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Differentiable Stacks and Gerbes
, 2008
"... We introduce differentiable stacks and explain the relationship with Lie groupoids. Then we study S¹bundles and S¹gerbes over differentiable stacks. In particular, we establish the relationship between S¹gerbes and groupoid S¹central extensions. We define connections and curvings for groupoid S¹ ..."
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Cited by 44 (4 self)
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We introduce differentiable stacks and explain the relationship with Lie groupoids. Then we study S¹bundles and S¹gerbes over differentiable stacks. In particular, we establish the relationship between S¹gerbes and groupoid S¹central extensions. We define connections and curvings for groupoid S
The volume of a differentiable stack
, 2009
"... We extend the notion of the cardinality of a discrete groupoid (equal to the Euler characteristic of the corresponding discrete orbifold) to the setting of Lie groupoids. Since this quantity is an invariant under equivalence of groupoids, we call it the volume of the associated stack rather than of ..."
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Cited by 3 (0 self)
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We extend the notion of the cardinality of a discrete groupoid (equal to the Euler characteristic of the corresponding discrete orbifold) to the setting of Lie groupoids. Since this quantity is an invariant under equivalence of groupoids, we call it the volume of the associated stack rather than
VECTOR FIELDS AND FLOWS ON DIFFERENTIABLE STACKS
"... Abstract. This paper introduces the notions of vector field and flow on a general differentiable stack. Our main theorem states that the flow of a vector field on a compact proper differentiable stack exists and is unique up to a uniquely determined 2cell. This extends the usual result on the exist ..."
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Cited by 8 (0 self)
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Abstract. This paper introduces the notions of vector field and flow on a general differentiable stack. Our main theorem states that the flow of a vector field on a compact proper differentiable stack exists and is unique up to a uniquely determined 2cell. This extends the usual result
Twisted Ktheory of differentiable stacks
 ANN. SCI. ÉCOLE NORM. SUP
, 2004
"... In this paper, we develop twisted Ktheory for stacks, where the twisted class is given by an S 1gerbe over the stack. General properties, including the Mayer–Vietoris property, Bott periodicity, and the product structure K i α ⊗K j β → Ki+j α+β are derived. Our approach provides a uniform framew ..."
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Cited by 75 (13 self)
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In this paper, we develop twisted Ktheory for stacks, where the twisted class is given by an S 1gerbe over the stack. General properties, including the Mayer–Vietoris property, Bott periodicity, and the product structure K i α ⊗K j β → Ki+j α+β are derived. Our approach provides a uniform
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ (1, and then the result is classical. A simple proof appears in EnriquesChisini [E, vol. 3, chap. 3], based on analyzing the totality of coverings of p1 of degree n, with a fixed number d of ordinary branch points. This method has been extended to char. p by William Fulton [F], using specializations from char. o to char. p provided that p> 2g qi. Unfortunately, attempts to extend this method to all p seem to get stuck on difficult questions of wild ramification. Nowadays, the Teichmtiller theory gives a thoroughly analytic but very profound insight into this irreducibility when kC. Our approach however is closest to Severi's incomplete proof ([Se], Anhang F; the error is on pp. 344345 and seems to be quite basic) and follows a suggestion of Grothendieck for using the result in char. o to deduce the result in char. p. The basis of both Severi's and Grothendieck's ideas is to construct families of curves X, some singular, with pa(X)=g, over nonsingular parameter spaces, which in some sense contain enough singular curves to link together any two components that Mg might have. The essential thing that makes this method work now is a recent " stable reduction theorem " for abelian varieties. This result was first proved independently in char. o by Grothendieck, using methods of etale cohomology (private correspondence with J. Tate), and by Mumford, applying the easy half of Theorem (2.5), to go from curves to abelian varieties (cf. [M2]). Grothendieck has recently strengthened his method so that it applies in all characteristics (SGA 7, ~968) 9 Mumford has also given a proof using theta functions in char. ~2. The result is this: Stable Reduction Theorem. Let R be a discrete valuation ring with quotient field K. Let A be an abelian variety over K. Then there exists a finite algebraic extension L of K such
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual CalabiYau manifolds V, W of dimension n (not necessarily equal to 3) one has dim H p (V, Ω q) = dim H n−p (W, Ω q). Physicists conjectured that conformal field theories associated with mirror varieties are equivalent. Mathematically, MS is considered now as a relation between numbers of rational curves on such a manifold and Taylor coefficients of periods of Hodge structures considered as functions on the moduli space of complex structures on a mirror manifold. Recently it has been realized that one can make predictions for numbers of curves of positive genera and also on CalabiYau manifolds of arbitrary dimensions. We will not describe here the complicated history of the subject and will not mention many beautiful contsructions, examples and conjectures motivated
Dynamic taint analysis for automatic detection, analysis, and signature generation of exploits on commodity software
 In Network and Distributed Systems Security Symposium
, 2005
"... Software vulnerabilities have had a devastating effect on the Internet. Worms such as CodeRed and Slammer can compromise hundreds of thousands of hosts within hours or even minutes, and cause millions of dollars of damage [32, 51]. To successfully combat these fast automatic Internet attacks, we nee ..."
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Cited by 634 (30 self)
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Software vulnerabilities have had a devastating effect on the Internet. Worms such as CodeRed and Slammer can compromise hundreds of thousands of hosts within hours or even minutes, and cause millions of dollars of damage [32, 51]. To successfully combat these fast automatic Internet attacks, we need fast automatic attack detection and filtering mechanisms. In this paper we propose dynamic taint analysis for automatic detection and analysis of overwrite attacks, which include most types of exploits. This approach does not need source code or special compilation for the monitored program, and hence works on commodity software. To demonstrate this idea, we have implemented TaintCheck, a mechanism that can perform dynamic taint analysis by performing binary rewriting at run time. We show that TaintCheck reliably detects most types of exploits. We found that TaintCheck produced no false positives for any of the many different programs that we tested. Further, we show how we can use a twotiered approach to build a hybrid exploit detector that enjoys the same accuracy as TaintCheck but have extremely low performance overhead. Finally, we propose a new type of automatic signature generation—semanticanalysis based signature generation. We show that by backtracing the chain of tainted data structure rooted at the detection point, TaintCheck can automatically identify which original flow and which part of the original flow have caused the attack and identify important invariants of the payload that can be used as signatures. Semanticanalysis based signature generation can be more accurate, resilient against polymorphic worms, and robust to attacks exploiting polymorphism than the patternextraction based signature generation methods.
Exokernel: An Operating System Architecture for ApplicationLevel Resource Management
, 1995
"... We describe an operating system architecture that securely multiplexes machine resources while permitting an unprecedented degree of applicationspecific customization of traditional operating system abstractions. By abstracting physical hardware resources, traditional operating systems have signifi ..."
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Cited by 724 (24 self)
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We describe an operating system architecture that securely multiplexes machine resources while permitting an unprecedented degree of applicationspecific customization of traditional operating system abstractions. By abstracting physical hardware resources, traditional operating systems have significantly limited the performance, flexibility, and functionality of applications. The exokernel architecture removes these limitations by allowing untrusted software to implement traditional operating system abstractions entirely at applicationlevel. We have implemented a prototype exokernelbased system that includes Aegis, an exokernel, and ExOS, an untrusted applicationlevel operating system. Aegis defines the lowlevel interface to machine resources. Applications can allocate and use machine resources, efficiently handle events, and participate in resource revocation. Measurements show that most primitive Aegis operations are 10–100 times faster than Ultrix,a mature monolithic UNIX operating system. ExOS implements processes, virtual memory, and interprocess communication abstractions entirely within a library. Measurements show that ExOS’s applicationlevel virtual memory and IPC primitives are 5–50 times faster than Ultrix’s primitives. These results demonstrate that the exokernel operating system design is practical and offers an excellent combination of performance and flexibility. 1
BDI Agents: From Theory to Practice
 IN PROCEEDINGS OF THE FIRST INTERNATIONAL CONFERENCE ON MULTIAGENT SYSTEMS (ICMAS95
, 1995
"... The study of computational agents capable of rational behaviour has received a great deal of attention in recent years. Theoretical formalizations of such agents and their implementations have proceeded in parallel with little or no connection between them. This paper explores a particular typ ..."
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Cited by 880 (3 self)
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The study of computational agents capable of rational behaviour has received a great deal of attention in recent years. Theoretical formalizations of such agents and their implementations have proceeded in parallel with little or no connection between them. This paper explores a particular type of rational agent, a BeliefDesire Intention (BDI) agent. The primary aim of this paper is to integrate (a) the theoretical foundations of BDI agents from both a quantitative decisiontheoretic perspective and a symbolic reasoning perspective; (b) the implementations of BDI agents from an ideal theoretical perspective and a more practical perspective; and (c) the building of largescale applications based on BDI agents. In particular, an airtraffic management application will be described from both a theoretical and an implementation perspective.
A theory of communicating sequential processes
, 1984
"... A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account. ..."
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Cited by 4135 (17 self)
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A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account.
Results 1  10
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166,710