Table Of ContentFrom Linear Operators to Computational Biology
Martin Davis (cid:2) Edmond Schonberg
Editors
From Linear
Operators to
Computational
Biology
Essays in Memory of Jacob T. Schwartz
Editors
MartinDavis EdmondSchonberg
Professor(emeritus)Mathematicsand Professor(emeritus)ComputerScience
ComputerScience Department
CourantInstituteofMathematicalScience CourantInstituteofMathematicalScience
NewYorkUniversity NewYorkUniversity
NewYork,USA NewYork,USA
ISBN978-1-4471-4281-2 ISBN978-1-4471-4282-9(eBook)
DOI10.1007/978-1-4471-4282-9
SpringerLondonHeidelbergNewYorkDordrecht
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JacobT.Schwartz,1930–2009
Recollecting Jack Schwartz
Jack had the most powerful mind of anyone I knew, except von Neumann. These
twohadincommonafantasticabilitytolearnanewsubjectextremelyrapidly;both
hadanincrediblywiderangeofinterest.
WhenJacklefttheDepartmentofMathematicstoleadtheDepartmentofCom-
puter Science newly created by him, he related to me that when he came to the
CourantInstitutehehaddecidedtoteachallcourseslistedinourbulletin,andthat
he had carried out his plan. When I pointed out that there must have been some
subjectsaboutwhichheknewlittleornothing,herepliedthatinthosecaseshetook
from the library the Summer before the leading text on the subject and learned it.
WhenIaskedhimiftherewasasubjecthehadtroublelearning,headmittedthathe
did,fluiddynamics.“Itisnotasubjectthatcanbeexpressedintermsoftheorems
andtheirproofs”.
Jackfirstcametotheattentionofthemathematicalcommunityasthecoauthor
ofDunford-Schwartz,animpressiveexpositionoffunctionalanalysis.Itwasmuch
morethanacompilationandorganizationofknownmaterial;thereismuchoriginal
workinit.Astrikingexampleisthetheoremthatthetraceofatraceclassoperatorin
Hibertspaceisthesumofitseigenvalues.Thistheoremanditsproofarepresented
in Vol. II, but no attribution is given to Lidskii, to whom it is due. Since D-S is
compulsive about giving references, this was mystifying, The explanation is that
D-S vol. II came out before the publication of the English translation of Lidskii’s
paper;Jackhadprovedtheresultindependently.
Jack has made valuable contributions to operator algabras, a subject founded
by von Neumann and Murray. Jack described von Neumann’s work as “coming
repeatedlytoastonewallandcrashingthroughit.”
Jackhadadelicioussenseofhumor.Inapapertitled“Theperniciousinfluenceof
mathematicsonscience”,hestartswiththeobservationthat“computerintelligence”
has three major shortcomings: single-mindedness, literal-mindedness, and simple-
mimdedness.Hethenmakesthepointthatmathematicsalsohastheseshortcomings,
althoughtoalesserextent.AsanexamplehepointstotheclaimthattheBirkhoff
ergodic theorem is the basis of the foundation of statistical mechanics, and then
neatlydemolishesit.
vii
viii RecollectingJackSchwartz
As another example Jack quotes Keynes’ criticism of some mathematical eco-
nomics as “...a mere concoction,as imprecise as the initial assumptionsthey rest
on,whichallowtheauthortolosesightofthecomplexitiesandinterdependencies
oftherealworldinamazeofpretensionsandunhelpfulsymbols.”
Hans Bethe once remarked,only half in jest,that von Neumann’s brain was an
upwardmutationofthehumanbrain;thesamecouldhavebeensaidaboutJack.
Weshallnotseethelikeofhimforalongtime.
CourantInstituteofMathematicalSciences PeterD.Lax
NYC,NY,USA
Contents
FromLinearOperatorstoComputationalBiology:EssaysinHonorof
JacobT.Schwartz . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
MartinDavisandEdmondSchonberg
NatureasQuantumComputer . . . . . . . . . . . . . . . . . . . . . . . . 5
DavidRitzFinkelstein
JackSchwartzMeetsKarlMarx . . . . . . . . . . . . . . . . . . . . . . . 23
MartinDavis
SETLandtheEvolutionofProgramming . . . . . . . . . . . . . . . . . . 39
RobertDewar
DecisionProceduresforElementarySublanguagesofSetTheory.XVII.
CommonlyOccurringDecidableExtensionsofMulti-levelSyllogistic 47
DomenicoCantone
JackSchwartzandRobotics:TheRoaringEighties . . . . . . . . . . . . 87
MichaSharir
Mathematics’MortuaManus:DiscoveringDexterity. . . . . . . . . . . . 105
B.Mishra
TheRefProof-CheckerandIts“CommonSharedScenario” . . . . . . . 121
EugenioG.Omodeo
ComputationalApproachestoRNAiandGeneSilencing. . . . . . . . . . 169
AlessandroLaganà, RosalbaGiugno, AlfredoPulvirenti, and
AlfredoFerro
TheLastTenYards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
MichaelWigler
SelectedBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
ix
Contributors
DomenicoCantone DipartimentodiMatematicaeInformatica,UniversitàdiCata-
nia,Catania,Italy
Martin Davis Courant Institute of Mathem. Science, New York University, New
York,NY,USA
RobertDewar CourantInstitute,NewYorkUniversity,NewYork,USA;AdaCore
Technologies,NewYork,USA
AlfredoFerro Dept.ofMathematicsandComputerSciences,UniversityofCata-
nia, Catania, Italy; Dept. of Biomedical Sciences, University of Catania, Catania,
Italy
DavidRitzFinkelstein GeorgiaInstituteofTechnology,Atlanta,GA,USA
Rosalba Giugno Dept. of Mathematics and Computer Sciences, University of
Catania,Catania,Italy
AlessandroLaganà Dept.of MathematicsandComputerSciences,Universityof
Catania,Catania,Italy;Dept.ofBiomedicalSciences,UniversityofCatania,Cata-
nia,Italy
B.Mishra CourantInstitute,NewYork,NY,USA
EugenioG.Omodeo DipartimentodiMatematicaeInformatica,UniversitàdiTri-
este,Trieste,Italy
Alfredo Pulvirenti Dept. of Mathematics and Computer Sciences, University of
Catania,Catania,Italy
EdmondSchonberg CourantInstituteofMathem.Science,NewYorkUniversity,
NewYork,NY,USA
MichaSharir SchoolofComputerScience,TelAvivUniversity,TelAviv,Israel;
CourantInstituteofMathematicalSciences,NewYorkUniversity,NewYork,NY,
USA
MichaelWigler ColdSpringHarborLaboratory,ColdSpringHarbor,NY,USA
xi
From Linear Operators to Computational
Biology: Essays in Honor of Jacob T. Schwartz
MartinDavisandEdmondSchonberg
Abstract WepresentathumbnailsketchofthescientificcareerofJackSchwartz,
inordertoplacetheessaysinthisvolumeintheproperchronologicalcontext.
1 Introduction
This volume of essays honors the memory of Jacob T. Schwartz (“Jack”) a dis-
tinguished mathematician and computer scientist who was our friend, colleague,
mentorandinspirationinthecourseofanamazinglyprolifictrajectoryasascientist
andteacher.
Inhislonganddistinguishedcareerasamathematicianandcomputerscientist,
JacobT.Schwartzmadenumerousimportantcontributionstoaremarkablevariety
of differentsubjectareas.His stylewas to entera newfield,to masterquicklythe
existing research literature, to add the stamp of his own forceful vision in a series
ofresearchcontributions,andfinallytoleavebehindanactiveresearchgroupthat
wouldcontinuefruitfulresearchformanyyearsalongthelineshelaiddown.Abrief
listofsomeoftheareastowhichSchwartzmademajorcontributionswillgivesome
notion of the breath of his interests: spectral theory of linear operators, von Neu-
mannalgebras,macroeconomics,themathematicsofquantumfieldtheory,parallel
computation,computertime-sharing,high-levelprogramminglanguages,compiler
optimization,transformationalprogramming,computationallogic,motionplanning
in robotics, multimedia and educational software, and finally computational biol-
ogy.Hehadanenormoustalentforconveyinghisenthusiasms,andtheessaysthat
follow reflect the impact that he has had on the scientific interests of his students
andcollaborators.
(cid:2)
M.Davis( )·E.Schonberg
CourantInstituteofMathem.Science,NewYorkUniversity,MercerStreet251,NewYork,10012
NY,USA
e-mail:[email protected]
E.Schonberg
e-mail:[email protected]
M.Davis,E.Schonberg(eds.),FromLinearOperatorstoComputationalBiology, 1
DOI10.1007/978-1-4471-4282-9_1,©Springer-VerlagLondon2013
