On Boolean Models for Quantified Boolean Horn Formulas

2004 ◽  
pp. 93-104 ◽  
Author(s):  
Hans Kleine Büning ◽  
K. Subramani ◽  
Xishun Zhao
Keyword(s):  
Boolean Models ◽  
Horn Formulas

scholarly journals Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 600 ◽  
Author(s):  
Marco Montalva-Medel ◽  
Thomas Ledger ◽  
Gonzalo A. Ruz ◽  
Eric Goles
Keyword(s):  
Escherichia Coli ◽  
Limit Cycles ◽  
The Other ◽  
Lac Operon ◽  
Boolean Models ◽  
Bistable Behavior

In Veliz-Cuba and Stigler 2011, Boolean models were proposed for the lac operon in Escherichia coli capable of reproducing the operon being OFF, ON and bistable for three (low, medium and high) and two (low and high) parameters, representing the concentration ranges of lactose and glucose, respectively. Of these 6 possible combinations of parameters, 5 produce results that match with the biological experiments of Ozbudak et al., 2004. In the remaining one, the models predict the operon being OFF while biological experiments show a bistable behavior. In this paper, we first explore the robustness of two such models in the sense of how much its attractors change against any deterministic update schedule. We prove mathematically that, in cases where there is no bistability, all the dynamics in both models lack limit cycles while, when bistability appears, one model presents 30% of its dynamics with limit cycles while the other only 23%. Secondly, we propose two alternative improvements consisting of biologically supported modifications; one in which both models match with Ozbudak et al., 2004 in all 6 combinations of parameters and, the other one, where we increase the number of parameters to 9, matching in all these cases with the biological experiments of Ozbudak et al., 2004.

scholarly journals Epidemics and Boolean Models

2001 ◽  
Vol 29 (4) ◽  
pp. 1515-1546 ◽  
Author(s):  
Mathew D. Penrose
Keyword(s):  
Boolean Models

On projected thick sections of stationary point processes and Boolean models

1996 ◽  
Vol 28 (2) ◽  
pp. 335-335
Author(s):  
Markus Kiderlen
Keyword(s):  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
Linear Subspace ◽  
Isotropic Case ◽  
Thick Section ◽  
Boolean Models ◽  
Dimensional Linear Subspace ◽  
Stationary Point Process ◽  
Stationary Point Processes

For a stationary point process X of convex particles in ℝd the projected thick section process X(L) on a q-dimensional linear subspace L is considered. Formulae connecting geometric functionals, e.g. the quermass densities of X and X(L), are presented. They generalize the classical results of Miles (1976) and Davy (1976) which hold only in the isotropic case.

scholarly journals The joy of implications, aka pure Horn formulas: Mainly a survey

2017 ◽  
Vol 658 ◽  
pp. 264-292 ◽  
Author(s):  
Marcel Wild
Keyword(s):  
Horn Formulas

Asymptotic properties of stereological estimators of volume fraction for stationary random sets

1982 ◽  
Vol 19 (1) ◽  
pp. 111-126 ◽  
Author(s):  
Shigeru Mase
Keyword(s):  
Volume Fraction ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Parametric Estimation ◽  
Random Sets ◽  
Stationary Time Series ◽  
Boolean Models ◽  
Window Functions ◽  
Spectral Density Functions ◽  
Point Estimators

We shall discuss asymptotic properties of stereological estimators of volume (area) fraction for stationary random sets (in the sense of Matheron) under natural and general assumptions. Results obtained are strong consistency, asymptotic normality, and asymptotic unbiasedness and consistency of asymptotic variance estimators. The method is analogous to the non-parametric estimation of spectral density functions of stationary time series using window functions. Proofs are given for areal estimators, but they are also valid for lineal and point estimators with slight modifications. Finally we show that stationary Boolean models satisfy the relevant assumptions reasonably well.

scholarly journals Minkowski tensor density formulas for Boolean models

2014 ◽  
Vol 55 ◽  
pp. 48-85 ◽  
Author(s):  
Julia Hörrmann ◽  
Daniel Hug ◽  
Michael Andreas Klatt ◽  
Klaus Mecke
Keyword(s):  
Boolean Models ◽  
Tensor Density ◽  
Minkowski Tensor

Variance reducing modifications for estimators of standardized moments of random sets

2000 ◽  
Vol 32 (03) ◽  
pp. 682-700
Author(s):  
Jeffrey D. Picka
Keyword(s):  
Statistical Analysis ◽  
Point Process ◽  
Random Sets ◽  
Boolean Models ◽  
Asymptotic Regime ◽  
Estimation Strategy ◽  
Moment Estimation ◽  
Second Moments ◽  
Simulation Results ◽  
Variance Result

In the statistical analysis of random sets, it is useful to have simple statistics that can be used to describe the realizations of these sets. The cumulants and several other standardized moments such as the correlation and second cumulant can be used for this purpose, but their estimators can be excessively variable if the most straightforward estimation strategy is used. Through exploitation of similarities between this estimation problem and a similar one for a point process statistic, two modifications are proposed. Analytical results concerning the effects of these modifications are found through use of a specialized asymptotic regime. Simulation results establish that the modifications are highly effective at reducing estimator standard deviations for Boolean models. The results suggest that the reductions in variance result from a balanced use of information in the estimation of the first and second moments, through eliminating the use of observations that are not used in second moment estimation.

Densities of mixed volumes for Boolean models

2001 ◽  
Vol 33 (1) ◽  
pp. 39-60 ◽  
Author(s):  
Wolfgang Weil
Keyword(s):  
Dimensional Space ◽  
Boolean Model ◽  
Boolean Models ◽  
Mixed Volumes ◽  
Explicit Formulae

In generalization of the well-known formulae for quermass densities of stationary and isotropic Boolean models, we prove corresponding results for densities of mixed volumes in the stationary situation and show how they can be used to determine the intensity of non-isotropic Boolean models Z in d-dimensional space for d = 2, 3, 4. We then consider non-stationary Boolean models and extend results of Fallert on quermass densities to densities of mixed volumes. In particular, we present explicit formulae for a planar inhomogeneous Boolean model with circular grains.

scholarly journals Second-order properties and central limit theorems for geometric functionals of Boolean models

2016 ◽  
Vol 26 (1) ◽  
pp. 73-135 ◽  
Author(s):  
Daniel Hug ◽  
Günter Last ◽  
Matthias Schulte
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Second Order ◽  
Central Limit Theorems ◽  
Boolean Models

Using Two-Point Set Statistics to Estimate the Diameter Distribution in Boolean Models with Circular Grains

2012 ◽  
Vol 44 (7) ◽  
pp. 805-822 ◽  
Author(s):  
Xavier Emery ◽  
Willy Kracht ◽  
Álvaro Egaña ◽  
Felipe Garrido
Keyword(s):  
Diameter Distribution ◽  
Boolean Models ◽  
Point Set
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