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Topics in Domain Theory and Pointfree Topology
, 2002
"... These notes for the course Domain Theory MN1 cover some topics not treated in the main textbook [MTD] such as interval arithmetic, digital topology, signeddigit expansions, abstract interpretation and Galois connections, combinatorics of partial orders, and gives a different treatment of formal spa ..."
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These notes for the course Domain Theory MN1 cover some topics not treated in the main textbook [MTD] such as interval arithmetic, digital topology, signeddigit expansions, abstract interpretation and Galois connections, combinatorics of partial orders, and gives a different treatment of formal
From intuitionistic topology to pointfree topology Pure and Applied Logic Colloquium,
, 2005
"... 1. Constructive continuity When computing the integral, calculating supremum or approximating zeroes of a continuous function f: [0,1] we use its uniform continuity. Using nonconstructive axioms, e.g. the Fan Theorem, one can show uniform continuity from pointwise continuity. ..."
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1. Constructive continuity When computing the integral, calculating supremum or approximating zeroes of a continuous function f: [0,1] we use its uniform continuity. Using nonconstructive axioms, e.g. the Fan Theorem, one can show uniform continuity from pointwise continuity.
Jacob VosmaerLogic, Algebra and Topology
"... Investigations into canonical extensions, duality theory and pointfree topology ..."
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Investigations into canonical extensions, duality theory and pointfree topology
The PointFree Approach to Sheafification
"... Let be an arbitrary frame, and consider the category Psh( of presheaves on ..."
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Let be an arbitrary frame, and consider the category Psh( of presheaves on
SPECIAL ISSUE ON POINTFREE GEOMETRY AND TOPOLOGY
"... Abstract. In the first section we briefly describe the methodological assumptions of pointfree geometry and topology. We also outline the history of geometrical theories based on the notion of a region. The second section is devoted to a concise presentation of the content of the LLP special issue ..."
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Abstract. In the first section we briefly describe the methodological assumptions of pointfree geometry and topology. We also outline the history of geometrical theories based on the notion of a region. The second section is devoted to a concise presentation of the content of the LLP special
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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as random graphs, it is increasingly recognized that the topology and evolution of real
ChernSimons Gauge Theory as a String Theory
, 2003
"... Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given spacetime interpretations. For instance, threedimensional ChernSimons gaug ..."
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Cited by 551 (14 self)
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Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given spacetime interpretations. For instance, threedimensional Chern
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number
A Simple, Fast, and Accurate Algorithm to Estimate Large Phylogenies by Maximum Likelihood
, 2003
"... The increase in the number of large data sets and the complexity of current probabilistic sequence evolution models necessitates fast and reliable phylogeny reconstruction methods. We describe a new approach, based on the maximumlikelihood principle, which clearly satisfies these requirements. The ..."
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Cited by 2109 (30 self)
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. The core of this method is a simple hillclimbing algorithm that adjusts tree topology and branch lengths simultaneously. This algorithm starts from an initial tree built by a fast distancebased method and modifies this tree to improve its likelihood at each iteration. Due to this simultaneous adjustment
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