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160
Algebraic Algorithms for Sampling from Conditional Distributions
 Annals of Statistics
, 1995
"... We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so a ..."
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Cited by 271 (20 self)
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We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so an excursion into computational algebraic geometry.
Decision Problems for Propositional Linear Logic
, 1990
"... Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, ..."
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Cited by 111 (19 self)
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Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes pspacecomplete. We also establish membership in np for the multiplicative fragment, npcompleteness for the multiplicative fragment extended with unrestricted weakening, and undecidability for certain fragments of noncommutative propositional linear logic. 1 Introduction Linear logic, introduced by Girard [14, 18, 17], is a refinement of classical logic which may be derived from a Gentzenstyle sequent calculus axiomatization of classical logic in three steps. The resulting sequent system Lincoln@CS.Stanford.EDU Department of Computer Science, Stanford University, Stanford, CA 94305, and the Computer Science Labo...
Reasoning with Concrete Domains
, 1999
"... Description logics are formalisms for the representation of and reasoning about conceptual knowledge on an abstract level. Concrete domains allow the integration of description logic reasoning with reasoning about concrete objects such as numbers, time intervals, or spatial regions. The importa ..."
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Cited by 65 (11 self)
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Description logics are formalisms for the representation of and reasoning about conceptual knowledge on an abstract level. Concrete domains allow the integration of description logic reasoning with reasoning about concrete objects such as numbers, time intervals, or spatial regions. The importance of this combined approach, especially for building realworld applications, is widely accepted. However, the complexity of reasoning with concrete domains has never been formally analyzed and efficient algorithms have not been developed. This paper closes the gap by providing a tight bound for the complexity of reasoning with concrete domains and presenting optimal algorithms. 1 Introduction Description logics are knowledge representation and reasoning formalisms dealing with conceptual knowledge on an abstract logical level. However, for a variety of applications, it is essential to integrate the abstract knowledge with knowledge of a more concrete nature. Examples of such "co...
Characteristicfree bounds for the Castelnuovo Mumford regularity
 Compos. Math
"... Abstract. In this paper we show how, given a complex of graded modules and knowing some partial CastelnuovoMumford regularities for all the modules in the complex and for all the positive homologies, it is possible to get a bound on the regularity of the zero homology. We use this to prove that if ..."
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Cited by 43 (2 self)
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Abstract. In this paper we show how, given a complex of graded modules and knowing some partial CastelnuovoMumford regularities for all the modules in the complex and for all the positive homologies, it is possible to get a bound on the regularity of the zero homology. We use this to prove that if dim TorR 1 (M, N) ≤ 1 then reg(M ⊗N) ≤ reg(M)+reg(N), generalizing results of Chandler, Conca and Herzog, and Sidman. Finally we give a description of the regularity of a module in terms of the postulation numbers of filter regular hyperplane restrictions. 1. introduction Let R = K[X1,..., Xn] be a polynomial ring over a field K, M a finitely generated graded Rmodule and let I ⊂ R be an ideal. Recently some work has been done to study when the CastelnuovoMumford regularity of Ir can be bounded by r times the regularity of I, and more generally when the regularity of IM can be bounded by the sum of the regularity of I and M. This is not always the case; see the papers of Sturmfels [St], and Conca, Herzog [CH] for counterexamples. On the
RESIDUE CURRENTS WITH PRESCRIBED ANNIHILATOR IDEALS
, 2007
"... Abstract. Given a coherent ideal sheaf J we construct locally a vectorvalued residue current R whose annihilator is precisely the given sheaf. In case J is a complete intersection, R is just the classical ColeffHerrera product. By means of these currents we can extend various results, previously k ..."
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Cited by 31 (11 self)
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Abstract. Given a coherent ideal sheaf J we construct locally a vectorvalued residue current R whose annihilator is precisely the given sheaf. In case J is a complete intersection, R is just the classical ColeffHerrera product. By means of these currents we can extend various results, previously known for a complete intersection, to general ideal sheaves. Combining with integral formulas we obtain a residue version of the EhrenpreisPalamodov fundamental principle. 1.
On the TimeSpace Complexity of Geometric Elimination Procedures
, 1999
"... In [25] and [22] a new algorithmic concept was introduced for the symbolic solution of a zero dimensional complete intersection polynomial equation system satisfying a certain generic smoothness condition. The main innovative point of this algorithmic concept consists in the introduction of a new ge ..."
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Cited by 29 (19 self)
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In [25] and [22] a new algorithmic concept was introduced for the symbolic solution of a zero dimensional complete intersection polynomial equation system satisfying a certain generic smoothness condition. The main innovative point of this algorithmic concept consists in the introduction of a new geometric invariant, called the degree of the input system, and the proof that the most common elimination problems have time complexity which is polynomial in this degree and the length of the input.