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A calculus of mobile processes, I
, 1992
"... We present the acalculus, a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage. The ..."
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Cited by 1183 (31 self)
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calculus of higherorder functions (the Icalculus and combinatory algebra), the transmission of processes as values, and the representation of data structures as processes. The paper continues by presenting the algebraic theory of strong bisimilarity and strong equivalence, including a new notion of equivalence
Representations of Rigid Solids: Theory, Methods, and Systems
 ACM Computing Surveys
, 1980
"... Computerbased ystems for modehng the geometry ofrigid solid objects are becoming increasingly important inmechanical nd civil engineering, architecture, computer graphics, computer vision, and other fields that deal with spatial phenomena. At the heart of such systems are symbol structures (represe ..."
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Cited by 254 (2 self)
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Computerbased ystems for modehng the geometry ofrigid solid objects are becoming increasingly important inmechanical nd civil engineering, architecture, computer graphics, computer vision, and other fields that deal with spatial phenomena. At the heart of such systems are symbol structures (representations) designating "abstract solids" (subsets of Euclidean space) that model physical solids. Representations arethe sources of data for procedures which compute useful properties ofobjects. The variety and uses of systems embodying representations f olids are growing rapidly, but so are the difficulties in assessing current designs, pecifying the characteristics that future systems should exhibit, and designing systems t9 meet such specifications. This paper esolves many of these difficulties by providing a coherent view, based on sound theoretical principles, of what is presently known about he representation of solids. The paper is divided into three parts. The first introduces a simple mathematical framework for characterizing certain important aspects of representations, for example, their semantic (geometric) ntegrity. The second part uses the framework to describe and compare all of the major knownschemes fo ~ representing solids. The third part briefly surveys extant geometric modeling systems and then applies the concepts developed in the paper to the highlevel design of a multiple*representation geometric modeling system which exhibits alevel of reliability and versatility supermr to that of systems currently used in industrial computeraided design and manufacturing.
Structure of the peak Hopf algebra of quasisymmetric functions
, 2002
"... Abstract. We analyze the structure of Stembridge’s peak algebra, showing it to be a free commutative algebra (specifically a shuffle algebra) over Q, a cofree graded coalgebra, and a free module over Schur’s Qfunction algebra. Our analysis builds on combinatorial properties of a new monomiallik ..."
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Cited by 5 (0 self)
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Abstract. We analyze the structure of Stembridge’s peak algebra, showing it to be a free commutative algebra (specifically a shuffle algebra) over Q, a cofree graded coalgebra, and a free module over Schur’s Qfunction algebra. Our analysis builds on combinatorial properties of a new monomial
Renormalization, Hopf algebras and Mellin transforms
 CONTEMPORARY MATHEMATICS
, 2014
"... This article aims to give a short introduction into Hopfalgebraic aspects of renormalization, enjoying growing attention for more than a decade by now. As most available literature is concerned with the minimal subtraction scheme, we like to point out properties of the kinematic subtraction scheme ..."
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[x] being a morphism of Hopf algebras to the polynomials in one indeterminate. Upon introduction of analytic regularization this results in efficient combinatorial recursions to calculate φR in terms of the Mellin transform. We find that different Feynman rules are related by a distinguished class of Hopf
The Dawn of an Algebraic . . .
, 2011
"... To me, 2010 looks as annus mirabilis, a miraculous year, in several areas of my mathematical interests. Below I list seven highlights and breakthroughs, mostly in discrete geometry, hoping to share some of my wonder and pleasure with the readers. Of course, hardly any of these great results have com ..."
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To me, 2010 looks as annus mirabilis, a miraculous year, in several areas of my mathematical interests. Below I list seven highlights and breakthroughs, mostly in discrete geometry, hoping to share some of my wonder and pleasure with the readers. Of course, hardly any of these great results have come out of the blue: usually the paper I refer to adds the last step to earlier ideas. Since this is an extended abstract (of a nonexistent paper), I will be rather brief, or sometimes completely silent, about the history, with apologies to the unmentioned giants on whose shoulders the authors I do mention have been standing. 1 A careful reader may notice that together with these great results, I will also advertise some smaller results of mine. • Larry Guth and Nets Hawk Katz [16] completed a bold project of György Elekes (whose previous stage is reported in [10]) and obtained a neartight bound for the Erdős distinct distances problem: they proved that every n points in the plane determine at least Ω(n / log n) distinct distances. This almost matches the best known upper bound of O(n / √ √ √ log n), attained for the n × n grid. Their proof and some related results and methods constitute the main topic of this note, and will be discussed later. • János Pach and Gábor Tardos [27] found tight lower bounds for the size of εnets for geometric set systems. 2 It has been known for a long time
Exponential Lower Bounds for the Pigeonhole Principle
, 1992
"... In this paper we prove an exponential lower bound on the size of boundeddepth Frege proofs for the pigeonhole principle (PHP). We also obtain an ~(log log rz)depth lower bound for any polynomialsized Frege proof of the pigeonhole principle. Our theorem nearly completes the search for the exact ..."
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Cited by 121 (27 self)
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In this paper we prove an exponential lower bound on the size of boundeddepth Frege proofs for the pigeonhole principle (PHP). We also obtain an ~(log log rz)depth lower bound for any polynomialsized Frege proof of the pigeonhole principle. Our theorem nearly completes the search for the exact
Topics in Algebraic Graph Theory
"... The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmo ..."
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Cited by 17 (0 self)
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The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic
Combinatorial frameworks for cluster algebras
 Int. Math. Res. Not., published online May
, 2015
"... Abstract. We develop a general approach to finding combinatorial models for cluster algebras. The approach is to construct a labeled graph called a framework. When a framework is constructed with certain properties, the result is a model incorporating information about exchange matrices, principal c ..."
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Cited by 8 (3 self)
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Abstract. We develop a general approach to finding combinatorial models for cluster algebras. The approach is to construct a labeled graph called a framework. When a framework is constructed with certain properties, the result is a model incorporating information about exchange matrices, principal
Some applications of algebra to combinatorics
 DISCRETE APPLIED MATHEMATICS 34 (1991) 241277
, 1991
"... In extremal combinatorics, it is often convenient to work in the context of partially ordered sets. First let us establish some notation and definitions. As general references on the subject of partially ordered sets we recommend [I; 28, Chapter 3]. ..."
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Cited by 6 (0 self)
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In extremal combinatorics, it is often convenient to work in the context of partially ordered sets. First let us establish some notation and definitions. As general references on the subject of partially ordered sets we recommend [I; 28, Chapter 3].
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