LINEAR ALGEBRA AND ITS APPLICATIONS
Special issue on Matrices and Mathematical Biology
Call for papers
In the last decade the field of mathematical biology has expanded very
rapidly. Biological research furnishes both data on and insight into the
workings of biological systems. However, qualitative and quantitative
modelling and simulation are still far from allowing current knowledge to
be organized into a well-understood structure. Further, the diversity
present in mathematical biology, coupled with the absence of a single
unifying approach, has inspired the formation of entirely new scientific
disciplines such as bioinformatics.
Theoretical research activity in mathematical biology is
naturally of an interdisciplinary character. It involves
mathematical and statistical investigations, sometimes in
combination with techniques originating from the computational
sciences. In many of these approaches, linear algebra is key to
solving the mathematical problems which arise. For instance, in
some population models, the asymptotic rate of increase of the
population turns out to be the spectral radius of a certain
matrix associated with the population, while the other
eigenvalues also yield information on the evolution of the
population's structure. Conversely, problems in mathematical
biology can enrich linear algebra. For example, in attempting to
measure the influence of a single matrix entry on a simple
eigenvalue, linear algebraists frequently employ the derivative
of that eigenvalue with respect to the entry. However, some
biologists have proposed the use of the elasticity, or a
logarithmic derivative, of an eigenvalue with respect to a matrix
entry in order to measure the effect on that eigenvalue of
perturbing a matrix entry. Thus linear algebraists are challenged
to deepen and develop the understanding of the ways in which the
effects of changes in the ecological conditions on the
populations can be measured through further theoretical
investigations.
A recent book by Caswell on matrix population models makes extensive use
of linear algebraic techniques. Quoting from the introduction to that
book: "Matrix population models -- carefully constructed, correctly
analyzed, and properly interpreted - provide a theoretical basis for
population models... A goal of this book is to raise the bar of what
constitutes rigorous analysis in population models.... The work of the
population biologist is too important to settle for less." But Caswell's
call for careful mathematical construction and analysis applies to areas
beyond the subject of population models; clearly a rigorous approach would
benefit all areas of interaction between biology and mathematics.
The Special Issue of LAA dedicated to Matrices and Mathematical Biology is
intended to both foster and accelerate cross fertilization between those
working primarily in linear algebra and those working primarily in
mathematical biology. The editors hope that such an issue of LAA will be
of benefit to both fields.
This special issue will be open for all submissions containing new and
meaningful results that advance interaction between linear algebra and
mathematical biology. The editors welcome submissions in which linear
algebraic methods play an important role for novel approaches to problems
arising in mathematical biology, or in which investigations in
mathematical biology motivate new tools and problems in linear algebra.
Survey papers which discuss specific areas involving the interaction
between biology and linear algebra, particularly where such interaction
has been successful, are also very welcome.
Areas and topics of interest for the special issue include, but are not
limited to:
metabolistic pathways
statistical data analysis
linear algebra problems in graph partitioning
matrix population models
model discrimination in biokinetics
linear algebra problems in network analysis and synchronization
subspace oriented eigenvalue problems
aggregation/disaggregation or related techniques
hidden Markov models
epidemic models
modelling phylogenetic trees
All papers submitted must meet the publication standards of Linear Algebra
and its Applications and will be refereed in the usual way. They should be
submitted to one of the special editors of this issue listed below by 30
November 2003.
Michael Dellnitz
Department of Mathematics and Computer Science
University of Paderborn
D-33095 Paderborn
Germany
dellnitz@upb.de
Steve Kirkland
Department of Mathematics and Statistics
University of Regina
Regina, Saskatchewan
Canada
S4S 0A2
kirkland@math.uregina.ca
Michael Neumann
Department of Mathematics
University of Connecticut
Storrs, Connecticut O6269-3OO9
USA
neumann@math.uconn.edu
Christof Schuette
Department of Mathematics & Computer Science
Numerical Mathematics/Scientific Computing
Free University Berlin
Arnimallee 2-6
D-14195 Berlin
Germany
schuette@math.fu-berlin.de