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Representation Theorems and the Foundations of Decision Theory∗†
"... Abstract Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that ..."
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Abstract Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief
A general Stone representation theorem
, 2008
"... This note contains a Stonestyle representation theorem for compact Hausdorff spaces. The note is very much inspired by some existing representation theorems and is expository in nature. The first representation theorem is by Jung and Sünderhauf in [JS] and there is also a version of it for compact ..."
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This note contains a Stonestyle representation theorem for compact Hausdorff spaces. The note is very much inspired by some existing representation theorems and is expository in nature. The first representation theorem is by Jung and Sünderhauf in [JS] and there is also a version of it for compact
A Unifying View of Representer Theorems
"... It is known that the solution of regularization and interpolation problems with Hilbertian penalties can be expressed as a linear combination of the data. This very useful property, called the representer theorem, has been widely studied and applied to machine learning problems. Analogous optimality ..."
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It is known that the solution of regularization and interpolation problems with Hilbertian penalties can be expressed as a linear combination of the data. This very useful property, called the representer theorem, has been widely studied and applied to machine learning problems. Analogous
A REFORMULATION OF BROWN REPRESENTABILITY THEOREM
, 2008
"... Abstract. A wellknown result says: If a triangulated category with small coproducts satisfies Brown Representability Theorem, then every triangulated coproduct preserving functor having as domain the respective category has a right adjoint. We wonder about the converse. In this paper we provide a ..."
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Abstract. A wellknown result says: If a triangulated category with small coproducts satisfies Brown Representability Theorem, then every triangulated coproduct preserving functor having as domain the respective category has a right adjoint. We wonder about the converse. In this paper we provide
Representation Theorems for Petri Nets
 Foundations of Computer Science: Potential  Theory  Cognition, to Wilfried Brauer on the occasion of his sixtieth birthday, volume 1337 of Lect. Notes in Comp. Science
"... . This paper retraces, collects, summarises, and mildly extends the contributions of the authors  both together and individually  on the theme of representing the space of computations of Petri nets in its mathematical essence. Introduction Among the semantics proposed for Petri nets [10] (se ..."
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Cited by 11 (10 self)
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. This paper retraces, collects, summarises, and mildly extends the contributions of the authors  both together and individually  on the theme of representing the space of computations of Petri nets in its mathematical essence. Introduction Among the semantics proposed for Petri nets [10] (see also [11, 13]), a relevant role is played by the various notions of process, e.g. [12, 5, 1], whose merit is to provide a faithful account of computations involving many different transitions and of the causal connections between the events occurring in computations. Bare process models, however, fail to bring to the foreground the algebraic structure of the space of computations of a net. Our interest, instead, resides on abstract models that capture the mathematical essence of such spaces, possibly axiomatically, roughly in the same way as a prime algebraic domain (or, equivalently, a prime event structure) models the computations of a safe net [9]. The research detailed in [6, 3, 4, 14,...
Representation Theorem for Stacks
"... Summary. In the paper the concept of stacks is formalized. As the main result the Theorem of Representation for Stacks is given. Formalization is done according to [13]. ..."
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Summary. In the paper the concept of stacks is formalized. As the main result the Theorem of Representation for Stacks is given. Formalization is done according to [13].
REPRESENTATION THEOREMS FOR QUANTALES
"... Abstract. In this paper we prove that any quantale Q is (isomorphic to) a quantale of suitable relations on Q. As a consequence two isomorphism theorems are also shown with suitable sets of functions of Q into Q. These theorems are the mathematical background one needs in order to give natural and c ..."
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Abstract. In this paper we prove that any quantale Q is (isomorphic to) a quantale of suitable relations on Q. As a consequence two isomorphism theorems are also shown with suitable sets of functions of Q into Q. These theorems are the mathematical background one needs in order to give natural
Representation Theorem for Heyting Lattices
"... this paper. Let us observe that every lower bound lattice which is Heyting is also implicative and every lattice which is implicative is also upperbounded. In the sequel T denotes a topological space and A, B denote subsets of the carrier of T . We now state two propositions: (1) A " Int(A ..."
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this paper. Let us observe that every lower bound lattice which is Heyting is also implicative and every lattice which is implicative is also upperbounded. In the sequel T denotes a topological space and A, B denote subsets of the carrier of T . We now state two propositions: (1) A " Int(A
Representation theorem for SPDEs
 ELECTRONIC COMMUNICATIONS IN PROBABILITY
, 2013
"... In this paper we establish a probabilistic representation for the spatial gradient of the viscosity solution to a quasilinear parabolic stochastic partial differential equations (SPDE, for short) in the spirit of the FeynmanKac formula, without using the derivatives of the coefficients of the corre ..."
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In this paper we establish a probabilistic representation for the spatial gradient of the viscosity solution to a quasilinear parabolic stochastic partial differential equations (SPDE, for short) in the spirit of the FeynmanKac formula, without using the derivatives of the coefficients
SKOROHOD REPRESENTATION THEOREM
"... Abstract. Let (µn: n ≥ 0) be Borel probabilities on a metric space S such that µn → µ0 weakly. Say that Skorohod representation holds if, on some probability space, there are Svalued random variables Xn satisfying Xn ∼ µn for all n and Xn → X0 in probability. By Skorohod’s theorem, Skorohod represe ..."
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Abstract. Let (µn: n ≥ 0) be Borel probabilities on a metric space S such that µn → µ0 weakly. Say that Skorohod representation holds if, on some probability space, there are Svalued random variables Xn satisfying Xn ∼ µn for all n and Xn → X0 in probability. By Skorohod’s theorem, Skorohod
Results 11  20
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