Index boundedness condition for mappings with bounded distortion

1968 ◽  
Vol 9 (2) ◽  
pp. 281-285 ◽  
Author(s):  
Yu. G. Reshetnyak
Keyword(s):  
Boundedness Condition ◽  
Bounded Distortion

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

Darboux chart on projective limit of weak symplectic Banach manifold

2015 ◽  
Vol 12 (07) ◽  
pp. 1550072 ◽  
Author(s):  
Pradip Mishra
Keyword(s):  
Banach Space ◽  
Symplectic Structure ◽  
Reflexive Banach Space ◽  
Projective Limit ◽  
Fréchet Space ◽  
Frechet Space ◽  
Banach Manifold ◽  
Boundedness Condition ◽  
Projective System ◽  
Banach Manifolds

Suppose M be the projective limit of weak symplectic Banach manifolds {(Mi, ϕij)}i, j∈ℕ, where Mi are modeled over reflexive Banach space and σ is compatible with the projective system (defined in the article). We associate to each point x ∈ M, a Fréchet space Hx. We prove that if Hx are locally identical, then with certain smoothness and boundedness condition, there exists a Darboux chart for the weak symplectic structure.

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.

A martingale approach to the PASTA property

1993 ◽  
Vol 30 (01) ◽  
pp. 252-257
Author(s):  
Michael Scheutzow
Keyword(s):  
Poisson Process ◽  
Queueing Theory ◽  
Point Processes ◽  
Law Of Large Numbers ◽  
Boundedness Condition ◽  
Martingale Approach ◽  
Large Numbers ◽  
Poisson Arrivals ◽  
Time Averages ◽  
Image Position

It is known (Weizsäcker and Winkler (1990)) that for bounded predictable functions H and a Poisson process with jump times exists almost surely, and that in this case both limits are equal. Here we relax the boundedness condition on H. Our tool is a law of large numbers for local L 2-martingales. We show by examples that our condition is close to optimal. Furthermore we indicate a generalization to point processes on more general spaces. The above property is called PASTA (‘Poisson arrivals see time averages') and is heavily used in queueing theory.

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