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Canalizing Boolean Functions Maximize the Mutual Information
[article]

2012
*
arXiv
*
pre-print

Using Fourier analysis we show that

arXiv:1207.7193v2
fatcat:oz2rsei22ncvnoyrajd6teef2u
*canalizing**functions**maximize*the*mutual**information*between an input variable and the outcome of the*function*. ... One measure to quantify this ability is the well known*mutual**information*. ... In this paper we combine two approaches to show that*canalizing**functions**maximize*the*mutual**information*for a given expectation value of the*functions*output. ...##
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CommentsComments on "Canalizing Boolean Functions Maximize Mutual Information"

2015
*
IEEE Transactions on Information Theory
*

In their recent paper "

doi:10.1109/tit.2014.2375183
fatcat:xielln3vlnelnhlknfmzmekqaq
*Canalizing**Boolean**Functions**Maximize**Mutual**Information*," Klotz et al. argued that*canalizing**Boolean**functions**maximize*certain*mutual**informations*by an argument involving Fourier ... Index Terms-*Boolean**functions*,*mutual**information*. ... showed that*canalizing**Boolean**functions**maximize*certain*mutual**informations*by way of an argument involving Fourier analysis on the hypercube [2] . ...##
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Maximizing local information transfer in Boolean networks

2018
*
New Journal of Physics
*

We study a

doi:10.1088/1367-2630/aadbc3
fatcat:6nkivdw7hncshngloe7rzrgff4
*Boolean*network model such that rules governing the time evolution of states are not given a priori but emerge from the*maximization*process of local*information*transfer and are stabilized ... We argue that the stabilized rules have generic properties of real-world gene regulatory networks, being both critical and highly*canalized*. ... Informax seeks the optimal*function*between its input and output by*maximizing*the average*mutual**information*subject to given external constraints. ...##
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The maximum mutual information between the output of a binary symmetric channel and a Boolean function of its input
[article]

2017
*
arXiv
*
pre-print

We prove the Courtade-Kumar conjecture, which states that the

arXiv:1604.05113v2
fatcat:lqvy2mwvv5e7zdkuatdvodqkee
*mutual**information*between any*Boolean**function*of an n-dimensional vector of independent and identically distributed inputs to a memoryless ... Let f:{0,1}^n →{0,1} be an n-dimensional*Boolean**function*. Then, MI(f(X),Y) ≤ 1-H(p). ... They show that this*mutual**information*between a*function*f that produces an output with fixed mean, µ = E [f (X)], and one input variable, X i , is*maximized*, if the*function*f is*canalizing*in the variable ...##
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Guiding the Self-organization of Random Boolean Networks
[article]

2010
*
arXiv
*
pre-print

Random

arXiv:1005.5733v2
fatcat:7l4fswkszfaclbjqxepisnxexu
*Boolean*networks (RBNs) are models of genetic regulatory networks. ... It has recently been found that RBNs near the critical regime*maximize**information*storage and coherent*information*transfer (Lizier et al, 2008) , as well as*maximize*Fisher*information*(Wang et al, ...*Boolean**functions*. n o p q r s ... ... ...##
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Logical Reduction of Biological Networks to Their Most Determinative Components

2016
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Bulletin of Mathematical Biology
*

The determinative power of a node is obtained by a summation of all

doi:10.1007/s11538-016-0193-x
pmid:27417985
pmcid:PMC4993808
fatcat:bqjjg5shlvclvjutqptngpihbu
*mutual**information*quantities over all nodes having the chosen node as a common input, thus representing a measure of*information*gain ... We consider a recently introduced method for reducing a*Boolean*network to its most determinative nodes that yield the highest*information*gain. ... In a subsequent paper by Klotz et al. (2014) , it is shown that*canalizing**Boolean**functions**maximize*the*mutual**information*under the same assumption as in Heckel et al. (2013) . ...##
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The maximum mutual information between the output of a discrete symmetric channel and several classes of Boolean functions of its input
[article]

2017
*
arXiv
*
pre-print

This conjecture states that the

arXiv:1701.05014v2
fatcat:jhplzh4f25br7ks6vexm7a6ieu
*mutual**information*between any*Boolean**function*of an n-dimensional vector of independent and identically distributed inputs to a memoryless binary symmetric channel and ... Let f:{0,1}^n →{0,1} be an n-dimensional*Boolean**function*. Then, MI(f(X),Y) ≤ 1-H(p). ... They show that this*mutual**information*between a*function*f that produces an output with fixed mean, µ = E [f (X)], and one input variable, X i , is*maximized*, if the*function*f is*canalizing*in the variable ...##
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Stratification and enumeration of Boolean functions by canalizing depth

2016
*
Physica D : Non-linear phenomena
*

Many of these networks use

doi:10.1016/j.physd.2015.09.016
fatcat:j7iy667s5ndsvlwex5e6cywwfu
*canalizing**Boolean**functions*, which has led to increased interest in the study of these*functions*. ... This generalizes recent work on the algebraic structure of nested*canalizing**functions*, and it yields a stratification of all*Boolean**functions*by their*canalizing*depth. ... Fourier analysis has shown that*canalizing**Boolean*networks*maximize**mutual**information*[KKBS14] , implying that*canalizing**Boolean*networks contain more*information*than general*Boolean*networks. ...##
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Guiding the self-organization of random Boolean networks

2011
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Theory in biosciences
*

Random

doi:10.1007/s12064-011-0144-x
pmid:22127955
pmcid:PMC3414703
fatcat:h3tp6gjvhzgkdjevgeubslzoye
*Boolean*networks (RBNs) are models of genetic regulatory networks. ... It has recently been found that RBNs near the critical regime*maximize**information*storage and coherent*information*transfer (Lizier et al. 2008) , as well as*maximize*Fisher*information*(Wang et al. ... -Increase the number of*canalizing**functions*. ...##
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Dynamical Instability in Boolean Networks as a Percolation Problem

2012
*
Physical Review Letters
*

*Boolean*networks, widely used to model gene regulation, exhibit a phase transition between regimes in which small perturbations either die out or grow exponentially. ... We now introduce a third case, in which we consider

*Boolean*networks with

*canalizing*

*functions*. ... The method used for our previous results can be extended to

*canalizing*

*functions*, but because the truth table elements in a

*canalizing*

*function*are not generated independently, we need to consider a new ...

##
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Stratification and enumeration of Boolean functions by canalizing depth
[article]

2015
*
arXiv
*
pre-print

Many of these networks use

arXiv:1504.07591v1
fatcat:ktit5t73angy7cydgjmk72minm
*canalizing**Boolean**functions*, which has led to increased interest in the study of these*functions*. ... This generalizes recent work on the algebraic structure of nested*canalizing**functions*, and it yields a stratification of all*Boolean**functions*by their*canalizing*depth. ... The evolution of*canalizing**Boolean*networks was studied in [SD07] . Fourier analysis has shown that*canalizing**Boolean*networks*maximize**mutual**information*[KKBS14] . ...##
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Identification of Boolean Network Models From Time Series Data Incorporating Prior Knowledge

2018
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Frontiers in Physiology
*

Using vector form of

doi:10.3389/fphys.2018.00695
pmid:29937735
pmcid:PMC6002699
fatcat:ngj7sxalarf5zmaztqwqnqtexu
*Boolean*variables and applying a generalized matrix multiplication called the semi-tensor product (STP), each*Boolean**function*can be equivalently converted into a matrix expression ... Results: We propose a new approach to identify*Boolean*networks from time series data incorporating prior knowledge, such as partial network structure,*canalizing*property, positive and negative unateness ... (B) Identified*Boolean*network without*canalizing**information*. (C) Identified*Boolean*network with prior knowlege. ...##
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Harmonic analysis of Boolean networks: determinative power and perturbations

2013
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EURASIP Journal on Bioinformatics and Systems Biology
*

We argue that the

doi:10.1186/1687-4153-2013-6
pmid:23642003
pmcid:PMC3748841
fatcat:p6emh3r4l5e4hbqf6lm2q26h7i
*mutual**information*(MI) between a given subset of the inputs X = X_1, ..., X_n of some node i and its associated*function*f_i(X) quantifies the determinative power of this set of inputs ... Consider a large*Boolean*network with a feed forward structure. ... We used Fourier analysis of*Boolean**functions*to study the*mutual**information*between a*function*f (X) and a set of its inputs X A , as a measure of determinative power of X A over f (X). ...##
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Which Boolean Functions Maximize Mutual Information on Noisy Inputs?

2014
*
IEEE Transactions on Information Theory
*

Index Terms-

doi:10.1109/tit.2014.2326877
fatcat:ckxbprw4abgvtpt4gs62rdbpxi
*Boolean**functions*,*mutual**information*, extremal inequality, isoperimetric inequality. ... We pose a simply stated conjecture regarding the maximum*mutual**information*a*Boolean**function*can reveal about noisy inputs. ... Intuitively, Conjecture 2 concerns the structure of*maximally*-*informative**Boolean**functions*, while Conjecture 3 handles the inequality component of Conjecture 1. ...##
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Which Boolean Functions are Most Informative?
[article]

2013
*
arXiv
*
pre-print

We introduce a simply stated conjecture regarding the maximum

arXiv:1302.2512v2
fatcat:o77abau4ovg7vimlxvhwjxydx4
*mutual**information*a*Boolean**function*can reveal about noisy inputs. Specifically, let X^n be i.i.d. ... For any*Boolean**function*b:{0,1}^n→{0,1}, we conjecture that I(b(X^n);Y^n)≤ 1-H(α). While the conjecture remains open, we provide substantial evidence supporting its validity. ... This work is supported in part by the Air Force grant FA9550-10-1-0124 and by NSF Center for Science of*Information*under grant agreement CCF-0939370. ...
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