A common language
The more we know, the less we understand. Hence the need of a common language with which mathematical models and statistical methods can help us understand the ever increasing amounts of scientific data collected.
By Eline Mørch Jensen
Few would describe mathematicians and statisticians as people who put much emphasis on intuition, chance and signal noise when it comes to analysing scientific data. Nevertheless it is exactly that which - combined with an unusually high degree of interdisciplinarity - is at stake in the research project "Dynamical systems: mathematical modelling and statistical methods in social science, health and science."
As the name suggests the overall objective of the project is to develop mathematical models and statistical methods for analysing and articulating complex dynamic systems within no fewer than seven research groups from the Natural and Life Sciences, Faculty of Health Science and Social Science.
In charge of the project, which has just received a grant of 28 million Danish kroner from the University of Copenhagen 2016 pool (UCPH Excellence Programme for Interdisciplinary Research), is professor of statistics Susanne Ditlevsen from the Department of Mathematical Sciences, University of Copenhagen. Regarding the background of the idea and collaboration, she says:
- We are a large group of researchers with expert specialty knowledge in our own fields, some of us even working with related issues although we do not call things by the same name. However, we basically don´t have a clue what everyone else is doing. Instead of staying within our own narrow field using our specialized terminology, perhaps even thinking the same but without understanding one another, the goal is finding a common language.
Would you in fact describe the interdisciplinary approach as the focal point of the project?
- Interdisciplinary research is basically about the creation of synergies between different fields and about detecting common points, so yes, definitely. What is specific to our project is the cooperation between people working on methodologies on the one side and substantive researchers on the other; that is, mathematicians and statisticians to researchers in econometrics, physiology, neuroscience, psychology and bioinformatics - all of whom are trying to understand how things develop over time.
Too much data, too little understanding
According to Susanne Ditlevsen the big challenge today is that technological advances have made it possible to measure and collect unimaginably large – and still increasing - amounts of scientific data while in turn the theoretical understanding of the underlying mechanisms lags far behind. In this respect she sees mathematics and statistics as an obvious bridge between empirical observations and theoretical explanations in finding simple structures of very complex data.
Have scientists become too skilled at measuring and gathering knowledge?
- The scientific world has certainly become so complex that our knowledge has necessarily become much more specialized and as we gain ever greater knowledge within our own areas it also becomes harder to keep up with what is happening in other fields, Susanne Ditlevsen explains.
- Fortunately there is a growing recognition that we need each other and the grant of 28 million is a clear expression of this, so I am very much looking forward to seeing how the expertise of researchers in specific areas will unfold in combination with our mathematical and statistical insight and intuition.
Susanne Ditlevsen mentions the nephron as an example: Nephrons are the functional units of the kidney, which among other things produce urine and cleanse the blood. Physiologists have found out that fluctuations occur in the nephrons, oscillations, where the concentration of substances constantly change with a certain regularity similar to what is observed in other biological and social systems. There is a desire to better understand these fluctuations.
- When I was doing my PhD in biostatistics in 2004 we were only able to measure one or two nephrons at a time, whereas today the numbers stand at between 70 and 100. Suddenly one can measure the entire network of nephrons and how they interact. It makes a huge difference and requires completely different models, says Susanne Ditlevsen, adding:
- But of course it is one thing to develop large, complex models and quite another to be able to analyse them satisfactorily! Of course you can look at what happens to the individual components, whether they do or do not synchronize, but the more complicated the data, the greater the risk of failures. That is exactly why we need scientists in several fields - to be better at deriving the underlying structures and causal relationships and to avoid fallacies.
The unplanned interaction
Susanne Ditlevsen expects that the meeting between researchers from different disciplines will make everyone think in new ways. She also feels certain that they will come up with unexpected results and develop new methods and thus meet the intentions of the University Strategy 2016.
- It is implicit in basic research that you do not know what you will find. You can choose to go for the safe target, for that which is close to what we already know, but if things are really going to move forward you have to take chances. So we can only talk about what we believe or expect to find, we cannot know for sure - and new research questions may also arise from this interaction, Susanne Ditlevsen emphasizes and elaborates:
- Even such a small thing as one of the researchers from Psychology having just borrowed a guest office here at the Mathematical Institute for a week is really important for the exchange of ideas. It is when we eat lunch together, drink a Friday beer or take a walk in the woods together that the unexpected occurs. It is the daily and unplanned interaction that makes us work together in the best possible way.
As an example Susanne Ditlevsen mentions the cooperation with psychologists in the area that deals with visual cognition: Psychologists work on a basis of two assumptions to try to understand how the brain processes visual information and determines what sort of object it is faced with. One assumption is that you only have one interpretation of the object at the time, a serial view. If, for example, you have a ball in front of you, you can have the assumption that it is a ping pong ball. The next moment you might switch to believe it is a tennis ball. This assumes that you completely forget that you just now thought it looked like a ping pong ball.
The second assumption might be called a parallel view because it assumes that the brain perceives two or more possibilities at one time, but where one possibility, for instance the ping pong ball, is paramount to all others and therefore ends up being the object the brain decides upon.
- Usually we are unaware of these processes as the brain quickly decides upon an unambiguous interpretation of the visual impression, but there are situations where we can experience it. For example if you look at the type of ambiguous images that most people probably know: Pictures that at the same time are depicting a young, beautiful woman and an old, wrinkled woman, but you can only perceive one image at the time, says Susanne Ditlevsen, adding:
- Another example could be if you were in a dark forest and therefore unsure whether the object you see in the distance is a bear or a tree. Because of the uncertainty the eye switches between multiple objects, but if, for instance, the lighting conditions improve it becomes clear what you have in front of you.
- In the same way we can set up models that assume that the process operates in either the one way or the other, and when one model fits the data which the psychologists come up with, i.e. these data fit well with a particular model, we can decide that there is a certain evidence that respectively one or the other assumption is correct. Maybe we can´t exactly prove that this is the case, but at least - hopefully - make the theory probable.
How to do it in practice?
The project “Dynamical Systems” is one of 18 projects that shared in the 400 million Danish kroner from the 2016 fund for interdisciplinary research. The project involves 22 researchers from seven research groups, nine of which are method-people (five from Mathematics and four from Biostatistics). The money will mostly pay for PhD and post-doc positions, all to be associated with at least two research groups.
Leading up to the final conference in 2017 both workshops and national and international conferences will be held, but how will such an interdisciplinary cooperation actually take place in practice - except for eating lunch together or having a Friday beer every now and then?
Normally the scientists don´t work together on a daily basis or speak the same professional language...
- As in the case of the psychologists we simply sit down and look at what kind of challenges the researchers face and how to meet them in the best way. For instance there is an increasing awareness of how dynamic developments of various biological and social systems occur over time and that this dynamic, this constant movement and change, may be required for the satisfactory functioning of the systems.
- Just look at for instance such a thing as circadian rhythm, i.e. that something varies during the course of the day and shuts down at night. If you can set up rules for such a phenomenon, put it in a formula so to speak, you can describe the regularity with which the dynamics occur.
- The interaction of many variables that are connected through complex correlations that regulate and control the system makes it difficult, if not impossible, to understand the dynamics without using mathematical models and computer simulations. Intuition is simply not enough to make reliable predictions or assumptions purely by using ordinary reasoning.
- The models provide a common framework for explaining and interpreting data and forming new predictions that can be tested experimentally. The mathematical structure that is repeated in the models of similar dynamic phenomena and which occurs in disparate biological and social system, helps us understand contexts and use tools from one research field to another. This is what I mean by finding a common language, Susanne Ditlevsen explains and elaborates:
- If we can analyse this mathematically we may get to understand what is cause and what is effect. Even though there will be deviations and all models are simplifications of course, but if we can develop some models that are working they can still make us wiser.
And you methodology-people get something in return because your models become more useful and targeted?
- Exactly! You can compare it with a map of the world where you have to simplify things if you want to find your way. If your map had be scaled 1:1 it would not be helpful - and not a map - but just the world...
- It is similar to studying a car, how it is designed and how it works in traffic, which may be just fine... But if you want to understand how traffic jams occur, knowing how each individual car works won’t help you. You need to move from unit to network, says Susanne Ditlevsen.
The good noise
For good reasons there will always be questions that can´t be solved or investigated in functioning organs such as a kidney as they reside inside a living human being. In the past researchers were forced to dissect organs from autopsied corpses, later to experiment with animals such as rats, the rat’s kidney serving as a model for the human kidney even though rat and human kidneys are not the same - for example, the rat' kidney has 30,000 nephrons while the human kidney has a million.
- Similarly, mathematics is used as a model of reality. It would be unethical to investigate what happens to people if you expose them to starvation, smoking or other stressful factors. What you can do is hope that rats react in the same way as humans when experimented upon, but in some areas there is no doubt that proper mathematical models are a better choice for simulating reality.
According to Susanne Ditlevsen the right model allows you to investigate the effect of extreme influences, of possible interventions or of long term effects through computer simulation, which can save both time and money and mean that you can avoid animal testing; in some cases it may even be the only option for decisive progress in your research.
- High dimensionally and non-linearly, the kidney is one of the most complex organs in the body. This can make it difficult to analyse, synthesize, and infer the important aspects of the increasing amounts of data available for measuring and collecting - understanding the dynamics regarding the dysfunctions of the kidneys that lead to high blood pressure, for instance.
- The models are easily made so extensive that it becomes difficult to clean , reduce and simplify the material, something which is necessary to extract the information stored in the data and avoid errors and wrong conclusions, but all these small effects can be described by stochastic models, explains Susanne Ditlevsen.
- Imagine listening for coincidences, or rather for line noise. Say you want to hear a certain tone, a whale’s song or whatever it may be. If the signal is below a certain threshold, if the note has too few decibels for us to capture the dynamics of sound, then adding some noise in the form of a curve with extra swings, helps transmit the signal, explains Susanne Ditlevsen, adding:
- In that sense noise can have a positive effect, so in my view there is actually no such thing as random coincidences. Coincidences also follow a structure which is important to understand and include in the models, especially when they, as in this example, help pass the information on through the system.
About Susanne Ditlevsen
Susanne Ditlevsen holds a MSc in mathematics from La Universidad Nacional de Educación a Distancia in Spain and in statistics from the University of Copenhagen.
She received a PhD in biostatistics in 2005 and later joined the Department of Biostatistics before she was hired by Department of Mathematical Sciences in 2007.
Since 2009 she has been research group leader, now head of the section, for the research group in statistics and probability theory of the department. Professor of statistics since 2011.
28 millions for research project
Professor in statistics Susanne Ditlevsen from Department of Mathematical Sciences, University of Copenhagen has with an 28DKK million grant from KU’s 2016 fund got a unique possibility for creating high profiled interdisciplinary research with other top scientists from University of Copenhagen.