Local homeomorphy of some mappings with bounded distortion and quasiconformality coefficient less than two

1995 ◽  
Vol 36 (2) ◽  
pp. 354-358
Author(s):  
V. I. Semënov
Keyword(s):  
Bounded Distortion ◽  
Quasiconformality Coefficient

Large-scale bounded distortion mappings

2015 ◽  
Vol 34 (6) ◽  
pp. 1-10 ◽  
Author(s):  
Shahar Z. Kovalsky ◽  
Noam Aigerman ◽  
Ronen Basri ◽  
Yaron Lipman
Keyword(s):  
Large Scale ◽  
Bounded Distortion

scholarly journals Protecting Private Inputs: Bounded Distortion Guarantees With Randomised Approximations

2020 ◽  
Vol 2020 (3) ◽  
pp. 284-303
Author(s):  
Patrick Ah-Fat ◽  
Michael Huth
Keyword(s):  
Experimental Work ◽  
Differential Privacy ◽  
Use Cases ◽  
Distortion Bounds ◽  
Low Probability ◽  
Bounded Distortion ◽  
Class Of Functions

AbstractComputing a function of some private inputs while maintaining the confidentiality of those inputs is an important problem, to which Differential Privacy and Secure Multi-party Computation can offer solutions under specific assumptions. Research in randomised algorithms aims at improving the privacy of such inputs by randomising the output of a computation while ensuring that large distortions of outputs occur with low probability. But use cases such as e-voting or auctions will not tolerate large distortions at all. Thus, we develop a framework for randomising the output of a privacypreserving computation, while guaranteeing that output distortions stay within a specified bound. We analyse the privacy gains of our approach and characterise them more precisely for our notion of sparse functions. We build randomisation algorithms, running in linearithmic time in the number of possible input values, for this class of functions and we prove that the computed randomisations maximise the inputs’ privacy. Experimental work demonstrates significant privacy gains when compared with existing approaches that guarantee distortion bounds, also for non-sparse functions.

Remarks on Livšic' theory for nonabelian cocycles

1999 ◽  
Vol 19 (3) ◽  
pp. 703-721 ◽  
Author(s):  
KLAUS SCHMIDT
Keyword(s):  
Dynamical System ◽  
Homomorphic Image ◽  
Periodic Points ◽  
Skew Product ◽  
Topologically Transitive ◽  
Polish Group ◽  
Bounded Distortion

Let $(X,\phi)$ be a hyperbolic dynamical system and let $(G,\delta)$ be a Polish group. Motivated by Nicol and Pollicott, and then by Parry we study conditions under which two Hölder maps $f,g: X\longrightarrow G$ are Hölder cohomologous.In the context of Nicol and Pollicott we show that if $f$ and $g$ are measurably cohomologous and the distortion of the metric $\delta $ by the cocycles defined by $f$ and $g$ is bounded in an appropriate sense, then $f$ and $g$ are Hölder cohomologous.Two further results extend the main theorems recently presented by Parry. Under the hypothesis of bounded distortion we show that, if $f$ and $g$ give equal weight to all periodic points of $\phi $, then $f$ and $g$ are Hölder cohomologous. If the metric $\delta $ is bi-invariant, and if the skew-product $\phi _f$ defined by $f$ is topologically transitive, then conjugacy of weights implies that $g$ is Hölder conjugate to $\alpha \cdot f$ for some isometric automorphism $\alpha $ of $G$. The weaker condition that $g$-weights of periodic points are close to the identity whenever their $f$-weights are close to the identity implies that $g$ is continuously cohomologous to a homomorphic image of $f$.

On bounded distortion in conformal mapping

1986 ◽  
Vol 7 (1-3) ◽  
pp. 161-180
Author(s):  
CH. Pommerenke ◽  
S. E. Warschawski
Keyword(s):  
Conformal Mapping ◽  
Bounded Distortion
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