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##
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On the Noise Sensitivity of Monotone Functions
[chapter]

2002
*
Mathematics and Computer Science II
*

It is natural to ask if

doi:10.1007/978-3-0348-8211-8_30
fatcat:6z3hiokzufaytjl3nz7t2klefq
*monotone**functions*can be as*sensitive*to*noise*as non-*monotone**functions*. ... By Parseval's identity,*Sensitivity**of**monotone**functions**The*parity*function*, f = u [n] = ⊕, is*the*boolean*function*most*sensitive*to*noise*: Z(f, η) = η n is minimal, and I(f ) = n is maximal. ... Since (14) happen with probability at least .85, it suffices to prove E x,x [(13)] ≥ Ω(1) conditioned*on*these three events holding. But in this case, ...##
###
On the noise sensitivity of monotone functions

2003
*
Random structures & algorithms (Print)
*

It is natural to ask if

doi:10.1002/rsa.10097
fatcat:x6cuxr4dsvbwbdwvqgszrf5any
*monotone**functions*can be as*sensitive*to*noise*as non-*monotone**functions*. ... By Parseval's identity,*Sensitivity**of**monotone**functions**The*parity*function*, f = u [n] = ⊕, is*the*boolean*function*most*sensitive*to*noise*: Z(f, η) = η n is minimal, and I(f ) = n is maximal. ... Since (14) happen with probability at least .85, it suffices to prove E x,x [(13)] ≥ Ω(1) conditioned*on*these three events holding. But in this case, ...##
###
Approximating the Noise Sensitivity of a Monotone Boolean Function

2019
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

*The*

*noise*

*sensitivity*

*of*a Boolean

*function*f : {0, 1} n → {0, 1} is

*one*

*of*its fundamental properties. For

*noise*parameter δ,

*the*

*noise*

*sensitivity*is denoted as N S δ [f ]. ... Therefore, we focus

*on*estimating

*the*

*noise*

*sensitivity*

*of*

*monotone*

*functions*, which form an important subclass

*of*Boolean

*functions*, since many

*functions*

*of*interest are either

*monotone*or can be simply ... For

*monotone*

*functions*, we are not aware

*of*previous lower bounds

*on*approximating

*the*bias or

*noise*

*sensitivity*. ...

##
###
On the noise sensitivity of monotone functions

2018

We also study

doi:10.1184/r1/6607997
fatcat:stwnb6w7ejdm3nshhpydjn4hce
*the*problem*of*achieving*the*best dependence*on*δ in*the*case that*the**noise*rate ϵ is at least a small constant;*the*results we obtain are tight to within logarithmic factors. ... It is known that for all*monotone**functions*f : {0, 1}n → {0, 1}, if x ∈ {0, 1}n is chosen uniformly at random and y is obtained from x by flipping each*of**the*bits*of*x independently with probability ... Acknowledgments: We would like to thank Gil Kalai for providing encouragement to write this paper and for Remark 2, Yuval Peres for interesting discussions, and*the*anonymous referees for helpful comments ...##
###
Effect of background noise on neuronal coding of interaural level difference cues in rat inferior colliculus

2015
*
European Journal of Neuroscience
*

To investigate

doi:10.1111/ejn.12914
pmid:25865218
pmcid:PMC4676293
fatcat:jleyelgq4rf3pett5fw6dxjn4y
*the*neural mechanisms underlying this, we studied*the*effect*of*background wide-band*noise**on*neural*sensitivity*to variations in interaural level difference (ILD),*the*predominant cue for ... At high signal-to-*noise*ratios (SNR), in most ILD*functions*(41%),*the*effect*of*background*noise*appeared to be due to effects*on*inputs from both ears, while for a large percentage (35.8%) appeared to ... change in*the*shape, namely category,*of**the*ILD*function*. ...##
###
Dynamical systems analysis of stack filters
[article]

2009
*
arXiv
*
pre-print

*of*Boolean networks constructed from

*the*corresponding

*monotone*

*functions*. ... We also examine

*the*dynamical behavior

*of*

*monotone*

*functions*corresponding to filters that are optimal in terms

*of*their

*noise*suppression capability, and find that

*the*optimal filters are dynamically ...

*The*class

*of*

*monotone*Boolean

*functions*is

*one*

*of*

*the*most widely used and studied classes

*of*Boolean

*functions*. ...

##
###
Pivotality versus noise stability for monotone transitive functions
[article]

2019
*
arXiv
*
pre-print

We show that such a sequence is volatile as well, and thus it is also an example

arXiv:1909.05375v1
fatcat:d4btxwoam5gbzadocqq7sboedy
*of*a volatile and*noise*stable sequence*of*transitive,*monotone**functions*. ... We construct a*noise*stable sequence*of*transitive,*monotone*increasing Boolean*functions*f_n: {-1,1}^k_n⟶{-1,1} which admit many pivotals with high probability. ... Research supported by ERC Consolidator Grant 772466*NOISE*. ...##
###
About the sensitivity of ordinal classifiers to non-monotone noise

2015
*
Artificial intelligence research
*

This research investigates for

doi:10.5430/air.v4n2p83
fatcat:wf57nsn2i5gofh5w3c7gr2jaga
*the*first time*the*effect*of*non-*monotone**noise**on**the*accuracy related rankings*of*ten classifiers in a controlled manner. ...*The*findings*of*this experiment are reported here. They clearly show that some models are more*sensitive*than others to non-*monotone**noise*. ...*The*experiment*The*purpose*of**the*experiment was to check*the**sensitivity**of*various classifiers to non-*monotone**noise*. ...##
###
Measuring Environmental Quantum Noise Exhibiting a Nonmonotonic Spectral Shape

2019
*
Physical Review Applied
*

*noise*spectroscopy: spectral decomposition based

*on*

*the*CPMG sequence,

*the*recently presented DYSCO sequence and a modified DYSCO sequence with a Gaussian envelope (gDYSCO).

*The*performance

*of*

*the*sequences ... is quantified by analytic and numeric determination

*of*

*the*frequency resolution, bandwidth and

*sensitivity*, revealing a supremacy

*of*gDYSCO to reconstruct non-trivial features.Utilizing an ensemble

*of*... When statistical

*noise*is added,

*the*limited

*sensitivity*

*of*gDYSCO alters

*the*results, but

*the*peak is still clearly visible as most

*of*

*the*

*noise*affects

*the*

*monotonous*"background". ...

##
###
Noise Sensitivity of Boolean Functions and Applications to Percolation
[article]

2000
*
arXiv
*
pre-print

*On*

*the*other hand, weighted majority

*functions*are shown to be

*noise*-stable. Several necessary and sufficient conditions for

*noise*

*sensitivity*and stability are given. ... It is shown that a large class

*of*events in a product probability space are highly

*sensitive*to

*noise*, in

*the*sense that with high probability,

*the*configuration with an arbitrary small percent

*of*random ... Many

*of*

*the*results

*on*influence and

*on*

*noise*

*sensitivity*should be extendible to measures

*on*Ω n for which

*the*coordinate variables are positively associated, namely, measures for which every two

*monotone*...

##
###
Book Review: Noise sensitivity of Boolean functions and percolation

2017
*
Bulletin of the American Mathematical Society
*

*The*catch phrase

*one*can learn from Benjamini, Kalai, and Schramm [3] is that

*functions*

*of*high frequency are

*noise*

*sensitive*and

*functions*

*of*low frequencies are

*noise*stable. ... We are now in a position to state

*one*

*of*

*the*main theorems in

*the*theory

*of*

*noise*

*sensitivity*: Theorem 7 ([3, Theorem 1.3]). Let {f n } be a sequence

*of*Boolean

*functions*. ...

##
###
Optimal Noise-Adding Mechanism in Additive Differential Privacy
[article]

2019
*
arXiv
*
pre-print

*on*

*the*origin occurs when δ > p/p+1. ... We explicitly derive

*the*optimal

*noise*distribution for general ℓ^p cost

*functions*, including ℓ^1 (for

*noise*magnitude) and ℓ^2 (for

*noise*power) cost

*functions*, and show that

*the*probability concentration ... Acknowledgment We would like to thank

*the*anonymous reviewers for their insightful comments and suggestions, which help us improve

*the*presentation

*of*this work. ...

##
###
The Optimal Noise-Adding Mechanism in Differential Privacy

2016
*
IEEE Transactions on Information Theory
*

We explicitly derive

doi:10.1109/tit.2015.2504967
fatcat:r6rbvv472jg27bmzsftjwu6wsm
*the*optimal*noise*distribution for general p cost*functions*, including 1 (for*noise*magnitude) and 2 (for*noise*power) cost*functions*, and show that*the*probability concentration*on*... Our result demonstrates an improvement over*the*existing Gaussian mechanisms by a factor*of*two and three for (0, δ)differential privacy in*the*high privacy regime in*the*context*of*minimizing*the**noise*... Acknowledgment We would like to thank*the*anonymous reviewers for their insightful comments and suggestions, which help us improve*the*presentation*of*this work. ...##
###
Noise Sensitivity and Chaos in Social Choice Theory
[chapter]

2010
*
Fete of Combinatorics and Computer Science
*

In this paper we study

doi:10.1007/978-3-642-13580-4_8
fatcat:2ozvqsym5jdmhd53ozwzlfz4ra
*the*social preferences obtained from*monotone*neutral social welfare*functions*for random individual preferences. ... > 0, if a small fraction*of*individuals change their preferences (randomly)*the*correlation between*the*resulting social preferences and*the*original*ones*tends to zero as*the*number*of*individuals in ... [Mossel, O'Donnell and Oleszkiewicz] A sequence*of*strong*monotone*simple games (G n ) with diminishing individual Banzhaf power has property [IAOUIO]. ...##
###
Noise Sensitivity of Boolean Functions and Applications to Percolation
[chapter]

2011
*
Selected Works of Oded Schramm
*

Many

doi:10.1007/978-1-4419-9675-6_12
fatcat:6gdfk7sjpvbczp7jj25g37xy6u
*of**the*results*on*influence and*on**noise**sensitivity*should be extendible to measures*on*.*on*for which th e coordinate variables are positively associated, namely, measures for which every two*monotone*... TeO and*noise*sensitiviry*Noise**sensitivity*seems related to another class*of*boolean*functions*-threshold circuits*of*bounded depths see [36, 22) . ...
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