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82
Jholomorphic curves, moment maps, and invariants of Hamiltonian group actions
, 1999
"... This paper outlines the construction of invariants of Hamiltonian group actions on symplectic manifolds. The invariants are derived from the solutions of a nonlinear rst order elliptic partial dierential equation involving the CauchyRiemann operator, the curvature, and the moment map (see (17) belo ..."
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Cited by 52 (5 self)
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This paper outlines the construction of invariants of Hamiltonian group actions on symplectic manifolds. The invariants are derived from the solutions of a nonlinear rst order elliptic partial dierential equation involving the CauchyRiemann operator, the curvature, and the moment map (see (17) below). They are related to the Gromov invariants of the reduced spaces. Our motivation arises from the proof of the AtiyahFloer conjecture in [17, 18, 19] which deals with the relation between holomorphic curves ! M S in the moduli space M S of at connections over a Riemann surface S and antiselfdual instantons over the 4manifold S. In [3] Atiyah and Bott interpret the space M S as a symplectic quotient of the space A S of connections on S by the action of the group G S of gauge transformations. A moment's thought shows that the various terms in the antiselfduality equations over S (see equation (64) below) can be interpreted symplectically. Hence they should give rise to meaningful equations in a context where the space A S is replaced by a nite dimensional symplectic manifold M and the gauge group G S by a compact Lie group G with a Hamiltonian action on M . In this paper 2 we show how the resulting equations give rise to invariants of Hamiltonian group actions. The same adiabatic limit argument as in [19] then leads to a correspondence between these invariants and the Gromov{Witten invariants of the quotient M==G (Conjecture 3.6). This correspondence is the subject of the PhD thesis [27] of the second author. In Section 2 we review the relevant background material about Hamiltonian group actions, gauge theory, equivariant cohomology, and holomorphic curves in symplectic quotients. The heart of this paper is Section 3, where we discuss the equations and the...
MIP: Theory and Practice  Closing the Gap
 SYSTEM MODELLING AND OPTIMIZATION: METHODS, THEORY, AND APPLICATIONS
, 2000
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Maximum Planar Subgraphs and Nice Embeddings: Practical Layout Tools
 ALGORITHMICA
, 1996
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Covering Conditions and Algorithms for the Synthesis of SpeedIndependent Circuits
 IEEE Transactions on ComputerAided Design
, 1998
"... This paper presents theory and algorithms for the synthesis of standard Cimplementations of speedindependent circuits. These implementations are blocklevel circuits which may consist of atomic gates to perform complex functions in order to ensure hazardfreedom. First, we present boolean covering ..."
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Cited by 14 (5 self)
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This paper presents theory and algorithms for the synthesis of standard Cimplementations of speedindependent circuits. These implementations are blocklevel circuits which may consist of atomic gates to perform complex functions in order to ensure hazardfreedom. First, we present boolean covering conditions that guarantee the standard Cimplementations operate correctly. Then, we present two algorithms that produce optimal solutions to the covering problem. The first algorithm is always applicable but does not complete on large circuits. The second algorithm, motivated by our observation that our covering problem can often be solved with a single cube, finds the optimal singlecube solution when such a solution exists. When applicable, the second algorithm is dramatically more efficient than the first, more general algorithm. We present results for benchmark specifications which indicate that our singlecube algorithm is applicable on most benchmark circuits and reduces runtimes by ...
Defining and researching disability: challenges and responses
 In C. Barnes and G. Mercer (Ed.), Exploring the Divide (pp
, 1996
"... It is something of a cliché to say that we are living in a period of rapid social change. Yet it seems clear that a fundamental process of cultural as well as economic and social transformation is underway, and on a global scale. Arguments have proliferated as to the ..."
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Cited by 10 (0 self)
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It is something of a cliché to say that we are living in a period of rapid social change. Yet it seems clear that a fundamental process of cultural as well as economic and social transformation is underway, and on a global scale. Arguments have proliferated as to the
A Model Checker for Statecharts (Linking CASE tools with Formal Methods)
, 1993
"... . ComputerAided Software Engineering (CASE) tools encourage users to codify the specification for the design of a system early in the development process. They often use graphical formalisms, simulation, and prototyping to help express ideas concisely and unambiguously. Some tools provide little ..."
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Cited by 8 (1 self)
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. ComputerAided Software Engineering (CASE) tools encourage users to codify the specification for the design of a system early in the development process. They often use graphical formalisms, simulation, and prototyping to help express ideas concisely and unambiguously. Some tools provide little more than syntax checking of the specification but others can test the model for reachability of conditions, nondeterminism, or deadlock. Formal methods include powerful tools like automatic model checking to exhaustively check a model against certain requirements. Integrating formal techniques into the system development process is an effective method of providing more thorough analysis of specifications than conventional approaches employed by ComputerAided Software Engineering (CASE) tools. In order to create this link, the formalism used by the CASE tool must have a precise formal semantics that can be understood by the verification tool. The CASE tool STATEMATE makes use of an...
The TemperleyLieb algebra and its generalizations in the Potts and XXZ models
 L02004 (2006) [hepth/0512273
"... We discuss generalizations of the TemperleyLieb algebra in the Potts and XXZ models. These can be used to describe the addition of different types of integrable boundary terms. We use the TemperleyLieb algebra and its oneboundary, twoboundary, and periodic extensions to classify different integr ..."
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We discuss generalizations of the TemperleyLieb algebra in the Potts and XXZ models. These can be used to describe the addition of different types of integrable boundary terms. We use the TemperleyLieb algebra and its oneboundary, twoboundary, and periodic extensions to classify different integrable boundary terms in the 2, 3, and 4state Potts models. The representations always lie at critical points where the algebras becomes nonsemisimple and possess indecomposable representations. In the oneboundary case we show how to use representation theory to extract the Potts spectrum from an XXZ model with particular boundary terms and hence obtain the finite size scaling of the Potts models. In the twoboundary case we find that the Potts spectrum can be obtained by combining several XXZ models with different boundary terms. As in the TemperleyLieb case there is a direct correspondence between representations of the lattice algebra and those in the continuum conformal field theory. 1
Moduli spaces of flat connections on 2manifolds, cobordism, and Witten’s volume formulas
"... According to AtiyahBott [AB],[A] the moduli space of flat connections on a compact oriented 2manifold with prescribed holonomies around the boundary is a finitedimensional symplectic manifold, possibly singular. A standard approach [W1, W2, V] to computing invariants (symplectic volumes, RiemannR ..."
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Cited by 6 (1 self)
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According to AtiyahBott [AB],[A] the moduli space of flat connections on a compact oriented 2manifold with prescribed holonomies around the boundary is a finitedimensional symplectic manifold, possibly singular. A standard approach [W1, W2, V] to computing invariants (symplectic volumes, RiemannRoch numbers, etc.) of the moduli
Multiple geodesics with the same direction
 Electron. Commun. Probab
, 2011
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