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44
A Relational Model of NonDeterministic Dataflow
 In CONCUR'98, volume 1466 of LNCS
, 1998
"... . We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits ..."
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Cited by 28 (13 self)
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. We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced monoidal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially the usual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higherorder dataflow as a biproduct, essentially by following the geometry of interaction programme. 1 Introduction A fundament...
A Tutte polynomial for signed graphs
 Discrete Appl. Math
, 1989
"... This paper introduces a generalization of the Tutte polynomial [14] that is defined for signed graphs. A signed graph is a graph whose edges are each labelled with a sign (+l or 1). The generalized polynomial will be denoted Q[G] = Q[G](A, B, d). Here G is the signed graph, and the letters A, B, d ..."
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Cited by 24 (0 self)
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This paper introduces a generalization of the Tutte polynomial [14] that is defined for signed graphs. A signed graph is a graph whose edges are each labelled with a sign (+l or 1). The generalized polynomial will be denoted Q[G] = Q[G](A, B, d). Here G is the signed graph, and the letters A, B, d denote three independent
Infinite families of links with trivial Jones polynomial
"... For each k >= 2, we exhibit infinite families of prime kcomponent links with Jones polynomial equal to that of the kcomponent unlink. ..."
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Cited by 20 (10 self)
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For each k >= 2, we exhibit infinite families of prime kcomponent links with Jones polynomial equal to that of the kcomponent unlink.
Interactive Topological Drawing
, 1998
"... The research presented here examines topological drawing, a new mode of constructing and interacting with mathematical objects in threedimensional space. In topological drawing, issues such as adjacency and connectedness, which are topological in nature, take precedence over purely geometric issues ..."
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Cited by 18 (1 self)
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The research presented here examines topological drawing, a new mode of constructing and interacting with mathematical objects in threedimensional space. In topological drawing, issues such as adjacency and connectedness, which are topological in nature, take precedence over purely geometric issues. Because the domain of application is mathematics, topological drawing is also concerned with the correct representation and display of these objects on a computer. By correctness we mean that the essential topological features of objects are maintained during interaction. We have chosen to limit the scope of topological drawing to knot theory, a domain that consists essentially of one class of object (embedded circles in threedimensional space) yet is rich enough to contain a wide variety of difficult problems of research interest. In knot theory, two embedded circles (knots) are considered equivalent if one may be smoothly deformed into the other without any cuts or selfintersections. This notion of equivalence may be thought of as the heart of knot theory. We present methods for the computer construction and interactive manipulation of a
Topological Quantum Field Theories For Surfaces With Spin Structure
, 1995
"... Refined quantum invariants for closed threemanifolds with links and spin structures are extended to a Topological Quantum Field Theory. By a `universal construction ', one associates, to surfaces with structure, modules which are shown to be free of finite rank. These modules satisfy the multiplica ..."
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Cited by 14 (4 self)
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Refined quantum invariants for closed threemanifolds with links and spin structures are extended to a Topological Quantum Field Theory. By a `universal construction ', one associates, to surfaces with structure, modules which are shown to be free of finite rank. These modules satisfy the multiplicativity axiom of TQFT in an extended Z=2graded sense, and their ranks are given by a spin refined version of the `Verlinde formula'. The relationship with the `unspun' theory is given by a natural `transfer map'. Introduction A Topological Quantum Field Theory (TQFT) in dimension 3 is a functor from a 2 + 1dimensional cobordism category to a category of modules, satisfying certain axioms. This terminology was introduced by Atiyah [1] following Witten's [32] interpretation, in terms of quantum field theory, of the Jones polynomial invariant of links in the 3sphere. The TQFTaxioms imply that the functor is determined by its values on closed bordisms. These lie in the ground ring, and are 3...
Relational Semantics of NonDeterministic Dataflow
, 1997
"... We recast dataflow in a modern categorical light using profunctors as a generalization of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fit ..."
Abstract

Cited by 12 (5 self)
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We recast dataflow in a modern categorical light using profunctors as a generalization of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced monoidal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially the usual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higherorder dataflow as a biproduct, essentially by following the geometry of interaction programme.
TemperleyLieb Algebra: From Knot Theory to . . .
"... Our aim in this paper is to trace some of the surprising and beautiful connections which are beginning to emerge between a number of apparently disparate topics. ..."
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Cited by 11 (2 self)
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Our aim in this paper is to trace some of the surprising and beautiful connections which are beginning to emerge between a number of apparently disparate topics.
Knot Theory and the Heuristics of Functional Integration
 PHYSICA A
, 2000
"... This paper is an exposition of the relationship between the heuristics of Witten's functional integral and the theory of knots and links in threedimensional space. ..."
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Cited by 9 (9 self)
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This paper is an exposition of the relationship between the heuristics of Witten's functional integral and the theory of knots and links in threedimensional space.
Topological Quantum Field Theories
"... Abstract. Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of topological quantum field theories were constructed in my pa ..."
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Cited by 9 (1 self)
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Abstract. Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of topological quantum field theories were constructed in my papers in late seventies) and I come to some new results, that were not published yet. 0. Introduction. I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I’ll start with old results (first examples of topological quantum field theories were constructed in my papers in late seventies) and I’ll come to some new results, that were not published
Skein modules of links in cylinders over surfaces
 Int. J. Math. Sci
"... Abstract. We define the Conway skein module C(M) of ordered based links in a 3manifold M. This module gives rise to C(M)valued invariants of usual links in M. We determine a basis of the Z[z]module C(Σ×[0, 1])/Tor(C(Σ×[0, 1])) where Σ is the real projective plane or a surface with boundary. For c ..."
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Cited by 6 (0 self)
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Abstract. We define the Conway skein module C(M) of ordered based links in a 3manifold M. This module gives rise to C(M)valued invariants of usual links in M. We determine a basis of the Z[z]module C(Σ×[0, 1])/Tor(C(Σ×[0, 1])) where Σ is the real projective plane or a surface with boundary. For cylinders over the Möbius strip or the projective plane we derive special properties of the Conway skein module, among them a refinement of a theorem of Hartley and Kawauchi about the Conway polynomial of strongly positive amphicheiral knots in S 3. In addition, we determine the Homfly and Kauffman skein modules of Σ × [0, 1] where Σ is an oriented surface with boundary.