Joint realizability of monotone Boolean functions

Crawford-Kahrl, Peter; Cummins, Bree; Gedeon, Tomáš

doi:10.1016/j.tcs.2022.04.045

Cited by 12 publications

(6 citation statements)

References 30 publications

(51 reference statements)

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“…Many problems with monotone Boolean functions (MBFs) appear in logical and physical level design of systems (Aslanyan et al, 2019), but also in artificial intelligence (Aslanyan and Sahakyan, 2009), data science and computational learning theory (Aslanyan et al, 2023a), hypergraph theory (Sahakyan, 2023;Sahakyan and Aslanyan, 2017) and other areas (e.g. Carlet et al, 2016;Kulhandjian et al, 2019;Crawford-Kahrl et al, 2022;Kabulov and Berdimurodov, 2021;Zhang et al, 2022). MBFs are used to encode extremely important constructions in various combinatorial optimizations providing a natural way of describing compatible subsets of sets of finite constraints (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Shadow Minimization Boolean Function Reconstruction

Aslanyan,

Katona,

Sahakyan

2024

Informatica

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A special class of monotone Boolean functions coming from shadow minimization theory of finite set-systems – KK-MBF functions – is considered. These functions are a descriptive model for systems of compatible groups of constraints, however, the class of all functions is unambiguously complex and it is sensible to study relatively simple subclasses of functions such as KK-MBF. Zeros of KK-MBF functions correspond to initial segments of lexicographic order on hypercube layers. This property is used to simplify the recognition. Lexicographic order applies priorities over constraints which is applicable property of practices. Query-based algorithms for KK-MBF functions are investigated in terms of their complexities.

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Section: Introductionmentioning

confidence: 99%

Shadow Minimization Boolean Function Reconstruction

Aslanyan,

Katona,

Sahakyan

2024

Informatica

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“…RACIPE 3 relies on random but judicious sampling of parameters and initial conditions with an ODE (Ordinary Differential Equation) based simulation that describes the interactions in the form of Hill functions, while DSGRN 4 – 7 uses combinatorial computations to analyze all multi-level Boolean models compatible with the network dynamics. DSGRN embeds 8 discrete Boolean models into a continuous framework of switching systems 9 – 16 , which then permits the use of ideas from bifurcation theory to understand changes in dynamics as a function of parameters. This close relationship between Boolean and ODE descriptions leads to rigorous mathematical results that link dynamics described by DSGRN and that of smooth ODE systems with sufficiently steep nonlinearities 17 , 18 .…”

Section: Introductionmentioning

confidence: 99%

Assessing biological network dynamics: comparing numerical simulations with analytical decomposition of parameter space

et al. 2023

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Mathematical modeling of the emergent dynamics of gene regulatory networks (GRN) faces a double challenge of (a) dependence of model dynamics on parameters, and (b) lack of reliable experimentally determined parameters. In this paper we compare two complementary approaches for describing GRN dynamics across unknown parameters: (1) parameter sampling and resulting ensemble statistics used by RACIPE (RAndom CIrcuit PErturbation), and (2) use of rigorous analysis of combinatorial approximation of the ODE models by DSGRN (Dynamic Signatures Generated by Regulatory Networks). We find a very good agreement between RACIPE simulation and DSGRN predictions for four different 2- and 3-node networks typically observed in cellular decision making. This observation is remarkable since the DSGRN approach assumes that the Hill coefficients of the models are very high while RACIPE assumes the values in the range 1-6. Thus DSGRN parameter domains, explicitly defined by inequalities between systems parameters, are highly predictive of ODE model dynamics within a biologically reasonable range of parameters.

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“…RACIPE [21] relies on random but judicious sampling of parameters and initial conditions with an ODE (Or-dinary Differential Equation) based simulation that describes the interactions in the form of Hill functions, while DSGRN [5,6,15,27] uses combinatorial computations to analyze all multi-level Boolean models compatible with the network dynamics. DSGRN embeds [4] discrete Boolean models into a continuous framework of switching systems [31,32,17,18,7,11,29,22], which then permits the use of ideas from bifurcation theory to understand changes in dynamics as a function of parameters. This close relationship between Boolean and ODE descriptions leads to rigorous mathematical results that link dynamics described by DSGRN and that of smooth ODE systems with sufficiently steep nonlinearities [14,10].…”

Section: Introductionmentioning

confidence: 99%

Assessing biological network dynamics: Comparing numerical simulations with analytical decomposition of parameter space

Hari

Duncan

Ibrahim

et al. 2022

Preprint

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Mathematical modeling of the emergent dynamics of gene regulatory networks (GRN) faces a double challenge of (a) dependence of model dynamics on parameters, and (b) lack of reliable experimentally determined parameters. In this paper we compare two complementary approaches for describing GRN dynamics across unknown parameters: (1) parameter sampling and resulting ensemble statistics used by RACIPE (RAndom CIrcuit PErturbation), and (2) use of rigorous analysis of combinatorial approximation of the ODE models by DSGRN (Dynamic Signatures Generated by Regulatory Networks). We find a very good agreement between RACIPE simulation and DSGRN predictions for four different 2- and 3-node networks typically observed in cellular decision making. This observation is remarkable since the DSGRN approach assumes that the Hill coefficients of the models are very high while RACIPE assumes the values in the range 1 to 6. Thus DSGRN parameter domains, explicitly defined by inequalities between systems parameters, are highly predictive of ODE model dynamics within a biologically reasonable range of parameters.

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Joint realizability of monotone Boolean functions

Cited by 12 publications

References 30 publications

Shadow Minimization Boolean Function Reconstruction

Shadow Minimization Boolean Function Reconstruction

Assessing biological network dynamics: comparing numerical simulations with analytical decomposition of parameter space

Assessing biological network dynamics: Comparing numerical simulations with analytical decomposition of parameter space

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