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Obfuscation via pitch-shifting for balancing privacy and diagnostic utility in voice-based cognitive assessment. [PDF]
Ahangaran M +5 more
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Preparing for the European Health Data Space: an open-source compiler for fast, transparent, and portable health data transformations. [PDF]
Beyer S +6 more
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Context-dependent structurally informed effective connectivity under psilocybin
Greaves MD +4 more
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Commuting measure-preserving transformations
Israel Journal of Mathematics, 1972Let φ1, ... ,φd be commuting measure-preserving transformations, \( \phi ^l \equiv \phi _1^{l_1 } \phi _2^{l_2 } \cdot \cdot \cdot \phi _d^{l_d } ,\Phi = \left\{ {\phi ^l } \right\} \). The Kakutani-Rokhlin tower theorem is proved in a refined form for non-periodic groups Φ, and the Shannon-McMillan theorem is extended to ergodic groups.
Katznelson, Yitzhak, Weiss, Benjamin
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Jointly ergodic measure-preserving transformations
Israel Journal of Mathematics, 1984The notion of ergodicity of a measure preserving transformation is generalized to finite sets of transformations. The main result is that, if \(T_ 1,T_ 2,...,T_ s\) are invertible commuting measure preserving transformations, of a probability space (X,\({\mathcal B},\mu)\), then \[ \frac{1}{N-M}\sum^{N-1}_{n=M}T^ n_ 1f_ 1\cdot T^ n_ 2f_ 2\cdot...\cdot ...
Berend, Daniel, Bergelson, Vitaly
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Measurability – Preserving Weakly Mixing Transformations
Sarajevo Journal of MathematicsIn this paper we investigate measure-theoretic properties of the class of all weakly mixing transformations on a finite measure space which preserve measurability. The main result in this paper is the following theorem: If $\phi $ is a weakly mixing transformation on a finite measure space $( S, \mathcal A , \mu )$ with the property that $\phi ...
Huse Fatkić
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Measure-preserving transformations, copulae and compatibility
2008We study the relationship between copulas and measure-preserving transformations on the Borel sets of the u it interval. This also allows to investigate the connection with a restricted compatibility problem for copulas. To this end, in order to construct a 3-copula from two given 2-copulas A and B, we modify the *-operation introduced by Darsow et al.,
KOLESAROVA, A +3 more
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Generic measure preserving transformations and the closed groups they generate
Inventiones Mathematicae, 2021We show that, for a generic measure preserving transformation T , the closed group generated by T is not isomorphic to the topological group $$L^0(\lambda , {{\mathbb {T}}})$$ L 0 ( λ , T ) of all Lebesgue measurable functions from [0, 1] to $${\mathbb ...
Slawomir Solecki
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On Groups of Measure Preserving Transformations. II
American Journal of Mathematics, 1959H. Dye
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