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Background: A novel data-driven Boolean model, namely, the fundamental Boolean model (FBM), has been proposed to draw genetic regulatory insights into gene activation, inhibition, and protein decay, published in 2018. This novel B...
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Background: A novel data-driven Boolean model, namely, the fundamental Boolean model (FBM), has been proposed to draw genetic regulatory insights into gene activation, inhibition, and protein decay, published in 2018. This novel Boolean model facilitates the analysis of the activation and inhibition pathways. However, the novel model does not handle the situation well, where genetic regulation might require more time steps to complete.Methods: Here, we propose extending the fundamental Boolean modelling to address the issue that some gene regulations might require more time steps to complete than others. We denoted this extension model as the temporal fundamental Boolean model (TFBM) and related networks as the temporal fundamental Boolean networks (TFBNs). The leukaemia microarray datasets downloaded from the National Centre for Biotechnology Information have been adopted to demonstrate the utility of the proposed TFBM and TFBNs.Results: We developed the TFBNs that contain 285 components and 2775 Boolean rules based on TFBM on the leukaemia microarray datasets, which are in the form of short-time series. The data contain gene expression measurements for 13 GC-sensitive children under therapy for acute lymphoblastic leukaemia, and each sample has three time points: 0 hour (before GC treatment), 6/8 hours (after GC treatment) and 24 hours (after GC treatment).Conclusion: We conclude that the proposed TFBM unlocks their predecessor's limitation, i.e., FBM, that could help pharmaceutical agents identify any side effects on clinic-related data. New hypotheses could be identified by analysing the extracted fundamental Boolean networks and analysing their up-regulatory and down-regulatory pathways.
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Boolean models of regulatory networks are assumed to be tolerant to perturbations. That qualitatively implies that each function can only depend on a few nodes. Biologically motivated constraints further show that functions found ...
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Boolean models of regulatory networks are assumed to be tolerant to perturbations. That qualitatively implies that each function can only depend on a few nodes. Biologically motivated constraints further show that functions found in Boolean regulatory networks belong to certain classes of functions, for example, the unate functions. It turns out that these classes have specific properties in the Fourier domain. That motivates us to study the problem of detecting controlling nodes in classes of Boolean networks using spectral techniques. We consider networks with unbalanced functions and functions of an average sensitivity less than where k is the number of controlling variables for a function. Further, we consider the class of 1-low networks which include unate networks, linear threshold networks, and networks with nested canalyzing functions. We show that the application of spectral learning algorithms leads to both better time and sample complexity for the detection of controlling nodes compared with algorithms based on exhaustive search. For a particular algorithm, we state analytical upper bounds on the number of samples needed to find the controlling nodes of the Boolean functions. Further, improved algorithms for detecting controlling nodes in large-scale unate networks are given and numerically studied.
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Motivation: We have hypothesized that the construction of transcriptional regulatory networks using a method that optimizes connectivity would lead to regulation consistent with biological expectations. A key expectation is that t...
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Motivation: We have hypothesized that the construction of transcriptional regulatory networks using a method that optimizes connectivity would lead to regulation consistent with biological expectations. A key expectation is that the hypothetical networks should produce a few, very strong attractors, highly similar to the original observations, mimicking biological state stability and determinism. Another central expectation is that, since it is expected that the biological control is distributed and mutually reinforcing, interpretation of the observations should lead to a very small number of connection schemes.Results: We propose a fully Bayesian approach to constructing probabilistic gene regulatory networks (PGRNs) that emphasizes network topology. The method computes the possible parent sets of each gene, the corresponding predictors and the associated probabilities based on a nonlinear perceptron model, using a reversible jump Markov chain Monte Carlo (MCMC) technique, and an MCMC method is employed to search the network configurations to find those with the highest Bayesian scores to construct the PGRN. The Bayesian method has been used to construct a PGRN based on the observed behavior of a set of genes whose expression patterns vary across a set of melanoma samples exhibiting two very different phenotypes with respect to cell motility and invasiveness. Key biological features have been faithfully reflected in the model. Its steady-state distribution contains attractors that are either identical or very similar to the states observed in the data, and many of the attractors are singletons, which mimics the biological propensity to stably occupy a given state. Most interestingly, the connectivity rules for the most optimal generated networks constituting the PGRN are remarkably similar, as would be expected for a network operating on a distributed basis, with strong interactions between the components.
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We describe the countably saturated models and prime models (up to isomorphism) of the theory Th_(prin) of Boolean algebras with a principal ideal, the theory Th_(max) of Boolean algebras with a maximal ideal, the theory Th_(ac) o...
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We describe the countably saturated models and prime models (up to isomorphism) of the theory Th_(prin) of Boolean algebras with a principal ideal, the theory Th_(max) of Boolean algebras with a maximal ideal, the theory Th_(ac) of atomic Boolean algebras with an ideal such that the supremum of the idea exists, and the theory Th_(sa) of atomless Boolean algebras with an ideal such that the supremum of the ideal exists. We prove than there are infinitely many completions of the theory of Boolean algebras with a distinguished ideal that do not have a countably saturated model. Also, we give a sufficient condition for a model of the theory T_X of Boolean algebras with distinguished ideals to be elementarily equivalent to a countably saturated model of T_X.
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We give a complete description of conditions of being strongly constructivizable for Boolean algebras of elementary characteristic (∞, 0, 0) in terms of being computable for a sequence of canonical Ershov–Tarski predicates on Boolean algebras.
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Counting spatially and temporally overlapping events in image sequences and estimating their shape-size and duration features are important issues in some applications. We propose a stochastic model, a particular case of the nonis...
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Counting spatially and temporally overlapping events in image sequences and estimating their shape-size and duration features are important issues in some applications. We propose a stochastic model, a particular case of the nonisotropic 3D Boolean model, for performing this analysis: the temporal Boolean model. Some probabilistic properties are derived and a methodology for parameter estimation from time-lapse image sequences is proposed using an explicit treatment of the temporal dimension. We estimate the mean number of germs per unit area and time, the mean grain size and the duration distribution. A wide simulation study in order to assess the proposed estimators showed promising results. The model was applied on biological image sequences of in-vivo cells in order to estimate new parameters such as the mean number and duration distribution of endocytic events. Our results show that the proposed temporal Boolean model is effective for obtaining information about dynamic processes which exhibit short-lived, but spatially and temporally overlapping events.
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Even though a Boolean query can express the information need precisely enough to select relevant documents, it is not easy to construct an appropriate Boolean query that covers all relevant documents. To utilize a Boolean query ef...
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Even though a Boolean query can express the information need precisely enough to select relevant documents, it is not easy to construct an appropriate Boolean query that covers all relevant documents. To utilize a Boolean query effectively, a mechanism to retrieve as many as possible relevant documents is therefore required. In accordance with this requirement, we propose a method for modifying a given Boolean query by using information from a relevant document set. The retrieval results, however, may deteriorate if some important query terms are removed by this reformulation. A further mechanism is thus required in order to use other query terms that are useful for finding more relevant documents, but are not strictly required in relevant documents. To meet this requirement, we propose a new method that combines the probabilistic IR and the Boolean IR models. We also introduce a new IR system—called appropriate Boolean query reformulation for information retrieval (ABRIR)—based on these two methods and the Okapi system. ABRIR uses both a word index and a phrase index formed from combinations of two adjacent noun words. The effectiveness of these two methods was confirmed according to the NTCIR-4 Web test collection.
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We prove that each computable Boolean algebra has a computable presentation in which for every computable family of automorphisms the set of atoms moved by at least one of its members is finite. This implies that each computable a...
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We prove that each computable Boolean algebra has a computable presentation in which for every computable family of automorphisms the set of atoms moved by at least one of its members is finite. This implies that each computable atomic Boolean algebra has a computable presentation in which its every computable family of automorphisms is finite. The priority argument is not used in the proof.
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The number of mathematical models for biological pathways is rapidly growing. In particular, Boolean modelling proved to be suited to describe large cellular signalling networks. Systems biology is at the threshold to holistic und...
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The number of mathematical models for biological pathways is rapidly growing. In particular, Boolean modelling proved to be suited to describe large cellular signalling networks. Systems biology is at the threshold to holistic understanding of comprehensive networks. In order to reach this goal, connection and integration of existing models of parts of cellular networks into more comprehensive network models is necessary. We discuss model combination approaches for Boolean models. Boolean modelling is qualitative rather than quantitative and does not require detailed kinetic information. We show that these models are useful precursors for large-scale quantitative models and that they are comparatively easy to combine. We propose modelling standards for Boolean models as a prerequisite for smooth model integration. Using these standards, we demonstrate the coupling of two logical models on two different examples concerning cellular interactions in the liver. In the first example, we show the integration of two Boolean models of two cell types in order to describe their interaction. In the second example, we demonstrate the combination of two models describing different parts of the network of a single cell type. Combination of partial models into comprehensive network models will take systems biology to the next level of understanding. The combination of logical models facilitated by modelling standards is a valuable example for the next step towards this goal.
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In cases where the same real-world system can be modeled both by an ODE system D and a Boolean system B, it is of interest to identify conditions under which the two systems will be consistent, that is, will make qualitatively equ...
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In cases where the same real-world system can be modeled both by an ODE system D and a Boolean system B, it is of interest to identify conditions under which the two systems will be consistent, that is, will make qualitatively equivalent predictions. In this note we introduce two broad classes of relatively simple models that provide a convenient framework for studying such questions. In contrast to the widely known class of Glass networks, the right-hand sides of our ODEs are Lipschitz-continuous. We prove that if B has certain structures, consistency between D and B is implied by sufficient separation of timescales in one class of our models. Namely, if the trajectories of B are "one-stepping" then we prove a strong form of consistency and if B has a certain monotonicity property then there is a weaker consistency between D and B. These results appear to point to more general structure properties that favor consistency between ODE and Boolean models.
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