postdoc Alexandra Muñoz have received funding from the Villum Foundation to think out of the box. Their projects can lead to radical breakthroughs within mathematics. If they succeed.

"The VILLUM Experiment" is a totally new way to distribute research funding. The applicant's CV or networks are not decisive. All applications will be treated anonymously by the reviewers.

Thus, VILLUM FONDEN wishes to support the very special research idea that challenge the norm and has the potential to fundamentally change the way we access important topics. The reviewers are asked to emphasize the ideas they regard as being genuinely innovative. Perhaps only one in ten projects will prove capable of yielding something unique.

The Foundation has just awarded DKK 71 million to 39 unorthodox and potentially ground-breaking experiments. Experiments that spans a wide range: Topics include everything from biology to quantum physics. Conversion of CO2 to climate-friendly material. Cars that change color. Systems that recognize insects without capturing them first.

17 of the 39 experiments will take place at the University of Copenhagen. Two of the researchers are from Department of Mathematical Sciences.

## Beyond the Genome

Postdoc Alexandra Muñoz et has received DKK 2 million for the project "Beyond the Genome: Re-theorizing the cellular system". Professor and research director Thomas Sinkjær from VILLUM Fonden presents Alexandra Muñoz's project as follows:

"The main hypothesis of the experiment is based on, is a bold challenge of one of the central doctrines in modern science - that an organism's cells are solely controlled by the genetic material, DNA. Just as quantum mechanics can describe a different layer of a physical system, this experiment will attempt to uncover another layer in the regulation of cells that functions when the genome is defective.

It is a high-risk experiment that can be anything or nothing. If the hypothesis turns out to be correct, the experiment will revolutionise and redefine our understanding of cell biology and have potentially ground-breaking influence on our understanding of, among other things, cancer. But the hypothesis may prove to be incorrect. Even then, the development of the proposed mathematical model, will offer a unique and valuable framework for the conceptualisation of the cells."

## Nonlinear quickest detection problems

Jesper Lund Pedersen, associate professor from the Section for Insurance and Economics, has received DKK 1.8 million for searching for mathematical solutions on an area, which today is considered to be out of reach. If successful, it can help improve performance of atomic clocks, controlling satellites, landing planes and detecting earthquakes.

Quickest detections problems arise from the need/desire to detect changes in the observed data as quickly as possible after they occur in real time. Problems of quickest detection date back to the 1960s in the context of radar detection. Today quickest real-time detection is of great importance in many applied settings of engineering and natural sciences - and a wide variety of other ﬁelds such as medicine and ﬁnance.

Translated into mathematical terms from modern probability theory, Jesper describes the project as follows:

We are observing a stochastic process with given probabilistic characteristics which change to some other probabilistic characteristics at some unknown time which is not directly observable. The problem is to detect the time of change as accurately as possible using only the observations of the stochastic process itself.

Since exact detection is impossible this ‘accurately’ means neither ‘too early’ (false alarm) nor ‘too late’ (detection delay).

The classic and modern theory of quickest detection is only developed for linear formulations of the problem, in the sense that ‘too early’ is expressed as the mean value related to false alarm and ‘too late’ is expressed as the mean value related to detection delay. Within this framework the problems are Markovian so that one can use the theory of Markov processes and exploit their connections to linear diﬀerential equations when solving the problem.

The research will open a novel way of looking at quickest detection where the central aim is to formulate and solve nonlinear quickest detection problems. In this context, a nonlinear formulation is obtained through nonlinear functions (e.g. variance) of the mean value related to false alarm and the mean value related to detection delay.

- This should lead to faster and more eﬃcient algorithms of quickest detection. The idea is fundamentally new and the approach creates unconventional scientiﬁc challenges that were never met in quickest detection before, explains Jesper.

## The VILLUM Experiment

- Support for the bold research idea that would have difficulty fitting into the conventional peer-review funding system.
- Created for the very special research projects that challenge the norm and have the potential to fundamentally alter the way we approach important topics.
- The reviewers are asked to emphasize the ideas they regard as being genuinely innovative. Perhaps only one in ten projects will prove capable of yielding something unique.
- Each of the reviewers has the opportunity to appoint one application with a decisive vote. If this happens, there must be quite significant arguments from the foundation’s board of directors to reject the project.
- The amount granted is DKK 1-2 million, which is to cover a research period of 1-2 years.
- The program is open to all researchers regardless of nationality and can be applied for by active researchers regardless of any age.

Read more about the VILLUM Experiment