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74
The many faces of alternatingsign matrices
, 2008
"... I give a survey of different combinatorial forms of alternatingsign matrices, starting with the original form introduced by Mills, Robbins and Rumsey as well as cornersum matrices, heightfunction matrices, threecolorings, monotone triangles, tetrahedral order ideals, square ice, gasketandbasket ..."
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Cited by 23 (0 self)
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I give a survey of different combinatorial forms of alternatingsign matrices, starting with the original form introduced by Mills, Robbins and Rumsey as well as cornersum matrices, heightfunction matrices, threecolorings, monotone triangles, tetrahedral order ideals, square ice, gasketandbasket tilings and full packings of loops. (This article has been published in a conference edition of the journal Discrete Mathematics and Theoretical
Distributing coalitional value calculations among cooperating agents
 In Proceedings of The Twentieth National Conference on Artificial Intelligence (AAAI05
, 2005
"... The process of forming coalitions of software agents generally requires calculating a value for every possible coalition which indicates how beneficial that coalition would be if it was formed. Now, instead of having a single agent calculate all these values (as is typically the case), it is more ef ..."
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Cited by 20 (13 self)
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The process of forming coalitions of software agents generally requires calculating a value for every possible coalition which indicates how beneficial that coalition would be if it was formed. Now, instead of having a single agent calculate all these values (as is typically the case), it is more efficient to distribute this calculation among the agents, thus using all the computational resources available to the system and avoiding the existence of a single point of failure. Given this, we present a novel algorithm for distributing this calculation among agents in cooperative environments. Specifically, by using our algorithm, each agent is assigned some part of the calculation such that the agents ’ shares are exhaustive and disjoint. Moreover, the algorithm is decentralized, requires no communication between the agents, has minimal memory requirements, and can reflect variations in the computational speeds of the agents. To evaluate the effectiveness of our algorithm, we compare it with the only other algorithm available in the literature for distributing the coalitional value calculations (due to Shehory and Kraus). This shows that for the case of 25 agents, the distribution process of our algorithm took less than 0.02 % of the time, the values were calculated using 0.000006 % of the memory, the calculation redundancy was reduced from 383229848 to 0, and the total number of bytes sent between the agents dropped from 1146989648 to 0 (note that for larger numbers of agents, these improvements become exponentially better). 1
A new operation on sequences: the boustrophedon transform
 J. Combin. Th. Ser. A
, 1996
"... A generalization of the SeidelEntringerArnold method for calculating the alternating permutation numbers (or secanttangent numbers) leads to a new operation on sequences, the boustrophedon transform. This paper was published (in a somewhat different form) in J. Combinatorial Theory, Series A, 76 ..."
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Cited by 12 (0 self)
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A generalization of the SeidelEntringerArnold method for calculating the alternating permutation numbers (or secanttangent numbers) leads to a new operation on sequences, the boustrophedon transform. This paper was published (in a somewhat different form) in J. Combinatorial Theory, Series A, 76 (1996), pp. 44–54.
On Angles Whose Squared Trigonometric Functions Are Rational
 Geom
"... We consider the rational linear relations between real numbers whose squared trigonometric values are rational, angles we call "geodetic". We construct a convenient basis for the vector space over Q generated by these angles. Geodetic angles, and rational linear combinations of geodetic angles, appe ..."
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Cited by 11 (2 self)
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We consider the rational linear relations between real numbers whose squared trigonometric values are rational, angles we call "geodetic". We construct a convenient basis for the vector space over Q generated by these angles. Geodetic angles, and rational linear combinations of geodetic angles, appear naturally in Euclidean geometry; for illustration we apply our results to equidecomposability of polyhedra. * Research supported in part by NSF Grant No. DMS9701444 ** Research supported in part by NSF Grant No. DMS9531584 and Texas ARP Grant 003658152 *** Research supported in part by NSF Grant No. DMS9626698 and Texas ARP Grant 003658152 0. Introduction Many well known geometric objects involve angles that are irrational when measured in degrees or are irrational multiples of ß in radian measure. For instance we might mention the dihedral angle ff (ß 70 ffi 31 0 44 00 ) of the regular tetrahedron, whose supplement (ß 109 ffi 28 0 16 00 ) is known to chemists as the c...
Implementation Of The AtkinGoldwasserKilian Primality Testing Algorithm
 Rapport de Recherche 911, INRIA, Octobre
, 1988
"... . We describe a primality testing algorithm, due essentially to Atkin, that uses elliptic curves over finite fields and the theory of complex multiplication. In particular, we explain how the use of class fields and genus fields can speed up certain phases of the algorithm. We sketch the actual impl ..."
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Cited by 9 (7 self)
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. We describe a primality testing algorithm, due essentially to Atkin, that uses elliptic curves over finite fields and the theory of complex multiplication. In particular, we explain how the use of class fields and genus fields can speed up certain phases of the algorithm. We sketch the actual implementation of this test and its use on testing large primes, the records being two numbers of more than 550 decimal digits. Finally, we give a precise answer to the question of the reliability of our computations, providing a certificate of primality for a prime number. IMPLEMENTATION DU TEST DE PRIMALITE D' ATKIN, GOLDWASSER, ET KILIAN R'esum'e. Nous d'ecrivons un algorithme de primalit'e, principalement du `a Atkin, qui utilise les propri'et'es des courbes elliptiques sur les corps finis et la th'eorie de la multiplication complexe. En particulier, nous expliquons comment l'utilisation du corps de classe et du corps de genre permet d'acc'el'erer les calculs. Nous esquissons l'impl'ementati...
Selection Theorem for Systems With Inheritance
"... Abstract. The problem of finitedimensional asymptotics of infinitedimensional dynamic systems is studied. A nonlinear kinetic system with conservation of supports for distributions has generically finitedimensional asymptotics. Such systems are apparent in many areas of biology, physics (the the ..."
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Cited by 8 (4 self)
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Abstract. The problem of finitedimensional asymptotics of infinitedimensional dynamic systems is studied. A nonlinear kinetic system with conservation of supports for distributions has generically finitedimensional asymptotics. Such systems are apparent in many areas of biology, physics (the theory of parametric wave interaction), chemistry and economics. This conservation of support has a biological interpretation: inheritance. The finitedimensional asymptotics demonstrates effects of “natural ” selection. Estimations of the asymptotic dimension are presented. After some initial time, solution of a kinetic equation with conservation of support becomes a finite set of narrow peaks that become increasingly narrow over time and move increasingly slowly. It is possible that these peaks do not tend to fixed positions, and the path covered tends to infinity as t → ∞. The drift equations for peak motion are obtained. Various types of distribution stability are studied: internal stability (stability with respect to perturbations that do not extend the support), external stability or uninvadability (stability with respect to strongly small perturbations that extend the support), and stable realizability (stability with respect to small shifts and extensions of the density peaks). Models of selfsynchronization of cell division are studied, as an example of selection in systems with additional symmetry. Appropriate construction of the notion of typicalness in infinitedimensional space is discussed, and the notion of “completely thin” sets is introduced.
Locating XML Documents in PeertoPeer Networks Using Distributed Hash Tables
, 2008
"... Abstract—One of the key challenges in a peertopeer (P2P) network is to efficiently locate relevant data sources across a large number of participating peers. With the increasing popularity of the extensible markup language (XML) as a standard for information interchange on the Internet, XML is com ..."
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Cited by 7 (4 self)
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Abstract—One of the key challenges in a peertopeer (P2P) network is to efficiently locate relevant data sources across a large number of participating peers. With the increasing popularity of the extensible markup language (XML) as a standard for information interchange on the Internet, XML is commonly used as an underlying data model for P2P applications to deal with the heterogeneity of data and enhance the expressiveness of queries. In this paper, we address the problem of efficiently locating relevant XML documents in a P2P network, where a user poses queries in a language such as XPath. We have developed a new system called psiX that runs on top of an existing distributed hashing framework. Under the psiX system, each XML document is mapped into an algebraic signature that captures the structural summary of the document. An XML query pattern is also mapped into a signature. The query’s signature is used to locate relevant document signatures. Our signature scheme supports holistic processing of query patterns without breaking them into multiple path queries and processing them individually. The participating peers in the network collectively maintain a collection of distributed hierarchical indexes for the document signatures. Value indexes are built to handle numeric and textual values in XML documents. These indexes are used to process queries with value predicates. Our experimental study on PlanetLab demonstrates that psiX provides an efficient location service in a P2P network for a wide variety of XML documents. Index Terms—XML indexing, XPath, peertopeer computing, distributed hash tables. Ç 1
Asymptotically Fair Scheduling on Fading Channels
 IEEE VTC Fall
, 2002
"... The problem of scheduling data for a DSCDMA downlink, over a fading channel is considered. We show that high speed downlink data is most efficiently supported by time division of the channel, by letting only one single user in each cell access the channel at a time. For efficient resource utilizati ..."
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Cited by 7 (1 self)
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The problem of scheduling data for a DSCDMA downlink, over a fading channel is considered. We show that high speed downlink data is most efficiently supported by time division of the channel, by letting only one single user in each cell access the channel at a time. For efficient resource utilization, some form of scheduling is required to determine which user should transmit at any given instant of time. Scheduling algorithms of different adaptation rate are suggested and compared. To avoid unfair performance, an algorithm that schedules a user to transmit when its channel is the "relatively best" is analyzed. We show that this algorithm asymptotically provides the same fairness as a round robin scheduler, but the throughput is significantly improved. For a Rayleigh fading channel, we show that the scheduling gain is in fact equal to the gain of a selection diversity scheme.
Are `Strong' Primes Needed for RSA?
 In The 1997 RSA Laboratories Seminar Series, Seminars Proceedings
, 1999
"... We review the arguments in favor of using socalled "strong primes" in the RSA publickey cryptosystem. There are two types of such arguments: those that say that strong primes are needed to protect against factoring attacks, and those that say that strong primes are needed to protect against "cy ..."
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Cited by 6 (1 self)
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We review the arguments in favor of using socalled "strong primes" in the RSA publickey cryptosystem. There are two types of such arguments: those that say that strong primes are needed to protect against factoring attacks, and those that say that strong primes are needed to protect against "cycling" attacks (based on repeated encryption).