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ofRenewalProcesses PhilippeFlajolet,WojtekSzpankowski
"... apport de recherche AnalyticVariationsonRedundancyRates RapportderechercheNovembre199812pages Theme2Genielogicieletcalculsymbolique ofRenewalProcesses ProjetAlgorithmes PhilippeFlajolet,WojtekSzpankowski providesarstnontrivialboundonredundancyforanonparametricfamilyofprocesses. Thepresentpaperp ..."
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apport de recherche AnalyticVariationsonRedundancyRates RapportderechercheNovembre199812pages Theme2Genielogicieletcalculsymbolique ofRenewalProcesses ProjetAlgorithmes PhilippeFlajolet,WojtekSzpankowski providesarstnon
Philippe Flajolet, Divide & Conquer Recurrences and The MellinPerron Formula
"... Most basic DivideandConquer Recurrence is in form Well known that if en = o(n) ⇒ fn = Θ(n) Θ(n) ⇒ fn = Θ(n log n) Θ(n k),k>1 ⇒ fn = Θ(n k) What’s left to do? The Problem Not so simple. When n is odd, set can't be split into two equal subsets. Use almost equal subsets. Recurrence becomes ..."
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periodic functions was adhoc and time consuming • As a master of techniques, Philippe realized that Mellintransform methods were applicable. He showed how they provided an “elementary ” derivationTwo Basic Examples ‣ Worst case number of comparisons used by recursive Mergesort when sorting n items
SIA: Secure Information Aggregation in Sensor Networks
, 2003
"... Sensor networks promise viable solutions to many monitoring problems. However, the practical deployment of sensor networks faces many challenges imposed by realworld demands. Sensor nodes often have limited computation and communication resources and battery power. Moreover, in many applications se ..."
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Cited by 250 (13 self)
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Sensor networks promise viable solutions to many monitoring problems. However, the practical deployment of sensor networks faces many challenges imposed by realworld demands. Sensor nodes often have limited computation and communication resources and battery power. Moreover, in many applications sensors are deployed in open environments, and hence are vulnerable to physical attacks, potentially compromising the sensor's cryptographic keys. One of the basic and indispensable functionalities of sensor networks is the ability to answer queries over the data acquired by the sensors. The resource constraints and security issues make designing mechanisms for information aggregation in large sensor networks particularly challenging.
Mellin Transforms And Asymptotics: Harmonic Sums
 Theoretical Computer Science
, 1995
"... . This survey presents a unified and essentially selfcontained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and the averagecase analysis of algorithms. It relies on the Mellin transform, a close relative of the ..."
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Cited by 212 (12 self)
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. This survey presents a unified and essentially selfcontained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and the averagecase analysis of algorithms. It relies on the Mellin transform, a close relative of the integral transforms of Laplace and Fourier. The method applies to harmonic sums that are superpositions of rather arbitrary "harmonics" of a common base function. Its principle is a precise correspondence between individual terms in the asymptotic expansion of an original function and singularities of the transformed function. The main applications are in the area of digital data structures, probabilistic algorithms, and communication theory. Die Theorie der reziproken Funktionen und Integrale ist ein centrales Gebiet, welches manche anderen Gebiete der Analysis miteinander verbindet.  Hjalmar Mellin Introduction Hjalmar Mellin (18541933, see [59] for a summary of his works) gave his ...
Joint String Complexity for Markov Sources Dedicated to our friend and mentor Philippe Flajolet
"... String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we define joint string complexity as the set of words that are common to both strings. We also relax this definition and introduce joint semicomplexity restricted to the commo ..."
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String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we define joint string complexity as the set of words that are common to both strings. We also relax this definition and introduce joint semicomplexity restricted to the common words appearing at least twice in both strings. In this paper we analyze joint complexity and joint semicomplexity when both strings are generated by a Markov source. The problem turns out to be quite challenging requiring subtle singularity analysis and saddle point method over infinity many saddle points leading to novel oscillatory phenomena with single and double periodicities. 1
An Algorithmic Proof Theory for Hypergeometric (ordinary and ``$q$'') Multisum/integral Identities
, 1991
"... this paper we show that these fast algorithms can be extended to the much larger class of multisum terminating hypergeometric (or equivalently, binomial coefficient) identities, to constant term identities of DysonMacdonald type, to MehtaDyson type integrals, and more generally, to identities inv ..."
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Cited by 199 (21 self)
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this paper we show that these fast algorithms can be extended to the much larger class of multisum terminating hypergeometric (or equivalently, binomial coefficient) identities, to constant term identities of DysonMacdonald type, to MehtaDyson type integrals, and more generally, to identities involving any (fixed) number of sums and integrals of products of special functions of hypergeometric type. The computergenerated proofs obtained by our algorithms are always short, are often very elegant, and like the singlesum case, sometimes yield the discovery and proof of new identities. We also do the same for single and multi (terminating) qhypergeometric identities, with continuous and/or discrete variables. Here we describe these algorithms in general, and prove their validity. The validity is an immediate consequence of what we call "The fundamental theorem of hypergeometric summation and integration", a result which we believe is of independent theoretical interest and beauty. The technical aspects of our algorithms, as well as their implementation in Maple, will be described in a forthcoming paper. It is possible, and sometimes preferable, to enjoy a magic show without understanding how the tricks are performed. Hence we invite casual readers to go directly to section 6, in which we give several examples of one or two line proofs generated by our method. In order to understand these proofs, and convince oneself of their correctness, one doesn't need to know how they were generated. Readers can generate many more examples on their own once they obtain a copy of our Maple program, that is available upon request from
OntheTranscendenceofFormalPowerSeries [summarybyPhilippeFlajolet] L.R.I.,UniversiteParisSud JeanPaulAllouche December1,1997
"... complexitylowerbound"onC.Forinstance,elementsofCcannotbeencodedbyanunambiguous contextfreegrammar.Accordingly,ifCalreadyadmitscontextfreedescriptions,allsuchdescripgories.tionsmustbeinherentlyambiguous. Conversely,atranscendenceresultforthegfofacombinatorialclassCmeansasortof\structural M ..."
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complexitylowerbound"onC.Forinstance,elementsofCcannotbeencodedbyanunambiguous contextfreegrammar.Accordingly,ifCalreadyadmitscontextfreedescriptions,allsuchdescripgories.tionsmustbeinherentlyambiguous. Conversely,atranscendenceresultforthegfofacombinatorialclassCmeansasortof\structural Methodsforestablishingthetranscendenceofgeneratingfunctionsfallbroadlyintotwocate {Arithmeticmethodsarebasedonnumbertheoreticpropertiesofcoecients.Themostfamous criterioninthisrangeisEisenstein'scriterion:IfaseriesofQ[[z]]isalgebraic,thenthe denominatorsofitscoecientscontainonlynitelymanyprimes.Forinstance,f(z)=exp(z) specicallyonthefollowingpowerfulapproach[2,3,4,10]. Theanalyticapproachisreviewedin[6].Thetalkfocusesonthearithmeticmethod,andmore {Analyticmethodsarebasedonthepresenceofatranscendentalelementinalocalbehaviour, manyprimes(byEuclid'stheorem!). usuallytakenatasingularpoint.Inthisperspective,f(z)=exp(z)istranscendental\because"itsgrowthistoofastatinnity,afactincompatiblewiththefactthatanalgebraic functionislocallydescribedbyaPuiseuxseries(i.e.,aseriesinvolvingfractionalpowers). istranscendental\because"itscoecientsfn=1n!havedenominatorsthatcontaininnitely
Correspondence Comments and notes Features Obituaries
, 2013
"... RES news p.25 Conference diary p.25 Crowded and late Members will receive this particular April issue a few days late since it went to press immediately after (a bitterly cold but otherwise very successful) Annual Conference at Royal Holloway University of London. This allows us to maintain the rece ..."
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at the Conference. As regards content in this issue, we have Angus Deaton’s slightly unsettling Letter from America, a substantial obituary of one illustrious past President by another and an unusual number of features. Regular readers will spot the various devices to which we have resorted to fit it all in. We
Automated Counting of Towers (À La Bordelaise) [Or: Footnote to p. 81 of the FlajoletSedgewick Chefd’œuvre]
"... À la mémoire de Philippe FLAJOLET One of our favorite theorems in enumerative combinatorics, whose prooffromthebook by Jean Bétréma and JeanGuy Penaud[BeP] is succinctly outlined on p. 81 of the FlajoletSedgewick[FS] bible, (that, in turn, is based on Mireille BousquetMélou’s “insightful prese ..."
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À la mémoire de Philippe FLAJOLET One of our favorite theorems in enumerative combinatorics, whose prooffromthebook by Jean Bétréma and JeanGuy Penaud[BeP] is succinctly outlined on p. 81 of the FlajoletSedgewick[FS] bible, (that, in turn, is based on Mireille BousquetMélou’s “insightful
Results 1  10
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