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Why do you think your paper is
highly cited?
The paper solves a fundamental problem in mathematical
tensor analysis, also called multi-way analysis. These
tensor methods can solve a number of problems in a radically
new way by what has been called "mathematical
chromatography."
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“Our paper provides the
necessary tool to easily verify whether the
model determined is meaningful or not and it
does so in a simple and intuitive way that has
appealed to users.” |
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For example in analytical chemistry, huge amounts of
money, time, and chemicals are used on a daily basis, e.g.,
in clinical analysis in order to provide accurate chemical
measurements. With mathematical chromatography, such results
can be obtained in seconds, based on measuring directly on a
complicated sample with non-invasive spectroscopic
instruments. The complex measurements can then be "un-mixed"
mathematically.
This is just one application of mathematical
chromatography, but it serves to illustrate that such tensor
approaches really can become a revolution in what is
possible—and at what cost. Our paper provides the necessary
tool to easily verify whether the model determined is
meaningful or not and it does so in a simple and intuitive
way that has appealed to users.
Does it describe a new discovery, methodology, or synthesis of
knowledge?
The paper describes a new approach to determining model
complexity for a specific class of models. It is based on a
fundamental understanding of the difference between low-rank
and subspace approaches in tensor analysis.
Would you summarize the significance of your paper in layman’s
terms?
With the results of the paper, it is more feasible for
non-experts to use advanced tensor models, for example, to
identify and quantify chemical analytes measured directly,
find underlying phenomena in EEG data, resolving magnetic
resonance data, detect and separate DS-CDMA systems, etc.
How did you become involved in this research and were there any
particular problems encountered along the way?
The research described in the paper is a core area of our
group. Within the last 13 years, we have established a very
strong team on both development and application of tensor
methods. We are trying to develop the theory and algorithms
and to target them towards specific applications. Through
development of free software, we are trying to make the
methods available to as many as possible.
Where do you see your research leading in the future?
In the not-so-distant future, the tools, algorithms, and
associated theory will be developed to an extent where the
tensor methods are in common use among scientists and
researchers as a simple tool built into various types of
instruments. At that stage, completely new applications will
be seen. For example, detailed analytical information can be
obtained directly from biological systems in vivo.
Rasmus Bro, Prof., Ph.D.
Faculty of Life Sciences
University of Copenhagen
Copenhagen, Denmark
www.models.life.ku.dk
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A Closer Look...
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Below
are images sent in by Rasmus Bro which correspond with the featured
paper, or current research. |
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Figure 1:
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Figure
1: An illustration of
the complex spectral patterns uncovered by
tensor analysis of NMR DOSY measurements. The
single measured sample is separated into signals
from the three individual consituents. |
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