Table Of ContentLecture Notes in Computer Science 6479
CommencedPublicationin1973
FoundingandFormerSeriesEditors:
GerhardGoos,JurisHartmanis,andJanvanLeeuwen
EditorialBoard
DavidHutchison
LancasterUniversity,UK
TakeoKanade
CarnegieMellonUniversity,Pittsburgh,PA,USA
JosefKittler
UniversityofSurrey,Guildford,UK
JonM.Kleinberg
CornellUniversity,Ithaca,NY,USA
AlfredKobsa
UniversityofCalifornia,Irvine,CA,USA
FriedemannMattern
ETHZurich,Switzerland
JohnC.Mitchell
StanfordUniversity,CA,USA
MoniNaor
WeizmannInstituteofScience,Rehovot,Israel
OscarNierstrasz
UniversityofBern,Switzerland
C.PanduRangan
IndianInstituteofTechnology,Madras,India
BernhardSteffen
TUDortmundUniversity,Germany
MadhuSudan
MicrosoftResearch,Cambridge,MA,USA
DemetriTerzopoulos
UniversityofCalifornia,LosAngeles,CA,USA
DougTygar
UniversityofCalifornia,Berkeley,CA,USA
GerhardWeikum
MaxPlanckInstituteforInformatics,Saarbruecken,Germany
Katsuhisa Horimoto Masahiko Nakatsui
Nikolaj Popov (Eds.)
Algebraic and
Numeric Biology
4th International Conference, ANB 2010
Hagenberg, Austria, July 31–August 2, 2010
Revised Selected Papers
1 3
VolumeEditors
KatsuhisaHorimoto
MasahikoNakatsui
NationalInstituteofAdvancedIndustrialScienceandTechnology(AIST)
ComputationalBiologyResearchCentre(CBRC)
Tokyo135-0064,Japan
E-mail:{k.horimoto,m.nakatsui}@aist.go.jp
NikolajPopov
JohannesKeplerUniversityofLinz
ResearchInstituteforSymbolicComputation(RISC)
4040Linz,Austria
E-mail:[email protected]
ISSN0302-9743 e-ISSN1611-3349
ISBN978-3-642-28066-5 e-ISBN978-3-642-28067-2
DOI10.1007/978-3-642-28067-2
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2011945509
CRSubjectClassification(1998):F.3.1,F.4,D.2.4,I.1,J.3
LNCSSublibrary:SL1–TheoreticalComputerScienceandGeneralIssues
©Springer-VerlagBerlinHeidelberg2012
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Preface
ThisvolumecontainstheproceedingsoftheInternationalConferenceonAlgebraic
andNumericBiology(ANB2010).ItwasheldduringJuly31–August2,2010in
theCastleofHagenberg,Austria,andwasorganizedbytheResearchInstitutefor
SymbolicComputation(RISC)oftheJohannesKeplerUniversity,Linz,Austria,
togetherwiththeNationalInstituteofAdvancedIndustrialScienceandTechnol-
ogy(AIST),Tokyo,Japan.
Algebraicandnumericbiologyistheinterdisciplinaryforumforthepresenta-
tionofresearchonallaspectsoftheapplicationofsymbolicandnumericcomputa-
tioninbiology.AlgebraicandNumericBiologywasrenamedafterourtraditional
name, Algebraic Biology, to consider its wider scope of mathematical methods,
especiallynumericcomputation.
TheAlgebraicandNumericBiologyconferenceisafollow-upoftheAlgebraic
Biology conference. Since 2005, we have been organizing an international con-
ference, Algebraic Biology,that focuses on the application of computer algebra,
automated reasoning, hybrid algebraic and numeric computation, which is also
called symbolic computation, to all types of problems from biology. The first
conference, AB 2005, was held in November 2005 in Tokyo, Japan. The second
conference, AB 2007, was held in July 2007 in Hagenberg, Austria. The third
conference, AB 2008, was held in July and August again in Hagenberg, Aus-
tria.Theseconferenceswerequitesuccessful.Forthisissueoftheconference,we
extended the range of mathematical methods.
The initiation of the series of these conferences was motivated by the re-
cent trends in symbolic and numeric computation and biology:In symbolic and
numeric computation, the recent advances in computer performance and algo-
rithmic methods have accelerated the extension of the scientific fields to which
symbolicandnumericcomputationcanbeapplied.Inbiology,thedetermination
ofcomplete genomicsequences andthe subsequentimprovementsofexperimen-
tal techniques have yielded large amounts of information about the biological
molecules underlying various biologicalphenomena. Under these circumstances,
the marriage of symbolic and numeric computation and biology is expected to
generate new mathematical models for biological phenomena and new symbolic
and numeric techniques for biological data analysis.
We receivedsubmissions from16 countries(Austria,Belgium, Chile,France,
Germany,HongKong,Ireland,Italy,Japan,Mexico,Portugal,Singapore,Spain,
UK, Ukraine, and USA) and 10 papers were accepted for presentation at the
conference. Each submission was assigned to at least two Program Committee
members, who carefully reviewed the papers, in some cases with the help of
external referees. The merits of the submissions were discussed by the Steering
Committee at the dedicated meeting in Hagenberg.
VI Preface
We are pleased to continue our collaboration with Springer, who agreed to
publish the conference proceedings in the Lecture Notes in Computer Science
series.
We, the ANB 2010organizersof the conference, are gratefulto the following
sponsors for their financial contributions toward its operation and success: the
DoctoralProgramComputationalMathematics atthe Johannes Kepler Univer-
sity supported by the Austrian Science Fund (FWF), the International Studies
forInformaticsHagenberg,LinzerHochschulfonds,theNationalInstituteofAd-
vancedIndustrialScienceandTechnology,andtheUpperAustrianGovernment.
Our thanks are also due to the members of the Program Committee and to
those who ensured the effective running of the conference.
July 2010 Bruno Buchberger
Katsuhisa Horimoto
Masahiko Nakatsui
Nikolaj Popov
Conference Organization
Steering Committee
Bruno Buchberger Johannes Kepler University of Linz, Austria
Katsuhisa Horimoto National Institute of Advanced Industrial
Science and Technology, Japan
Reinhard Laubenbacher Virginia Bioinformatics Institute, USA
Bud Mishra New York University, USA
Nikolaj Popov Johannes Kepler University of Linz, Austria
Program Chairs and Proceedings Editors
Katsuhisa Horimoto National Institute of Advanced Industrial
Science and Technology, Japan
Masahiko Nakatsui National Institute of Advanced Industrial
Science and Technology, Japan
Nikolaj Popov Johannes Kepler University of Linz, Austria
Program Committee
Tatsuya Akutsu Kyoto University, Japan
Hirokazu Anai Kyushu University, Japan
Niko Beerenwinkel Swiss Federal Institute of Technology Zurich,
Switzerland
Armin Biere Johannes Kepler University of Linz, Austria
Franc¸ois Boulier University of Lille I, France
Bruno Buchberger Johannes Kepler University of Linz, Austria
Luca Cardelli Microsoft Research, Cambridge, UK
Luonan Chen Osaka Sangyo University, Japan
Wai-Ki Ching University of Hong Kong, China
Kwang-Hyun Cho Korea Advanced Institute of Science and
Technology, Korea
Franck Delaplace Evry University, France
Hoon Hong North Carolina State University, USA
Katsuhisa Horimoto National Institute of Advanced Industrial
Science and Technology, Japan
Peter Huggins Carnegie Mellon University, USA
Abdul Salam Jarrah Virginia Bioinformatics Institute, USA
Erich Kaltofen North Carolina State University, USA
Hans Kestler University of Ulm, Germany
Temur Kutsia Johannes Kepler University of Linz, Austria
VIII Conference Organization
Philipp Ku¨gler RICAM, Austria and University of Stuttgart,
Germany
Doheon Lee Korea Advanced Institute of Science and
Technology, Korea
James Lynch Clarkson University, USA
Manfred Minimair Seton Hall University, USA
Stefan Mu¨ller RICAM, Austria
Masahiko Nakatsui National Institute of Advanced Industrial
Science and Technology, Japan
Masahiro Okamoto Kyushu University Japan
Eugenio Omodeo University of Trieste, Italy
Sonja Petrovic University of Illinois at Chicago, USA
Nikolaj Popov Johannes Kepler University of Linz, Austria
Georg Regensburger RICAM, Austria
Carolyn Talcott SRI International, USA
Ashish Tiwari SRI International, USA
Hiroyuki Toh Kyushu University, Japan
Dongming Wang Beihang University, China and UPMC-CNRS,
France
Limsoon Wong National University of Singapore
Ruriko Yoshida University of Kentucky, USA
Local Organization Chair
Nikolaj Popov Johannes Kepler University of Linz, Austria
Table of Contents
P -Matrix Products of Matrices (Invited Talk)....................... 1
0
Murad Banaji
A Formal Model for Databases in DNA ............................. 18
Joris J.M. Gillis and Jan Van den Bussche
Efficient and Accurate Haplotype Inference by Combining Parsimony
and Pedigree Information ......................................... 38
Ana Grac¸a, Inˆes Lynce, Joa˜o Marques-Silva, and Arlindo L. Oliveira
MABSys: Modeling and Analysis of Biological Systems ............... 57
Franc¸ois Lemaire and Asli U¨rgu¨plu¨
Models of Stochastic Gene Expressionand Weyl Algebra.............. 76
Samuel Vidal, Michel Petitot, Franc¸ois Boulier,
Franc¸ois Lemaire, and C´eline Kuttler
Reconciling Competing Models: A Case Study of Wine Fermentation
Kinetics ........................................................ 98
Rodrigo Assar, Felipe A. Vargas, and David J. Sherman
Computational Modeling and Verification of Signaling Pathways
in Cancer ....................................................... 117
Haijun Gong, Paolo Zuliani, Anvesh Komuravelli,
James R. Faeder, and Edmund M. Clarke
Composability: Perspectives in EcologicalModeling .................. 136
Ozan Kahramano˘gulları, Ferenc Jorda´n, and Corrado Priami
A General Procedure for Accurate Parameter Estimation in Dynamic
Systems Using New Estimation Errors.............................. 149
Masahiko Nakatsui, Alexandre Sedoglavic, Franc¸ois Lemaire,
Franc¸ois Boulier, Asli U¨rgu¨plu¨, and Katsuihisa Horimoto
Analyzing Pathways Using ASP-Based Approaches................... 167
Oliver Ray, Takehide Soh, and Katsumi Inoue
Author Index.................................................. 185
P -Matrix Products of Matrices
0
Murad Banaji
Departmentof Mathematics, University of Portsmouth, Lion Gate Building,
Lion Terrace, Portsmouth, Hampshire PO1 3HF, UK
Abstract. The question of when the product of two matrices lies in
the closure of the P-matrices is discussed. Both sufficient and neces-
sary conditionsfor thistooccur are derived.Suchresults areapplicable
to questions on the injectivity of functions, and consequently the pos-
sibility of multiple fixed points of maps and flows. General results and
special cases are presented, and the concepts illustrated with numerous
examples.Graph-theoreticcorollaries tothematrix-theoreticresultsare
touched upon.
Keywords: P-matrix; P0-matrix; matrix factorisation; injectivity;
stability.
1 Introduction
WewillbeinterestedinP-matricesandcertaincloselyrelatedclassesofmatrices.
In each of the definitions below, A is a real square matrix:
Definition 1. A is a P-matrix if all of its principal minors are positive.
Definition 2. A is a P -matrix if all of its principal minors are nonnegative.
0
Definition 3. A is a P(−)-matrix if −A is a P-matrix.
Definition 4. A is P(−)-matrix if −A is a P -matrix.
0 0
Matrices belonging to any of these classes will be termed P-type matrices.
P-type matrices play important roles in various applications, including to the
linear complementarity problem [1], and to a variety of questions in biology [2].
This paperexploresnecessaryandsufficientconditionsfortheproductoftwo
matricesto be aP -matrix.The workis motivatedprimarily(but notsolely)by
0
two observations:
1. Differentiable functions with P-matrixJacobiansoncertaindomains arein-
jective[3].ThesameistrueforfunctionswithP -matrixJacobians,provided
0
certainadditionalconditionsaresatisfied[4].Suchresultshavebeenapplied
to problems in economics [5], biology [6] and chemistry [7].
2. Matrices which arise as Jacobian matrices in various areas of application
often have natural factorisations as a consequence of physical constraints
[7,8]. In practice, it is often the case that some of the factors are constant,
while only the sign pattern of others is known. Determining whether all
allowed products are P-type matrices is a nontrivial problem.
K.Horimoto,M.Nakatsu,andN.Popov(Eds.):ANB2011,LNCS6479,pp.1–17,2012.
(cid:2)c Springer-VerlagBerlinHeidelberg2012
2 M. Banaji
Here, ratherthanfocussingonthe applications,anumber ofmatrix-theoretic
results which have proved useful are reviewed and generalised, while previously
published applications are referenced. The results are in most cases amenable
tostraightforwardalgorithmicimplementation.Elementaryproofsarepresented
and some graph-theoretic corollaries are touched upon.
1.1 Some Properties of P-Type Matrices
It follows from elementary properties of P-matrices that any P -matrix plus a
0
positive diagonal matrix is a P-matrix. In fact, the P -matrices can be charac-
0
terised as follows:
Lemma 1. A square matrix A is a P -matrix if and only if det(A+D)>0 for
0
every positive diagonal matrix D.
Proof. See Section 3.2 in [8]. (cid:2)(cid:3)
Eigenvalues and Stability. Other properties ofP-matricesinclude that their
eigenvalues are excluded from a certain wedge aroundthe negative real axis [9],
implying that real eigenvaluesof P-matrices arepositive, and further that 2×2
P-matrices are positive stable (i.e., have eigenvalues with positive real part).
Positive stability for P-matrices satisfying additional constraints can also be
deduced in higher dimensions, and a result in this direction of Hershkowitz and
Keller (Theorem 1.1 in [10]) will be applied later to prove that certain matrices
are positive stable.
Injectivity of Functions. Define a rectangular domain in Rn to be the
productofintervalsonthecoordinateaxes,eachofwhichmaybeopen,closedor
semi-open.ThefollowingresultofGaleandNikaidohasprovedhighlyapplicable:
given a rectangular domain X ⊆ Rn, each differentiable function f : X → Rn
with P-matrix Jacobian is injective on X (Theorem 4 and subsequent remarks
in[3]).IfX is,additionally,open,thenitsufficesfortheJacobianmatrixtobea
nonsingular P -matrix (Theorem 4w in [3], and see also [4]). For simplicity, the
0
resultspresentedbelowinvolveP-andP -matrices,but,sinceinjectivityof−f is
0
equivalenttoinjectivity off,allresultshaveeasydualsstatedintermsofP(−)-
and P(−)-matrices. It is the dual results which generally arise in practice, and
0
mostofthepreviousresultsreferencedactuallyinvolveP(−)-andP(−)-matrices.
0
This point will not be laboured.
1.2 The Main Question
Notation. LetRn×m denotetherealn×m matrices.Define P tobethe setof
0
P0-matrices, and P0,n ⊆Rn×n to be the set of n×n P0-matrices. Clearly, P0,n
is the closure of the set of n×n P-matrices.
