Contents
Preface . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . v
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
Symbolic Calculation in the
Life Sciences — Some Trends and Prospects
M. P. Barnett .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .1
Petri Net Based Description and
Modeling of Biological Pathways
M. Nagasaki, A. Doi, H. Matsuno, and S. Miyano . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 19
Algebraic Models in Systems
Biology
R. Laubenbacher .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 33
Maximum Likelihood
Estimation of Phylogenetic Tree and Substitution Rates via Generalized Neighbor-Joining and the
EM Algorithm
A. Hobolth and R. Yoshida. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 41
Controllability Analysis for
Gene Regulation Networks and Its Application to Luminescence Bacterium
E. Yanagisawa, S. Azuma, and J. Imura. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 51
Independent Dynamics Hybrid
Automata in System Biology
A. Casagrande, V. Mysore, C. Piazza, and B. Mishra. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 61
Algebraic Analysis of Stability
for Some Biological Systems
D. Wang and B. Xia. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 75
A New Approach for
Symbolic-Numeric Optimization in Biological Kinetic Models
S. Orii, H. Anai, and K. Horimoto. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 85
Mathematical Mechanism of
Quarantine Measures for SARS Epidemic
C. Jiang. . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 97
Inquiry into Conditions for
Cell–Type Diversity of Multicellular Organisms by Quantifier Elimination
H. Yoshida, H. Anai, S. Orii, and K. Horimoto. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 105
A Self-Referential Equation,
f(f) = f,
Obtained by Using the Theory of (M,R) Systems: Overview and Applications
J. C. Letelier, T. Kuboyama, H. Yasuda, M. L. Cardenas, and
A. Cornish-Bowden. . . . .
. . 115
Computational Polynomial
Algebra and Its Biological Applications
D. Wang. . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 127
Algebraic Methods for
Solving Real Polynomial Constraints and their Applications in Biology
H. Anai. . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 139
Estimation of Gene
Interaction Models (Extended Abstract)
K. Hiraishi. .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 149
Mathematical Models with
Maple
T. Yamaguchi. .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .151
Graphical Models for Gene Expression
Profile Analyses
S. Aburatni, S. Saito, and K. Horimoto . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 157
Author Index. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 173