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Additivity and Chain Rules for Quantum Entropies via Multi-index Schatten Norms. [PDF]
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Australian & New Zealand Journal of Statistics, 2014
Summary A Bayes linear space is a linear space of equivalence classes of proportional σ‐finite measures, including probability measures. Measures are identified with their density functions. Addition is given by Bayes' rule and substraction by Radon–Nikodym derivatives.
Boogaart, K. Gerald van den +2 more
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Summary A Bayes linear space is a linear space of equivalence classes of proportional σ‐finite measures, including probability measures. Measures are identified with their density functions. Addition is given by Bayes' rule and substraction by Radon–Nikodym derivatives.
Boogaart, K. Gerald van den +2 more
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SIAM Review, 1973
Resolution space, recently introduced for the study of causality in an operator theoretic setting, is employed to formulate an abstract state concept which generalizes the state space theory commonly used in the study of finite-dimensional dynamical systems. After formulating the state concept as an operator factorization and verifying the existence of
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Resolution space, recently introduced for the study of causality in an operator theoretic setting, is employed to formulate an abstract state concept which generalizes the state space theory commonly used in the study of finite-dimensional dynamical systems. After formulating the state concept as an operator factorization and verifying the existence of
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On Symmetrizable Operators on Hilbert Spaces
Acta Applicandae Mathematicae, 2008Letting \(G\) be a bounded linear operator and \(S\) a bounded nonnegative selfadjoint operator on a complex Hilbert space such that \(SG\) is selfadjoint, spectral properties of \(G\) are derived, in particular lower bounds (and in some cases exact values) for its spectral radius, and the compactness of \(SG\) when \(G\) is power compact.
Mokhtar-Kharroubi, Mustapha +1 more
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SIAM Review, 1970
A new formalism, termed the resolution space, is presented within which the theory of causal systems may be unified and extended. The resulting formalism, which is defined as a Hilbert space together with a resolution of the identity, readily includes the commonly encountered function and sequence space causality concepts yet is sufficiently ...
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A new formalism, termed the resolution space, is presented within which the theory of causal systems may be unified and extended. The resulting formalism, which is defined as a Hilbert space together with a resolution of the identity, readily includes the commonly encountered function and sequence space causality concepts yet is sufficiently ...
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Behavioral and Brain Sciences, 2013
AbstractUse of quantum probability as a top-down model of cognition will be enhanced by consideration of the underlying complex-valued wave function, which allows a better account of interference effects and of the structure of learned and ad hoc question operators.
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AbstractUse of quantum probability as a top-down model of cognition will be enhanced by consideration of the underlying complex-valued wave function, which allows a better account of interference effects and of the structure of learned and ad hoc question operators.
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Proceedings of the London Mathematical Society, 1988
In a recent paper by \textit{V. D. Milman} and the author [Isr. J. Math. 54, 139-158 (1986; Zbl 0611.46022)] the notion of weak cotype 2 and weak type 2 Banach spaces were introduced. In the present paper the author considers the class of Banach spaces which are both of weak type 2 and weak cotype 2.
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In a recent paper by \textit{V. D. Milman} and the author [Isr. J. Math. 54, 139-158 (1986; Zbl 0611.46022)] the notion of weak cotype 2 and weak type 2 Banach spaces were introduced. In the present paper the author considers the class of Banach spaces which are both of weak type 2 and weak cotype 2.
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On the Performance of Clustering in Hilbert Spaces
IEEE Transactions on Information Theory, 2008Based on randomly drawn vectors in a separable Hilbert space, one may construct a k-means clustering scheme by minimizing an empirical squared error. We investigate the risk of such a clustering scheme, defined as the expected squared distance of a random vector X from the set of cluster centers.
Biau, Gérard, Devroye, L., Lugosi, G.
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Mathematika, 2010
A covering \((C_n)\) of a Banach space is said to be a \textit{tiling} if the interiors of \(C_n\) are pairwise disjoint. Answering a question originating from the work of \textit{V.\,Klee} [Math.\ Ann.\ 257, 251--260 (1981; Zbl 0453.41021)], the author proves that a separable Hilbert space has a tiling by closed convex sets whose outer radii are ...
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A covering \((C_n)\) of a Banach space is said to be a \textit{tiling} if the interiors of \(C_n\) are pairwise disjoint. Answering a question originating from the work of \textit{V.\,Klee} [Math.\ Ann.\ 257, 251--260 (1981; Zbl 0453.41021)], the author proves that a separable Hilbert space has a tiling by closed convex sets whose outer radii are ...
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