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Sample records for boolean network models

  1. Boolean networks as modelling framework

    Directory of Open Access Journals (Sweden)

    Florian eGreil

    2012-08-01

    Full Text Available In a network, the components of a given system are represented as nodes, the interactions are abstracted as links between the nodes. Boolean networks refer to a class of dynamics on networks, in fact it is the simplest possible dynamics where each node has a value 0 or 1. This allows to investigate extensively the dynamics both analytically and by numerical experiments. The present article focuses on the theoretical concept of relevant components and the immediate application in plant biology, references for more in-depths treatment of the mathematical details are also given.

  2. Random Boolean network models and the yeast transcriptional network

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    Kauffman, Stuart; Peterson, Carsten; Samuelsson, Björn; Troein, Carl

    2003-12-01

    The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean networks. We find that for ensembles of generated models, those with canalyzing Boolean rules are remarkably stable, whereas those with random Boolean rules are only marginally stable. Furthermore, substantial parts of the generated networks are frozen, in the sense that they reach the same state regardless of initial state. Thus, our ensemble approach suggests that the yeast network shows highly ordered dynamics.

  3. Boolean network model predicts knockout mutant phenotypes of fission yeast.

    Directory of Open Access Journals (Sweden)

    Maria I Davidich

    Full Text Available BOOLEAN NETWORKS (OR: networks of switches are extremely simple mathematical models of biochemical signaling networks. Under certain circumstances, Boolean networks, despite their simplicity, are capable of predicting dynamical activation patterns of gene regulatory networks in living cells. For example, the temporal sequence of cell cycle activation patterns in yeasts S. pombe and S. cerevisiae are faithfully reproduced by Boolean network models. An interesting question is whether this simple model class could also predict a more complex cellular phenomenology as, for example, the cell cycle dynamics under various knockout mutants instead of the wild type dynamics, only. Here we show that a Boolean network model for the cell cycle control network of yeast S. pombe correctly predicts viability of a large number of known mutants. So far this had been left to the more detailed differential equation models of the biochemical kinetics of the yeast cell cycle network and was commonly thought to be out of reach for models as simplistic as Boolean networks. The new results support our vision that Boolean networks may complement other mathematical models in systems biology to a larger extent than expected so far, and may fill a gap where simplicity of the model and a preference for an overall dynamical blueprint of cellular regulation, instead of biochemical details, are in the focus.

  4. Boolean Network Model Predicts Knockout Mutant Phenotypes of Fission Yeast

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    Davidich, Maria I.; Bornholdt, Stefan

    2013-01-01

    Boolean networks (or: networks of switches) are extremely simple mathematical models of biochemical signaling networks. Under certain circumstances, Boolean networks, despite their simplicity, are capable of predicting dynamical activation patterns of gene regulatory networks in living cells. For example, the temporal sequence of cell cycle activation patterns in yeasts S. pombe and S. cerevisiae are faithfully reproduced by Boolean network models. An interesting question is whether this simple model class could also predict a more complex cellular phenomenology as, for example, the cell cycle dynamics under various knockout mutants instead of the wild type dynamics, only. Here we show that a Boolean network model for the cell cycle control network of yeast S. pombe correctly predicts viability of a large number of known mutants. So far this had been left to the more detailed differential equation models of the biochemical kinetics of the yeast cell cycle network and was commonly thought to be out of reach for models as simplistic as Boolean networks. The new results support our vision that Boolean networks may complement other mathematical models in systems biology to a larger extent than expected so far, and may fill a gap where simplicity of the model and a preference for an overall dynamical blueprint of cellular regulation, instead of biochemical details, are in the focus. PMID:24069138

  5. Piecewise linear and Boolean models of chemical reaction networks.

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    Veliz-Cuba, Alan; Kumar, Ajit; Josić, Krešimir

    2014-12-01

    Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions ([Formula: see text]). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent [Formula: see text] is large. However, while the case of small constant [Formula: see text] appears in practice, it is not well understood. We provide a mathematical analysis of this limit and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed-form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator.

  6. Piecewise linear and Boolean models of chemical reaction networks

    Science.gov (United States)

    Veliz-Cuba, Alan; Kumar, Ajit; Josić, Krešimir

    2014-01-01

    Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions (xn/(Jn + xn)). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent n is large. However, while the case of small constant J appears in practice, it is not well understood. We provide a mathematical analysis of this limit, and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator. PMID:25412739

  7. Canalization and symmetry in Boolean models for genetic regulatory networks

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    Reichhardt, C J Olson [Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Bassler, Kevin E [Department of Physics, University of Houston, Houston, TX 77204-5005 (United States)

    2007-04-20

    Canalization of genetic regulatory networks has been argued to be favoured by evolutionary processes due to the stability that it can confer to phenotype expression. We explore whether a significant amount of canalization and partial canalization can arise in purely random networks in the absence of evolutionary pressures. We use a mapping of the Boolean functions in the Kauffman N-K model for genetic regulatory networks onto a k-dimensional Ising hypercube (where k = K) to show that the functions can be divided into different classes strictly due to geometrical constraints. The classes can be counted and their properties determined using results from group theory and isomer chemistry. We demonstrate that partially canalizing functions completely dominate all possible Boolean functions, particularly for higher k. This indicates that partial canalization is extremely common, even in randomly chosen networks, and has implications for how much information can be obtained in experiments on native state genetic regulatory networks.

  8. Autonomous Boolean modelling of developmental gene regulatory networks

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    Cheng, Xianrui; Sun, Mengyang; Socolar, Joshua E. S.

    2013-01-01

    During early embryonic development, a network of regulatory interactions among genes dynamically determines a pattern of differentiated tissues. We show that important timing information associated with the interactions can be faithfully represented in autonomous Boolean models in which binary variables representing expression levels are updated in continuous time, and that such models can provide a direct insight into features that are difficult to extract from ordinary differential equation (ODE) models. As an application, we model the experimentally well-studied network controlling fly body segmentation. The Boolean model successfully generates the patterns formed in normal and genetically perturbed fly embryos, permits the derivation of constraints on the time delay parameters, clarifies the logic associated with different ODE parameter sets and provides a platform for studying connectivity and robustness in parameter space. By elucidating the role of regulatory time delays in pattern formation, the results suggest new types of experimental measurements in early embryonic development. PMID:23034351

  9. Boolean network models of cellular regulation: prospects and limitations.

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    Bornholdt, Stefan

    2008-08-06

    Computer models are valuable tools towards an understanding of the cell's biochemical regulatory machinery. Possible levels of description of such models range from modelling the underlying biochemical details to top-down approaches, using tools from the theory of complex networks. The latter, coarse-grained approach is taken where regulatory circuits are classified in graph-theoretical terms, with the elements of the regulatory networks being reduced to simply nodes and links, in order to obtain architectural information about the network. Further, considering dynamics on networks at such an abstract level seems rather unlikely to match dynamical regulatory activity of biological cells. Therefore, it came as a surprise when recently examples of discrete dynamical network models based on very simplistic dynamical elements emerged which in fact do match sequences of regulatory patterns of their biological counterparts. Here I will review such discrete dynamical network models, or Boolean networks, of biological regulatory networks. Further, we will take a look at such models extended with stochastic noise, which allow studying the role of network topology in providing robustness against noise. In the end, we will discuss the interesting question of why at all such simple models can describe aspects of biology despite their simplicity. Finally, prospects of Boolean models in exploratory dynamical models for biological circuits and their mutants will be discussed.

  10. Experimental design schemes for learning Boolean network models

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    Atias, Nir; Gershenzon, Michal; Labazin, Katia; Sharan, Roded

    2014-01-01

    Motivation: A holy grail of biological research is a working model of the cell. Current modeling frameworks, especially in the protein–protein interaction domain, are mostly topological in nature, calling for stronger and more expressive network models. One promising alternative is logic-based or Boolean network modeling, which was successfully applied to model signaling regulatory circuits in human. Learning such models requires observing the system under a sufficient number of different conditions. To date, the amount of measured data is the main bottleneck in learning informative Boolean models, underscoring the need for efficient experimental design strategies. Results: We developed novel design approaches that greedily select an experiment to be performed so as to maximize the difference or the entropy in the results it induces with respect to current best-fit models. Unique to our maximum difference approach is the ability to account for all (possibly exponential number of) Boolean models displaying high fit to the available data. We applied both approaches to simulated and real data from the EFGR and IL1 signaling systems in human. We demonstrate the utility of the developed strategies in substantially improving on a random selection approach. Our design schemes highlight the redundancy in these datasets, leading up to 11-fold savings in the number of experiments to be performed. Availability and implementation: Source code will be made available upon acceptance of the manuscript. Contact: roded@post.tau.ac.il PMID:25161232

  11. Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.

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    Klarner, Hannes; Siebert, Heike

    2015-01-01

    This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: "faithfulness" which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, "univocality" which requires that there is a unique attractor in each trap space, and "completeness" which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks.

  12. Boolean networks with multiexpressions and parameters.

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    Zou, Yi Ming

    2013-01-01

    To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean models, both synchronous and asynchronous, have been proposed in the literature. However, analytical study of these more general Boolean networks models is lagging. This paper aims to develop a concise theory for these different Boolean logic-based modeling methods. Boolean models for networks where each node can have more than two levels of expression and Boolean models with parameters are defined algebraically with examples provided. Certain classes of random asynchronous Boolean networks and deterministic moduli asynchronous Boolean networks are investigated in detail using the setting introduced in this paper. The derived theorems provide a clear picture for the attractor structures of these asynchronous Boolean networks.

  13. Boolean network model predicts cell cycle sequence of fission yeast.

    Directory of Open Access Journals (Sweden)

    Maria I Davidich

    Full Text Available A Boolean network model of the cell-cycle regulatory network of fission yeast (Schizosaccharomyces Pombe is constructed solely on the basis of the known biochemical interaction topology. Simulating the model in the computer faithfully reproduces the known activity sequence of regulatory proteins along the cell cycle of the living cell. Contrary to existing differential equation models, no parameters enter the model except the structure of the regulatory circuitry. The dynamical properties of the model indicate that the biological dynamical sequence is robustly implemented in the regulatory network, with the biological stationary state G1 corresponding to the dominant attractor in state space, and with the biological regulatory sequence being a strongly attractive trajectory. Comparing the fission yeast cell-cycle model to a similar model of the corresponding network in S. cerevisiae, a remarkable difference in circuitry, as well as dynamics is observed. While the latter operates in a strongly damped mode, driven by external excitation, the S. pombe network represents an auto-excited system with external damping.

  14. Learning restricted Boolean network model by time-series data.

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    Ouyang, Hongjia; Fang, Jie; Shen, Liangzhong; Dougherty, Edward R; Liu, Wenbin

    2014-01-01

    Restricted Boolean networks are simplified Boolean networks that are required for either negative or positive regulations between genes. Higa et al. (BMC Proc 5:S5, 2011) proposed a three-rule algorithm to infer a restricted Boolean network from time-series data. However, the algorithm suffers from a major drawback, namely, it is very sensitive to noise. In this paper, we systematically analyze the regulatory relationships between genes based on the state switch of the target gene and propose an algorithm with which restricted Boolean networks may be inferred from time-series data. We compare the proposed algorithm with the three-rule algorithm and the best-fit algorithm based on both synthetic networks and a well-studied budding yeast cell cycle network. The performance of the algorithms is evaluated by three distance metrics: the normalized-edge Hamming distance [Formula: see text], the normalized Hamming distance of state transition [Formula: see text], and the steady-state distribution distance μ (ssd). Results show that the proposed algorithm outperforms the others according to both [Formula: see text] and [Formula: see text], whereas its performance according to μ (ssd) is intermediate between best-fit and the three-rule algorithms. Thus, our new algorithm is more appropriate for inferring interactions between genes from time-series data.

  15. Learning restricted Boolean network model by time-series data

    Science.gov (United States)

    2014-01-01

    Restricted Boolean networks are simplified Boolean networks that are required for either negative or positive regulations between genes. Higa et al. (BMC Proc 5:S5, 2011) proposed a three-rule algorithm to infer a restricted Boolean network from time-series data. However, the algorithm suffers from a major drawback, namely, it is very sensitive to noise. In this paper, we systematically analyze the regulatory relationships between genes based on the state switch of the target gene and propose an algorithm with which restricted Boolean networks may be inferred from time-series data. We compare the proposed algorithm with the three-rule algorithm and the best-fit algorithm based on both synthetic networks and a well-studied budding yeast cell cycle network. The performance of the algorithms is evaluated by three distance metrics: the normalized-edge Hamming distance μhame, the normalized Hamming distance of state transition μhamst, and the steady-state distribution distance μssd. Results show that the proposed algorithm outperforms the others according to both μhame and μhamst, whereas its performance according to μssd is intermediate between best-fit and the three-rule algorithms. Thus, our new algorithm is more appropriate for inferring interactions between genes from time-series data. PMID:25093019

  16. Modeling Integrated Cellular Machinery Using Hybrid Petri-Boolean Networks

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    Berestovsky, Natalie; Zhou, Wanding; Nagrath, Deepak; Nakhleh, Luay

    2013-01-01

    The behavior and phenotypic changes of cells are governed by a cellular circuitry that represents a set of biochemical reactions. Based on biological functions, this circuitry is divided into three types of networks, each encoding for a major biological process: signal transduction, transcription regulation, and metabolism. This division has generally enabled taming computational complexity dealing with the entire system, allowed for using modeling techniques that are specific to each of the components, and achieved separation of the different time scales at which reactions in each of the three networks occur. Nonetheless, with this division comes loss of information and power needed to elucidate certain cellular phenomena. Within the cell, these three types of networks work in tandem, and each produces signals and/or substances that are used by the others to process information and operate normally. Therefore, computational techniques for modeling integrated cellular machinery are needed. In this work, we propose an integrated hybrid model (IHM) that combines Petri nets and Boolean networks to model integrated cellular networks. Coupled with a stochastic simulation mechanism, the model simulates the dynamics of the integrated network, and can be perturbed to generate testable hypotheses. Our model is qualitative and is mostly built upon knowledge from the literature and requires fine-tuning of very few parameters. We validated our model on two systems: the transcriptional regulation of glucose metabolism in human cells, and cellular osmoregulation in S. cerevisiae. The model produced results that are in very good agreement with experimental data, and produces valid hypotheses. The abstract nature of our model and the ease of its construction makes it a very good candidate for modeling integrated networks from qualitative data. The results it produces can guide the practitioner to zoom into components and interconnections and investigate them using such more

  17. Modeling integrated cellular machinery using hybrid Petri-Boolean networks.

    Directory of Open Access Journals (Sweden)

    Natalie Berestovsky

    Full Text Available The behavior and phenotypic changes of cells are governed by a cellular circuitry that represents a set of biochemical reactions. Based on biological functions, this circuitry is divided into three types of networks, each encoding for a major biological process: signal transduction, transcription regulation, and metabolism. This division has generally enabled taming computational complexity dealing with the entire system, allowed for using modeling techniques that are specific to each of the components, and achieved separation of the different time scales at which reactions in each of the three networks occur. Nonetheless, with this division comes loss of information and power needed to elucidate certain cellular phenomena. Within the cell, these three types of networks work in tandem, and each produces signals and/or substances that are used by the others to process information and operate normally. Therefore, computational techniques for modeling integrated cellular machinery are needed. In this work, we propose an integrated hybrid model (IHM that combines Petri nets and Boolean networks to model integrated cellular networks. Coupled with a stochastic simulation mechanism, the model simulates the dynamics of the integrated network, and can be perturbed to generate testable hypotheses. Our model is qualitative and is mostly built upon knowledge from the literature and requires fine-tuning of very few parameters. We validated our model on two systems: the transcriptional regulation of glucose metabolism in human cells, and cellular osmoregulation in S. cerevisiae. The model produced results that are in very good agreement with experimental data, and produces valid hypotheses. The abstract nature of our model and the ease of its construction makes it a very good candidate for modeling integrated networks from qualitative data. The results it produces can guide the practitioner to zoom into components and interconnections and investigate them

  18. Effects of a silenced gene in Boolean network models

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    Emir Haliki

    2017-03-01

    Full Text Available Gene regulation and their regulatory networks are one of the most challenging research problems of computational biology and complexity sciences. Gene regulation is formed by indirect interaction between DNA segments which are protein coding genes to configure the expression level of one another. Prevention of expression of any genes in gene regulation at the levels of transcription or translation indicates the gene silencing event. The present study examined what types of results in gene silencing would bring about in the dynamics of Boolean genetic regulatory mechanisms. The analytical study was performed in gene expression variations of Boolean dynamics first, then the related numerical analysis was simulated in real networks in the literature.

  19. Steady state analysis of Boolean molecular network models via model reduction and computational algebra

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    2014-01-01

    Background A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. Results This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. Conclusions The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate

  20. Boolean network model of the Pseudomonas aeruginosa quorum sensing circuits.

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    Dallidis, Stylianos E; Karafyllidis, Ioannis G

    2014-09-01

    To coordinate their behavior and virulence and to synchronize attacks against their hosts, bacteria communicate by continuously producing signaling molecules (called autoinducers) and continuously monitoring the concentration of these molecules. This communication is controlled by biological circuits called quorum sensing (QS) circuits. Recently QS circuits and have been recognized as an alternative target for controlling bacterial virulence and infections without the use of antibiotics. Pseudomonas aeruginosa is a Gram-negative bacterium that infects insects, plants, animals and humans and can cause acute infections. This bacterium has three interconnected QS circuits that form a very complex and versatile QS system, the operation of which is still under investigation. Here we use Boolean networks to model the complete QS system of Pseudomonas aeruginosa and we simulate and analyze its operation in both synchronous and asynchronous modes. The state space of the QS system is constructed and it turned out to be very large, hierarchical, modular and scale-free. Furthermore, we developed a simulation tool that can simulate gene knock-outs and study their effect on the regulons controlled by the three QS circuits. The model and tools we developed will give to life scientists a deeper insight to this complex QS system.

  1. Boolean universes above Boolean models

    OpenAIRE

    Wehrung, Friedrich

    1993-01-01

    We establish several first- or second-order properties of models of first-order theories by considering their elements as atoms of a new universe of set theory, and by extending naturally any structure of Boolean model on the atoms to the whole universe. For example, complete f-rings are ``boundedly algebraically compact" in the language $( + , - , . , \\wedge , \\vee , \\leq )$, and the positive cone of a complete l-group with infinity adjoined is algebraically compact in the language $( + , \\v...

  2. Synchronization of Asynchronous Switched Boolean Network.

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    Zhang, Hao; Wang, Xingyuan; Lin, Xiaohui

    2015-01-01

    In this paper, the complete synchronizations for asynchronous switched Boolean network with free Boolean sequence controllers and close-loop controllers are studied. First, the basic asynchronous switched Boolean network model is provided. With the method of semi-tensor product, the Boolean dynamics is translated into linear representation. Second, necessary and sufficient conditions for ASBN synchronization with free Boolean sequence control and close-loop control are derived, respectively. Third, some illustrative examples are provided to show the efficiency of the proposed methods.

  3. Relative stability of network states in Boolean network models of gene regulation in development.

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    Zhou, Joseph Xu; Samal, Areejit; d'Hérouël, Aymeric Fouquier; Price, Nathan D; Huang, Sui

    2016-01-01

    Progress in cell type reprogramming has revived the interest in Waddington's concept of the epigenetic landscape. Recently researchers developed the quasi-potential theory to represent the Waddington's landscape. The Quasi-potential U(x), derived from interactions in the gene regulatory network (GRN) of a cell, quantifies the relative stability of network states, which determine the effort required for state transitions in a multi-stable dynamical system. However, quasi-potential landscapes, originally developed for continuous systems, are not suitable for discrete-valued networks which are important tools to study complex systems. In this paper, we provide a framework to quantify the landscape for discrete Boolean networks (BNs). We apply our framework to study pancreas cell differentiation where an ensemble of BN models is considered based on the structure of a minimal GRN for pancreas development. We impose biologically motivated structural constraints (corresponding to specific type of Boolean functions) and dynamical constraints (corresponding to stable attractor states) to limit the space of BN models for pancreas development. In addition, we enforce a novel functional constraint corresponding to the relative ordering of attractor states in BN models to restrict the space of BN models to the biological relevant class. We find that BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics of pancreas cell differentiation. This framework can also determine the genes' influence on cell state transitions, and thus can facilitate the rational design of cell reprogramming protocols.

  4. Stochastic Boolean networks: An efficient approach to modeling gene regulatory networks

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    Liang Jinghang

    2012-08-01

    Full Text Available Abstract Background Various computational models have been of interest due to their use in the modelling of gene regulatory networks (GRNs. As a logical model, probabilistic Boolean networks (PBNs consider molecular and genetic noise, so the study of PBNs provides significant insights into the understanding of the dynamics of GRNs. This will ultimately lead to advances in developing therapeutic methods that intervene in the process of disease development and progression. The applications of PBNs, however, are hindered by the complexities involved in the computation of the state transition matrix and the steady-state distribution of a PBN. For a PBN with n genes and N Boolean networks, the complexity to compute the state transition matrix is O(nN22n or O(nN2n for a sparse matrix. Results This paper presents a novel implementation of PBNs based on the notions of stochastic logic and stochastic computation. This stochastic implementation of a PBN is referred to as a stochastic Boolean network (SBN. An SBN provides an accurate and efficient simulation of a PBN without and with random gene perturbation. The state transition matrix is computed in an SBN with a complexity of O(nL2n, where L is a factor related to the stochastic sequence length. Since the minimum sequence length required for obtaining an evaluation accuracy approximately increases in a polynomial order with the number of genes, n, and the number of Boolean networks, N, usually increases exponentially with n, L is typically smaller than N, especially in a network with a large number of genes. Hence, the computational efficiency of an SBN is primarily limited by the number of genes, but not directly by the total possible number of Boolean networks. Furthermore, a time-frame expanded SBN enables an efficient analysis of the steady-state distribution of a PBN. These findings are supported by the simulation results of a simplified p53 network, several randomly generated networks and a

  5. Stochastic coupling of two random Boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Ho, M.-C. [Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan (China)]. E-mail: t1603@nknucc.nknu.edu.tw; Hung, Y.-C. [Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan (China)]. E-mail: d9123801@student.nsysu.edu.tw; Jiang, I-M. [Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan (China)

    2005-08-29

    We study the dynamics of two coupled random Boolean networks. Based on the Boolean model studied by Andrecut and Ali [Int. J. Mod. Phys. B 15 (2001) 17] and the stochastic coupling techniques, the density evolution of networks is precisely described by two deterministic coupled polynomial maps. The iteration results of the model match the real networks well. By using MSE and the maximal Lyapunov exponents, the synchronization phenomena of coupled networks is also under our discussion.

  6. Boolean Networks with Multi-Expressions and Parameters.

    Science.gov (United States)

    Zou, Yi Ming

    2013-07-01

    To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean models, both synchronous and asynchronous, have been proposed in the literature. However, analytical study of these more general Boolean networks models is lagging. This paper aims to develop a concise theory for these different Boolean logic based modeling methods. Boolean models for networks where each node can have more than two levels of expression and Boolean models with parameters are defined algebraically with examples provided. Certain classes of random asynchronous Boolean networks and deterministic moduli asynchronous Boolean networks are investigated in detail using the setting introduced in this paper. The derived theorems provide a clear picture for the attractor structures of these asynchronous Boolean networks.

  7. Reverse Engineering Boolean Networks: From Bernoulli Mixture Models to Rule Based Systems

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    Saeed, Mehreen; Ijaz, Maliha; Javed, Kashif; Babri, Haroon Atique

    2012-01-01

    A Boolean network is a graphical model for representing and analyzing the behavior of gene regulatory networks (GRN). In this context, the accurate and efficient reconstruction of a Boolean network is essential for understanding the gene regulation mechanism and the complex relations that exist therein. In this paper we introduce an elegant and efficient algorithm for the reverse engineering of Boolean networks from a time series of multivariate binary data corresponding to gene expression data. We call our method ReBMM, i.e., reverse engineering based on Bernoulli mixture models. The time complexity of most of the existing reverse engineering techniques is quite high and depends upon the indegree of a node in the network. Due to the high complexity of these methods, they can only be applied to sparsely connected networks of small sizes. ReBMM has a time complexity factor, which is independent of the indegree of a node and is quadratic in the number of nodes in the network, a big improvement over other techniques and yet there is little or no compromise in accuracy. We have tested ReBMM on a number of artificial datasets along with simulated data derived from a plant signaling network. We also used this method to reconstruct a network from real experimental observations of microarray data of the yeast cell cycle. Our method provides a natural framework for generating rules from a probabilistic model. It is simple, intuitive and illustrates excellent empirical results. PMID:23284654

  8. On the underlying assumptions of threshold Boolean networks as a model for genetic regulatory network behavior

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    Tran, Van; McCall, Matthew N.; McMurray, Helene R.; Almudevar, Anthony

    2013-01-01

    Boolean networks (BoN) are relatively simple and interpretable models of gene regulatory networks. Specifying these models with fewer parameters while retaining their ability to describe complex regulatory relationships is an ongoing methodological challenge. Additionally, extending these models to incorporate variable gene decay rates, asynchronous gene response, and synergistic regulation while maintaining their Markovian nature increases the applicability of these models to genetic regulatory networks (GRN). We explore a previously-proposed class of BoNs characterized by linear threshold functions, which we refer to as threshold Boolean networks (TBN). Compared to traditional BoNs with unconstrained transition functions, these models require far fewer parameters and offer a more direct interpretation. However, the functional form of a TBN does result in a reduction in the regulatory relationships which can be modeled. We show that TBNs can be readily extended to permit self-degradation, with explicitly modeled degradation rates. We note that the introduction of variable degradation compromises the Markovian property fundamental to BoN models but show that a simple state augmentation procedure restores their Markovian nature. Next, we study the effect of assumptions regarding self-degradation on the set of possible steady states. Our findings are captured in two theorems relating self-degradation and regulatory feedback to the steady state behavior of a TBN. Finally, we explore assumptions of synchronous gene response and asynergistic regulation and show that TBNs can be easily extended to relax these assumptions. Applying our methods to the budding yeast cell-cycle network revealed that although the network is complex, its steady state is simplified by the presence of self-degradation and lack of purely positive regulatory cycles. PMID:24376454

  9. Robust Reachability of Boolean Control Networks.

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    Li, Fangfei; Tang, Yang

    2016-04-20

    Boolean networks serve a powerful tool in analysis of genetic regulatory networks since it emphasizes the fundamental principles and establishes a nature framework for capturing the dynamics of regulation of cellular states. In this paper, the robust reachability of Boolean control networks is investigated by means of semi-tensor product. Necessary and sufficient conditions for the robust reachability of Boolean control networks are provided, in which control inputs relying on disturbances or not are considered, respectively. Besides, the corresponding control algorithms are developed for these two cases. A reduced model of the lac operon in the Escherichia coli is presented to show the effectiveness of the presented results.

  10. On the underlying assumptions of threshold Boolean networks as a model for genetic regulatory network behavior

    Directory of Open Access Journals (Sweden)

    Van eTran

    2013-12-01

    Full Text Available Boolean networks (BoN are relatively simple and interpretable models of gene regulatorynetworks. Specifying these models with fewer parameters while retaining their ability to describe complex regulatory relationships is an ongoing methodological challenge. Additionally, extending these models to incorporate variable gene decay rates, asynchronous gene response, and synergistic regulation while maintaining their Markovian nature increases the applicability of these models to genetic regulatory networks.We explore a previously-proposed class of BoNs characterized by linear threshold functions, which we refer to as threshold Boolean networks (TBN. Compared to traditional BoNs with unconstrained transition functions, these models require far fewer parameters and offer a more direct interpretation. However, the functional form of a TBN does result in a reduction in the regulatory relationships which can be modeled.We show that TBNs can be readily extended to permit self-degradation, with explicitly modeled degradation rates. We note that the introduction of variable degradation compromises the Markovian property fundamental to BoN models but show that a simple state augmentation procedure restores their Markovian nature. Next, we study the effect of assumptions regarding self-degradation on the set of possible steady states. Our findings are captured in two theorems relating self-degradation and regulatory feedback to the steady state behavior of a TBN. Finally, we explore assumptions of synchronous gene response and asynergistic regulation and show that TBNs can be easily extended to relax these assumptions.Applying our methods to the budding yeast cell-cycle network revealed that although the network is complex, its steady state is simplified by the presence of self-degradation and lack of purely positive regulatory cycles.

  11. Computing preimages of Boolean networks

    Science.gov (United States)

    2013-01-01

    In this paper we present an algorithm based on the sum-product algorithm that finds elements in the preimage of a feed-forward Boolean networks given an output of the network. Our probabilistic method runs in linear time with respect to the number of nodes in the network. We evaluate our algorithm for randomly constructed Boolean networks and a regulatory network of Escherichia coli and found that it gives a valid solution in most cases. PMID:24267277

  12. Boolean modeling identifies Greatwall/MASTL as an important regulator in the AURKA network of neuroblastoma.

    Science.gov (United States)

    Dahlhaus, Meike; Burkovski, Andre; Hertwig, Falk; Mussel, Christoph; Volland, Ruth; Fischer, Matthias; Debatin, Klaus-Michael; Kestler, Hans A; Beltinger, Christian

    2016-02-01

    Aurora Kinase A (AURKA) is often overexpressed in neuroblastoma (NB) with poor outcome. The causes of AURKA overexpression in NB are unknown. Here, we describe a gene regulatory network consisting of core regulators of AURKA protein expression and activation during mitosis to identify potential causes. This network was transformed to a dynamic Boolean model. Simulated activation of the serine/threonine protein kinase Greatwall (GWL, encoded by MASTL) that attenuates the pivotal AURKA inhibitor PP2A, predicted stabilization of AURKA. Consistent with this notion, gene set enrichment analysis showed enrichment of mitotic spindle assembly genes and MYCN target genes in NB with high GWL/MASTL expression. In line with the prediction of GWL/MASTL enhancing AURKA, elevated expression of GWL/MASTL was associated with NB risk factors and poor survival of patients. These results establish Boolean network modeling of oncogenic pathways in NB as a useful means for guided discovery in this enigmatic cancer.

  13. Boolean networks with veto functions

    Science.gov (United States)

    Ebadi, Haleh; Klemm, Konstantin

    2014-08-01

    Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give analytical expressions for the sensitivity of these functions and provide evidence for their role in natural systems. In an intracellular signal transduction network [Helikar et al., Proc. Natl. Acad. Sci. USA 105, 1913 (2008), 10.1073/pnas.0705088105], the functions with veto are over-represented by a factor exceeding the over-representation of threshold functions and canalyzing functions in the same system. In Boolean networks for control of the yeast cell cycle [Li et al., Proc. Natl. Acad. Sci. USA 101, 4781 (2004), 10.1073/pnas.0305937101; Davidich et al., PLoS ONE 3, e1672 (2008), 10.1371/journal.pone.0001672], no or minimal changes to the wiring diagrams are necessary to formulate their dynamics in terms of the veto functions introduced here.

  14. An extended gene protein/products boolean network model including post-transcriptional regulation

    Science.gov (United States)

    2014-01-01

    Background Networks Biology allows the study of complex interactions between biological systems using formal, well structured, and computationally friendly models. Several different network models can be created, depending on the type of interactions that need to be investigated. Gene Regulatory Networks (GRN) are an effective model commonly used to study the complex regulatory mechanisms of a cell. Unfortunately, given their intrinsic complexity and non discrete nature, the computational study of realistic-sized complex GRNs requires some abstractions. Boolean Networks (BNs), for example, are a reliable model that can be used to represent networks where the possible state of a node is a boolean value (0 or 1). Despite this strong simplification, BNs have been used to study both structural and dynamic properties of real as well as randomly generated GRNs. Results In this paper we show how it is possible to include the post-transcriptional regulation mechanism (a key process mediated by small non-coding RNA molecules like the miRNAs) into the BN model of a GRN. The enhanced BN model is implemented in a software toolkit (EBNT) that allows to analyze boolean GRNs from both a structural and a dynamic point of view. The open-source toolkit is compatible with available visualization tools like Cytoscape and allows to run detailed analysis of the network topology as well as of its attractors, trajectories, and state-space. In the paper, a small GRN built around the mTOR gene is used to demonstrate the main capabilities of the toolkit. Conclusions The extended model proposed in this paper opens new opportunities in the study of gene regulation. Several of the successful researches done with the support of BN to understand high-level characteristics of regulatory networks, can now be improved to better understand the role of post-transcriptional regulation for example as a network-wide noise-reduction or stabilization mechanisms. PMID:25080304

  15. Stability of Boolean Multiplex Networks

    CERN Document Server

    Cozzo, Emanuele; Moreno, Yamir

    2012-01-01

    We extend the formalism of Random Boolean Networks with canalizing rules to multilevel complex networks. The formalism allows to model genetic networks in which each gene might take part in more than one signaling pathway. We use a semi-annealed approach to study the stability of this class of models when coupled in a multiplex network and show that the analytical results are in good agreement with numerical simulations. Our main finding is that the multiplex structure provides a mechanism for the stabilization of the system and of chaotic regimes of individual layers. Our results help understanding why some genetic networks that are theoretically expected to operate in the chaotic regime can actually display dynamical stability.

  16. Integer programming-based method for designing synthetic metabolic networks by Minimum Reaction Insertion in a Boolean model.

    Science.gov (United States)

    Lu, Wei; Tamura, Takeyuki; Song, Jiangning; Akutsu, Tatsuya

    2014-01-01

    In this paper, we consider the Minimum Reaction Insertion (MRI) problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA)-based model, the solution of the FBA-based model tends to include more reactions than that of the Boolean model. However, solving MRI using the Boolean model is computationally more expensive than using the FBA-based model since the Boolean model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database, we have found that the developed method can appropriately solve MRI in the Boolean model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean model. Our developed software is available at "http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html."

  17. Integer programming-based method for designing synthetic metabolic networks by Minimum Reaction Insertion in a Boolean model.

    Directory of Open Access Journals (Sweden)

    Wei Lu

    Full Text Available In this paper, we consider the Minimum Reaction Insertion (MRI problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA-based model, the solution of the FBA-based model tends to include more reactions than that of the Boolean model. However, solving MRI using the Boolean model is computationally more expensive than using the FBA-based model since the Boolean model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG database, we have found that the developed method can appropriately solve MRI in the Boolean model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean model. Our developed software is available at "http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html."

  18. Integer Programming-Based Method for Designing Synthetic Metabolic Networks by Minimum Reaction Insertion in a Boolean Model

    Science.gov (United States)

    Song, Jiangning; Akutsu, Tatsuya

    2014-01-01

    In this paper, we consider the Minimum Reaction Insertion (MRI) problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA)-based model, the solution of the FBA-based model tends to include more reactions than that of the Boolean model. However, solving MRI using the Boolean model is computationally more expensive than using the FBA-based model since the Boolean model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database, we have found that the developed method can appropriately solve MRI in the Boolean model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean model. Our developed software is available at “http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html.” PMID:24651476

  19. Boolean genetic network model for the control of C. elegans early embryonic cell cycles

    Science.gov (United States)

    2013-01-01

    Background In Caenorhabditis elegans early embryo, cell cycles only have two phases: DNA synthesis and mitosis, which are different from the typical 4-phase cell cycle. Modeling this cell-cycle process into network can fill up the gap in C. elegans cell-cycle study and provide a thorough understanding on the cell-cycle regulations and progressions at the network level. Methods In this paper, C. elegans early embryonic cell-cycle network has been constructed based on the knowledge of key regulators and their interactions from literature studies. A discrete dynamical Boolean model has been applied in computer simulations to study dynamical properties of this network. The cell-cycle network is compared with random networks and tested under several perturbations to analyze its robustness. To investigate whether our proposed network could explain biological experiment results, we have also compared the network simulation results with gene knock down experiment data. Results With the Boolean model, this study showed that the cell-cycle network was stable with a set of attractors (fixed points). A biological pathway was observed in the simulation, which corresponded to a whole cell-cycle progression. The C. elegans network was significantly robust when compared with random networks of the same size because there were less attractors and larger basins than random networks. Moreover, the network was also robust under perturbations with no significant change of the basin size. In addition, the smaller number of attractors and the shorter biological pathway from gene knock down network simulation interpreted the shorter cell-cycle lengths in mutant from the RNAi gene knock down experiment data. Hence, we demonstrated that the results in network simulation could be verified by the RNAi gene knock down experiment data. Conclusions A C. elegans early embryonic cell cycles network was constructed and its properties were analyzed and compared with those of random networks

  20. Evolving sensitivity balances Boolean Networks.

    Directory of Open Access Journals (Sweden)

    Jamie X Luo

    Full Text Available We investigate the sensitivity of Boolean Networks (BNs to mutations. We are interested in Boolean Networks as a model of Gene Regulatory Networks (GRNs. We adopt Ribeiro and Kauffman's Ergodic Set and use it to study the long term dynamics of a BN. We define the sensitivity of a BN to be the mean change in its Ergodic Set structure under all possible loss of interaction mutations. In silico experiments were used to selectively evolve BNs for sensitivity to losing interactions. We find that maximum sensitivity was often achievable and resulted in the BNs becoming topologically balanced, i.e. they evolve towards network structures in which they have a similar number of inhibitory and excitatory interactions. In terms of the dynamics, the dominant sensitivity strategy that evolved was to build BNs with Ergodic Sets dominated by a single long limit cycle which is easily destabilised by mutations. We discuss the relevance of our findings in the context of Stem Cell Differentiation and propose a relationship between pluripotent stem cells and our evolved sensitive networks.

  1. Steady-State Analysis of Genetic Regulatory Networks Modelled by Probabilistic Boolean Networks

    Directory of Open Access Journals (Sweden)

    Wei Zhang

    2006-04-01

    Full Text Available Probabilistic Boolean networks (PBNs have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs can be analysed in the context of Markov chains. A key goal is the determination of the steady-state (long-run behaviour of a PBN by analysing the corresponding Markov chain. This allows one to compute the long-term influence of a gene on another gene or determine the long-term joint probabilistic behaviour of a few selected genes. Because matrix-based methods quickly become prohibitive for large sizes of networks, we propose the use of Monte Carlo methods. However, the rate of convergence to the stationary distribution becomes a central issue. We discuss several approaches for determining the number of iterations necessary to achieve convergence of the Markov chain corresponding to a PBN. Using a recently introduced method based on the theory of two-state Markov chains, we illustrate the approach on a sub-network designed from human glioma gene expression data and determine the joint steadystate probabilities for several groups of genes.

  2. An efficient algorithm for computing fixed length attractors based on bounded model checking in synchronous Boolean networks with biochemical applications.

    Science.gov (United States)

    Li, X Y; Yang, G W; Zheng, D S; Guo, W S; Hung, W N N

    2015-01-01

    Genetic regulatory networks are the key to understanding biochemical systems. One condition of the genetic regulatory network under different living environments can be modeled as a synchronous Boolean network. The attractors of these Boolean networks will help biologists to identify determinant and stable factors. Existing methods identify attractors based on a random initial state or the entire state simultaneously. They cannot identify the fixed length attractors directly. The complexity of including time increases exponentially with respect to the attractor number and length of attractors. This study used the bounded model checking to quickly locate fixed length attractors. Based on the SAT solver, we propose a new algorithm for efficiently computing the fixed length attractors, which is more suitable for large Boolean networks and numerous attractors' networks. After comparison using the tool BooleNet, empirical experiments involving biochemical systems demonstrated the feasibility and efficiency of our approach.

  3. Altered Micro-RNA Degradation Promotes Tumor Heterogeneity: A Result from Boolean Network Modeling.

    Science.gov (United States)

    Wu, Yunyi; Krueger, Gerhard R F; Wang, Guanyu

    2016-02-01

    Cancer heterogeneity may reflect differential dynamical outcomes of the regulatory network encompassing biomolecules at both transcriptional and post-transcriptional levels. In other words, differential gene-expression profiles may correspond to different stable steady states of a mathematical model for simulation of biomolecular networks. To test this hypothesis, we simplified a regulatory network that is important for soft-tissue sarcoma metastasis and heterogeneity, comprising of transcription factors, micro-RNAs, and signaling components of the NOTCH pathway. We then used a Boolean network model to simulate the dynamics of this network, and particularly investigated the consequences of differential miRNA degradation modes. We found that efficient miRNA degradation is crucial for sustaining a homogenous and healthy phenotype, while defective miRNA degradation may lead to multiple stable steady states and ultimately to carcinogenesis and heterogeneity.

  4. Boolean Network Model for Cancer Pathways: Predicting Carcinogenesis and Targeted Therapy Outcomes

    Science.gov (United States)

    Fumiã, Herman F.; Martins, Marcelo L.

    2013-01-01

    A Boolean dynamical system integrating the main signaling pathways involved in cancer is constructed based on the currently known protein-protein interaction network. This system exhibits stationary protein activation patterns – attractors – dependent on the cell's microenvironment. These dynamical attractors were determined through simulations and their stabilities against mutations were tested. In a higher hierarchical level, it was possible to group the network attractors into distinct cell phenotypes and determine driver mutations that promote phenotypic transitions. We find that driver nodes are not necessarily central in the network topology, but at least they are direct regulators of central components towards which converge or through which crosstalk distinct cancer signaling pathways. The predicted drivers are in agreement with those pointed out by diverse census of cancer genes recently performed for several human cancers. Furthermore, our results demonstrate that cell phenotypes can evolve towards full malignancy through distinct sequences of accumulated mutations. In particular, the network model supports routes of carcinogenesis known for some tumor types. Finally, the Boolean network model is employed to evaluate the outcome of molecularly targeted cancer therapies. The major find is that monotherapies were additive in their effects and that the association of targeted drugs is necessary for cancer eradication. PMID:23922675

  5. From Boolean Network Model to Continuous Model Helps in Design of Functional Circuits

    Science.gov (United States)

    Zhang, Dongliang; Wu, Jiayi; Ouyang, Qi

    2015-01-01

    Computational circuit design with desired functions in a living cell is a challenging task in synthetic biology. To achieve this task, numerous methods that either focus on small scale networks or use evolutionary algorithms have been developed. Here, we propose a two-step approach to facilitate the design of functional circuits. In the first step, the search space of possible topologies for target functions is reduced by reverse engineering using a Boolean network model. In the second step, continuous simulation is applied to evaluate the performance of these topologies. We demonstrate the usefulness of this method by designing an example biological function: the SOS response of E. coli. Our numerical results show that the desired function can be faithfully reproduced by candidate networks with different parameters and initial conditions. Possible circuits are ranked according to their robustness against perturbations in parameter and gene expressions. The biological network is among the candidate networks, yet novel designs can be generated. Our method provides a scalable way to design robust circuits that can achieve complex functions, and makes it possible to uncover design principles of biological networks. PMID:26061094

  6. Modeling the Normal and Neoplastic Cell Cycle with 'Realistic Boolean Genetic Networks': Their Application for Understanding Carcinogenesis and Assessing Therapeutic Strategies

    Science.gov (United States)

    Szallasi, Zoltan; Liang, Shoudan

    2000-01-01

    In this paper we show how Boolean genetic networks could be used to address complex problems in cancer biology. First, we describe a general strategy to generate Boolean genetic networks that incorporate all relevant biochemical and physiological parameters and cover all of their regulatory interactions in a deterministic manner. Second, we introduce 'realistic Boolean genetic networks' that produce time series measurements very similar to those detected in actual biological systems. Third, we outline a series of essential questions related to cancer biology and cancer therapy that could be addressed by the use of 'realistic Boolean genetic network' modeling.

  7. Computing smallest intervention strategies for multiple metabolic networks in a boolean model.

    Science.gov (United States)

    Lu, Wei; Tamura, Takeyuki; Song, Jiangning; Akutsu, Tatsuya

    2015-02-01

    This article considers the problem whereby, given two metabolic networks N1 and N2, a set of source compounds, and a set of target compounds, we must find the minimum set of reactions whose removal (knockout) ensures that the target compounds are not producible in N1 but are producible in N2. Similar studies exist for the problem of finding the minimum knockout with the smallest side effect for a single network. However, if technologies of external perturbations are advanced in the near future, it may be important to develop methods of computing the minimum knockout for multiple networks (MKMN). Flux balance analysis (FBA) is efficient if a well-polished model is available. However, that is not always the case. Therefore, in this article, we study MKMN in Boolean models and an elementary mode (EM)-based model. Integer linear programming (ILP)-based methods are developed for these models, since MKMN is NP-complete for both the Boolean model and the EM-based model. Computer experiments are conducted with metabolic networks of clostridium perfringens SM101 and bifidobacterium longum DJO10A, respectively known as bad bacteria and good bacteria for the human intestine. The results show that larger networks are more likely to have MKMN solutions. However, solving for these larger networks takes a very long time, and often the computation cannot be completed. This is reasonable, because small networks do not have many alternative pathways, making it difficult to satisfy the MKMN condition, whereas in large networks the number of candidate solutions explodes. Our developed software minFvskO is available online.

  8. Computing Smallest Intervention Strategies for Multiple Metabolic Networks in a Boolean Model

    Science.gov (United States)

    Lu, Wei; Song, Jiangning; Akutsu, Tatsuya

    2015-01-01

    Abstract This article considers the problem whereby, given two metabolic networks N1 and N2, a set of source compounds, and a set of target compounds, we must find the minimum set of reactions whose removal (knockout) ensures that the target compounds are not producible in N1 but are producible in N2. Similar studies exist for the problem of finding the minimum knockout with the smallest side effect for a single network. However, if technologies of external perturbations are advanced in the near future, it may be important to develop methods of computing the minimum knockout for multiple networks (MKMN). Flux balance analysis (FBA) is efficient if a well-polished model is available. However, that is not always the case. Therefore, in this article, we study MKMN in Boolean models and an elementary mode (EM)-based model. Integer linear programming (ILP)-based methods are developed for these models, since MKMN is NP-complete for both the Boolean model and the EM-based model. Computer experiments are conducted with metabolic networks of clostridium perfringens SM101 and bifidobacterium longum DJO10A, respectively known as bad bacteria and good bacteria for the human intestine. The results show that larger networks are more likely to have MKMN solutions. However, solving for these larger networks takes a very long time, and often the computation cannot be completed. This is reasonable, because small networks do not have many alternative pathways, making it difficult to satisfy the MKMN condition, whereas in large networks the number of candidate solutions explodes. Our developed software minFvskO is available online. PMID:25684199

  9. Dynamic Boolean models

    OpenAIRE

    Berg, van den, Aad; Meester, R.; White, Damien

    1997-01-01

    Consider an ordinary Boolean model, that is, a homogeneous Poisson point process in Rd, where the points are all centres of random balls with i.i.d. radii. Now let these points move around according to i.i.d. stochastic processes. It is not hard to show that at each xed time t we again have a Boolean model with the original distribution. Hence if the original model is supercritical then, for any t, the probability of having an unbounded occupied component at time t equals 1. We show that unde...

  10. Analysis of feedback loops and robustness in network evolution based on Boolean models

    Directory of Open Access Journals (Sweden)

    Cho Kwang-Hyun

    2007-11-01

    Full Text Available Abstract Background Many biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. Preferential attachment has been considered as the most plausible evolutionary growth model to explain this topological property. Although various studies have been undertaken to investigate the structural characteristics of a network obtained using this growth model, its dynamical characteristics have received relatively less attention. Results In this paper, we focus on the robustness of a network that is acquired during its evolutionary process. Through simulations using Boolean network models, we found that preferential attachment increases the number of coupled feedback loops in the course of network evolution. Whereas, if networks evolve to have more coupled feedback loops rather than following preferential attachment, the resulting networks are more robust than those obtained through preferential attachment, although both of them have similar degree distributions. Conclusion The presented analysis demonstrates that coupled feedback loops may play an important role in network evolution to acquire robustness. The result also provides a hint as to why various biological networks have evolved to contain a number of coupled feedback loops.

  11. Boolean network-based model of the Bcl-2 family mediated MOMP regulation

    Science.gov (United States)

    2013-01-01

    Background Mitochondrial outer membrane permeabilization (MOMP) is one of the most important points in the majority of apoptotic signaling cascades and it is controlled by a network of interactions between the members of the Bcl-2 family. Methods To understand the role of individual members of this family within the MOMP regulation, we have constructed a Boolean network-based model of interactions between the Bcl-2 proteins. Results Computational simulations have revealed the existence of trapping states which, independently from the incoming stimuli, block the occurrence of MOMP. Our results emphasize the role of the antiapoptotic protein Mcl-1 in the majority of these configurations. We demonstrate here the importance of the Bid and Bim for activation of effectors Bax and Bak, and the irreversibility of this activation. The model further points to the antiapoptotic protein Bcl-w as a key factor preventing Bax activation. Conclusions In spite of relative simplicity, the Boolean network-based model provides useful insight into main functioning logic of the Bcl-2 switch, consistent with experimental findings. PMID:23767791

  12. Reconstructing Boolean Models of Signaling

    Science.gov (United States)

    Karp, Richard M.

    2013-01-01

    Abstract Since the first emergence of protein–protein interaction networks more than a decade ago, they have been viewed as static scaffolds of the signaling–regulatory events taking place in cells, and their analysis has been mainly confined to topological aspects. Recently, functional models of these networks have been suggested, ranging from Boolean to constraint-based methods. However, learning such models from large-scale data remains a formidable task, and most modeling approaches rely on extensive human curation. Here we provide a generic approach to learning Boolean models automatically from data. We apply our approach to growth and inflammatory signaling systems in humans and show how the learning phase can improve the fit of the model to experimental data, remove spurious interactions, and lead to better understanding of the system at hand. PMID:23286509

  13. Partial stability and stabilisation of Boolean networks

    Science.gov (United States)

    Chen, Hong-Wei; Sun, Liang-Jie; Liu, Yang

    2016-07-01

    In this paper, we investigate the stability of Boolean networks and the stabilisation of Boolean control networks with respect to part of the system's states. First, an algebraic expression of the Boolean (control) network is derived by the semi-tensor product of matrices. Then, some necessary and sufficient conditions for partial stability of Boolean networks are given. Finally, the stabilisation of Boolean control networks by a free control sequence and a state-feedback control is investigated and the respective necessary and sufficient conditions are obtained. Examples are provided to illustrate the efficiency of the obtained results.

  14. Using synchronous Boolean networks to model several phenomena of collective behavior.

    Directory of Open Access Journals (Sweden)

    Stepan Kochemazov

    Full Text Available In this paper, we propose an approach for modeling and analysis of a number of phenomena of collective behavior. By collectives we mean multi-agent systems that transition from one state to another at discrete moments of time. The behavior of a member of a collective (agent is called conforming if the opinion of this agent at current time moment conforms to the opinion of some other agents at the previous time moment. We presume that at each moment of time every agent makes a decision by choosing from the set {0,1} (where 1-decision corresponds to action and 0-decision corresponds to inaction. In our approach we model collective behavior with synchronous Boolean networks. We presume that in a network there can be agents that act at every moment of time. Such agents are called instigators. Also there can be agents that never act. Such agents are called loyalists. Agents that are neither instigators nor loyalists are called simple agents. We study two combinatorial problems. The first problem is to find a disposition of instigators that in several time moments transforms a network from a state where the majority of simple agents are inactive to a state with the majority of active agents. The second problem is to find a disposition of loyalists that returns the network to a state with the majority of inactive agents. Similar problems are studied for networks in which simple agents demonstrate the contrary to conforming behavior that we call anticonforming. We obtained several theoretical results regarding the behavior of collectives of agents with conforming or anticonforming behavior. In computational experiments we solved the described problems for randomly generated networks with several hundred vertices. We reduced corresponding combinatorial problems to the Boolean satisfiability problem (SAT and used modern SAT solvers to solve the instances obtained.

  15. Using Synchronous Boolean Networks to Model Several Phenomena of Collective Behavior

    Science.gov (United States)

    Kochemazov, Stepan; Semenov, Alexander

    2014-01-01

    In this paper, we propose an approach for modeling and analysis of a number of phenomena of collective behavior. By collectives we mean multi-agent systems that transition from one state to another at discrete moments of time. The behavior of a member of a collective (agent) is called conforming if the opinion of this agent at current time moment conforms to the opinion of some other agents at the previous time moment. We presume that at each moment of time every agent makes a decision by choosing from the set (where 1-decision corresponds to action and 0-decision corresponds to inaction). In our approach we model collective behavior with synchronous Boolean networks. We presume that in a network there can be agents that act at every moment of time. Such agents are called instigators. Also there can be agents that never act. Such agents are called loyalists. Agents that are neither instigators nor loyalists are called simple agents. We study two combinatorial problems. The first problem is to find a disposition of instigators that in several time moments transforms a network from a state where the majority of simple agents are inactive to a state with the majority of active agents. The second problem is to find a disposition of loyalists that returns the network to a state with the majority of inactive agents. Similar problems are studied for networks in which simple agents demonstrate the contrary to conforming behavior that we call anticonforming. We obtained several theoretical results regarding the behavior of collectives of agents with conforming or anticonforming behavior. In computational experiments we solved the described problems for randomly generated networks with several hundred vertices. We reduced corresponding combinatorial problems to the Boolean satisfiability problem (SAT) and used modern SAT solvers to solve the instances obtained. PMID:25526612

  16. Effect of memory in non-Markovian Boolean networks

    CERN Document Server

    Ebadi, Haleh; Ausloos, Marcel; Jafari, GholamReza

    2016-01-01

    One successful model of interacting biological systems is the Boolean network. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self organizing features of biological phenomena and their intelligent nature should raise some doubt about ignoring the history of their time evolution. Here, we extend the Boolean network Markovian approach: we involve the effect of memory on the dynamics. This can be explored by modifying Boolean functions into non-Markovian functions, for example, by investigating the usual non-Markovian threshold function, - one of the most applied Boolean functions. By applying the non-Markovian threshold function on the dynamical process of a cell cycle network, we discover a power law memory with a more robust dynamics than the Markovian dynamics.

  17. Modeling and controlling the two-phase dynamics of the p53 network: a Boolean network approach

    Science.gov (United States)

    Lin, Guo-Qiang; Ao, Bin; Chen, Jia-Wei; Wang, Wen-Xu; Di, Zeng-Ru

    2014-12-01

    Although much empirical evidence has demonstrated that p53 plays a key role in tumor suppression, the dynamics and function of the regulatory network centered on p53 have not yet been fully understood. Here, we develop a Boolean network model to reproduce the two-phase dynamics of the p53 network in response to DNA damage. In particular, we map the fates of cells into two types of Boolean attractors, and we find that the apoptosis attractor does not exist for minor DNA damage, reflecting that the cell is reparable. As the amount of DNA damage increases, the basin of the repair attractor shrinks, accompanied by the rising of the apoptosis attractor and the expansion of its basin, indicating that the cell becomes more irreparable with more DNA damage. For severe DNA damage, the repair attractor vanishes, and the apoptosis attractor dominates the state space, accounting for the exclusive fate of death. Based on the Boolean network model, we explore the significance of links, in terms of the sensitivity of the two-phase dynamics, to perturbing the weights of links and removing them. We find that the links are either critical or ordinary, rather than redundant. This implies that the p53 network is irreducible, but tolerant of small mutations at some ordinary links, and this can be interpreted with evolutionary theory. We further devised practical control schemes for steering the system into the apoptosis attractor in the presence of DNA damage by pinning the state of a single node or perturbing the weight of a single link. Our approach offers insights into understanding and controlling the p53 network, which is of paramount importance for medical treatment and genetic engineering.

  18. A boolean model of the cardiac gene regulatory network determining first and second heart field identity.

    Directory of Open Access Journals (Sweden)

    Franziska Herrmann

    Full Text Available Two types of distinct cardiac progenitor cell populations can be identified during early heart development: the first heart field (FHF and second heart field (SHF lineage that later form the mature heart. They can be characterized by differential expression of transcription and signaling factors. These regulatory factors influence each other forming a gene regulatory network. Here, we present a core gene regulatory network for early cardiac development based on published temporal and spatial expression data of genes and their interactions. This gene regulatory network was implemented in a Boolean computational model. Simulations reveal stable states within the network model, which correspond to the regulatory states of the FHF and the SHF lineages. Furthermore, we are able to reproduce the expected temporal expression patterns of early cardiac factors mimicking developmental progression. Additionally, simulations of knock-down experiments within our model resemble published phenotypes of mutant mice. Consequently, this gene regulatory network retraces the early steps and requirements of cardiogenic mesoderm determination in a way appropriate to enhance the understanding of heart development.

  19. A Boolean Model of the Cardiac Gene Regulatory Network Determining First and Second Heart Field Identity

    Science.gov (United States)

    Zhou, Dao; Kestler, Hans A.; Kühl, Michael

    2012-01-01

    Two types of distinct cardiac progenitor cell populations can be identified during early heart development: the first heart field (FHF) and second heart field (SHF) lineage that later form the mature heart. They can be characterized by differential expression of transcription and signaling factors. These regulatory factors influence each other forming a gene regulatory network. Here, we present a core gene regulatory network for early cardiac development based on published temporal and spatial expression data of genes and their interactions. This gene regulatory network was implemented in a Boolean computational model. Simulations reveal stable states within the network model, which correspond to the regulatory states of the FHF and the SHF lineages. Furthermore, we are able to reproduce the expected temporal expression patterns of early cardiac factors mimicking developmental progression. Additionally, simulations of knock-down experiments within our model resemble published phenotypes of mutant mice. Consequently, this gene regulatory network retraces the early steps and requirements of cardiogenic mesoderm determination in a way appropriate to enhance the understanding of heart development. PMID:23056457

  20. Non-monotony and Boolean automata networks

    CERN Document Server

    Noual, Mathilde; Sené, Sylvain

    2011-01-01

    This paper aims at setting the keystone of a prospective theoretical study on the role of non-monotone interactions in biological regulation networks. Focusing on discrete models of these networks, namely, Boolean automata networks, we propose to analyse the contribution of non-monotony to the diversity and complexity in their dynamical behaviours. More precisely, in this paper, we start by detailing some motivations, both mathematical and biological, for our interest in non-monotony, and we discuss how it may account for phenomena that cannot be produced by monotony only. Then, to build some understanding in this direction, we propose some preliminary results on the dynamical behaviour of some specific non-monotone Boolean automata networks called XOR circulant networks.

  1. Boolean modeling: a logic-based dynamic approach for understanding signaling and regulatory networks and for making useful predictions.

    Science.gov (United States)

    Albert, Réka; Thakar, Juilee

    2014-01-01

    The biomolecules inside or near cells form a complex interacting system. Cellular phenotypes and behaviors arise from the totality of interactions among the components of this system. A fruitful way of modeling interacting biomolecular systems is by network-based dynamic models that characterize each component by a state variable, and describe the change in the state variables due to the interactions in the system. Dynamic models can capture the stable state patterns of this interacting system and can connect them to different cell fates or behaviors. A Boolean or logic model characterizes each biomolecule by a binary state variable that relates the abundance of that molecule to a threshold abundance necessary for downstream processes. The regulation of this state variable is described in a parameter free manner, making Boolean modeling a practical choice for systems whose kinetic parameters have not been determined. Boolean models integrate the body of knowledge regarding the components and interactions of biomolecular systems, and capture the system's dynamic repertoire, for example the existence of multiple cell fates. These models were used for a variety of systems and led to important insights and predictions. Boolean models serve as an efficient exploratory model, a guide for follow-up experiments, and as a foundation for more quantitative models.

  2. Synchronization of Boolean Networks with Different Update Schemes.

    Science.gov (United States)

    Zhang, Hao; Wang, Xingyuan; Lin, Xiaohui

    2014-01-01

    In this paper, the synchronizations of Boolean networks with different update schemes (synchronized Boolean networks and asynchronous Boolean networks) are investigated. All nodes in Boolean network are represented in terms of semi-tensor product. First, we give the concept of inner synchronization and observe that all nodes in a Boolean network are synchronized with each other. Second, we investigate the outer synchronization between a driving Boolean network and a corresponding response Boolean network. We provide not only the concept of traditional complete synchronization, but also the anti-synchronization and get the anti-synchronization in simulation. Third, we extend the outer synchronization to asynchronous Boolean network and get the complete synchronization between an asynchronous Boolean network and a response Boolean network. Consequently, theorems for synchronization of Boolean networks and asynchronous Boolean networks are derived. Examples are provided to show the correctness of our theorems.

  3. Boolean network robotics: a proof of concept

    CERN Document Server

    Roli, Andrea; Pinciroli, Carlo; Birattari, Mauro

    2011-01-01

    Dynamical systems theory and complexity science provide powerful tools for analysing artificial agents and robots. Furthermore, they have been recently proposed also as a source of design principles and guidelines. Boolean networks are a prominent example of complex dynamical systems and they have been shown to effectively capture important phenomena in gene regulation. From an engineering perspective, these models are very compelling, because they can exhibit rich and complex behaviours, in spite of the compactness of their description. In this paper, we propose the use of Boolean networks for controlling robots' behaviour. The network is designed by means of an automatic procedure based on stochastic local search techniques. We show that this approach makes it possible to design a network which enables the robot to accomplish a task that requires the capability of navigating the space using a light stimulus, as well as the formation and use of an internal memory.

  4. Intervention in Context-Sensitive Probabilistic Boolean Networks Revisited

    Directory of Open Access Journals (Sweden)

    Babak Faryabi

    2009-01-01

    Full Text Available An approximate representation for the state space of a context-sensitive probabilistic Boolean network has previously been proposed and utilized to devise therapeutic intervention strategies. Whereas the full state of a context-sensitive probabilistic Boolean network is specified by an ordered pair composed of a network context and a gene-activity profile, this approximate representation collapses the state space onto the gene-activity profiles alone. This reduction yields an approximate transition probability matrix, absent of context, for the Markov chain associated with the context-sensitive probabilistic Boolean network. As with many approximation methods, a price must be paid for using a reduced model representation, namely, some loss of optimality relative to using the full state space. This paper examines the effects on intervention performance caused by the reduction with respect to various values of the model parameters. This task is performed using a new derivation for the transition probability matrix of the context-sensitive probabilistic Boolean network. This expression of transition probability distributions is in concert with the original definition of context-sensitive probabilistic Boolean network. The performance of optimal and approximate therapeutic strategies is compared for both synthetic networks and a real case study. It is observed that the approximate representation describes the dynamics of the context-sensitive probabilistic Boolean network through the instantaneously random probabilistic Boolean network with similar parameters.

  5. An Extended, Boolean Model of the Septation Initiation Network in S.Pombe Provides Insights into Its Regulation.

    Science.gov (United States)

    Chasapi, Anastasia; Wachowicz, Paulina; Niknejad, Anne; Collin, Philippe; Krapp, Andrea; Cano, Elena; Simanis, Viesturs; Xenarios, Ioannis

    2015-01-01

    Cytokinesis in fission yeast is controlled by the Septation Initiation Network (SIN), a protein kinase signaling network using the spindle pole body as scaffold. In order to describe the qualitative behavior of the system and predict unknown mutant behaviors we decided to adopt a Boolean modeling approach. In this paper, we report the construction of an extended, Boolean model of the SIN, comprising most SIN components and regulators as individual, experimentally testable nodes. The model uses CDK activity levels as control nodes for the simulation of SIN related events in different stages of the cell cycle. The model was optimized using single knock-out experiments of known phenotypic effect as a training set, and was able to correctly predict a double knock-out test set. Moreover, the model has made in silico predictions that have been validated in vivo, providing new insights into the regulation and hierarchical organization of the SIN.

  6. Boolean networks with reliable dynamics

    CERN Document Server

    Peixoto, Tiago P

    2009-01-01

    We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states which is independent of the order in which the nodes are updated. We explored numerically the topology, the update functions, and the state space structure of these networks, which we constructed using a minimum number of links and the simplest update functions. We found that the clustering coefficient is larger than in random networks, and that the probability distribution of three-node motifs is similar to that found in gene regulation networks. Among the update functions, only a subset of all possible functions occur, and they can be classified according to their probability. More homogeneous functions occur more often, leading to a dominance of canalyzing functions. Finally, we studied the entire state space of the networks. We observed that with increasing systems size, fixed points become more dominant, moving the networks close to the frozen...

  7. A Full Bayesian Approach for Boolean Genetic Network Inference

    Science.gov (United States)

    Han, Shengtong; Wong, Raymond K. W.; Lee, Thomas C. M.; Shen, Linghao; Li, Shuo-Yen R.; Fan, Xiaodan

    2014-01-01

    Boolean networks are a simple but efficient model for describing gene regulatory systems. A number of algorithms have been proposed to infer Boolean networks. However, these methods do not take full consideration of the effects of noise and model uncertainty. In this paper, we propose a full Bayesian approach to infer Boolean genetic networks. Markov chain Monte Carlo algorithms are used to obtain the posterior samples of both the network structure and the related parameters. In addition to regular link addition and removal moves, which can guarantee the irreducibility of the Markov chain for traversing the whole network space, carefully constructed mixture proposals are used to improve the Markov chain Monte Carlo convergence. Both simulations and a real application on cell-cycle data show that our method is more powerful than existing methods for the inference of both the topology and logic relations of the Boolean network from observed data. PMID:25551820

  8. A full bayesian approach for boolean genetic network inference.

    Directory of Open Access Journals (Sweden)

    Shengtong Han

    Full Text Available Boolean networks are a simple but efficient model for describing gene regulatory systems. A number of algorithms have been proposed to infer Boolean networks. However, these methods do not take full consideration of the effects of noise and model uncertainty. In this paper, we propose a full Bayesian approach to infer Boolean genetic networks. Markov chain Monte Carlo algorithms are used to obtain the posterior samples of both the network structure and the related parameters. In addition to regular link addition and removal moves, which can guarantee the irreducibility of the Markov chain for traversing the whole network space, carefully constructed mixture proposals are used to improve the Markov chain Monte Carlo convergence. Both simulations and a real application on cell-cycle data show that our method is more powerful than existing methods for the inference of both the topology and logic relations of the Boolean network from observed data.

  9. Delay synchronization of temporal Boolean networks

    Science.gov (United States)

    Wei, Qiang; Xie, Cheng-jun; Liang, Yi; Niu, Yu-jun; Lin, Da

    2016-01-01

    This paper investigates the delay synchronization between two temporal Boolean networks base on semi-tensor product method, which improve complete synchronization. Necessary and sufficient conditions for delay synchronization are drawn base on algebraic expression of temporal Boolean networks. A example is presented to show the effectiveness of theoretical analysis.

  10. Energy and criticality in random Boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Andrecut, M. [Institute for Biocomplexity and Informatics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada)], E-mail: mandrecu@ucalgary.ca; Kauffman, S.A. [Institute for Biocomplexity and Informatics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada)

    2008-06-30

    The central issue of the research on the Random Boolean Networks (RBNs) model is the characterization of the critical transition between ordered and chaotic phases. Here, we discuss an approach based on the 'energy' associated with the unsatisfiability of the Boolean functions in the RBNs model, which provides an upper bound estimation for the energy used in computation. We show that in the ordered phase the RBNs are in a 'dissipative' regime, performing mostly 'downhill' moves on the 'energy' landscape. Also, we show that in the disordered phase the RBNs have to 'hillclimb' on the 'energy' landscape in order to perform computation. The analytical results, obtained using Derrida's approximation method, are in complete agreement with numerical simulations.

  11. optPBN: An Optimisation Toolbox for Probabilistic Boolean Networks

    Science.gov (United States)

    Trairatphisan, Panuwat; Mizera, Andrzej; Pang, Jun; Tantar, Alexandru Adrian; Sauter, Thomas

    2014-01-01

    Background There exist several computational tools which allow for the optimisation and inference of biological networks using a Boolean formalism. Nevertheless, the results from such tools yield only limited quantitative insights into the complexity of biological systems because of the inherited qualitative nature of Boolean networks. Results We introduce optPBN, a Matlab-based toolbox for the optimisation of probabilistic Boolean networks (PBN) which operates under the framework of the BN/PBN toolbox. optPBN offers an easy generation of probabilistic Boolean networks from rule-based Boolean model specification and it allows for flexible measurement data integration from multiple experiments. Subsequently, optPBN generates integrated optimisation problems which can be solved by various optimisers. In term of functionalities, optPBN allows for the construction of a probabilistic Boolean network from a given set of potential constitutive Boolean networks by optimising the selection probabilities for these networks so that the resulting PBN fits experimental data. Furthermore, the optPBN pipeline can also be operated on large-scale computational platforms to solve complex optimisation problems. Apart from exemplary case studies which we correctly inferred the original network, we also successfully applied optPBN to study a large-scale Boolean model of apoptosis where it allows identifying the inverse correlation between UVB irradiation, NFκB and Caspase 3 activations, and apoptosis in primary hepatocytes quantitatively. Also, the results from optPBN help elucidating the relevancy of crosstalk interactions in the apoptotic network. Summary The optPBN toolbox provides a simple yet comprehensive pipeline for integrated optimisation problem generation in the PBN formalism that can readily be solved by various optimisers on local or grid-based computational platforms. optPBN can be further applied to various biological studies such as the inference of gene regulatory

  12. Inference of gene regulatory networks with the strong-inhibition Boolean model

    Energy Technology Data Exchange (ETDEWEB)

    Xia Qinzhi; Liu Lulu; Ye Weiming; Hu Gang, E-mail: ganghu@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)

    2011-08-15

    The inference of gene regulatory networks (GRNs) is an important topic in biology. In this paper, a logic-based algorithm that infers the strong-inhibition Boolean genetic regulatory networks (where regulation by any single repressor can definitely suppress the expression of the gene regulated) from time series is discussed. By properly ordering various computation steps, we derive for the first time explicit formulae for the probabilities at which different interactions can be inferred given a certain number of data. With the formulae, we can predict the precision of reconstructions of regulation networks when the data are insufficient. Numerical simulations coincide well with the analytical results. The method and results are expected to be applicable to a wide range of general dynamic networks, where logic algorithms play essential roles in the network dynamics and the probabilities of various logics can be estimated well.

  13. Synchronization in an array of coupled Boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Li, Rui, E-mail: rui.li@pku.edu.cn [State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871 (China); Chu, Tianguang, E-mail: chutg@pku.edu.cn [State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871 (China)

    2012-10-01

    This Letter presents an analytical study of synchronization in an array of coupled deterministic Boolean networks. A necessary and sufficient criterion for synchronization is established based on algebraic representations of logical dynamics in terms of the semi-tensor product of matrices. Some basic properties of a synchronized array of Boolean networks are then derived for the existence of transient states and the upper bound of the number of fixed points. Particularly, an interesting consequence indicates that a “large” mismatch between two coupled Boolean networks in the array may result in loss of synchrony in the entire system. Examples, including the Boolean model of coupled oscillations in the cell cycle, are given to illustrate the present results. -- Highlights: ► We analytically study synchronization in an array of coupled Boolean networks. ► The study is based on the algebraic representations of logical dynamics. ► A necessary and sufficient algebraic criterion for synchronization is established. ► It reveals some basic properties of a synchronized array of Boolean networks. ► A large mismatch between two coupled networks may result in the loss of synchrony.

  14. Symmetry in critical random Boolean network dynamics

    Science.gov (United States)

    Hossein, Shabnam; Reichl, Matthew D.; Bassler, Kevin E.

    2014-04-01

    Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.

  15. Symmetry in critical random Boolean network dynamics.

    Science.gov (United States)

    Hossein, Shabnam; Reichl, Matthew D; Bassler, Kevin E

    2014-04-01

    Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.

  16. Partial Synchronization of Interconnected Boolean Networks.

    Science.gov (United States)

    Chen, Hongwei; Liang, Jinling; Lu, Jianquan

    2017-01-01

    This paper addresses the partial synchronization problem for the interconnected Boolean networks (BNs) via the semi-tensor product (STP) of matrices. First, based on an algebraic state space representation of BNs, a necessary and sufficient criterion is presented to ensure the partial synchronization of the interconnected BNs. Second, by defining an induced digraph of the partial synchronized states set, an equivalent graphical description for the partial synchronization of the interconnected BNs is established. Consequently, the second partial synchronization criterion is derived in terms of adjacency matrix of the induced digraph. Finally, two examples (including an epigenetic model) are provided to illustrate the efficiency of the obtained results.

  17. Forced synchronization of autonomous dynamical Boolean networks.

    Science.gov (United States)

    Rivera-Durón, R R; Campos-Cantón, E; Campos-Cantón, I; Gauthier, Daniel J

    2015-08-01

    We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics.

  18. Forced synchronization of autonomous dynamical Boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Rivera-Durón, R. R., E-mail: roberto.rivera@ipicyt.edu.mx; Campos-Cantón, E., E-mail: eric.campos@ipicyt.edu.mx [División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica A. C., Camino a la Presa San José 2055, Col. Lomas 4 Sección, C.P. 78216, San Luis Potosí, S.L.P. (Mexico); Campos-Cantón, I. [Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, C.P. 78000, San Luis Potosí, S.L.P. (Mexico); Gauthier, Daniel J. [Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Box 90305, Durham, North Carolina 27708 (United States)

    2015-08-15

    We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics.

  19. Inferring Boolean network states from partial information

    Science.gov (United States)

    2013-01-01

    Networks of molecular interactions regulate key processes in living cells. Therefore, understanding their functionality is a high priority in advancing biological knowledge. Boolean networks are often used to describe cellular networks mathematically and are fitted to experimental datasets. The fitting often results in ambiguities since the interpretation of the measurements is not straightforward and since the data contain noise. In order to facilitate a more reliable mapping between datasets and Boolean networks, we develop an algorithm that infers network trajectories from a dataset distorted by noise. We analyze our algorithm theoretically and demonstrate its accuracy using simulation and microarray expression data. PMID:24006954

  20. The Influence of Canalization on the Robustness of Boolean Networks

    CERN Document Server

    Kadelka, Claus; Laubenbacher, Reinhard

    2016-01-01

    Time- and state-discrete dynamical systems are frequently used to model molecular networks. This paper provides a collection of mathematical and computational tools for the study of robustness in Boolean network models. The focus is on networks governed by $k$-canalizing functions, a recently introduced class of Boolean functions that contains the well-studied class of nested canalizing functions. The activities and sensitivity of a function quantify the impact of input changes on the function output. This paper generalizes the latter concept to $c$-sensitivity and provides formulas for the activities and $c$-sensitivity of general $k$-canalizing functions as well as canalizing functions with more precisely defined structure. A popular measure for the robustness of a network, the Derrida value, can be expressed as a weighted sum of the $c$-sensitivities of the governing canalizing functions, and can also be calculated for a stochastic extension of Boolean networks. These findings provide a computationally eff...

  1. Controllability of asynchronous Boolean multiplex control networks

    Science.gov (United States)

    Luo, Chao; Wang, Xingyuan; Liu, Hong

    2014-09-01

    In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) is studied. First, the model of Boolean multiplex control networks under Harvey' asynchronous update is presented. By means of semi-tensor product approach, the logical dynamics is converted into linear representation, and a generalized formula of control-depending network transition matrices is achieved. Second, a necessary and sufficient condition is proposed to verify that only control-depending fixed points of ABMCNs can be controlled with probability one. Third, using two types of controls, the controllability of system is studied and formulae are given to show: (a) when an initial state is given, the reachable set at time s under a group of specified controls; (b) the reachable set at time s under arbitrary controls; (c) the specific probability values from a given initial state to destination states. Based on the above formulae, an algorithm to calculate overall reachable states from a specified initial state is presented. Moreover, we also discuss an approach to find the particular control sequence which steers the system between two states with maximum probability. Examples are shown to illustrate the feasibility of the proposed scheme.

  2. Controllability of asynchronous Boolean multiplex control networks.

    Science.gov (United States)

    Luo, Chao; Wang, Xingyuan; Liu, Hong

    2014-09-01

    In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) is studied. First, the model of Boolean multiplex control networks under Harvey' asynchronous update is presented. By means of semi-tensor product approach, the logical dynamics is converted into linear representation, and a generalized formula of control-depending network transition matrices is achieved. Second, a necessary and sufficient condition is proposed to verify that only control-depending fixed points of ABMCNs can be controlled with probability one. Third, using two types of controls, the controllability of system is studied and formulae are given to show: (a) when an initial state is given, the reachable set at time s under a group of specified controls; (b) the reachable set at time s under arbitrary controls; (c) the specific probability values from a given initial state to destination states. Based on the above formulae, an algorithm to calculate overall reachable states from a specified initial state is presented. Moreover, we also discuss an approach to find the particular control sequence which steers the system between two states with maximum probability. Examples are shown to illustrate the feasibility of the proposed scheme.

  3. Optimization-Based Approaches to Control of Probabilistic Boolean Networks

    Directory of Open Access Journals (Sweden)

    Koichi Kobayashi

    2017-02-01

    Full Text Available Control of gene regulatory networks is one of the fundamental topics in systems biology. In the last decade, control theory of Boolean networks (BNs, which is well known as a model of gene regulatory networks, has been widely studied. In this review paper, our previously proposed methods on optimal control of probabilistic Boolean networks (PBNs are introduced. First, the outline of PBNs is explained. Next, an optimal control method using polynomial optimization is explained. The finite-time optimal control problem is reduced to a polynomial optimization problem. Furthermore, another finite-time optimal control problem, which can be reduced to an integer programming problem, is also explained.

  4. Reaction-contingency based bipartite Boolean modelling

    Science.gov (United States)

    2013-01-01

    Background Intracellular signalling systems are highly complex, rendering mathematical modelling of large signalling networks infeasible or impractical. Boolean modelling provides one feasible approach to whole-network modelling, but at the cost of dequantification and decontextualisation of activation. That is, these models cannot distinguish between different downstream roles played by the same component activated in different contexts. Results Here, we address this with a bipartite Boolean modelling approach. Briefly, we use a state oriented approach with separate update rules based on reactions and contingencies. This approach retains contextual activation information and distinguishes distinct signals passing through a single component. Furthermore, we integrate this approach in the rxncon framework to support automatic model generation and iterative model definition and validation. We benchmark this method with the previously mapped MAP kinase network in yeast, showing that minor adjustments suffice to produce a functional network description. Conclusions Taken together, we (i) present a bipartite Boolean modelling approach that retains contextual activation information, (ii) provide software support for automatic model generation, visualisation and simulation, and (iii) demonstrate its use for iterative model generation and validation. PMID:23835289

  5. An efficient approach of attractor calculation for large-scale Boolean gene regulatory networks.

    Science.gov (United States)

    He, Qinbin; Xia, Zhile; Lin, Bin

    2016-11-07

    Boolean network models provide an efficient way for studying gene regulatory networks. The main dynamics of a Boolean network is determined by its attractors. Attractor calculation plays a key role for analyzing Boolean gene regulatory networks. An approach of attractor calculation was proposed in this study, which improved the predecessor-based approach. Furthermore, the proposed approach combined with the identification of constant nodes and simplified Boolean networks to accelerate attractor calculation. The proposed algorithm is effective to calculate all attractors for large-scale Boolean gene regulatory networks. If the average degree of the network is not too large, the algorithm can get all attractors of a Boolean network with dozens or even hundreds of nodes.

  6. Symmetry in Critical Random Boolean Networks Dynamics

    Science.gov (United States)

    Bassler, Kevin E.; Hossein, Shabnam

    2014-03-01

    Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used to both greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. Classes of functions occur at the same frequency. These classes are orbits of the controlling symmetry group. We find the nature of the symmetry that controls the dynamics of critical random Boolean networks by determining the frequency of output functions utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using symmetry to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems. This work was supported by the NSF through grants DMR-0908286 and DMR-1206839, and by the AFSOR and DARPA through grant FA9550-12-1-0405.

  7. Mental Models of Boolean Concepts

    Science.gov (United States)

    Goodwin, Geoffrey P.; Johnson-Laird, P. N.

    2011-01-01

    Negation, conjunction, and disjunction are major building blocks in the formation of concepts. This article presents a new model-based theory of these Boolean components. It predicts that individuals simplify the models of instances of concepts. Evidence corroborates the theory and challenges alternative accounts, such as those based on minimal…

  8. Reduction Mappings between Probabilistic Boolean Networks

    Directory of Open Access Journals (Sweden)

    Ivan Ivanov

    2004-01-01

    Full Text Available Probabilistic Boolean networks (PBNs comprise a model describing a directed graph with rule-based dependences between its nodes. The rules are selected, based on a given probability distribution which provides a flexibility when dealing with the uncertainty which is typical for genetic regulatory networks. Given the computational complexity of the model, the characterization of mappings reducing the size of a given PBN becomes a critical issue. Mappings between PBNs are important also from a theoretical point of view. They provide means for developing a better understanding about the dynamics of PBNs. This paper considers two kinds of mappings reduction and projection and their effect on the original probability structure of a given PBN.

  9. An Evaluation of Methods for Inferring Boolean Networks from Time-Series Data.

    Science.gov (United States)

    Berestovsky, Natalie; Nakhleh, Luay

    2013-01-01

    Regulatory networks play a central role in cellular behavior and decision making. Learning these regulatory networks is a major task in biology, and devising computational methods and mathematical models for this task is a major endeavor in bioinformatics. Boolean networks have been used extensively for modeling regulatory networks. In this model, the state of each gene can be either 'on' or 'off' and that next-state of a gene is updated, synchronously or asynchronously, according to a Boolean rule that is applied to the current-state of the entire system. Inferring a Boolean network from a set of experimental data entails two main steps: first, the experimental time-series data are discretized into Boolean trajectories, and then, a Boolean network is learned from these Boolean trajectories. In this paper, we consider three methods for data discretization, including a new one we propose, and three methods for learning Boolean networks, and study the performance of all possible nine combinations on four regulatory systems of varying dynamics complexities. We find that employing the right combination of methods for data discretization and network learning results in Boolean networks that capture the dynamics well and provide predictive power. Our findings are in contrast to a recent survey that placed Boolean networks on the low end of the "faithfulness to biological reality" and "ability to model dynamics" spectra. Further, contrary to the common argument in favor of Boolean networks, we find that a relatively large number of time points in the time-series data is required to learn good Boolean networks for certain data sets. Last but not least, while methods have been proposed for inferring Boolean networks, as discussed above, missing still are publicly available implementations thereof. Here, we make our implementation of the methods available publicly in open source at http://bioinfo.cs.rice.edu/.

  10. Synchronization of coupled large-scale Boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Li, Fangfei, E-mail: li-fangfei@163.com [Department of Mathematics, East China University of Science and Technology, No. 130, Meilong Road, Shanghai, Shanghai 200237 (China)

    2014-03-15

    This paper investigates the complete synchronization and partial synchronization of two large-scale Boolean networks. First, the aggregation algorithm towards large-scale Boolean network is reviewed. Second, the aggregation algorithm is applied to study the complete synchronization and partial synchronization of large-scale Boolean networks. Finally, an illustrative example is presented to show the efficiency of the proposed results.

  11. Synchronization of coupled large-scale Boolean networks

    Science.gov (United States)

    Li, Fangfei

    2014-03-01

    This paper investigates the complete synchronization and partial synchronization of two large-scale Boolean networks. First, the aggregation algorithm towards large-scale Boolean network is reviewed. Second, the aggregation algorithm is applied to study the complete synchronization and partial synchronization of large-scale Boolean networks. Finally, an illustrative example is presented to show the efficiency of the proposed results.

  12. Synchronization in output-coupled temporal Boolean networks

    Science.gov (United States)

    Lu, Jianquan; Zhong, Jie; Tang, Yang; Huang, Tingwen; Cao, Jinde; Kurths, Jürgen

    2014-09-01

    This paper presents an analytical study of synchronization in an array of output-coupled temporal Boolean networks. A temporal Boolean network (TBN) is a logical dynamic system developed to model Boolean networks with regulatory delays. Both state delay and output delay are considered, and these two delays are assumed to be different. By referring to the algebraic representations of logical dynamics and using the semi-tensor product of matrices, the output-coupled TBNs are firstly converted into a discrete-time algebraic evolution system, and then the relationship between the states of coupled TBNs and the initial state sequence is obtained. Then, some necessary and sufficient conditions are derived for the synchronization of an array of TBNs with an arbitrary given initial state sequence. Two numerical examples including one epigenetic model are finally given to illustrate the obtained results.

  13. Probabilistic Boolean Network Modelling and Analysis Framework for mRNA Translation.

    Science.gov (United States)

    Zhao, Yun-Bo; Krishnan, J

    2016-01-01

    mRNA translation is a complex process involving the progression of ribosomes on the mRNA, resulting in the synthesis of proteins, and is subject to multiple layers of regulation. This process has been modelled using different formalisms, both stochastic and deterministic. Recently, we introduced a Probabilistic Boolean modelling framework for mRNA translation, which possesses the advantage of tools for numerically exact computation of steady state probability distribution, without requiring simulation. Here, we extend this model to incorporate both random sequential and parallel update rules, and demonstrate its effectiveness in various settings, including its flexibility in accommodating additional static and dynamic biological complexities and its role in parameter sensitivity analysis. In these applications, the results from the model analysis match those of TASEP model simulations. Importantly, the proposed modelling framework maintains the stochastic aspects of mRNA translation and provides a way to exactly calculate probability distributions, providing additional tools of analysis in this context. Finally, the proposed modelling methodology provides an alternative approach to the understanding of the mRNA translation process, by bridging the gap between existing approaches, providing new analysis tools, and contributing to a more robust platform for modelling and understanding translation.

  14. Model Checking of Boolean Process Models

    CERN Document Server

    Schneider, Christoph

    2011-01-01

    In the field of Business Process Management formal models for the control flow of business processes have been designed since more than 15 years. Which methods are best suited to verify the bulk of these models? The first step is to select a formal language which fixes the semantics of the models. We adopt the language of Boolean systems as reference language for Boolean process models. Boolean systems form a simple subclass of coloured Petri nets. Their characteristics are low tokens to model explicitly states with a subsequent skipping of activations and arbitrary logical rules of type AND, XOR, OR etc. to model the split and join of the control flow. We apply model checking as a verification method for the safeness and liveness of Boolean systems. Model checking of Boolean systems uses the elementary theory of propositional logic, no modal operators are needed. Our verification builds on a finite complete prefix of a certain T-system attached to the Boolean system. It splits the processes of the Boolean sy...

  15. Stability of biological networks as represented in Random Boolean Nets.

    Energy Technology Data Exchange (ETDEWEB)

    Slepoy, Alexander; Thompson, Marshall

    2004-09-01

    We explore stability of Random Boolean Networks as a model of biological interaction networks. We introduce surface-to-volume ratio as a measure of stability of the network. Surface is defined as the set of states within a basin of attraction that maps outside the basin by a bit-flip operation. Volume is defined as the total number of states in the basin. We report development of an object-oriented Boolean network analysis code (Attract) to investigate the structure of stable vs. unstable networks. We find two distinct types of stable networks. The first type is the nearly trivial stable network with a few basins of attraction. The second type contains many basins. We conclude that second type stable networks are extremely rare.

  16. Estimation of delays in generalized asynchronous Boolean networks.

    Science.gov (United States)

    Das, Haimabati; Layek, Ritwik Kumar

    2016-10-20

    A new generalized asynchronous Boolean network (GABN) model has been proposed in this paper. This continuous-time discrete-state model captures the biological reality of cellular dynamics without compromising the computational efficiency of the Boolean framework. The GABN synthesis procedure is based on the prior knowledge of the logical structure of the regulatory network, and the experimental transcriptional parameters. The novelty of the proposed methodology lies in considering different delays associated with the activation and deactivation of a particular protein (especially the transcription factors). A few illustrative examples of some well-studied network motifs have been provided to explore the scope of using the GABN model for larger networks. The GABN model of the p53-signaling pathway in response to γ-irradiation has also been simulated in the current paper to provide an indirect validation of the proposed schema.

  17. Dynamic network-based epistasis analysis: Boolean examples

    Directory of Open Access Journals (Sweden)

    Eugenio eAzpeitia

    2011-12-01

    Full Text Available In this review we focus on how the hierarchical and single-path assumptions of epistasis analysis can bias the topologies of gene interactions infered. This has been acknowledged in several previous papers and reviews, but here we emphasize the critical importance of dynamic analyses, and specifically illustrate the use of Boolean network models. Epistasis in a broad sense refers to gene interactions, however, as originally proposed by Bateson (herein, classical epistasis, defined as the blocking of a particular allelic effect due to the effect of another allele at a different locus. Classical epistasis analysis has proven powerful and useful, allowing researchers to infer and assign directionality to gene interactions. As larger data sets are becoming available, the analysis of classical epistasis is being complemented with computer science tools and system biology approaches. We show that when the hierarchical and single-path assumptions are not met in classical epistasis analysis, the access to relevant information and the correct gene interaction topologies are hindered, and it becomes necessary to consider the temporal dynamics of gene interactions. The use of dynamical networks can overcome these limitations. We particularly focus on the use of Boolean networks that, like classical epistasis analysis, relies on logical formalisms, and hence can complement classical epistasis analysis and relax its assumptions. We develop a couple of theoretical examples and analyze them from a dynamic Boolean network model perspective. Boolean networks could help to guide additional experiments and discern among alternative regulatory schemes that would be impossible or difficult to infer without the elimination of these assumption from the classical epistasis analysis. We also use examples from the literature to show how a Boolean network-based approach has resolved ambiguities and guided epistasis analysis. Our review complements previous accounts, not

  18. Properties of Boolean networks and methods for their tests

    Science.gov (United States)

    2013-01-01

    Transcriptional regulation networks are often modeled as Boolean networks. We discuss certain properties of Boolean functions (BFs), which are considered as important in such networks, namely, membership to the classes of unate or canalizing functions. Of further interest is the average sensitivity (AS) of functions. In this article, we discuss several algorithms to test the properties of interest. To test canalizing properties of functions, we apply spectral techniques, which can also be used to characterize the AS of functions as well as the influences of variables in unate BFs. Further, we provide and review upper and lower bounds on the AS of unate BFs based on the spectral representation. Finally, we apply these methods to a transcriptional regulation network of Escherichia coli, which controls central parts of the E. coli metabolism. We find that all functions are unate. Also the analysis of the AS of the network reveals an exceptional robustness against transient fluctuations of the binary variables.a PMID:23311536

  19. Boolean network representation of contagion dynamics during a financial crisis

    Science.gov (United States)

    Caetano, Marco Antonio Leonel; Yoneyama, Takashi

    2015-01-01

    This work presents a network model for representation of the evolution of certain patterns of economic behavior. More specifically, after representing the agents as points in a space in which each dimension associated to a relevant economic variable, their relative "motions" that can be either stationary or discordant, are coded into a boolean network. Patterns with stationary averages indicate the maintenance of status quo, whereas discordant patterns represent aggregation of new agent into the cluster or departure from the former policies. The changing patterns can be embedded into a network representation, particularly using the concept of autocatalytic boolean networks. As a case study, the economic tendencies of the BRIC countries + Argentina were studied. Although Argentina is not included in the cluster formed by BRIC countries, it tends to follow the BRIC members because of strong commercial ties.

  20. Controllability and observability of Boolean networks arising from biology.

    Science.gov (United States)

    Li, Rui; Yang, Meng; Chu, Tianguang

    2015-02-01

    Boolean networks are currently receiving considerable attention as a computational scheme for system level analysis and modeling of biological systems. Studying control-related problems in Boolean networks may reveal new insights into the intrinsic control in complex biological systems and enable us to develop strategies for manipulating biological systems using exogenous inputs. This paper considers controllability and observability of Boolean biological networks. We propose a new approach, which draws from the rich theory of symbolic computation, to solve the problems. Consequently, simple necessary and sufficient conditions for reachability, controllability, and observability are obtained, and algorithmic tests for controllability and observability which are based on the Gröbner basis method are presented. As practical applications, we apply the proposed approach to several different biological systems, namely, the mammalian cell-cycle network, the T-cell activation network, the large granular lymphocyte survival signaling network, and the Drosophila segment polarity network, gaining novel insights into the control and/or monitoring of the specific biological systems.

  1. Improved Time Complexities for Learning Boolean Networks

    Directory of Open Access Journals (Sweden)

    Chee Keong Kwoh

    2013-09-01

    Full Text Available Existing algorithms for learning Boolean networks (BNs have time complexities of at least O(N · n0:7(k+1, where n is the number of variables, N is the number of samples and k is the number of inputs in Boolean functions. Some recent studies propose more efficient methods with O(N · n2 time complexities. However, these methods can only be used to learn monotonic BNs, and their performances are not satisfactory when the sample size is small. In this paper, we mathematically prove that OR/AND BNs, where the variables are related with logical OR/AND operations, can be found with the time complexity of O(k·(N+ logn·n2, if there are enough noiseless training samples randomly generated from a uniform distribution. We also demonstrate that our method can successfully learn most BNs, whose variables are not related with exclusive OR and Boolean equality operations, with the same order of time complexity for learning OR/AND BNs, indicating our method has good efficiency for learning general BNs other than monotonic BNs. When the datasets are noisy, our method can still successfully identify most BNs with the same efficiency. When compared with two existing methods with the same settings, our method achieves a better comprehensive performance than both of them, especially for small training sample sizes. More importantly, our method can be used to learn all BNs. However, of the two methods that are compared, one can only be used to learn monotonic BNs, and the other one has a much worse time complexity than our method. In conclusion, our results demonstrate that Boolean networks can be learned with improved time complexities.

  2. Algorithms for Finding Small Attractors in Boolean Networks

    Directory of Open Access Journals (Sweden)

    Hayashida Morihiro

    2007-01-01

    Full Text Available A Boolean network is a model used to study the interactions between different genes in genetic regulatory networks. In this paper, we present several algorithms using gene ordering and feedback vertex sets to identify singleton attractors and small attractors in Boolean networks. We analyze the average case time complexities of some of the proposed algorithms. For instance, it is shown that the outdegree-based ordering algorithm for finding singleton attractors works in time for , which is much faster than the naive time algorithm, where is the number of genes and is the maximum indegree. We performed extensive computational experiments on these algorithms, which resulted in good agreement with theoretical results. In contrast, we give a simple and complete proof for showing that finding an attractor with the shortest period is NP-hard.

  3. Control of Large-Scale Boolean Networks via Network Aggregation.

    Science.gov (United States)

    Zhao, Yin; Ghosh, Bijoy K; Cheng, Daizhan

    2016-07-01

    A major challenge to solve problems in control of Boolean networks is that the computational cost increases exponentially when the number of nodes in the network increases. We consider the problem of controllability and stabilizability of Boolean control networks, address the increasing cost problem by partitioning the network graph into several subnetworks, and analyze the subnetworks separately. Easily verifiable necessary conditions for controllability and stabilizability are proposed for a general aggregation structure. For acyclic aggregation, we develop a sufficient condition for stabilizability. It dramatically reduces the computational complexity if the number of nodes in each block of the acyclic aggregation is small enough compared with the number of nodes in the entire Boolean network.

  4. Inference of asynchronous Boolean network from biological pathways.

    Science.gov (United States)

    Das, Haimabati; Layek, Ritwik Kumar

    2015-01-01

    Gene regulation is a complex process with multiple levels of interactions. In order to describe this complex dynamical system with tractable parameterization, the choice of the dynamical system model is of paramount importance. The right abstraction of the modeling scheme can reduce the complexity in the inference and intervention design, both computationally and experimentally. This article proposes an asynchronous Boolean network framework to capture the transcriptional regulation as well as the protein-protein interactions in a genetic regulatory system. The inference of asynchronous Boolean network from biological pathways information and experimental evidence are explained using an algorithm. The suitability of this paradigm for the variability of several reaction rates is also discussed. This methodology and model selection open up new research challenges in understanding gene-protein interactive system in a coherent way and can be beneficial for designing effective therapeutic intervention strategy.

  5. A more robust Boolean model describing inhibitor binding

    Institute of Scientific and Technical Information of China (English)

    Zhaoqian Steven XIE; Chao TANG

    2008-01-01

    From the first application of the Boolean model to the cell cycle regulation network of budding yeast, new regulative pathways have been discovered, par-ticularly in the G1/S transition circuit. This discovery called for finer modeling to study the essential biology, and the resulting outcomes are first introduced in the ar-ticle. A traditional Boolean network model set up for the new G1/S transition circuit shows that it cannot correctly simulate real biology unless the model parameters are fine tuned. The deficiency is caused by an overly coarse-grained description of the inhibitor binding process, which shall be overcome by a two-vector model proposed whose robustness is surveyed using random perturba-tions. Simulations show that the proposed two-vector model is much more robust in describing inhibitor binding processes within the Boolean framework.

  6. A SAT-based algorithm for finding attractors in synchronous Boolean networks.

    Science.gov (United States)

    Dubrova, Elena; Teslenko, Maxim

    2011-01-01

    This paper addresses the problem of finding attractors in synchronous Boolean networks. The existing Boolean decision diagram-based algorithms have limited capacity due to the excessive memory requirements of decision diagrams. The simulation-based algorithms can be applied to larger networks, however, they are incomplete. We present an algorithm, which uses a SAT-based bounded model checking to find all attractors in a Boolean network. The efficiency of the presented algorithm is evaluated by analyzing seven networks models of real biological processes, as well as 150,000 randomly generated Boolean networks of sizes between 100 and 7,000. The results show that our approach has a potential to handle an order of magnitude larger models than currently possible.

  7. Boolean networks with robust and reliable trajectories

    Energy Technology Data Exchange (ETDEWEB)

    Schmal, Christoph; Peixoto, Tiago P; Drossel, Barbara, E-mail: schmal@physik.uni-bielefeld.d, E-mail: tiago@fkp.tu-darmstadt.d, E-mail: drossel@fkp.tu-darmstadt.d [Institut fuer Festkoerperphysik, TU Darmstadt, Hochschulstrasse 6, 64289 Darmstadt (Germany)

    2010-11-15

    We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule and which is also robust against noise. Robustness is quantified as the probability that the dynamics return to the reliable trajectory after a perturbation of the state of a single node. In order to achieve high robustness, we navigate through the space of possible update functions by using an evolutionary algorithm. We constrain the networks to those having the minimum number of connections required to obtain the reliable trajectory. Surprisingly, we find that robustness always reaches values close to 100% during the evolutionary optimization process. The set of update functions can be evolved such that it differs only slightly from that of networks that were not optimized with respect to robustness. The state space of the optimized networks is dominated by the basin of attraction of the reliable trajectory.

  8. On Natural Genetic Engineering: Structural Dynamism in Random Boolean Networks

    CERN Document Server

    Bull, Larry

    2012-01-01

    This short paper presents an abstract, tunable model of genomic structural change within the cell lifecycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include changes in node connectivity based upon the current cell state, e.g., via transposable elements. The underlying behaviour of the resulting dynamical networks is investigated before their evolvability is explored using a version of the NK model of fitness landscapes. Structural dynamism is found to be selected for in non-stationary environments and subsequently shown capable of providing a mechanism for evolutionary innovation when such reorganizations are inherited.

  9. Stabilization of perturbed Boolean network attractors through compensatory interactions

    Science.gov (United States)

    2014-01-01

    Background Understanding and ameliorating the effects of network damage are of significant interest, due in part to the variety of applications in which network damage is relevant. For example, the effects of genetic mutations can cascade through within-cell signaling and regulatory networks and alter the behavior of cells, possibly leading to a wide variety of diseases. The typical approach to mitigating network perturbations is to consider the compensatory activation or deactivation of system components. Here, we propose a complementary approach wherein interactions are instead modified to alter key regulatory functions and prevent the network damage from triggering a deregulatory cascade. Results We implement this approach in a Boolean dynamic framework, which has been shown to effectively model the behavior of biological regulatory and signaling networks. We show that the method can stabilize any single state (e.g., fixed point attractors or time-averaged representations of multi-state attractors) to be an attractor of the repaired network. We show that the approach is minimalistic in that few modifications are required to provide stability to a chosen attractor and specific in that interventions do not have undesired effects on the attractor. We apply the approach to random Boolean networks, and further show that the method can in some cases successfully repair synchronous limit cycles. We also apply the methodology to case studies from drought-induced signaling in plants and T-LGL leukemia and find that it is successful in both stabilizing desired behavior and in eliminating undesired outcomes. Code is made freely available through the software package BooleanNet. Conclusions The methodology introduced in this report offers a complementary way to manipulating node expression levels. A comprehensive approach to evaluating network manipulation should take an "all of the above" perspective; we anticipate that theoretical studies of interaction modification

  10. Networking development by Boolean logic

    Science.gov (United States)

    Tu, Shikui; Pederson, Thoru; Weng, Zhiping

    2013-01-01

    Eric Davidson at Caltech has spent several decades investigating the molecular basis of animal development using the sea urchin embryo as an experimental system1,2 although his scholarship extends to all of embryology as embodied in several editions of his landmark book.3 In recent years his laboratory has become a leading force in constructing gene regulatory networks (GRNs) operating in sea urchin development.4 This axis of his work has its roots in this laboratory’s cDNA cloning of an actin mRNA from the sea urchin embryo (for the timeline, see ref. 1)—one of the first eukaryotic mRNAs to be cloned as it turned out. From that point of departure, the Davidson lab has drilled down into other genes and gene families and the factors that regulate their coordinated regulation, leading them into the GRN era (a field they helped to define) and the development of the computational tools needed to consolidate and advance the GRN field. PMID:23412653

  11. An attractor-based complexity measurement for Boolean recurrent neural networks.

    Directory of Open Access Journals (Sweden)

    Jérémie Cabessa

    Full Text Available We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of ω-automata, and then translating the most refined classification of ω-automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits.

  12. An attractor-based complexity measurement for Boolean recurrent neural networks.

    Science.gov (United States)

    Cabessa, Jérémie; Villa, Alessandro E P

    2014-01-01

    We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of ω-automata, and then translating the most refined classification of ω-automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits.

  13. Effect of memory in non-Markovian Boolean networks illustrated with a case study: A cell cycling process

    Science.gov (United States)

    Ebadi, H.; Saeedian, M.; Ausloos, M.; Jafari, G. R.

    2016-11-01

    The Boolean network is one successful model to investigate discrete complex systems such as the gene interacting phenomenon. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self-organizing features of biological phenomena and their intelligent nature should raise some doubt about ignoring the history of their time evolution. Here, we extend the Boolean network Markovian approach: we involve the effect of memory on the dynamics. This can be explored by modifying Boolean functions into non-Markovian functions, for example, by investigating the usual non-Markovian threshold function —one of the most applied Boolean functions. By applying the non-Markovian threshold function on the dynamical process of the yeast cell cycle network, we discover a power-law-like memory with a more robust dynamics than the Markovian dynamics.

  14. A parallel attractor-finding algorithm based on Boolean satisfiability for genetic regulatory networks.

    Directory of Open Access Journals (Sweden)

    Wensheng Guo

    Full Text Available In biological systems, the dynamic analysis method has gained increasing attention in the past decade. The Boolean network is the most common model of a genetic regulatory network. The interactions of activation and inhibition in the genetic regulatory network are modeled as a set of functions of the Boolean network, while the state transitions in the Boolean network reflect the dynamic property of a genetic regulatory network. A difficult problem for state transition analysis is the finding of attractors. In this paper, we modeled the genetic regulatory network as a Boolean network and proposed a solving algorithm to tackle the attractor finding problem. In the proposed algorithm, we partitioned the Boolean network into several blocks consisting of the strongly connected components according to their gradients, and defined the connection between blocks as decision node. Based on the solutions calculated on the decision nodes and using a satisfiability solving algorithm, we identified the attractors in the state transition graph of each block. The proposed algorithm is benchmarked on a variety of genetic regulatory networks. Compared with existing algorithms, it achieved similar performance on small test cases, and outperformed it on larger and more complex ones, which happens to be the trend of the modern genetic regulatory network. Furthermore, while the existing satisfiability-based algorithms cannot be parallelized due to their inherent algorithm design, the proposed algorithm exhibits a good scalability on parallel computing architectures.

  15. A parallel attractor-finding algorithm based on Boolean satisfiability for genetic regulatory networks.

    Science.gov (United States)

    Guo, Wensheng; Yang, Guowu; Wu, Wei; He, Lei; Sun, Mingyu

    2014-01-01

    In biological systems, the dynamic analysis method has gained increasing attention in the past decade. The Boolean network is the most common model of a genetic regulatory network. The interactions of activation and inhibition in the genetic regulatory network are modeled as a set of functions of the Boolean network, while the state transitions in the Boolean network reflect the dynamic property of a genetic regulatory network. A difficult problem for state transition analysis is the finding of attractors. In this paper, we modeled the genetic regulatory network as a Boolean network and proposed a solving algorithm to tackle the attractor finding problem. In the proposed algorithm, we partitioned the Boolean network into several blocks consisting of the strongly connected components according to their gradients, and defined the connection between blocks as decision node. Based on the solutions calculated on the decision nodes and using a satisfiability solving algorithm, we identified the attractors in the state transition graph of each block. The proposed algorithm is benchmarked on a variety of genetic regulatory networks. Compared with existing algorithms, it achieved similar performance on small test cases, and outperformed it on larger and more complex ones, which happens to be the trend of the modern genetic regulatory network. Furthermore, while the existing satisfiability-based algorithms cannot be parallelized due to their inherent algorithm design, the proposed algorithm exhibits a good scalability on parallel computing architectures.

  16. Synchronization of Arbitrarily Switched Boolean Networks.

    Science.gov (United States)

    Chen, Hongwei; Liang, Jinling; Huang, Tingwen; Cao, Jinde

    2017-03-01

    This paper investigates the complete synchronization problem for the drive-response switched Boolean networks (SBNs) under arbitrary switching signals, where the switching signals of the response SBN follow those generated by the drive SBN at each time instant. First, the definition of complete synchronization is introduced for the drive-response SBNs under arbitrary switching signals. Second, the concept of switching reachable set starting from a given initial state set is put forward. Based on it, a necessary and sufficient condition is derived for the complete synchronization of the drive-response SBNs. Last, we give a simple algebraic expression for the switching reachable set in a given number of time steps, and two computable algebraic criteria are obtained for the complete synchronization of the SBNs. A biological example is given to demonstrate the effectiveness of the obtained main results.

  17. Adaptive Local Information Transfer in Random Boolean Networks.

    Science.gov (United States)

    Haruna, Taichi

    2017-01-01

    Living systems such as gene regulatory networks and neuronal networks have been supposed to work close to dynamical criticality, where their information-processing ability is optimal at the whole-system level. We investigate how this global information-processing optimality is related to the local information transfer at each individual-unit level. In particular, we introduce an internal adjustment process of the local information transfer and examine whether the former can emerge from the latter. We propose an adaptive random Boolean network model in which each unit rewires its incoming arcs from other units to balance stability of its information processing based on the measurement of the local information transfer pattern. First, we show numerically that random Boolean networks can self-organize toward near dynamical criticality in our model. Second, the proposed model is analyzed by a mean-field theory. We recognize that the rewiring rule has a bootstrapping feature. The stationary indegree distribution is calculated semi-analytically and is shown to be close to dynamical criticality in a broad range of model parameter values.

  18. Perturbation propagation in random and evolved Boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Fretter, Christoph [Instistut fuer Informatik, Martin-Luther-Universitaet Halle-Wittenberg, Von-Seckendorffplatz 1, 06120 Halle (Germany); Szejka, Agnes; Drossel, Barbara [Institut fuer Festkoerperphysik, Technische Universitaet Darmstadt, Hochschulstrasse 6, 64289 Darmstadt (Germany)], E-mail: Christoph.Fretter@informatik.uni-halle.de

    2009-03-15

    In this paper, we investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and its modifications. We show that even small random Boolean networks agree well with the predictions of the annealed approximation, but nonrandom networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conclusion is that the simple distinction between frozen, critical and chaotic networks is no longer useful, since such evolved networks can display the properties of all three types of networks. Furthermore, we evaluate a simplified empirical network and show how its specific state space properties are reflected in the modified Derrida plots.

  19. EXACT SIMULATION OF A BOOLEAN MODEL

    Directory of Open Access Journals (Sweden)

    Christian Lantuéjoul

    2013-06-01

    Full Text Available A Boolean model is a union of independent objects (compact random subsets located at Poisson points. Two algorithms are proposed for simulating a Boolean model in a bounded domain. The first one applies only to stationary models. It generates the objects prior to their Poisson locations. Two examples illustrate its applicability. The second algorithm applies to stationary and non-stationary models. It generates the Poisson points prior to the objects. Its practical difficulties of implementation are discussed. Both algorithms are based on importance sampling techniques, and the generated objects are weighted.

  20. Towards a theory of modelling with Boolean automata networks - I. Theorisation and observations

    CERN Document Server

    Noual, Mathilde

    2011-01-01

    Although models are built on the basis of some observations of reality, the concepts that derive theoretically from their definitions as well as from their characteristics and properties are not necessarily direct consequences of these initial observations. Indeed, many of them rather follow from chains of theoretical inferences that are only based on the precise model definitions and rely strongly, in addition, on some consequential working hypotheses. Thus, it is important to address the question of which features of a model effectively carry some modelling meaning and which only result from the task of formalising observations of reality into a mathematical language. In this article, we address this question with a theoretical point view that sets our discussion strictly between the two stages of the modelling process that require knowledge of real systems, that is, between the initial stage that chooses a global theoretical framework to build the model and the final stage that exploits its formal predicti...

  1. Control of random Boolean networks via average sensitivity of Boolean functions

    Institute of Scientific and Technical Information of China (English)

    Chen Shi-Jian; Hong Yi-Guang

    2011-01-01

    In this paper, we discuss how to transform the disordered phase into an ordered phase in random Boolean networks. To increase the effectiveness, a control scheme is proposed, which periodically freezes a fraction of the network based on the average sensitivity of Boolean functions of the nodes. Theoretical analysis is carried out to estimate the expected critical value of the fraction, and shows that the critical value is reduced using this scheme compared to that of randomly freezing a fraction of the nodes. Finally, the simulation is given for illustrating the effectiveness of the proposed method.

  2. On the robustness of NK-Kauffman networks against changes in their connections and Boolean functions

    Science.gov (United States)

    Zertuche, Federico

    2009-04-01

    NK-Kauffman networks LKN are a subset of the Boolean functions on N Boolean variables to themselves, ΛN={ξ :Z2N→Z2N}. To each NK-Kauffman network it is possible to assign a unique Boolean function on N variables through the function Ψ :LKN→ΛN. The probability PK that Ψ(f )=Ψ(f'), when f' is obtained through f by a change in one of its K-Boolean functions (bK:Z2K→Z2), and/or connections, is calculated. The leading term of the asymptotic expansion of PK, for N ≫1, turns out to depend on the probability to extract the tautology and contradiction Boolean functions, and in the average value of the distribution of probability of the Boolean functions, the other terms decay as O(1/N). In order to accomplish this, a classification of the Boolean functions in terms of what I have called their irreducible degree of connectivity is established. The mathematical findings are discussed in the biological context, where Ψ is used to model the genotype-phenotype map.

  3. Control of Boolean networks: hardness results and algorithms for tree structured networks.

    Science.gov (United States)

    Akutsu, Tatsuya; Hayashida, Morihiro; Ching, Wai-Ki; Ng, Michael K

    2007-02-21

    Finding control strategies of cells is a challenging and important problem in the post-genomic era. This paper considers theoretical aspects of the control problem using the Boolean network (BN), which is a simplified model of genetic networks. It is shown that finding a control strategy leading to the desired global state is computationally intractable (NP-hard) in general. Furthermore, this hardness result is extended for BNs with considerably restricted network structures. These results justify existing exponential time algorithms for finding control strategies for probabilistic Boolean networks (PBNs). On the other hand, this paper shows that the control problem can be solved in polynomial time if the network has a tree structure. Then, this algorithm is extended for the case where the network has a few loops and the number of time steps is small. Though this paper focuses on theoretical aspects, biological implications of the theoretical results are also discussed.

  4. Stability depends on positive autoregulation in Boolean gene regulatory networks.

    Directory of Open Access Journals (Sweden)

    Ricardo Pinho

    2014-11-01

    Full Text Available Network motifs have been identified as building blocks of regulatory networks, including gene regulatory networks (GRNs. The most basic motif, autoregulation, has been associated with bistability (when positive and with homeostasis and robustness to noise (when negative, but its general importance in network behavior is poorly understood. Moreover, how specific autoregulatory motifs are selected during evolution and how this relates to robustness is largely unknown. Here, we used a class of GRN models, Boolean networks, to investigate the relationship between autoregulation and network stability and robustness under various conditions. We ran evolutionary simulation experiments for different models of selection, including mutation and recombination. Each generation simulated the development of a population of organisms modeled by GRNs. We found that stability and robustness positively correlate with autoregulation; in all investigated scenarios, stable networks had mostly positive autoregulation. Assuming biological networks correspond to stable networks, these results suggest that biological networks should often be dominated by positive autoregulatory loops. This seems to be the case for most studied eukaryotic transcription factor networks, including those in yeast, flies and mammals.

  5. Stability Depends on Positive Autoregulation in Boolean Gene Regulatory Networks

    Science.gov (United States)

    Pinho, Ricardo; Garcia, Victor; Irimia, Manuel; Feldman, Marcus W.

    2014-01-01

    Network motifs have been identified as building blocks of regulatory networks, including gene regulatory networks (GRNs). The most basic motif, autoregulation, has been associated with bistability (when positive) and with homeostasis and robustness to noise (when negative), but its general importance in network behavior is poorly understood. Moreover, how specific autoregulatory motifs are selected during evolution and how this relates to robustness is largely unknown. Here, we used a class of GRN models, Boolean networks, to investigate the relationship between autoregulation and network stability and robustness under various conditions. We ran evolutionary simulation experiments for different models of selection, including mutation and recombination. Each generation simulated the development of a population of organisms modeled by GRNs. We found that stability and robustness positively correlate with autoregulation; in all investigated scenarios, stable networks had mostly positive autoregulation. Assuming biological networks correspond to stable networks, these results suggest that biological networks should often be dominated by positive autoregulatory loops. This seems to be the case for most studied eukaryotic transcription factor networks, including those in yeast, flies and mammals. PMID:25375153

  6. Polynomial-Time Algorithm for Controllability Test of a Class of Boolean Biological Networks

    Directory of Open Access Journals (Sweden)

    Koichi Kobayashi

    2010-01-01

    Full Text Available In recent years, Boolean-network-model-based approaches to dynamical analysis of complex biological networks such as gene regulatory networks have been extensively studied. One of the fundamental problems in control theory of such networks is the problem of determining whether a given substance quantity can be arbitrarily controlled by operating the other substance quantities, which we call the controllability problem. This paper proposes a polynomial-time algorithm for solving this problem. Although the algorithm is based on a sufficient condition for controllability, it is easily computable for a wider class of large-scale biological networks compared with the existing approaches. A key to this success in our approach is to give up computing Boolean operations in a rigorous way and to exploit an adjacency matrix of a directed graph induced by a Boolean network. By applying the proposed approach to a neurotransmitter signaling pathway, it is shown that it is effective.

  7. Using Boolean Logic Modeling of Gene Regulatory Networks to Exploit the Links Between Cancer and Metabolism for Therapeutic Purposes.

    Science.gov (United States)

    Arshad, Osama A; Venkatasubramani, Priyadharshini S; Datta, Aniruddha; Venkatraj, Jijayanagaram

    2016-01-01

    The uncontrolled cell proliferation that is characteristically associated with cancer is usually accompanied by alterations in the genome and cell metabolism. Indeed, the phenomenon of cancer cells metabolizing glucose using a less efficient anaerobic process even in the presence of normal oxygen levels, termed the Warburg effect, is currently considered to be one of the hallmarks of cancer. Diabetes, much like cancer, is defined by significant metabolic changes. Recent epidemiological studies have shown that diabetes patients treated with the antidiabetic drug Metformin have significantly lowered risk of cancer as compared to patients treated with other antidiabetic drugs. We utilize a Boolean logic model of the pathways commonly mutated in cancer to not only investigate the efficacy of Metformin for cancer therapeutic purposes but also demonstrate how Metformin in concert with other cancer drugs could provide better and less toxic clinical outcomes as compared to using cancer drugs alone.

  8. Predicting Variabilities in Cardiac Gene Expression with a Boolean Network Incorporating Uncertainty.

    Science.gov (United States)

    Grieb, Melanie; Burkovski, Andre; Sträng, J Eric; Kraus, Johann M; Groß, Alexander; Palm, Günther; Kühl, Michael; Kestler, Hans A

    2015-01-01

    Gene interactions in cells can be represented by gene regulatory networks. A Boolean network models gene interactions according to rules where gene expression is represented by binary values (on / off or {1, 0}). In reality, however, the gene's state can have multiple values due to biological properties. Furthermore, the noisy nature of the experimental design results in uncertainty about a state of the gene. Here we present a new Boolean network paradigm to allow intermediate values on the interval [0, 1]. As in the Boolean network, fixed points or attractors of such a model correspond to biological phenotypes or states. We use our new extension of the Boolean network paradigm to model gene expression in first and second heart field lineages which are cardiac progenitor cell populations involved in early vertebrate heart development. By this we are able to predict additional biological phenotypes that the Boolean model alone is not able to identify without utilizing additional biological knowledge. The additional phenotypes predicted by the model were confirmed by published biological experiments. Furthermore, the new method predicts gene expression propensities for modelled but yet to be analyzed genes.

  9. Evolution and Controllability of Cancer Networks: A Boolean Perspective.

    Science.gov (United States)

    Srihari, Sriganesh; Raman, Venkatesh; Leong, Hon Wai; Ragan, Mark A

    2014-01-01

    Cancer forms a robust system capable of maintaining stable functioning (cell sustenance and proliferation) despite perturbations. Cancer progresses as stages over time typically with increasing aggressiveness and worsening prognosis. Characterizing these stages and identifying the genes driving transitions between them is critical to understand cancer progression and to develop effective anti-cancer therapies. In this work, we propose a novel model for the `cancer system' as a Boolean state space in which a Boolean network, built from protein-interaction and gene-expression data from different stages of cancer, transits between Boolean satisfiability states by "editing" interactions and "flipping" genes. Edits reflect rewiring of the PPI network while flipping of genes reflect activation or silencing of genes between stages. We formulate a minimization problem min flip to identify these genes driving the transitions. The application of our model (called BoolSpace) on three case studies-pancreatic and breast tumours in human and post spinal-cord injury (SCI) in rats-reveals valuable insights into the phenomenon of cancer progression: (i) interactions involved in core cell-cycle and DNA-damage repair pathways are significantly rewired in tumours, indicating significant impact to key genome-stabilizing mechanisms; (ii) several of the genes flipped are serine/threonine kinases which act as biological switches, reflecting cellular switching mechanisms between stages; and (iii) different sets of genes are flipped during the initial and final stages indicating a pattern to tumour progression. Based on these results, we hypothesize that robustness of cancer partly stems from "passing of the baton" between genes at different stages-genes from different biological processes and/or cellular components are involved in different stages of tumour progression thereby allowing tumour cells to evade targeted therapy, and therefore an effective therapy should target a "cover set" of

  10. ILP/SMT-Based Method for Design of Boolean Networks Based on Singleton Attractors.

    Science.gov (United States)

    Kobayashi, Koichi; Hiraishi, Kunihiko

    2014-01-01

    Attractors in gene regulatory networks represent cell types or states of cells. In system biology and synthetic biology, it is important to generate gene regulatory networks with desired attractors. In this paper, we focus on a singleton attractor, which is also called a fixed point. Using a Boolean network (BN) model, we consider the problem of finding Boolean functions such that the system has desired singleton attractors and has no undesired singleton attractors. To solve this problem, we propose a matrix-based representation of BNs. Using this representation, the problem of finding Boolean functions can be rewritten as an Integer Linear Programming (ILP) problem and a Satisfiability Modulo Theories (SMT) problem. Furthermore, the effectiveness of the proposed method is shown by a numerical example on a WNT5A network, which is related to melanoma. The proposed method provides us a basic method for design of gene regulatory networks.

  11. An optimal control approach to probabilistic Boolean networks

    Science.gov (United States)

    Liu, Qiuli

    2012-12-01

    External control of some genes in a genetic regulatory network is useful for avoiding undesirable states associated with some diseases. For this purpose, a number of stochastic optimal control approaches have been proposed. Probabilistic Boolean networks (PBNs) as powerful tools for modeling gene regulatory systems have attracted considerable attention in systems biology. In this paper, we deal with a problem of optimal intervention in a PBN with the help of the theory of discrete time Markov decision process. Specifically, we first formulate a control model for a PBN as a first passage model for discrete time Markov decision processes and then find, using a value iteration algorithm, optimal effective treatments with the minimal expected first passage time over the space of all possible treatments. In order to demonstrate the feasibility of our approach, an example is also displayed.

  12. Controllability of Boolean networks via input controls under Harvey's update scheme

    Science.gov (United States)

    Luo, Chao; Zhang, Xiaolin; Shao, Rui; Zheng, YuanJie

    2016-02-01

    In this article, the controllability of Boolean networks via input controls under Harvey's update scheme is investigated. First, the model of Boolean control networks under Harvey's stochastic update is proposed, by means of semi-tensor product approach, which is converted into discrete-time linear representation. And, a general formula of control-depending network transition matrix is provided. Second, based on discrete-time dynamics, controllability of the proposed model is analytically discussed by revealing the necessary and sufficient conditions of the reachable sets, respectively, for three kinds of controls, i.e., free Boolean control sequence, input control networks, and close-loop control. Examples are showed to demonstrate the effectiveness and feasibility of the proposed scheme.

  13. Controllability of Boolean networks via input controls under Harvey's update scheme.

    Science.gov (United States)

    Luo, Chao; Zhang, Xiaolin; Shao, Rui; Zheng, YuanJie

    2016-02-01

    In this article, the controllability of Boolean networks via input controls under Harvey's update scheme is investigated. First, the model of Boolean control networks under Harvey's stochastic update is proposed, by means of semi-tensor product approach, which is converted into discrete-time linear representation. And, a general formula of control-depending network transition matrix is provided. Second, based on discrete-time dynamics, controllability of the proposed model is analytically discussed by revealing the necessary and sufficient conditions of the reachable sets, respectively, for three kinds of controls, i.e., free Boolean control sequence, input control networks, and close-loop control. Examples are showed to demonstrate the effectiveness and feasibility of the proposed scheme.

  14. Finite size effects and symmetry breaking in the evolution of networks of competing Boolean nodes

    Energy Technology Data Exchange (ETDEWEB)

    Liu, M; Bassler, K E, E-mail: bassler@uh.edu [Department of Physics, University of Houston, 617 Science and Research 1, Houston, TX 77204-5005 (United States)

    2011-01-28

    Finite size effects on the evolutionary dynamics of Boolean networks are analyzed. In the model considered, Boolean networks evolve via a competition between nodes that punishes those in the majority. Previous studies have found that large networks evolve to a statistical steady state that is both critical and highly canalized, and that the evolution of canalization, which is a form of robustness found in genetic regulatory networks, is associated with a particular symmetry of the evolutionary dynamics. Here, it is found that finite size networks evolve in a fundamentally different way than infinitely large networks do. The symmetry of the evolutionary dynamics of infinitely large networks that selects for canalizing Boolean functions is broken in the evolutionary dynamics of finite size networks. In finite size networks, there is an additional selection for input-inverting Boolean functions that output a value opposite to the majority of input values. The reason for the symmetry breaking in the evolutionary dynamics is found to be due to the need for nodes in finite size networks to behave differently in order to cooperate so that the system collectively performs as efficiently as possible. The results suggest that both finite size effects and symmetry are fundamental for understanding the evolution of real-world complex networks, including genetic regulatory networks.

  15. Simulating Quantitative Cellular Responses Using Asynchronous Threshold Boolean Network Ensembles

    Directory of Open Access Journals (Sweden)

    Shah Imran

    2011-07-01

    Full Text Available Abstract Background With increasing knowledge about the potential mechanisms underlying cellular functions, it is becoming feasible to predict the response of biological systems to genetic and environmental perturbations. Due to the lack of homogeneity in living tissues it is difficult to estimate the physiological effect of chemicals, including potential toxicity. Here we investigate a biologically motivated model for estimating tissue level responses by aggregating the behavior of a cell population. We assume that the molecular state of individual cells is independently governed by discrete non-deterministic signaling mechanisms. This results in noisy but highly reproducible aggregate level responses that are consistent with experimental data. Results We developed an asynchronous threshold Boolean network simulation algorithm to model signal transduction in a single cell, and then used an ensemble of these models to estimate the aggregate response across a cell population. Using published data, we derived a putative crosstalk network involving growth factors and cytokines - i.e., Epidermal Growth Factor, Insulin, Insulin like Growth Factor Type 1, and Tumor Necrosis Factor α - to describe early signaling events in cell proliferation signal transduction. Reproducibility of the modeling technique across ensembles of Boolean networks representing cell populations is investigated. Furthermore, we compare our simulation results to experimental observations of hepatocytes reported in the literature. Conclusion A systematic analysis of the results following differential stimulation of this model by growth factors and cytokines suggests that: (a using Boolean network ensembles with asynchronous updating provides biologically plausible noisy individual cellular responses with reproducible mean behavior for large cell populations, and (b with sufficient data our model can estimate the response to different concentrations of extracellular ligands. Our

  16. Broad edge of chaos in strongly heterogeneous Boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Deok-Sun [Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115 (United States); Rieger, Heiko [Theoretische Physik, Universitaet des Saarlandes, 66041 Saarbruecken (Germany)

    2008-10-17

    The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations. This turns out to behave in a universal way close to the phase boundary only for in-degree distributions with a finite second moment. In-degree distributions of the form P{sub d}(k) {approx} k{sup -{gamma}} with 2 < {gamma} < 3, thus having a diverging second moment, lead to a slower increase of the Hamming distance when moving towards the unstable phase and to a broadening of the phase boundary for finite N with decreasing {gamma}. We conclude that the heterogeneous regulatory network connectivity facilitates the balancing between robustness and evolvability in living organisms.

  17. Recent development and biomedical applications of probabilistic Boolean networks

    Science.gov (United States)

    2013-01-01

    Probabilistic Boolean network (PBN) modelling is a semi-quantitative approach widely used for the study of the topology and dynamic aspects of biological systems. The combined use of rule-based representation and probability makes PBN appealing for large-scale modelling of biological networks where degrees of uncertainty need to be considered. A considerable expansion of our knowledge in the field of theoretical research on PBN can be observed over the past few years, with a focus on network inference, network intervention and control. With respect to areas of applications, PBN is mainly used for the study of gene regulatory networks though with an increasing emergence in signal transduction, metabolic, and also physiological networks. At the same time, a number of computational tools, facilitating the modelling and analysis of PBNs, are continuously developed. A concise yet comprehensive review of the state-of-the-art on PBN modelling is offered in this article, including a comparative discussion on PBN versus similar models with respect to concepts and biomedical applications. Due to their many advantages, we consider PBN to stand as a suitable modelling framework for the description and analysis of complex biological systems, ranging from molecular to physiological levels. PMID:23815817

  18. Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence

    Directory of Open Access Journals (Sweden)

    Le Yu

    2007-05-01

    Full Text Available The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation is that the characteristics of a single Boolean network without perturbation may be determined by its pairwise transitions. Because the network function is fixed and there are no perturbations, a given state will always be followed by a unique state at the succeeding time point. Thus, a transition counting matrix compiled over a data sequence will be sparse and contain only one entry per line. If the network also has perturbations, with small perturbation probability, then the transition counting matrix would have some insignificant nonzero entries replacing some (or all of the zeros. If a data sequence is sufficiently long to adequately populate the matrix, then determination of the functions and inputs underlying the model is straightforward. The difficulty comes when the transition counting matrix consists of data derived from more than one Boolean network. We address the PBN inference procedure in several steps: (1 separate the data sequence into “pure” subsequences corresponding to constituent Boolean networks; (2 given a subsequence, infer a Boolean network; and (3 infer the probabilities of perturbation, the probability of there being a switch between constituent Boolean networks, and the selection probabilities governing which network is to be selected given a switch. Capturing the full dynamic behavior of probabilistic Boolean networks, be they binary or multivalued, will require the use of temporal data, and a great deal of it. This should not be surprising given the complexity of the model and the number of parameters, both transitional and static, that must be estimated. In addition to providing an inference algorithm

  19. Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence

    Directory of Open Access Journals (Sweden)

    Xiao Yufei

    2007-01-01

    Full Text Available The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation is that the characteristics of a single Boolean network without perturbation may be determined by its pairwise transitions. Because the network function is fixed and there are no perturbations, a given state will always be followed by a unique state at the succeeding time point. Thus, a transition counting matrix compiled over a data sequence will be sparse and contain only one entry per line. If the network also has perturbations, with small perturbation probability, then the transition counting matrix would have some insignificant nonzero entries replacing some (or all of the zeros. If a data sequence is sufficiently long to adequately populate the matrix, then determination of the functions and inputs underlying the model is straightforward. The difficulty comes when the transition counting matrix consists of data derived from more than one Boolean network. We address the PBN inference procedure in several steps: (1 separate the data sequence into "pure" subsequences corresponding to constituent Boolean networks; (2 given a subsequence, infer a Boolean network; and (3 infer the probabilities of perturbation, the probability of there being a switch between constituent Boolean networks, and the selection probabilities governing which network is to be selected given a switch. Capturing the full dynamic behavior of probabilistic Boolean networks, be they binary or multivalued, will require the use of temporal data, and a great deal of it. This should not be surprising given the complexity of the model and the number of parameters, both transitional and static, that must be estimated. In addition to providing an inference algorithm, this paper

  20. An in silico target identification using Boolean network attractors: Avoiding pathological phenotypes.

    Science.gov (United States)

    Poret, Arnaud; Boissel, Jean-Pierre

    2014-12-01

    Target identification aims at identifying biomolecules whose function should be therapeutically altered to cure the considered pathology. An algorithm for in silico target identification using Boolean network attractors is proposed. It assumes that attractors correspond to phenotypes produced by the modeled biological network. It identifies target combinations which allow disturbed networks to avoid attractors associated with pathological phenotypes. The algorithm is tested on a Boolean model of the mammalian cell cycle and its applications are illustrated on a Boolean model of Fanconi anemia. Results show that the algorithm returns target combinations able to remove attractors associated with pathological phenotypes and then succeeds in performing the proposed in silico target identification. However, as with any in silico evidence, there is a bridge to cross between theory and practice. Nevertheless, it is expected that the algorithm is of interest for target identification.

  1. Boolean Chaos

    OpenAIRE

    Zhang, Rui; Cavalcante, Hugo L. D. de S.; Gao, Zheng; Gauthier, Daniel J.; Socolar, Joshua E. S.; Adams, Matthew M.; Lathrop, Daniel P.

    2009-01-01

    We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may fin...

  2. Estimation for the simple linear Boolean model

    OpenAIRE

    2006-01-01

    We consider the simple linear Boolean model, a fundamental coverage process also known as the Markov/General/infinity queue. In the model, line segments of independent and identically distributed length are located at the points of a Poisson process. The segments may overlap, resulting in a pattern of "clumps"-regions of the line that are covered by one or more segments-alternating with uncovered regions or "spacings". Study and application of the model have been impeded by the difficult...

  3. Boolean Models of Biological Processes Explain Cascade-Like Behavior.

    Science.gov (United States)

    Chen, Hao; Wang, Guanyu; Simha, Rahul; Du, Chenghang; Zeng, Chen

    2016-01-29

    Biological networks play a key role in determining biological function and therefore, an understanding of their structure and dynamics is of central interest in systems biology. In Boolean models of such networks, the status of each molecule is either "on" or "off" and along with the molecules interact with each other, their individual status changes from "on" to "off" or vice-versa and the system of molecules in the network collectively go through a sequence of changes in state. This sequence of changes is termed a biological process. In this paper, we examine the common perception that events in biomolecular networks occur sequentially, in a cascade-like manner, and ask whether this is likely to be an inherent property. In further investigations of the budding and fission yeast cell-cycle, we identify two generic dynamical rules. A Boolean system that complies with these rules will automatically have a certain robustness. By considering the biological requirements in robustness and designability, we show that those Boolean dynamical systems, compared to an arbitrary dynamical system, statistically present the characteristics of cascadeness and sequentiality, as observed in the budding and fission yeast cell- cycle. These results suggest that cascade-like behavior might be an intrinsic property of biological processes.

  4. Boolean network identification from perturbation time series data combining dynamics abstraction and logic programming.

    Science.gov (United States)

    Ostrowski, M; Paulevé, L; Schaub, T; Siegel, A; Guziolowski, C

    2016-11-01

    Boolean networks (and more general logic models) are useful frameworks to study signal transduction across multiple pathways. Logic models can be learned from a prior knowledge network structure and multiplex phosphoproteomics data. However, most efficient and scalable training methods focus on the comparison of two time-points and assume that the system has reached an early steady state. In this paper, we generalize such a learning procedure to take into account the time series traces of phosphoproteomics data in order to discriminate Boolean networks according to their transient dynamics. To that end, we identify a necessary condition that must be satisfied by the dynamics of a Boolean network to be consistent with a discretized time series trace. Based on this condition, we use Answer Set Programming to compute an over-approximation of the set of Boolean networks which fit best with experimental data and provide the corresponding encodings. Combined with model-checking approaches, we end up with a global learning algorithm. Our approach is able to learn logic models with a true positive rate higher than 78% in two case studies of mammalian signaling networks; for a larger case study, our method provides optimal answers after 7min of computation. We quantified the gain in our method predictions precision compared to learning approaches based on static data. Finally, as an application, our method proposes erroneous time-points in the time series data with respect to the optimal learned logic models.

  5. Complex network analysis of state spaces for random Boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Shreim, Amer [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Berdahl, Andrew [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Sood, Vishal [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Grassberger, Peter [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Paczuski, Maya [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada)

    2008-01-15

    We apply complex network analysis to the state spaces of random Boolean networks (RBNs). An RBN contains N Boolean elements each with K inputs. A directed state space network (SSN) is constructed by linking each dynamical state, represented as a node, to its temporal successor. We study the heterogeneity of these SSNs at both local and global scales, as well as sample to-sample fluctuations within an ensemble of SSNs. We use in-degrees of nodes as a local topological measure, and the path diversity (Shreim A et al 2007 Phys. Rev. Lett. 98 198701) of an SSN as a global topological measure. RBNs with 2 {<=} K {<=} 5 exhibit non-trivial fluctuations at both local and global scales, while K = 2 exhibits the largest sample-to-sample (possibly non-self-averaging) fluctuations. We interpret the observed 'multi scale' fluctuations in the SSNs as indicative of the criticality and complexity of K = 2 RBNs. 'Garden of Eden' (GoE) states are nodes on an SSN that have in-degree zero. While in-degrees of non-GoE nodes for K > 1 SSNs can assume any integer value between 0 and 2{sup N}, for K = 1 all the non-GoE nodes in a given SSN have the same in-degree which is always a power of two.

  6. Identifying a Probabilistic Boolean Threshold Network From Samples.

    Science.gov (United States)

    Melkman, Avraham A; Cheng, Xiaoqing; Ching, Wai-Ki; Akutsu, Tatsuya

    2017-01-25

    This paper studies the problem of exactly identifying the structure of a probabilistic Boolean network (PBN) from a given set of samples, where PBNs are probabilistic extensions of Boolean networks. Cheng et al. studied the problem while focusing on PBNs consisting of pairs of AND/OR functions. This paper considers PBNs consisting of Boolean threshold functions while focusing on those threshold functions that have unit coefficients. The treatment of Boolean threshold functions, and triplets and n-tuplets of such functions, necessitates a deepening of the theoretical analyses. It is shown that wide classes of PBNs with such threshold functions can be exactly identified from samples under reasonable constraints, which include: 1) PBNs in which any number of threshold functions can be assigned provided that all have the same number of input variables and 2) PBNs consisting of pairs of threshold functions with different numbers of input variables. It is also shown that the problem of deciding the equivalence of two Boolean threshold functions is solvable in pseudopolynomial time but remains co-NP complete.

  7. Feedback Controller Design for the Synchronization of Boolean Control Networks.

    Science.gov (United States)

    Liu, Yang; Sun, Liangjie; Lu, Jianquan; Liang, Jinling

    2016-09-01

    This brief investigates the partial and complete synchronization of two Boolean control networks (BCNs). Necessary and sufficient conditions for partial and complete synchronization are established by the algebraic representations of logical dynamics. An algorithm is obtained to construct the feedback controller that guarantees the synchronization of master and slave BCNs. Two biological examples are provided to illustrate the effectiveness of the obtained results.

  8. Identification of Boolean Networks Using Premined Network Topology Information.

    Science.gov (United States)

    Zhang, Xiaohua; Han, Huaxiang; Zhang, Weidong

    2017-02-01

    This brief aims to reduce the data requirement for the identification of Boolean networks (BNs) by using the premined network topology information. First, a matching table is created and used for sifting the true from the false dependences among the nodes in the BNs. Then, a dynamic extension to matching table is developed to enable the dynamic locating of matching pairs to start as soon as possible. Next, based on the pseudocommutative property of the semitensor product, a position-transform mining is carried out to further improve data utilization. Combining the above, the topology of the BNs can be premined for the subsequent identification. Examples are given to illustrate the efficiency of reducing the data requirement. Some excellent features, such as the online and parallel processing ability, are also demonstrated.

  9. Boolean models of biosurfactants production in Pseudomonas fluorescens.

    Directory of Open Access Journals (Sweden)

    Adrien Richard

    Full Text Available Cyclolipopeptides (CLPs are biosurfactants produced by numerous Pseudomonas fluorescens strains. CLP production is known to be regulated at least by the GacA/GacS two-component pathway, but the full regulatory network is yet largely unknown. In the clinical strain MFN1032, CLP production is abolished by a mutation in the phospholipase C gene (plcC and not restored by plcC complementation. Their production is also subject to phenotypic variation. We used a modelling approach with Boolean networks, which takes into account all these observations concerning CLP production without any assumption on the topology of the considered network. Intensive computation yielded numerous models that satisfy these properties. All models minimizing the number of components point to a bistability in CLP production, which requires the presence of a yet unknown key self-inducible regulator. Furthermore, all suggest that a set of yet unexplained phenotypic variants might also be due to this epigenetic switch. The simplest of these Boolean networks was used to propose a biological regulatory network for CLP production. This modelling approach has allowed a possible regulation to be unravelled and an unusual behaviour of CLP production in P. fluorescens to be explained.

  10. Boolean Queries and Term Dependencies in Probabilistic Retrieval Models.

    Science.gov (United States)

    Croft, W. Bruce

    1986-01-01

    Proposes approach to integrating Boolean and statistical systems where Boolean queries are interpreted as a means of specifying term dependencies in relevant set of documents. Highlights include series of retrieval experiments designed to test retrieval strategy based on term dependence model and relation of results to other work. (18 references)…

  11. Robust Boolean Operation for Sculptured Models

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    To enhance the ability of current modeling system, an uniformed representation is designed to represent wire-frame, solid, surface models. We present an algorithm for Boolean operation between the models under this representation. Accuracy, efficiency and robustness are the main consideration. The geometric information is represented with trimmed parametric patches and trimmed parametric splines. The topological information is represented with an extended half-edge data structure. In the process of intersection calculation, hierarchy intersection method is applied for unified classification. Tracing the intersection curve to overcome degenerate cases that occur frequently in practice. The algorithm has been implemented as the modeling kernel of a feature based modeling system named GS-CAD98, which was developed on Windows/NT platform.

  12. Pulse-transmission Oscillators: Autonomous Boolean Models and the Yeast Cell Cycle

    Science.gov (United States)

    Sevim, Volkan; Gong, Xinwei; Socolar, Joshua

    2010-03-01

    Models of oscillatory gene expression typically involve a constitutively expressed or positively autoregulated gene which is repressed by a negative feedback loop. In Boolean representations of such systems, which include the repressilator and relaxation oscillators, dynamical stability stems from the impossibility of satisfying all of the Boolean rules at once. We consider a different class of networks, in which oscillations are due to the transmission of a pulse of gene activation around a ring. Using autonomous Boolean modeling methods, we show how the circulating pulse can be stabilized by decoration of the ring with certain feedback and feed-forward motifs. We then discuss the relation of these models to ODE models of transcriptional networks, emphasizing the role of explicit time delays. Finally, we show that a network recently proposed as a generator of cell cycle oscillations in yeast contains the motifs required to support stable transmission oscillations.

  13. Overview of methods of reverse engineering of gene regulatory networks: Boolean and Bayesian networks

    Directory of Open Access Journals (Sweden)

    Frolova A. O.

    2012-06-01

    Full Text Available Reverse engineering of gene regulatory networks is an intensively studied topic in Systems Biology as it reconstructs regulatory interactions between all genes in the genome in the most complete form. The extreme computational complexity of this problem and lack of thorough reviews on reconstruction methods of gene regulatory network is a significant obstacle to further development of this area. In this article the two most common methods for modeling gene regulatory networks are surveyed: Boolean and Bayesian networks. The mathematical description of each method is given, as well as several algorithmic approaches to modeling gene networks using these methods; the complexity of algorithms and the problems that arise during its implementation are also noted.

  14. A Semiquantitative Framework for Gene Regulatory Networks: Increasing the Time and Quantitative Resolution of Boolean Networks

    Science.gov (United States)

    Kerkhofs, Johan; Geris, Liesbet

    2015-01-01

    Boolean models have been instrumental in predicting general features of gene networks and more recently also as explorative tools in specific biological applications. In this study we introduce a basic quantitative and a limited time resolution to a discrete (Boolean) framework. Quantitative resolution is improved through the employ of normalized variables in unison with an additive approach. Increased time resolution stems from the introduction of two distinct priority classes. Through the implementation of a previously published chondrocyte network and T helper cell network, we show that this addition of quantitative and time resolution broadens the scope of biological behaviour that can be captured by the models. Specifically, the quantitative resolution readily allows models to discern qualitative differences in dosage response to growth factors. The limited time resolution, in turn, can influence the reachability of attractors, delineating the likely long term system behaviour. Importantly, the information required for implementation of these features, such as the nature of an interaction, is typically obtainable from the literature. Nonetheless, a trade-off is always present between additional computational cost of this approach and the likelihood of extending the model’s scope. Indeed, in some cases the inclusion of these features does not yield additional insight. This framework, incorporating increased and readily available time and semi-quantitative resolution, can help in substantiating the litmus test of dynamics for gene networks, firstly by excluding unlikely dynamics and secondly by refining falsifiable predictions on qualitative behaviour. PMID:26067297

  15. Is the optimal intervention policy UC superior to the suboptimal policy MFPT over inferred probabilistic Boolean network models?

    Science.gov (United States)

    Zan, X Z; Liu, W B; Hu, M X; Shen, L Z

    2016-12-19

    A salient problem in translational genomics is the use of gene regulatory networks to determine therapeutic intervention strategies. Theoretically, in a complete network, the optimal policy performs better than the suboptimal policy. However, this theory may not hold if we intervene in a system based on a control policy derived from imprecise inferred networks, especially in the small-sample scenario. In this paper, we compare the performance of the unconstrained (UC) policy with that of the mean-first-passage-time (MFPT) policy in terms of the quality of the determined control gene and the effectiveness of the policy. Our simulation results reveal that the quality of the control gene determined by the robust MFPT policy is better in the small-sample scenario, whereas the sensitive UC policy performs better in the large-sample scenario. Furthermore, given the same control gene, the MFPT policy is more efficient than the UC policy for the small-sample scenario. Owing to these two features, the MFPT policy performs better in the small-sample scenario and the UC policy performs better only in the large-sample scenario. Additionally, using a relatively complex model (gene number N is more than 1) is beneficial for the intervention process, especially for the sensitive UC policy.

  16. A Boolean Approach to Airline Business Model Innovation

    DEFF Research Database (Denmark)

    Hvass, Kristian Anders

    analyzes the business models of North America low-cost carriers from 2001 to 2010 using a Boolean minimization algorithm to identify which combinations of business model activities lead to operational profitability. The research aim is threefold: complement airline literature in the realm of business model...... innovation, introduce Boolean minimization methods to the field, and propose alternative business model activities to North American carriers striving for positive operating results....

  17. Design of Probabilistic Boolean Networks Based on Network Structure and Steady-State Probabilities.

    Science.gov (United States)

    Kobayashi, Koichi; Hiraishi, Kunihiko

    2016-06-06

    In this brief, we consider the problem of finding a probabilistic Boolean network (PBN) based on a network structure and desired steady-state properties. In systems biology and synthetic biology, such problems are important as an inverse problem. Using a matrix-based representation of PBNs, a solution method for this problem is proposed. The problem of finding a BN has been studied so far. In the problem of finding a PBN, we must calculate not only the Boolean functions, but also the probabilities of selecting a Boolean function and the number of candidates of the Boolean functions. Hence, the problem of finding a PBN is more difficult than that of finding a BN. The effectiveness of the proposed method is presented by numerical examples.

  18. Coevolution of Information Processing and Topology in Hierarchical Adaptive Random Boolean Networks

    CERN Document Server

    Gorski, Piotr J; Holyst, Janusz A

    2015-01-01

    Random Boolean networks (RBNs) are frequently employed for modelling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive RBN (HARBN) as a system consisting of distinct adaptive RBNs - subnetworks - connected by a set of permanent interlinks. Information measures and internal subnetworks topology of HARBN coevolve and reach steady-states that are specific for a given network structure. We investigate mean node information, mean edge information as well as a mean node degree as functions of model parameters and demonstrate HARBN's ability to describe complex hierarchical systems.

  19. Chaos synchronization of two stochastically coupled random Boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Hung, Y.-C. [Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan (China) and Nonlinear Science Group, Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan (China)]. E-mail: d9123801@student.nsysu.edu.tw; Ho, M.-C. [Nonlinear Science Group, Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan (China)]. E-mail: t1603@nknucc.nknu.edu.tw; Lih, J.-S. [Department of Physics and Geoscience, National Pingtung University of Education, Pingtung, Taiwan (China); Nonlinear Science Group, Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan (China); Jiang, I-M. [Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan (China); Nonlinear Science Group, Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan (China)

    2006-07-24

    In this Letter, we study the chaos synchronization of two stochastically coupled random Boolean networks (RBNs). Instead of using the 'site-by-site and all-to-all' coupling, the coupling mechanism we consider here is that: the nth cell in a network is linked by an arbitrarily chosen cell in the other network with probability {rho}, and it possesses no links with probability 1-{rho}. The mechanism is useful to investigate the coevolution of biological species via horizontal genetic exchange. We show that the density evolution of networks can be described by two deterministic coupled polynomial maps. The complete synchronization occurs when the coupling parameter exceeds a critical value. Moreover, the reverse bifurcations in inhomogeneous condition are observed and under our discussion.

  20. Harmonic Analysis of Boolean Networks: Determinative Power and Perturbations

    CERN Document Server

    Heckel, Reinhard; Bossert, Martin

    2011-01-01

    Consider a large Boolean network with a feed forward structure. Given a probability distribution for the inputs, can one find-possibly small-collections of input nodes that determine the states of most other nodes in the network? To identify these nodes, a notion that quantifies the determinative power of an input over states in the network is needed. We argue that the mutual information (MI) between a subset of the inputs X = {X_1, ..., X_n} of node i and the function f_i(X)$ associated with node i quantifies the determinative power of this subset of inputs over node i. To study the relation of determinative power to sensitivity to perturbations, we relate the MI to measures of perturbations, such as the influence of a variable, in terms of inequalities. The result shows that, maybe surprisingly, an input that has large influence does not necessarily have large determinative power. The main tool for the analysis is Fourier analysis of Boolean functions. Whether a function is sensitive to perturbations or not...

  1. Evolution of a designless nanoparticle network into reconfigurable Boolean logic

    Science.gov (United States)

    Bose, S. K.; Lawrence, C. P.; Liu, Z.; Makarenko, K. S.; van Damme, R. M. J.; Broersma, H. J.; van der Wiel, W. G.

    2015-12-01

    Natural computers exploit the emergent properties and massive parallelism of interconnected networks of locally active components. Evolution has resulted in systems that compute quickly and that use energy efficiently, utilizing whatever physical properties are exploitable. Man-made computers, on the other hand, are based on circuits of functional units that follow given design rules. Hence, potentially exploitable physical processes, such as capacitive crosstalk, to solve a problem are left out. Until now, designless nanoscale networks of inanimate matter that exhibit robust computational functionality had not been realized. Here we artificially evolve the electrical properties of a disordered nanomaterials system (by optimizing the values of control voltages using a genetic algorithm) to perform computational tasks reconfigurably. We exploit the rich behaviour that emerges from interconnected metal nanoparticles, which act as strongly nonlinear single-electron transistors, and find that this nanoscale architecture can be configured in situ into any Boolean logic gate. This universal, reconfigurable gate would require about ten transistors in a conventional circuit. Our system meets the criteria for the physical realization of (cellular) neural networks: universality (arbitrary Boolean functions), compactness, robustness and evolvability, which implies scalability to perform more advanced tasks. Our evolutionary approach works around device-to-device variations and the accompanying uncertainties in performance. Moreover, it bears a great potential for more energy-efficient computation, and for solving problems that are very hard to tackle in conventional architectures.

  2. Intrinsic noise and deviations from criticality in Boolean gene-regulatory networks

    Science.gov (United States)

    Villegas, Pablo; Ruiz-Franco, José; Hidalgo, Jorge; Muñoz, Miguel A.

    2016-01-01

    Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline between their ordered and disordered phases. Critical networks have been argued to lead to a number of functional advantages such as maximal dynamical range, maximal sensitivity to environmental changes, as well as to an excellent tradeoff between stability and flexibility. Here, we study the effect of noise within the context of Boolean networks trained to learn complex tasks under supervision. We verify that quasi-critical networks are the ones learning in the fastest possible way –even for asynchronous updating rules– and that the larger the task complexity the smaller the distance to criticality. On the other hand, when additional sources of intrinsic noise in the network states and/or in its wiring pattern are introduced, the optimally performing networks become clearly subcritical. These results suggest that in order to compensate for inherent stochasticity, regulatory and other type of biological networks might become subcritical rather than being critical, all the most if the task to be performed has limited complexity. PMID:27713479

  3. Intrinsic noise and deviations from criticality in Boolean gene-regulatory networks

    Science.gov (United States)

    Villegas, Pablo; Ruiz-Franco, José; Hidalgo, Jorge; Muñoz, Miguel A.

    2016-10-01

    Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline between their ordered and disordered phases. Critical networks have been argued to lead to a number of functional advantages such as maximal dynamical range, maximal sensitivity to environmental changes, as well as to an excellent tradeoff between stability and flexibility. Here, we study the effect of noise within the context of Boolean networks trained to learn complex tasks under supervision. We verify that quasi-critical networks are the ones learning in the fastest possible way –even for asynchronous updating rules– and that the larger the task complexity the smaller the distance to criticality. On the other hand, when additional sources of intrinsic noise in the network states and/or in its wiring pattern are introduced, the optimally performing networks become clearly subcritical. These results suggest that in order to compensate for inherent stochasticity, regulatory and other type of biological networks might become subcritical rather than being critical, all the most if the task to be performed has limited complexity.

  4. Detecting small attractors of large Boolean networks by function-reduction-based strategy.

    Science.gov (United States)

    Zheng, Qiben; Shen, Liangzhong; Shang, Xuequn; Liu, Wenbin

    2016-04-01

    Boolean networks (BNs) are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long-term behaviour of systems. A central aim of Boolean-network analysis is to find attractors that correspond to various cellular states, such as cell types or the stage of cell differentiation. This problem is NP-hard and various algorithms have been used to tackle it with considerable success. The idea is that a singleton attractor corresponds to n consistent subsequences in the truth table. To find these subsequences, the authors gradually reduce the entire truth table of Boolean functions by extending a partial gene activity profile (GAP). Not only does this process delete inconsistent subsequences in truth tables, it also directly determines values for some nodes not extended, which means it can abandon the partial GAPs that cannot lead to an attractor as early as possible. The results of simulation show that the proposed algorithm can detect small attractors with length p = 4 in BNs of up to 200 nodes with average indegree K = 2.

  5. Gene perturbation and intervention in context-sensitive stochastic Boolean networks

    Science.gov (United States)

    2014-01-01

    Background In a gene regulatory network (GRN), gene expressions are affected by noise, and stochastic fluctuations exist in the interactions among genes. These stochastic interactions are context dependent, thus it becomes important to consider noise in a context-sensitive manner in a network model. As a logical model, context-sensitive probabilistic Boolean networks (CSPBNs) account for molecular and genetic noise in the temporal context of gene functions. In a CSPBN with n genes and k contexts, however, a computational complexity of O(nk222n ) (or O(nk2 n )) is required for an accurate (or approximate) computation of the state transition matrix (STM) of the size (2 n ∙ k) × (2 n ∙ k) (or 2 n × 2 n ). The evaluation of a steady state distribution (SSD) is more challenging. Recently, stochastic Boolean networks (SBNs) have been proposed as an efficient implementation of an instantaneous PBN. Results The notion of stochastic Boolean networks (SBNs) is extended for the general model of PBNs, i.e., CSPBNs. This yields a novel structure of context-sensitive SBNs (CSSBNs) for modeling the stochasticity in a GRN. A CSSBN enables an efficient simulation of a CSPBN with a complexity of O(nLk2 n ) for computing the state transition matrix, where L is a factor related to the required sequence length in CSSBN for achieving a desired accuracy. A time-frame expanded CSSBN can further efficiently simulate the stationary behavior of a CSPBN and allow for a tunable tradeoff between accuracy and efficiency. The CSSBN approach is more efficient than an analytical method and more accurate than an approximate analysis. Conclusions Context-sensitive stochastic Boolean networks (CSSBNs) are proposed as an efficient approach to modeling the effects of gene perturbation and intervention in gene regulatory networks. A CSSBN analysis provides biologically meaningful insights into the oscillatory dynamics of the p53-Mdm2 network in a context-switching environment. It is shown that

  6. Synchronization Analysis of Master-Slave Probabilistic Boolean Networks

    Science.gov (United States)

    Lu, Jianquan; Zhong, Jie; Li, Lulu; Ho, Daniel W. C.; Cao, Jinde

    2015-01-01

    In this paper, we analyze the synchronization problem of master-slave probabilistic Boolean networks (PBNs). The master Boolean network (BN) is a deterministic BN, while the slave BN is determined by a series of possible logical functions with certain probability at each discrete time point. In this paper, we firstly define the synchronization of master-slave PBNs with probability one, and then we investigate synchronization with probability one. By resorting to new approach called semi-tensor product (STP), the master-slave PBNs are expressed in equivalent algebraic forms. Based on the algebraic form, some necessary and sufficient criteria are derived to guarantee synchronization with probability one. Further, we study the synchronization of master-slave PBNs in probability. Synchronization in probability implies that for any initial states, the master BN can be synchronized by the slave BN with certain probability, while synchronization with probability one implies that master BN can be synchronized by the slave BN with probability one. Based on the equivalent algebraic form, some efficient conditions are derived to guarantee synchronization in probability. Finally, several numerical examples are presented to show the effectiveness of the main results. PMID:26315380

  7. Synchronization Analysis of Master-Slave Probabilistic Boolean Networks.

    Science.gov (United States)

    Lu, Jianquan; Zhong, Jie; Li, Lulu; Ho, Daniel W C; Cao, Jinde

    2015-01-01

    In this paper, we analyze the synchronization problem of master-slave probabilistic Boolean networks (PBNs). The master Boolean network (BN) is a deterministic BN, while the slave BN is determined by a series of possible logical functions with certain probability at each discrete time point. In this paper, we firstly define the synchronization of master-slave PBNs with probability one, and then we investigate synchronization with probability one. By resorting to new approach called semi-tensor product (STP), the master-slave PBNs are expressed in equivalent algebraic forms. Based on the algebraic form, some necessary and sufficient criteria are derived to guarantee synchronization with probability one. Further, we study the synchronization of master-slave PBNs in probability. Synchronization in probability implies that for any initial states, the master BN can be synchronized by the slave BN with certain probability, while synchronization with probability one implies that master BN can be synchronized by the slave BN with probability one. Based on the equivalent algebraic form, some efficient conditions are derived to guarantee synchronization in probability. Finally, several numerical examples are presented to show the effectiveness of the main results.

  8. Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation.

    Science.gov (United States)

    Stötzel, Claudia; Röblitz, Susanna; Siebert, Heike

    2015-01-01

    In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.

  9. Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation.

    Directory of Open Access Journals (Sweden)

    Claudia Stötzel

    Full Text Available In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.

  10. Detection of attractors of large Boolean networks via exhaustive enumeration of appropriate subspaces of the state space

    Science.gov (United States)

    2013-01-01

    Background Boolean models are increasingly used to study biological signaling networks. In a Boolean network, nodes represent biological entities such as genes, proteins or protein complexes, and edges indicate activating or inhibiting influences of one node towards another. Depending on the input of activators or inhibitors, Boolean networks categorize nodes as either active or inactive. The formalism is appealing because for many biological relationships, we lack quantitative information about binding constants or kinetic parameters and can only rely on a qualitative description of the type “A activates (or inhibits) B”. A central aim of Boolean network analysis is the determination of attractors (steady states and/or cycles). This problem is known to be computationally complex, its most important parameter being the number of network nodes. Various algorithms tackle it with considerable success. In this paper we present an algorithm, which extends the size of analyzable networks thanks to simple and intuitive arguments. Results We present lnet, a software package which, in fully asynchronous updating mode and without any network reduction, detects the fixed states of Boolean networks with up to 150 nodes and a good part of any present cycles for networks with up to half the above number of nodes. The algorithm goes through a complete enumeration of the states of appropriately selected subspaces of the entire network state space. The size of these relevant subspaces is small compared to the full network state space, allowing the analysis of large networks. The subspaces scanned for the analyses of cycles are larger, reducing the size of accessible networks. Importantly, inherent in cycle detection is a classification scheme based on the number of non-frozen nodes of the cycle member states, with cycles characterized by fewer non-frozen nodes being easier to detect. It is further argued that these detectable cycles are also the biologically more important ones

  11. Coevolution of information processing and topology in hierarchical adaptive random Boolean networks

    Science.gov (United States)

    Górski, Piotr J.; Czaplicka, Agnieszka; Hołyst, Janusz A.

    2016-02-01

    Random Boolean Networks (RBNs) are frequently used for modeling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive random Boolean Network (HARBN) as a system consisting of distinct adaptive RBNs (ARBNs) - subnetworks - connected by a set of permanent interlinks. We investigate mean node information, mean edge information as well as mean node degree. Information measures and internal subnetworks topology of HARBN coevolve and reach steady-states that are specific for a given network structure. The main natural feature of ARBNs, i.e. their adaptability, is preserved in HARBNs and they evolve towards critical configurations which is documented by power law distributions of network attractor lengths. The mean information processed by a single node or a single link increases with the number of interlinks added to the system. The mean length of network attractors and the mean steady-state connectivity possess minima for certain specific values of the quotient between the density of interlinks and the density of all links in networks. It means that the modular network displays extremal values of its observables when subnetworks are connected with a density a few times lower than a mean density of all links.

  12. Algorithms and Complexity Analyses for Control of Singleton Attractors in Boolean Networks

    Directory of Open Access Journals (Sweden)

    Wai-Ki Ching

    2008-09-01

    Full Text Available A Boolean network (BN is a mathematical model of genetic networks. We propose several algorithms for control of singleton attractors in BN. We theoretically estimate the average-case time complexities of the proposed algorithms, and confirm them by computer experiments. The results suggest the importance of gene ordering. Especially, setting internal nodes ahead yields shorter computational time than setting external nodes ahead in various types of algorithms. We also present a heuristic algorithm which does not look for the optimal solution but for the solution whose computational time is shorter than that of the exact algorithms.

  13. Harmonic analysis of Boolean networks: determinative power and perturbations

    Science.gov (United States)

    2013-01-01

    Consider a large Boolean network with a feed forward structure. Given a probability distribution on the inputs, can one find, possibly small, collections of input nodes that determine the states of most other nodes in the network? To answer this question, a notion that quantifies the determinative power of an input over the states of the nodes in the network is needed. We argue that the mutual information (MI) between a given subset of the inputs X={X1,...,Xn} of some node i and its associated function fi(X) quantifies the determinative power of this set of inputs over node i. We compare the determinative power of a set of inputs to the sensitivity to perturbations to these inputs, and find that, maybe surprisingly, an input that has large sensitivity to perturbations does not necessarily have large determinative power. However, for unate functions, which play an important role in genetic regulatory networks, we find a direct relation between MI and sensitivity to perturbations. As an application of our results, we analyze the large-scale regulatory network of Escherichia coli. We identify the most determinative nodes and show that a small subset of those reduces the overall uncertainty of the network state significantly. Furthermore, the network is found to be tolerant to perturbations of its inputs. PMID:23642003

  14. Boolean networks using the chi-square test for inferring large-scale gene regulatory networks

    Directory of Open Access Journals (Sweden)

    Lee Jae K

    2007-02-01

    Full Text Available Abstract Background Boolean network (BN modeling is a commonly used method for constructing gene regulatory networks from time series microarray data. However, its major drawback is that its computation time is very high or often impractical to construct large-scale gene networks. We propose a variable selection method that are not only reduces BN computation times significantly but also obtains optimal network constructions by using chi-square statistics for testing the independence in contingency tables. Results Both the computation time and accuracy of the network structures estimated by the proposed method are compared with those of the original BN methods on simulated and real yeast cell cycle microarray gene expression data sets. Our results reveal that the proposed chi-square testing (CST-based BN method significantly improves the computation time, while its ability to identify all the true network mechanisms was effectively the same as that of full-search BN methods. The proposed BN algorithm is approximately 70.8 and 7.6 times faster than the original BN algorithm when the error sizes of the Best-Fit Extension problem are 0 and 1, respectively. Further, the false positive error rate of the proposed CST-based BN algorithm tends to be less than that of the original BN. Conclusion The CST-based BN method dramatically improves the computation time of the original BN algorithm. Therefore, it can efficiently infer large-scale gene regulatory network mechanisms.

  15. "Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis

    Directory of Open Access Journals (Sweden)

    Arellano Gustavo

    2011-12-01

    Full Text Available Abstract Background In Thomas' formalism for modeling gene regulatory networks (GRNs, branching time, where a state can have more than one possible future, plays a prominent role. By representing a certain degree of unpredictability, branching time can model several important phenomena, such as (a asynchrony, (b incompletely specified behavior, and (c interaction with the environment. Introducing more than one possible future for a state, however, creates a difficulty for ordinary simulators, because infinitely many paths may appear, limiting ordinary simulators to statistical conclusions. Model checkers for branching time, by contrast, are able to prove properties in the presence of infinitely many paths. Results We have developed Antelope ("Analysis of Networks through TEmporal-LOgic sPEcifications", http://turing.iimas.unam.mx:8080/AntelopeWEB/, a model checker for analyzing and constructing Boolean GRNs. Currently, software systems for Boolean GRNs use branching time almost exclusively for asynchrony. Antelope, by contrast, also uses branching time for incompletely specified behavior and environment interaction. We show the usefulness of modeling these two phenomena in the development of a Boolean GRN of the Arabidopsis thaliana root stem cell niche. There are two obstacles to a direct approach when applying model checking to Boolean GRN analysis. First, ordinary model checkers normally only verify whether or not a given set of model states has a given property. In comparison, a model checker for Boolean GRNs is preferable if it reports the set of states having a desired property. Second, for efficiency, the expressiveness of many model checkers is limited, resulting in the inability to express some interesting properties of Boolean GRNs. Antelope tries to overcome these two drawbacks: Apart from reporting the set of all states having a given property, our model checker can express, at the expense of efficiency, some properties that ordinary

  16. Feedback control design for the complete synchronisation of two coupled Boolean networks

    Science.gov (United States)

    Li, Fangfei

    2016-09-01

    In the literatures, to design state feedback controllers to make the response Boolean network synchronise with the drive Boolean network is rarely considered. Motivated by this, feedback control design for the complete synchronisation of two coupled Boolean networks is investigated in this paper. A necessary condition for the existence of a state feedback controller achieving the complete synchronisation is established first. Then, based on the necessary condition, the feedback control law is proposed. Finally, an example is worked out to illustrate the proposed design procedure.

  17. Minimum energy control and optimal-satisfactory control of Boolean control network

    Energy Technology Data Exchange (ETDEWEB)

    Li, Fangfei, E-mail: li_fangfei@163.com; Lu, Xiwen

    2013-12-09

    In the literatures, to transfer the Boolean control network from the initial state to the desired state, the expenditure of energy has been rarely considered. Motivated by this, this Letter investigates the minimum energy control and optimal-satisfactory control of Boolean control network. Based on the semi-tensor product of matrices and Floyd's algorithm, minimum energy, constrained minimum energy and optimal-satisfactory control design for Boolean control network are given respectively. A numerical example is presented to illustrate the efficiency of the obtained results.

  18. Sampled-Data State Feedback Stabilization of Boolean Control Networks.

    Science.gov (United States)

    Liu, Yang; Cao, Jinde; Sun, Liangjie; Lu, Jianquan

    2016-04-01

    In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.

  19. Synchronization for the Realization-Dependent Probabilistic Boolean Networks.

    Science.gov (United States)

    Chen, Hongwei; Liang, Jinling; Lu, Jianquan; Qiu, Jianlong

    2017-01-24

    This paper investigates the synchronization problem for the realization-dependent probabilistic Boolean networks (PBNs) coupled unidirectionally in the drive-response configuration. The realization of the response PBN is assumed to be uniquely determined by the realization signal generated by the drive PBN at each discrete time instant. First, the drive-response PBNs are expressed in their algebraic forms based on the semitensor product method, and then, a necessary and sufficient condition is presented for the synchronization of the PBNs. Second, by resorting to a newly defined matrix operator, the reachable set from any initial state is expressed by a column vector. Consequently, an easily computable algebraic criterion is derived assuring the synchronization of the drive-response PBNs. Finally, three illustrative examples are employed to demonstrate the applicability and usefulness of the developed theoretical results.

  20. Super-transient scaling in time-delay autonomous Boolean network motifs.

    Science.gov (United States)

    D'Huys, Otti; Lohmann, Johannes; Haynes, Nicholas D; Gauthier, Daniel J

    2016-09-01

    Autonomous Boolean networks are commonly used to model the dynamics of gene regulatory networks and allow for the prediction of stable dynamical attractors. However, most models do not account for time delays along the network links and noise, which are crucial features of real biological systems. Concentrating on two paradigmatic motifs, the toggle switch and the repressilator, we develop an experimental testbed that explicitly includes both inter-node time delays and noise using digital logic elements on field-programmable gate arrays. We observe transients that last millions to billions of characteristic time scales and scale exponentially with the amount of time delays between nodes, a phenomenon known as super-transient scaling. We develop a hybrid model that includes time delays along network links and allows for stochastic variation in the delays. Using this model, we explain the observed super-transient scaling of both motifs and recreate the experimentally measured transient distributions.

  1. Super-transient scaling in time-delay autonomous Boolean network motifs

    Science.gov (United States)

    D'Huys, Otti; Lohmann, Johannes; Haynes, Nicholas D.; Gauthier, Daniel J.

    2016-09-01

    Autonomous Boolean networks are commonly used to model the dynamics of gene regulatory networks and allow for the prediction of stable dynamical attractors. However, most models do not account for time delays along the network links and noise, which are crucial features of real biological systems. Concentrating on two paradigmatic motifs, the toggle switch and the repressilator, we develop an experimental testbed that explicitly includes both inter-node time delays and noise using digital logic elements on field-programmable gate arrays. We observe transients that last millions to billions of characteristic time scales and scale exponentially with the amount of time delays between nodes, a phenomenon known as super-transient scaling. We develop a hybrid model that includes time delays along network links and allows for stochastic variation in the delays. Using this model, we explain the observed super-transient scaling of both motifs and recreate the experimentally measured transient distributions.

  2. Discrete interference modeling via boolean algebra.

    Science.gov (United States)

    Beckhoff, Gerhard

    2011-01-01

    Two types of boolean functions are considered, the locus function of n variables, and the interval function of ν = n - 1 variables. A 1-1 mapping is given that takes elements (cells) of the interval function to antidual pairs of elements in the locus function, and vice versa. A set of ν binary codewords representing the intervals are defined and used to generate the codewords of all genomic regions. Next a diallelic three-point system is reviewed in the light of boolean functions, which leads to redefining complete interference by a logic function. Together with the upper bound of noninterference already defined by a boolean function, it confines the region of interference. Extensions of these two functions to any finite number of ν are straightforward, but have been also made in terms of variables taken from the inclusion-exclusion principle (expressing "at least" and "exactly equal to" a decimal integer). Two coefficients of coincidence for systems with more than three loci are defined and discussed, one using the average of several individual coefficients and the other taking as coefficient a real number between zero and one. Finally, by way of a malfunction of the mod-2 addition, it is shown that a four-point system may produce two different functions, one of which exhibiting loss of a class of odd recombinants.

  3. Characterizing short-term stability for Boolean networks over any distribution of transfer functions

    Science.gov (United States)

    Seshadhri, C.; Smith, Andrew M.; Vorobeychik, Yevgeniy; Mayo, Jackson R.; Armstrong, Robert C.

    2016-07-01

    We present a characterization of short-term stability of Kauffman's N K (random) Boolean networks under arbitrary distributions of transfer functions. Given such a Boolean network where each transfer function is drawn from the same distribution, we present a formula that determines whether short-term chaos (damage spreading) will happen. Our main technical tool which enables the formal proof of this formula is the Fourier analysis of Boolean functions, which describes such functions as multilinear polynomials over the inputs. Numerical simulations on mixtures of threshold functions and nested canalyzing functions demonstrate the formula's correctness.

  4. A new approach for global controllability of higher order Boolean control network.

    Science.gov (United States)

    Chen, Hao; Sun, Jitao

    2013-03-01

    Using the semi-tensor product, the global control problem of the higher order Boolean control network with avoiding set is considered. First, the number of different control sequences that drive the higher order Boolean control network from the initial state to the destination state while avoiding undesirable set is provided. Then, the definition of global controllability of higher order Boolean control network is given. Third, by using the classical theory of nonnegative matrices, the necessary and sufficient condition for the global controllability of higher order Boolean control network with avoiding set is presented. Furthermore, a sufficient condition for k fixed-time global controllability of the system is also obtained. At last, an example is given to illustrate the main results.

  5. Critical line in undirected Kauffman Boolean networks - the role of percolation

    Energy Technology Data Exchange (ETDEWEB)

    Fronczak, Piotr; Fronczak, Agata [Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw (Poland)], E-mail: fronczak@if.pw.edu.pl

    2008-06-06

    We show that to describe correctly the position of the critical line in Kauffman random Boolean networks one must take into account percolation phenomena underlying the process of damage spreading. For this reason, since the issue of percolation transition is much simpler in random undirected networks than in the directed ones, we study the Kauffman model in undirected networks. We derive the mean field formula for the critical line in the giant components of these networks, and show that the critical line characterizing the whole network results from the fact that the ordered behavior of small clusters shields the chaotic behavior of the giant component. We also show a possible attitude towards the analytical description of the shielding effect. The theoretical derivations given in this paper very much tally with the numerical simulations done for classical random graphs.

  6. Feedback control and output feedback control for the stabilisation of switched Boolean networks

    Science.gov (United States)

    Li, Fangfei; Yu, Zhaoxu

    2016-02-01

    This paper presents the feedback control and output feedback control for the stabilisation of switched Boolean network. A necessary condition for the existence of a state feedback controller for the stabilisation of switched Boolean networks under arbitrary switching signal is derived first, and constructive procedures for feedback control and output feedback control design are provided. An example is introduced to show the effectiveness of this paper.

  7. Optimal computation of symmetric Boolean functions in Tree networks

    CERN Document Server

    Kowshik, Hemant

    2010-01-01

    In this paper, we address the scenario where nodes with sensor data are connected in a tree network, and every node wants to compute a given symmetric Boolean function of the sensor data. We first consider the problem of computing a function of two nodes with integer measurements. We allow for block computation to enhance data fusion efficiency, and determine the minimum worst-case total number of bits to be exchanged to perform the desired computation. We establish lower bounds using fooling sets, and provide a novel scheme which attains the lower bounds, using information theoretic tools. For a class of functions called sum-threshold functions, this scheme is shown to be optimal. We then turn to tree networks and derive a lower bound for the number of bits exchanged on each link by viewing it as a two node problem. We show that the protocol of recursive innetwork aggregation achieves this lower bound in the case of sumthreshold functions. Thus we have provided a communication and in-network computation stra...

  8. Optimal Control of Gene Regulatory Networks with Effectiveness of Multiple Drugs: A Boolean Network Approach

    Science.gov (United States)

    Kobayashi, Koichi; Hiraishi, Kunihiko

    2013-01-01

    Developing control theory of gene regulatory networks is one of the significant topics in the field of systems biology, and it is expected to apply the obtained results to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of gene regulatory networks, and gene expression is expressed by a binary value (0 or 1). In the control problem, we assume that the concentration level of a part of genes is arbitrarily determined as the control input. However, there are cases that no gene satisfying this assumption exists, and it is important to consider structural control via external stimuli. Furthermore, these controls are realized by multiple drugs, and it is also important to consider multiple effects such as duration of effect and side effects. In this paper, we propose a BN model with two types of the control inputs and an optimal control method with duration of drug effectiveness. First, a BN model and duration of drug effectiveness are discussed. Next, the optimal control problem is formulated and is reduced to an integer linear programming problem. Finally, numerical simulations are shown. PMID:24058904

  9. Selection of probability based weighting models for Boolean retrieval system

    Energy Technology Data Exchange (ETDEWEB)

    Ebinuma, Y. (Japan Atomic Energy Research Inst., Tokai, Ibaraki. Tokai Research Establishment)

    1981-09-01

    Automatic weighting models based on probability theory were studied if they can be applied to boolean search logics including logical sum. The INIS detabase was used for searching of one particular search formula. Among sixteen models three with good ranking performance were selected. These three models were further applied to searching of nine search formulas in the same database. It was found that two models among them show slightly better average ranking performance while the other model, the simplest one, seems also practical.

  10. Damage spreading in spatial and small-world random boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Lu, Qiming [Los Alamos National Laboratory; Teuscher, Christof [Los Alamos National Laboratory

    2008-01-01

    Random Boolean Networks (RBNs) are often used as generic models for certain dynamics of complex systems, ranging from social networks, neural networks, to gene or protein interaction networks. Traditionally, RBNs are interconnected randomly and without considering any spatial arrangement of the links and nodes. However, most real-world networks are spatially extended and arranged with regular, small-world, or other non-random connections. Here we explore the RBN network topology between extreme local connections, random small-world, and random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the relevant component at very low connectivities ({bar K} << 1) and that the critical connectivity of stability K{sub s} changes compared to random networks. At higher {bar K}, this scaling remains unchanged. We also show that the relevant component of spatially local networks scales with a power-law as the system size N increases, but with a different exponent for local and small-world networks. The scaling behaviors are obtained by finite-size scaling. We further investigate the wiring cost of the networks. From an engineering perspective, our new findings provide the key trade-offs between damage spreading (robustness), the network wiring cost, and the network's communication characteristics.

  11. Boolean model of Yeast Apoptosis as a tool to study yeast and human apoptotic regulations

    Directory of Open Access Journals (Sweden)

    Laleh eKazemzadeh

    2012-12-01

    Full Text Available Programmed cell death (PCD is an essential cellular mechanism that is evolutionary conserved, mediated through various pathways and acts by integrating different stimuli. Many diseases such as neurodegenerative diseases and cancers are found to be caused by, or associated with, regulations in the cell death pathways. Yeast Saccharomyces cerevisiae, is a unicellular eukaryotic organism that shares with human cells components and pathways of the PCD and is therefore used as a model organism. Boolean modelling is becoming promising approach to capture qualitative behaviour and describe essential properties of such complex networks. Here we present large literature-based and to our knowledge first Boolean model that combines pathways leading to apoptosis (a type of PCD in yeast. Analysis of the yeast model confirmed experimental findings of anti-apoptotic role of Bir1p and pro-apoptotic role of Stm1p and revealed activation of the stress protein kinase Hog proposing the maximal level of activation upon heat stress. In addition we extended the yeast model and created an in silico humanized yeast in which human pro- and anti-apoptotic regulators Bcl-2 family and Valosin-contain protein (VCP are included in the model. We showed that accumulation of Bax in in silico humanized yeast shows apoptotic markers and that VCP is essential target of Akt Signaling. The presented Boolean model provides comprehensive description of yeast apoptosis network behaviour. Extended model of humanized yeast gives new insights of how complex human disease like neurodegenration can initially be tested.

  12. Boolean Model of Yeast Apoptosis as a Tool to Study Yeast and Human Apoptotic Regulations

    Science.gov (United States)

    Kazemzadeh, Laleh; Cvijovic, Marija; Petranovic, Dina

    2012-01-01

    Programmed cell death (PCD) is an essential cellular mechanism that is evolutionary conserved, mediated through various pathways and acts by integrating different stimuli. Many diseases such as neurodegenerative diseases and cancers are found to be caused by, or associated with, regulations in the cell death pathways. Yeast Saccharomyces cerevisiae, is a unicellular eukaryotic organism that shares with human cells components and pathways of the PCD and is therefore used as a model organism. Boolean modeling is becoming promising approach to capture qualitative behavior and describe essential properties of such complex networks. Here we present large literature-based and to our knowledge first Boolean model that combines pathways leading to apoptosis (a type of PCD) in yeast. Analysis of the yeast model confirmed experimental findings of anti-apoptotic role of Bir1p and pro-apoptotic role of Stm1p and revealed activation of the stress protein kinase Hog proposing the maximal level of activation upon heat stress. In addition we extended the yeast model and created an in silico humanized yeast in which human pro- and anti-apoptotic regulators Bcl-2 family and Valosin-contain protein (VCP) are included in the model. We showed that accumulation of Bax in silico humanized yeast shows apoptotic markers and that VCP is essential target of Akt Signaling. The presented Boolean model provides comprehensive description of yeast apoptosis network behavior. Extended model of humanized yeast gives new insights of how complex human disease like neurodegeneration can initially be tested. PMID:23233838

  13. Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update.

    Science.gov (United States)

    Luo, Chao; Wang, Xingyuan; Liu, Hong

    2014-12-17

    In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) with time delay is studied. Firstly, dynamical model of Boolean multiplex control networks is constructed, which is assumed to be under Harvey' asynchronous update and time delay is introduced both in states and controls. By using of semi-tensor product (STP) approach, the logical dynamics is converted into an equivalent algebraic form by obtaining the control-depending network transition matrices of delayed system. Secondly, a necessary and sufficient condition is proved that only control-depending fixed points of the studied dynamics can be controlled with probability one. Thirdly, respectively for two types of controls, the controllability of dynamical control system is investigated. When initial states and time delay are given, formulae are obtained to show a) the reachable set at time s under specified controls; b) the reachable set at time s under arbitrary controls; c) the reachable probabilities to different destination states. Furthermore, an approach is discussed to find a precise control sequence which can steer dynamical system into a specified target with the maximum reachable probability. Examples are shown to illustrate the feasibility of the proposed scheme.

  14. Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update

    Science.gov (United States)

    Luo, Chao; Wang, Xingyuan; Liu, Hong

    2014-01-01

    In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) with time delay is studied. Firstly, dynamical model of Boolean multiplex control networks is constructed, which is assumed to be under Harvey' asynchronous update and time delay is introduced both in states and controls. By using of semi-tensor product (STP) approach, the logical dynamics is converted into an equivalent algebraic form by obtaining the control-depending network transition matrices of delayed system. Secondly, a necessary and sufficient condition is proved that only control-depending fixed points of the studied dynamics can be controlled with probability one. Thirdly, respectively for two types of controls, the controllability of dynamical control system is investigated. When initial states and time delay are given, formulae are obtained to show a) the reachable set at time s under specified controls; b) the reachable set at time s under arbitrary controls; c) the reachable probabilities to different destination states. Furthermore, an approach is discussed to find a precise control sequence which can steer dynamical system into a specified target with the maximum reachable probability. Examples are shown to illustrate the feasibility of the proposed scheme. PMID:25516009

  15. FPGA implementation of a stochastic neural network for monotonic pseudo-Boolean optimization.

    Science.gov (United States)

    Grossi, Giuliano; Pedersini, Federico

    2008-08-01

    In this paper a FPGA implementation of a novel neural stochastic model for solving constrained NP-hard problems is proposed and developed. The model exploits pseudo-Boolean functions both to express the constraints and to define the cost function, interpreted as energy of a neural network. A wide variety of NP-hard problems falls in the class of problems that can be solved by this model, particularly those having a quadratic pseudo-Boolean penalty function. The proposed hardware implementation provides high computation speed by exploiting parallelism, as the neuron update and the constraint violation check can be performed in parallel over the whole network. The neural system has been tested on random and benchmark graphs, showing good performance with respect to the same heuristic for the same problems. Furthermore, the computational speed of the FPGA implementation has been measured and compared to software implementation. The developed architecture featured dramatically faster computation, with respect to the software implementation, even adopting a low-cost FPGA chip.

  16. Damage Spreading in Spatial and Small-world Random Boolean Networks

    Energy Technology Data Exchange (ETDEWEB)

    Lu, Qiming [Fermilab; Teuscher, Christof [Portland State U.

    2014-02-18

    The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean Networks (RBNs) are commonly used a simple generic model for certain dynamics of complex systems. Traditionally, RBNs are interconnected randomly and without considering any spatial extension and arrangement of the links and nodes. However, most real-world networks are spatially extended and arranged with regular, power-law, small-world, or other non-random connections. Here we explore the RBN network topology between extreme local connections, random small-world, and pure random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the relevant component at very low connectivities ($\\bar{K} \\ll 1$) and that the critical connectivity of stability $K_s$ changes compared to random networks. At higher $\\bar{K}$, this scaling remains unchanged. We also show that the relevant component of spatially local networks scales with a power-law as the system size N increases, but with a different exponent for local and small-world networks. The scaling behaviors are obtained by finite-size scaling. We further investigate the wiring cost of the networks. From an engineering perspective, our new findings provide the key design trade-offs between damage spreading (robustness), the network's wiring cost, and the network's communication characteristics.

  17. Decisional Processes with Boolean Neural Network: the Emergence of Mental Schemes

    CERN Document Server

    Barnabei, Graziano; Conversano, Ciro; Lensi, Elena

    2010-01-01

    Human decisional processes result from the employment of selected quantities of relevant information, generally synthesized from environmental incoming data and stored memories. Their main goal is the production of an appropriate and adaptive response to a cognitive or behavioral task. Different strategies of response production can be adopted, among which haphazard trials, formation of mental schemes and heuristics. In this paper, we propose a model of Boolean neural network that incorporates these strategies by recurring to global optimization strategies during the learning session. The model characterizes as well the passage from an unstructured/chaotic attractor neural network typical of data-driven processes to a faster one, forward-only and representative of schema-driven processes. Moreover, a simplified version of the Iowa Gambling Task (IGT) is introduced in order to test the model. Our results match with experimental data and point out some relevant knowledge coming from psychological domain.

  18. PATHLOGIC-S: a scalable Boolean framework for modelling cellular signalling.

    Directory of Open Access Journals (Sweden)

    Liam G Fearnley

    Full Text Available Curated databases of signal transduction have grown to describe several thousand reactions, and efficient use of these data requires the development of modelling tools to elucidate and explore system properties. We present PATHLOGIC-S, a Boolean specification for a signalling model, with its associated GPL-licensed implementation using integer programming techniques. The PATHLOGIC-S specification has been designed to function on current desktop workstations, and is capable of providing analyses on some of the largest currently available datasets through use of Boolean modelling techniques to generate predictions of stable and semi-stable network states from data in community file formats. PATHLOGIC-S also addresses major problems associated with the presence and modelling of inhibition in Boolean systems, and reduces logical incoherence due to common inhibitory mechanisms in signalling systems. We apply this approach to signal transduction networks including Reactome and two pathways from the Panther Pathways database, and present the results of computations on each along with a discussion of execution time. A software implementation of the framework and model is freely available under a GPL license.

  19. ViSiBooL-visualization and simulation of Boolean networks with temporal constraints.

    Science.gov (United States)

    Schwab, Julian; Burkovski, Andre; Siegle, Lea; Müssel, Christoph; Kestler, Hans A

    2016-10-22

    : Mathematical models and their simulation are increasingly used to gain insights into cellular pathways and regulatory networks. Dynamics of regulatory factors can be modeled using Boolean networks (BNs), among others. Text-based representations of models are precise descriptions, but hard to understand and interpret. ViSiBooL aims at providing a graphical way of modeling and simulating networks. By providing visualizations of static and dynamic network properties simultaneously, it is possible to directly observe the effects of changes in the network structure on the behavior. In order to address the challenges of clear design and a user-friendly graphical user interface (GUI), ViSiBooL implements visual representations of BNs. Additionally temporal extensions of the BNs for the modeling of regulatory time delays are incorporated. The GUI of ViSiBooL allows to model, organize, simulate and visualize BNs as well as corresponding simulation results such as attractors. Attractor searches are performed in parallel to the modeling process. Hence, changes in the network behavior are visualized at the same time.

  20. Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics

    CERN Document Server

    Silva, A Castro e

    2009-01-01

    We study two types of simplified Boolean dynamics over scale-free networks, both with synchronous update. Assigning only Boolean functions AND and XOR to the nodes with probability $1-p$ and $p$, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamic as its own input (self-regulation) or not. The same conclusion holds for the Kauffman KN model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation, and (ii) disagree for small $p$ when self-regulation is present in the model.

  1. Mean-field and non-mean-field behaviors in scale-free networks with random Boolean dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Castro e Silva, A [Departamento de Fisica, Universidade Federal de Ouro Preto, Campus Universitario, 35.400-000 Ouro Preto, Minas Gerais (Brazil); Kamphorst Leal da Silva, J, E-mail: alcidescs@gmail.co, E-mail: jaff@fisica.ufmg.b [Departamento de Fisica, Universidade Federal de Minas Gerais, Caixa Postal 702, 30.161-970, Belo Horizonte, Minas Gerais (Brazil)

    2010-06-04

    We study two types of simplified Boolean dynamics in scale-free networks, both with a synchronous update. Assigning only the Boolean functions AND and XOR to the nodes with probabilities 1 - p and p, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamics as its own input (self-regulation) or not. The same conclusion holds for the Kauffman NK model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation and (ii) disagree for small p when self-regulation is present in the model.

  2. MILES FORMULAE FOR BOOLEAN MODELS OBSERVED ON LATTICES

    Directory of Open Access Journals (Sweden)

    Joachim Ohser

    2011-05-01

    Full Text Available The densities of the intrinsic volumes – in 3D the volume density, surface density, the density of the integral of the mean curvature and the density of the Euler number – are a very useful collection of geometric characteristics of random sets. Combining integral and digital geometry we develop a method for efficient and simultaneous calculation of the intrinsic volumes of random sets observed in binary images in arbitrary dimensions. We consider isotropic and reflection invariant Boolean models sampled on homogeneous lattices and compute the expectations of the estimators of the intrinsic volumes. It turns out that the estimator for the surface density is proved to be asymptotically unbiased and thusmultigrid convergent for Boolean models with convex grains. The asymptotic bias of the estimators for the densities of the integral of the mean curvature and of the Euler number is assessed for Boolean models of balls of random diameters. Miles formulae with corresponding correction terms are derived for the 3D case.

  3. Local digital estimators of intrinsic volumes for Boolean models and in the design based setting

    DEFF Research Database (Denmark)

    Svane, Anne Marie

    In order to estimate the specific intrinsic volumes of a planar Boolean model from a binary image, we consider local digital algorithms based on weigted sums of 2×2 configuration counts. For Boolean models with balls as grains, explicit formulas for the bias of such algorithms are derived...... for the bias obtained for Boolean models are applied to existing algorithms in order to compare their accuracy....

  4. An efficient algorithm for computing attractors of synchronous and asynchronous Boolean networks.

    Directory of Open Access Journals (Sweden)

    Desheng Zheng

    Full Text Available Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD, we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly [Formula: see text] faster in computing attractors for empirical experimental systems.The software package is available at https://sites.google.com/site/desheng619/download.

  5. An Efficient Algorithm for Computing Attractors of Synchronous And Asynchronous Boolean Networks

    Science.gov (United States)

    Zheng, Desheng; Yang, Guowu; Li, Xiaoyu; Wang, Zhicai; Liu, Feng; He, Lei

    2013-01-01

    Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD), we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly faster in computing attractors for empirical experimental systems. Availability The software package is available at https://sites.google.com/site/desheng619/download. PMID:23585840

  6. Chaos Control in Random Boolean Networks by Reducing Mean Damage Percolation Rate

    Institute of Scientific and Technical Information of China (English)

    JIANG Nan; CHEN Shi-Jian

    2011-01-01

    Chaos control in random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase. However, controlled nodes are only viewed as passive blocks to prevent perturbation spread. We propose a new control method in which controlled nodes can exert an active impact on the network.Controlled nodes and frozen values are deliberately selected according to the information of connection and Boolean functions. Simulation results showy that the number of nodes needed to achieve control is largely reduced compared to the previous method. Theoretical analysis is also given to estimate the least fraction of nodes needed to achieve control.%Chaos control in random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase.However, controlled nodes are only viewed as passive blocks to prevent perturbation spread.We propose a new control method in which controlled nodes can exert an active impact on the network.Controlled nodes and frozen values are deliberately selected according to the information of connection and Boolean functions.Simulation results show that the number of nodes needed to achieve control is largely reduced compared to the previous method.Theoretical analysis is also given to estimate the least fraction of nodes needed to achieve control

  7. Calculation Method for Reliability of Agricultural Distribution Power Networks while Applying Functions of Boolean Algebra

    Directory of Open Access Journals (Sweden)

    V. Rusan

    2012-01-01

    Full Text Available The paper considers calculation methods for reliability of  agricultural distribution power networks while using Boolean algebra functions and analytical method. Reliability of 10 kV overhead line circuits with automatic sectionalization points and automatic standby activation has been investigated in the paper.

  8. Analysis and control of Boolean networks a semi-tensor product approach

    CERN Document Server

    Cheng, Daizhan; Li, Zhiqiang

    2010-01-01

    This book presents a new approach to the investigation of Boolean control networks, using the semi-tensor product (STP), which can express a logical function as a conventional discrete-time linear system. This makes it possible to analyze basic control problems.

  9. Influence of a Structure on System's Dynamics on Example of Boolean Networks

    OpenAIRE

    Kirillova, O.

    1999-01-01

    In this work we study the Boolean Networks of different geometric shape and lattice organization. It was revealed that no only a spatial shape but also type of lattice are very important for definition of the structure-dynamics relation. The regular structures do not give a critical regime in the investigated cases. Hierarchy together with the irregular structure reveals characteristic features of criticality.

  10. Boolean Variables in Economic Models Solved by Linear Programming

    Directory of Open Access Journals (Sweden)

    Lixandroiu D.

    2014-12-01

    Full Text Available The article analyses the use of logical variables in economic models solved by linear programming. Focus is given to the presentation of the way logical constraints are obtained and of the definition rules based on predicate logic. Emphasis is also put on the possibility to use logical variables in constructing a linear objective function on intervals. Such functions are encountered when costs or unitary receipts are different on disjunct intervals of production volumes achieved or sold. Other uses of Boolean variables are connected to constraint systems with conditions and the case of a variable which takes values from a finite set of integers.

  11. Seismic imaging and evaluation of channels modeled by boolean approach

    Energy Technology Data Exchange (ETDEWEB)

    Spinola, M.; Aggio, A. [PETROBRAS, Rio de Janeiro, RJ (Brazil). Centro de Pesquisas

    1999-07-01

    The seismic method attempt to image the subsurface architecture and has been able to significantly contribute to detect areal and vertical changes in rock properties. This work presents a seismic imaging study of channel objects generated using the boolean technique. Three channels having different thicknesses were simulated, using the same width, sinuosity and direction. A velocity model was constructed in order to allow seismic contrasts between the interior of channels and the embedding rock. To examine the seismic response for different channel thicknesses, a 3D ray tracing with a normal incident point survey was performed. The three channels were resolved and the way the seismic could image them was studied. (author)

  12. An Application of Invertibility of Boolean Control Networks to the Control of the Mammalian Cell Cycle.

    Science.gov (United States)

    Zhang, Kuize; Zhang, Lijun; Mou, Shaoshuai

    2017-01-01

    In Fauré et al. (2006), the dynamics of the core network regulating the mammalian cell cycle is formulated as a Boolean control network (BCN) model consisting of nine proteins as state nodes and a tenth protein (protein CycD) as the control input node. In this model, one of the state nodes, protein Cdc20, plays a central role in the separation of sister chromatids. Hence, if any Cdc20 sequence can be obtained, fully controlling the mammalian cell cycle is feasible. Motivated by this fact, we study whether any Cdc20 sequence can be obtained theoretically. We formulate the foregoing problem as the invertibility of BCNs, that is, whether one can obtain any Cdc20 sequence by designing input (i.e., protein CycD) sequences. We give an algorithm to verify the invertibility of any BCN, and find that the BCN model for the core network regulating the mammalian cell cycle is not invertible, that is, one cannot obtain any Cdc20 sequence. We further present another algorithm to test whether a finite Cdc20 sequence can be generated by the BCN model, which leads to a series of periodic infinite Cdc20 sequences with alternately active and inactive Cdc20 segments. States of these sequences are alternated between the two attractors in the proposed model, which reproduces correctly how a cell exits the cell cycle to enter the quiescent state, or the opposite.

  13. The phase diagram of random Boolean networks with nested canalizing functions

    CERN Document Server

    Peixoto, Tiago P

    2010-01-01

    We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $\\lambda$, and we compare with numerical simulations of quenched networks. We find that, contrary to what was reported by Kauffman et al. [Proc. Natl. Acad. Sci. 2004 101 49 17102-7], these networks have a rich phase diagram, were both the "chaotic" and frozen phases are present, as well as an oscillatory regime of the value of $b_t$. We argue that the presence of only the frozen phase in the work of Kauffman et al. was due simply to the specific parametrization used, and is not an inherent feature of this class of functions. However, these networks are significantly more stable than the variants where all possible Boolean functions are allowed.

  14. Antigen profiling analysis of vaccinia virus injected canine tumors: oncolytic virus efficiency predicted by boolean models.

    Science.gov (United States)

    Cecil, Alexander; Gentschev, Ivaylo; Adelfinger, Marion; Nolte, Ingo; Dandekar, Thomas; Szalay, Aladar A

    2014-01-01

    Virotherapy on the basis of oncolytic vaccinia virus (VACV) strains is a novel approach for cancer therapy. In this study we describe for the first time the use of dynamic boolean modeling for tumor growth prediction of vaccinia virus GLV-1h68-injected canine tumors including canine mammary adenoma (ZMTH3), canine mammary carcinoma (MTH52c), canine prostate carcinoma (CT1258), and canine soft tissue sarcoma (STSA-1). Additionally, the STSA-1 xenografted mice were injected with either LIVP 1.1.1 or LIVP 5.1.1 vaccinia virus strains.   Antigen profiling data of the four different vaccinia virus-injected canine tumors were obtained, analyzed and used to calculate differences in the tumor growth signaling network by type and tumor type. Our model combines networks for apoptosis, MAPK, p53, WNT, Hedgehog, TK cell, Interferon, and Interleukin signaling networks. The in silico findings conform with in vivo findings of tumor growth. Boolean modeling describes tumor growth and remission semi-quantitatively with a good fit to the data obtained for all cancer type variants. At the same time it monitors all signaling activities as a basis for treatment planning according to antigen levels. Mitigation and elimination of VACV- susceptible tumor types as well as effects on the non-susceptible type CT1258 are predicted correctly. Thus the combination of Antigen profiling and semi-quantitative modeling optimizes the therapy already before its start.

  15. Direct relations between morphology and transport in Boolean models.

    Science.gov (United States)

    Scholz, Christian; Wirner, Frank; Klatt, Michael A; Hirneise, Daniel; Schröder-Turk, Gerd E; Mecke, Klaus; Bechinger, Clemens

    2015-10-01

    We study the relation of permeability and morphology for porous structures composed of randomly placed overlapping circular or elliptical grains, so-called Boolean models. Microfluidic experiments and lattice Boltzmann simulations allow us to evaluate a power-law relation between the Euler characteristic of the conducting phase and its permeability. Moreover, this relation is so far only directly applicable to structures composed of overlapping grains where the grain density is known a priori. We develop a generalization to arbitrary structures modeled by Boolean models and characterized by Minkowski functionals. This generalization works well for the permeability of the void phase in systems with overlapping grains, but systematic deviations are found if the grain phase is transporting the fluid. In the latter case our analysis reveals a significant dependence on the spatial discretization of the porous structure, in particular the occurrence of single isolated pixels. To link the results to percolation theory we performed Monte Carlo simulations of the Euler characteristic of the open cluster, which reveals different regimes of applicability for our permeability-morphology relations close to and far away from the percolation threshold.

  16. Majority Rules with Random Tie-Breaking in Boolean Gene Regulatory Networks

    Science.gov (United States)

    Chaouiya, Claudine; Ourrad, Ouerdia; Lima, Ricardo

    2013-01-01

    We consider threshold Boolean gene regulatory networks, where the update function of each gene is described as a majority rule evaluated among the regulators of that gene: it is turned ON when the sum of its regulator contributions is positive (activators contribute positively whereas repressors contribute negatively) and turned OFF when this sum is negative. In case of a tie (when contributions cancel each other out), it is often assumed that the gene keeps it current state. This framework has been successfully used to model cell cycle control in yeast. Moreover, several studies consider stochastic extensions to assess the robustness of such a model. Here, we introduce a novel, natural stochastic extension of the majority rule. It consists in randomly choosing the next value of a gene only in case of a tie. Hence, the resulting model includes deterministic and probabilistic updates. We present variants of the majority rule, including alternate treatments of the tie situation. Impact of these variants on the corresponding dynamical behaviours is discussed. After a thorough study of a class of two-node networks, we illustrate the interest of our stochastic extension using a published cell cycle model. In particular, we demonstrate that steady state analysis can be rigorously performed and can lead to effective predictions; these relate for example to the identification of interactions whose addition would ensure that a specific state is absorbing. PMID:23922761

  17. Majority rules with random tie-breaking in Boolean gene regulatory networks.

    Directory of Open Access Journals (Sweden)

    Claudine Chaouiya

    Full Text Available We consider threshold boolean gene regulatory networks, where the update function of each gene is described as a majority rule evaluated among the regulators of that gene: it is turned ON when the sum of its regulator contributions is positive (activators contribute positively whereas repressors contribute negatively and turned OFF when this sum is negative. In case of a tie (when contributions cancel each other out, it is often assumed that the gene keeps it current state. This framework has been successfully used to model cell cycle control in yeast. Moreover, several studies consider stochastic extensions to assess the robustness of such a model. Here, we introduce a novel, natural stochastic extension of the majority rule. It consists in randomly choosing the next value of a gene only in case of a tie. Hence, the resulting model includes deterministic and probabilistic updates. We present variants of the majority rule, including alternate treatments of the tie situation. Impact of these variants on the corresponding dynamical behaviours is discussed. After a thorough study of a class of two-node networks, we illustrate the interest of our stochastic extension using a published cell cycle model. In particular, we demonstrate that steady state analysis can be rigorously performed and can lead to effective predictions; these relate for example to the identification of interactions whose addition would ensure that a specific state is absorbing.

  18. Improving the User Query for the Boolean Model Using Genetic Algorithms

    CERN Document Server

    Nassar, Mohammad Othman; Mashagba, Eman Al

    2011-01-01

    The Use of genetic algorithms in the Information retrieval (IR) area, especially in optimizing a user query in Arabic data collections is presented in this paper. Very little research has been carried out on Arabic text collections. Boolean model have been used in this research. To optimize the query using GA we used different fitness functions, different mutation strategies to find which is the best strategy and fitness function that can be used with Boolean model when the data collection is the Arabic language. Our results show that the best GA strategy for the Boolean model is the GA (M2, Precision) method.

  19. Stability of Boolean networks: The joint effects of topology and update rules

    Science.gov (United States)

    Squires, Shane; Pomerance, Andrew; Girvan, Michelle; Ott, Edward

    2014-08-01

    We study the stability of orbits in large Boolean networks. We treat the case in which the network has a given complex topology, and we do not assume a specific form for the update rules, which may be correlated with local topological properties of the network. While recent past work has addressed the separate effects of complex network topology and certain classes of update rules on stability, only crude results exist about how these effects interact. We present a widely applicable solution to this problem. Numerical simulations confirm our theory and show that local correlations between topology and update rules can have profound effects on the qualitative behavior of these systems.

  20. Controllability and observability of Boolean control networks with time-variant delays in states.

    Science.gov (United States)

    Zhang, Lijun; Zhang, Kuize

    2013-09-01

    This brief investigates the controllability and observability of Boolean control networks with (not necessarily bounded) time-variant delays in states. After a brief introduction to converting a Boolean control network to an equivalent discrete-time bilinear dynamical system via the semi-tensor product of matrices, the system is split into a finite number of subsystems (constructed forest) with no time delays by using the idea of splitting time that is proposed in this brief. Then, the controllability and observability of the system are investigated by verifying any so-called controllability constructed path and any so-called observability constructed paths in the above forest, respectively, which generalize some recent relevant results. Matrix test criteria for the controllability and observability are given. The corresponding control design algorithms based on the controllability theorems are given. We also show that the computing complexity of our algorithm is much less than that of the existing algorithms.

  1. Boolean Modeling of Cellular and Molecular Pathways Involved in Influenza Infection

    Science.gov (United States)

    Anderson, Christopher S.; DeDiego, Marta L.; Topham, David J.; Thakar, Juilee

    2016-01-01

    Systems virology integrates host-directed approaches with molecular profiling to understand viral pathogenesis. Self-contained statistical approaches that combine expression profiles of genes with the available databases defining the genes involved in the pathways (gene-sets) have allowed characterization of predictive gene-signatures associated with outcome of the influenza virus (IV) infection. However, such enrichment techniques do not take into account interactions among pathways that are responsible for the IV infection pathogenesis. We investigate dendritic cell response to seasonal H1N1 influenza A/New Caledonia/20/1999 (NC) infection and infer the Boolean logic rules underlying the interaction network of ligand induced signaling pathways and transcription factors. The model reveals several novel regulatory modes and provides insights into mechanism of cross talk between NFκB and IRF mediated signaling. Additionally, the logic rule underlying the regulation of IL2 pathway that was predicted by the Boolean model was experimentally validated. Thus, the model developed in this paper integrates pathway analysis tools with the dynamic modeling approaches to reveal the regulation between signaling pathways and transcription factors using genome-wide transcriptional profiles measured upon influenza infection. PMID:26981147

  2. Boolean Modeling of Cellular and Molecular Pathways Involved in Influenza Infection

    Directory of Open Access Journals (Sweden)

    Christopher S. Anderson

    2016-01-01

    Full Text Available Systems virology integrates host-directed approaches with molecular profiling to understand viral pathogenesis. Self-contained statistical approaches that combine expression profiles of genes with the available databases defining the genes involved in the pathways (gene-sets have allowed characterization of predictive gene-signatures associated with outcome of the influenza virus (IV infection. However, such enrichment techniques do not take into account interactions among pathways that are responsible for the IV infection pathogenesis. We investigate dendritic cell response to seasonal H1N1 influenza A/New Caledonia/20/1999 (NC infection and infer the Boolean logic rules underlying the interaction network of ligand induced signaling pathways and transcription factors. The model reveals several novel regulatory modes and provides insights into mechanism of cross talk between NFκB and IRF mediated signaling. Additionally, the logic rule underlying the regulation of IL2 pathway that was predicted by the Boolean model was experimentally validated. Thus, the model developed in this paper integrates pathway analysis tools with the dynamic modeling approaches to reveal the regulation between signaling pathways and transcription factors using genome-wide transcriptional profiles measured upon influenza infection.

  3. Boolean Modeling of Cellular and Molecular Pathways Involved in Influenza Infection.

    Science.gov (United States)

    Anderson, Christopher S; DeDiego, Marta L; Topham, David J; Thakar, Juilee

    2016-01-01

    Systems virology integrates host-directed approaches with molecular profiling to understand viral pathogenesis. Self-contained statistical approaches that combine expression profiles of genes with the available databases defining the genes involved in the pathways (gene-sets) have allowed characterization of predictive gene-signatures associated with outcome of the influenza virus (IV) infection. However, such enrichment techniques do not take into account interactions among pathways that are responsible for the IV infection pathogenesis. We investigate dendritic cell response to seasonal H1N1 influenza A/New Caledonia/20/1999 (NC) infection and infer the Boolean logic rules underlying the interaction network of ligand induced signaling pathways and transcription factors. The model reveals several novel regulatory modes and provides insights into mechanism of cross talk between NFκB and IRF mediated signaling. Additionally, the logic rule underlying the regulation of IL2 pathway that was predicted by the Boolean model was experimentally validated. Thus, the model developed in this paper integrates pathway analysis tools with the dynamic modeling approaches to reveal the regulation between signaling pathways and transcription factors using genome-wide transcriptional profiles measured upon influenza infection.

  4. Phase transition in NK-Kauffman networks and its correction for Boolean irreducibility

    Science.gov (United States)

    Zertuche, Federico

    2014-05-01

    In a series of articles published in 1986, Derrida and his colleagues studied two mean field treatments (the quenched and the annealed) for NK-Kauffman networks. Their main results lead to a phase transition curve Kc 2 pc(1-pc)=1 (0Boolean functions, called Boolean irreducibility, permitted the study of new phenomena of NK-Kauffman networks. In the present work we study once again the mean field treatment for NK-Kauffman networks, correcting it for Boolean irreducibility. A shifted phase transition curve is found. In particular, for pc=1/2 the predicted value Kc=2 by Derrida et al. changes to Kc=2.62140224613…. We support our results with numerical simulations.

  5. A novel mutual information-based Boolean network inference method from time-series gene expression data

    Science.gov (United States)

    Barman, Shohag; Kwon, Yung-Keun

    2017-01-01

    Background Inferring a gene regulatory network from time-series gene expression data in systems biology is a challenging problem. Many methods have been suggested, most of which have a scalability limitation due to the combinatorial cost of searching a regulatory set of genes. In addition, they have focused on the accurate inference of a network structure only. Therefore, there is a pressing need to develop a network inference method to search regulatory genes efficiently and to predict the network dynamics accurately. Results In this study, we employed a Boolean network model with a restricted update rule scheme to capture coarse-grained dynamics, and propose a novel mutual information-based Boolean network inference (MIBNI) method. Given time-series gene expression data as an input, the method first identifies a set of initial regulatory genes using mutual information-based feature selection, and then improves the dynamics prediction accuracy by iteratively swapping a pair of genes between sets of the selected regulatory genes and the other genes. Through extensive simulations with artificial datasets, MIBNI showed consistently better performance than six well-known existing methods, REVEAL, Best-Fit, RelNet, CST, CLR, and BIBN in terms of both structural and dynamics prediction accuracy. We further tested the proposed method with two real gene expression datasets for an Escherichia coli gene regulatory network and a fission yeast cell cycle network, and also observed better results using MIBNI compared to the six other methods. Conclusions Taken together, MIBNI is a promising tool for predicting both the structure and the dynamics of a gene regulatory network. PMID:28178334

  6. Invariance Under Quasi-isometries of Subcritical and Supercritical Behavior in the Boolean Model of Percolation

    Science.gov (United States)

    Coletti, Cristian F.; Miranda, Daniel; Mussini, Filipe

    2016-02-01

    In this work we study the Poisson Boolean model of percolation in locally compact Polish metric spaces and we prove the invariance of subcritical and supercritical phases under mm-quasi-isometries. More precisely, we prove that if a metric space M is mm-quasi-isometric to another metric space N and the Poisson Boolean model in M exhibits any of the following: (a) a subcritical phase; (b) a supercritical phase; or (c) a phase transition, then respectively so does the Poisson Boolean model of percolation in N. Then we use these results in order to understand the phase transition phenomenon in a large family of metric spaces. Indeed, we study the Poisson Boolean model of percolation in the context of Riemannian manifolds, in a large family of nilpotent Lie groups and in Cayley graphs. Also, we prove the existence of a subcritical phase in Gromov spaces with bounded growth at some scale.

  7. Stability of Boolean networks: The joint effects of topology and update rules

    CERN Document Server

    Squires, Shane; Girvan, Michelle; Ott, Edward

    2013-01-01

    We study the stability of orbits in large Boolean networks with given complex topology. We impose no restrictions on the form of the update rules, which may be correlated with local topological properties of the network. While recent past work has addressed the separate effects of nontrivial network topology and certain special classes of update rules on stability, only crude results exist about how these effects interact. We present a widely applicable solution to this problem. Numerical experiments confirm our theory and show that local correlations between topology and update rules can have profound effects on the qualitative behavior of these systems.

  8. Model construction from orthographic views as Pseudo Boolean constraint satisfaction problem

    Energy Technology Data Exchange (ETDEWEB)

    Itoh, Kiyoshi; Suzuki, Shigemich [Sophia Univ., Tokyo (Japan)

    1996-12-31

    A surface model representation of a solid can be constructed in straightforward fashion from a set of three orthographic views. The surface model may include ghost vertexes, ghost edges and ghost faces. The authors` project, called Sophia-Alsovig, treats the problem for obtaining valid combination of surfaces and edges as Pseudo Boolean constraint satisfaction problem (CSP). It can remove such ghosts. As CSP, Sophia-Alsovig adopts a set of units consisting of edges and surfaces, a set of Boolean labels, and a set of constraints with the formulation of a collection of topological/geometrical rules for edges and surfaces by Pseudo Boolean equations. Sophia-Alsovig obtains solutions by Pseudo Boolean Nonlinear Programming.

  9. Sensitivity analysis of biological Boolean networks using information fusion based on nonadditive set functions

    Science.gov (United States)

    2014-01-01

    Background An algebraic method for information fusion based on nonadditive set functions is used to assess the joint contribution of Boolean network attributes to the sensitivity of the network to individual node mutations. The node attributes or characteristics under consideration are: in-degree, out-degree, minimum and average path lengths, bias, average sensitivity of Boolean functions, and canalizing degrees. The impact of node mutations is assessed using as target measure the average Hamming distance between a non-mutated/wild-type network and a mutated network. Results We find that for a biochemical signal transduction network consisting of several main signaling pathways whose nodes represent signaling molecules (mainly proteins), the algebraic method provides a robust classification of attribute contributions. This method indicates that for the biochemical network, the most significant impact is generated mainly by the combined effects of two attributes: out-degree, and average sensitivity of nodes. Conclusions The results support the idea that both topological and dynamical properties of the nodes need to be under consideration. The algebraic method is robust against the choice of initial conditions and partition of data sets in training and testing sets for estimation of the nonadditive set functions of the information fusion procedure. PMID:25189194

  10. HSP70 mediates survival in apoptotic cells-Boolean network prediction and experimental validation.

    Science.gov (United States)

    Vasaikar, Suhas V; Ghosh, Sourish; Narain, Priyam; Basu, Anirban; Gomes, James

    2015-01-01

    Neuronal stress or injury results in the activation of proteins, which regulate the balance between survival and apoptosis. However, the complex mechanism of cell signaling involving cell death and survival, activated in response to cellular stress is not yet completely understood. To bring more clarity about these mechanisms, a Boolean network was constructed that represented the apoptotic pathway in neuronal cells. FasL and neurotrophic growth factor (NGF) were considered as inputs in the absence and presence of heat shock proteins known to shift the balance toward survival by rescuing pro-apoptotic cells. The probabilities of survival, DNA repair and apoptosis as cellular fates, in the presence of either the growth factor or FasL, revealed a survival bias encoded in the network. Boolean predictions tested by measuring the mRNA level of caspase-3, caspase-8, and BAX in neuronal Neuro2a (N2a) cell line with NGF and FasL as external input, showed positive correlation with the observed experimental results for survival and apoptotic states. It was observed that HSP70 contributed more toward rescuing cells from apoptosis in comparison to HSP27, HSP40, and HSP90. Overexpression of HSP70 in N2a transfected cells showed reversal of cellular fate from FasL-induced apoptosis to survival. Further, the pro-survival role of the proteins BCL2, IAP, cFLIP, and NFκB determined by vertex perturbation analysis was experimentally validated through protein inhibition experiments using EM20-25, Embelin and Wedelolactone, which resulted in 1.27-, 1.26-, and 1.46-fold increase in apoptosis of N2a cells. The existence of a one-to-one correspondence between cellular fates and attractor states shows that Boolean networks may be employed with confidence in qualitative analytical studies of biological networks.

  11. Boolean logic functions of a synthetic peptide network.

    Science.gov (United States)

    Ashkenasy, Gonen; Ghadiri, M Reza

    2004-09-15

    Living cells can process rapidly and simultaneously multiple extracellular input signals through the complex networks of evolutionary selected biomolecular interactions and chemical transformations. Recent approaches to molecular computation have increasingly sought to mimic or exploit various aspects of biology. A number of studies have adapted nucleic acids and proteins to the design of molecular logic gates and computational systems, while other works have affected computation in living cells via biochemical pathway engineering. Here we report that de novo designed synthetic peptide networks can also mimic some of the basic logic functions of the more complex biological networks. We show that segments of a small network whose graph structure is composed of five nodes and 15 directed edges can express OR, NOR, and NOTIF logic.

  12. Boolean Modelling Reveals New Regulatory Connections between Transcription Factors Orchestrating the Development of the Ventral Spinal Cord

    Science.gov (United States)

    Lovrics, Anna; Gao, Yu; Juhász, Bianka; Bock, István; Byrne, Helen M.; Dinnyés, András; Kovács, Krisztián A.

    2014-01-01

    We have assembled a network of cell-fate determining transcription factors that play a key role in the specification of the ventral neuronal subtypes of the spinal cord on the basis of published transcriptional interactions. Asynchronous Boolean modelling of the network was used to compare simulation results with reported experimental observations. Such comparison highlighted the need to include additional regulatory connections in order to obtain the fixed point attractors of the model associated with the five known progenitor cell types located in the ventral spinal cord. The revised gene regulatory network reproduced previously observed cell state switches between progenitor cells observed in knock-out animal models or in experiments where the transcription factors were overexpressed. Furthermore the network predicted the inhibition of Irx3 by Nkx2.2 and this prediction was tested experimentally. Our results provide evidence for the existence of an as yet undescribed inhibitory connection which could potentially have significance beyond the ventral spinal cord. The work presented in this paper demonstrates the strength of Boolean modelling for identifying gene regulatory networks. PMID:25398016

  13. Boolean modelling reveals new regulatory connections between transcription factors orchestrating the development of the ventral spinal cord.

    KAUST Repository

    Lovrics, Anna

    2014-11-14

    We have assembled a network of cell-fate determining transcription factors that play a key role in the specification of the ventral neuronal subtypes of the spinal cord on the basis of published transcriptional interactions. Asynchronous Boolean modelling of the network was used to compare simulation results with reported experimental observations. Such comparison highlighted the need to include additional regulatory connections in order to obtain the fixed point attractors of the model associated with the five known progenitor cell types located in the ventral spinal cord. The revised gene regulatory network reproduced previously observed cell state switches between progenitor cells observed in knock-out animal models or in experiments where the transcription factors were overexpressed. Furthermore the network predicted the inhibition of Irx3 by Nkx2.2 and this prediction was tested experimentally. Our results provide evidence for the existence of an as yet undescribed inhibitory connection which could potentially have significance beyond the ventral spinal cord. The work presented in this paper demonstrates the strength of Boolean modelling for identifying gene regulatory networks.

  14. Variances as order parameter and complexity measure for random Boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Luque, Bartolo [Departamento de Matematica Aplicada y EstadIstica, Escuela Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, Madrid 28040 (Spain); Ballesteros, Fernando J [Observatori Astronomic, Universitat de Valencia, Ed. Instituts d' Investigacio, Pol. La Coma s/n, E-46980 Paterna, Valencia (Spain); Fernandez, Manuel [Departamento de Matematica Aplicada y EstadIstica, Escuela Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, Madrid 28040 (Spain)

    2005-02-04

    Several order parameters have been considered to predict and characterize the transition between ordered and disordered phases in random Boolean networks, such as the Hamming distance between replicas or the stable core, which have been successfully used. In this work, we propose a natural and clear new order parameter: the temporal variance. We compute its value analytically and compare it with the results of numerical experiments. Finally, we propose a complexity measure based on the compromise between temporal and spatial variances. This new order parameter and its related complexity measure can be easily applied to other complex systems.

  15. Evolution of a designless nanoparticle network into reconfigurable Boolean logic

    NARCIS (Netherlands)

    Bose, S.K.; Lawrence, C.P.; Liu, Z.; Makarenko, K.S.; Damme, van R.M.J.; Broersma, H.J.; Wiel, van der W.G.

    2015-01-01

    Natural computers exploit the emergent properties and massive parallelism of interconnected networks of locally active components. Evolution has resulted in systems that compute quickly and that use energy efficiently, utilizing whatever physical properties are exploitable. Man-made computers, on th

  16. Effective Boolean dynamics analysis to identify functionally important genes in large-scale signaling networks.

    Science.gov (United States)

    Trinh, Hung-Cuong; Kwon, Yung-Keun

    2015-11-01

    Efficiently identifying functionally important genes in order to understand the minimal requirements of normal cellular development is challenging. To this end, a variety of structural measures have been proposed and their effectiveness has been investigated in recent literature; however, few studies have shown the effectiveness of dynamics-based measures. This led us to investigate a dynamic measure to identify functionally important genes, and the effectiveness of which was verified through application on two large-scale human signaling networks. We specifically consider Boolean sensitivity-based dynamics against an update-rule perturbation (BSU) as a dynamic measure. Through investigations on two large-scale human signaling networks, we found that genes with relatively high BSU values show slower evolutionary rate and higher proportions of essential genes and drug targets than other genes. Gene-ontology analysis showed clear differences between the former and latter groups of genes. Furthermore, we compare the identification accuracies of essential genes and drug targets via BSU and five well-known structural measures. Although BSU did not always show the best performance, it effectively identified the putative set of genes, which is significantly different from the results obtained via the structural measures. Most interestingly, BSU showed the highest synergy effect in identifying the functionally important genes in conjunction with other measures. Our results imply that Boolean-sensitive dynamics can be used as a measure to effectively identify functionally important genes in signaling networks.

  17. 高阶布尔网络的结构%Structure of higher order Boolean networks*

    Institute of Scientific and Technical Information of China (English)

    李志强; 赵寅; 程代展

    2011-01-01

    The higher order Boolean (control) network is introduced and its topological structure is studied.Using semi-tensor product of matrices,its dynamics is converted into two algebraic forms,which are standard discrete-time dynamic systems.The one-to-one correspondence of the network dynamics and its first algebraic form is proved,and certain topological structures,including fixed points,cycles,and transient time,of higher order Boolean (control) networks are revealed.The relationship between the original system and its second algebraic form is also studied.%介绍高阶布尔(控制)网络,并研究了其拓扑结构.以矩阵的半张量积作为工具,把高阶布尔网络的动态过程转化为2种标准离散事件动态系统的代数形式.证明了高阶布尔网络和第1代数形式的一一对应关系,并由此得到其拓扑结构(不动点、极限圈以及暂态期等).还研究了高阶布尔网络系统与它第2代数形式的关系.

  18. TESTING HISTOLOGICAL IMAGES OF MAMMARY TISSUES ON COMPATIBILITY WITH THE BOOLEAN MODEL OF RANDOM SETS

    Directory of Open Access Journals (Sweden)

    Tomáš Mrkvička

    2011-03-01

    Full Text Available Methods for testing the Boolean model assumption from binary images are briefly reviewed. Two hundred binary images of mammary cancer tissue and 200 images of mastopathic tissue were tested individually on the Boolean model assumption. In a previous paper, it had been found that a Monte Carlo method based on the approximation of the envelopes by a multi-normal distribution with the normalized intrinsic volume densities of parallel sets as a summary statistics had the highest power for this purpose. Hence, this method was used here as its first application to real biomedical data. It was found that mastopathic tissue deviates from the Boolean model significantly more strongly than mammary cancer tissue does.

  19. Boolean nested canalizing functions: a comprehensive analysis

    CERN Document Server

    Li, Yuan; Murrugarra, David; Aguilar, Boris; Laubenbacher, Reinhard

    2012-01-01

    Boolean network models of molecular regulatory networks have been used successfully in computational systems biology. The Boolean functions that appear in published models tend to have special properties, in particular the property of being nested canalizing, a property inspired by the concept of canalization in evolutionary biology. It has been shown that networks comprised of nested canalizing functions have dynamic properties that make them suitable for modeling molecular regulatory networks, namely a small number of (large) attractors, as well as relatively short limit cycles. This paper contains a detailed analysis of this class of functions, based on a novel normal form as polynomial functions over the Boolean field. The concept of layer is introduced that stratifies variables into different classes depending on their level of dominance. Using this layer concept a closed form formula is derived for the number of nested canalizing functions with a given number of variables. Additional metrics analyzed in...

  20. Problems in modeling a weighted Boolean retrieval system

    Energy Technology Data Exchange (ETDEWEB)

    Kraft, D.H.; Waller, W.G.

    1979-01-01

    The use of weights to denote a query representation and/or the indexing of a document is analyzed as a generalization of a Boolean retrieval system. Criteria are given for the functions used to evaluate the relevance of the records to a specific query. Various mechanisms for evaluating the relevance of records with regard to a given query are tested and found to be less than satisfactory. A new approach is suggested to avoid some of the perils.

  1. Dynamics of Random Boolean Networks under Fully Asynchronous Stochastic Update Based on Linear Representation

    Science.gov (United States)

    Luo, Chao; Wang, Xingyuan

    2013-01-01

    A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs). In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of length in ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme. PMID:23785502

  2. Stratification and enumeration of Boolean functions by canalizing depth

    CERN Document Server

    He, Qijun

    2015-01-01

    Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The canalizing depth of a function describes how many canalizing variables can be recursively picked off, until a non-canalizing function remains. In this paper, we show how every Boolean function has a unique algebraic form involving extended monomial layers and a well-defined core polynomial. 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. As a result, we obtain closed formulas for the number of n-variable Boolean functions with depth k, which simultaneously generalizes enumeration formulas for canalizing, and nested canalizing functions.

  3. Stratification and enumeration of Boolean functions by canalizing depth

    Science.gov (United States)

    He, Qijun; Macauley, Matthew

    2016-01-01

    Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The canalizing depth of a function describes how many canalizing variables can be recursively "picked off", until a non-canalizing function remains. In this paper, we show how every Boolean function has a unique algebraic form involving extended monomial layers and a well-defined core polynomial. 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. As a result, we obtain closed formulas for the number of n-variable Boolean functions with depth k, which simultaneously generalizes enumeration formulas for canalizing, and nested canalizing functions.

  4. A comprehensive approach to the molecular determinants of lifespan using a Boolean model of geroconversion.

    Science.gov (United States)

    Verlingue, Loic; Dugourd, Aurélien; Stoll, Gautier; Barillot, Emmanuel; Calzone, Laurence; Londoño-Vallejo, Arturo

    2016-09-09

    Altered molecular responses to insulin and growth factors (GF) are responsible for late-life shortening diseases such as type-2 diabetes mellitus (T2DM) and cancers. We have built a network of the signaling pathways that control S-phase entry and a specific type of senescence called geroconversion. We have translated this network into a Boolean model to study possible cell phenotype outcomes under diverse molecular signaling conditions. In the context of insulin resistance, the model was able to reproduce the variations of the senescence level observed in tissues related to T2DM's main morbidity and mortality. Furthermore, by calibrating the pharmacodynamics of mTOR inhibitors, we have been able to reproduce the dose-dependent effect of rapamycin on liver degeneration and lifespan expansion in wild-type and HER2-neu mice. Using the model, we have finally performed an in silico prospective screen of the risk-benefit ratio of rapamycin dosage for healthy lifespan expansion strategies. We present here a comprehensive prognostic and predictive systems biology tool for human aging.

  5. On a Boolean-valued Model of the Strict Implication System(Continuous)

    Institute of Scientific and Technical Information of China (English)

    LI Na; LIU Hua-ke

    2004-01-01

    The reference [4] proved the consistency of S 1 and S 2 among Lewis'five strict implicationsystems in the modal logic by using the method of the Boolean-valued model. But, in this method, the consistency of S 3 , S 4 and S 5 in Lewis'five strictimplication systems is not decided. This paper makes use of the properties : (1) the equivalence of the modal systems S 3 andP 3 , S 4 and P 4 ; (2) the modal systems P 3 and P 4 all contained the modal axiom T(□p) ; (3) the modal axiom T is correspondence to the reflexiveproperty in VB . Hence, the paper proves: (a) |A S 31|=1 ; (b) |A S 41|=1 ;(c) |A S 51|=1 in the model (where B is a complete Boolean algebra, R is reflexive property in VB ). Therefore, the paper finallyproves that the Boolean-valued model VB of the ZFC axiomsystem in set theory is also a Boolean-valued model of Lewis'the strict implication system S 3 , S 4 and S 5 .

  6. Application of fuzzy logic to Boolean models for digital soil assessment

    NARCIS (Netherlands)

    Gruijter, de J.J.; Walvoort, D.J.J.; Bragato, G.

    2011-01-01

    Boolean models based on expert knowledge are often used to classify soils into a limited number of classes of a difficult-to-measure soil attribute. Although the primary data used for these classifications contain information on whether the soil is a typical class member or a boundary case between t

  7. Using whole number models with Boolean variables for solving optimization problems in the oil industry

    Energy Technology Data Exchange (ETDEWEB)

    Smorodinskiy, B.I.

    1984-01-01

    A theoretical justification is given for a method for solving one of the common problems in whole number linear programming with Boolean variables. It is shown that a number of optimization problems in the oil industry can be reduced to this model.

  8. A Boolean model of the Pseudomonas syringae hrp regulon predicts a tightly regulated system.

    Directory of Open Access Journals (Sweden)

    Daniel MacLean

    Full Text Available The Type III secretion system (TTSS is a protein secretion machinery used by certain gram-negative bacterial pathogens of plants and animals to deliver effector molecules to the host and is at the core of the ability to cause disease. Extensive molecular and biochemical study has revealed the components and their interactions within this system but reductive approaches do not consider the dynamical properties of the system as a whole. In order to gain a better understanding of these dynamical behaviours and to create a basis for the refinement of the experimentally derived knowledge we created a Boolean model of the regulatory interactions within the hrp regulon of Pseudomonas syringae pathovar tomato strain DC3000 Pseudomonas syringae. We compared simulations of the model with experimental data and found them to be largely in accordance, though the hrpV node shows some differences in state changes to that expected. Our simulations also revealed interesting dynamical properties not previously predicted. The model predicts that the hrp regulon is a biologically stable two-state system, with each of the stable states being strongly attractive, a feature indicative of selection for a tightly regulated and responsive system. The model predicts that the state of the GacS/GacA node confers control, a prediction that is consistent with experimental observations that the protein has a role as master regulator. Simulated gene "knock out" experiments with the model predict that HrpL is a central information processing point within the network.

  9. An efficient algorithm to identify the optimal one-bit perturbation based on the basin-of-state size of Boolean networks.

    Science.gov (United States)

    Hu, Mingxiao; Shen, Liangzhong; Zan, Xiangzhen; Shang, Xuequn; Liu, Wenbin

    2016-05-19

    Boolean networks are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long-term behavior of systems. In this paper, we investigate the less-studied one-bit perturbation, which falls under the category of structural intervention. Previous works focused on finding the optimal one-bit perturbation to maximally alter the steady-state distribution (SSD) of undesirable states through matrix perturbation theory. However, the application of the SSD is limited to Boolean networks with about ten genes. In 2007, Xiao et al. proposed to search the optimal one-bit perturbation by altering the sizes of the basin of attractions (BOAs). However, their algorithm requires close observation of the state-transition diagram. In this paper, we propose an algorithm that efficiently determines the BOA size after a perturbation. Our idea is that, if we construct the basin of states for all states, then the size of the BOA of perturbed networks can be obtained just by updating the paths of the states whose transitions have been affected. Results from both synthetic and real biological networks show that the proposed algorithm performs better than the exhaustive SSD-based algorithm and can be applied to networks with about 25 genes.

  10. Random sampling versus exact enumeration of attractors in random Boolean networks

    Energy Technology Data Exchange (ETDEWEB)

    Berdahl, Andrew; Shreim, Amer; Sood, Vishal; Paczuski, Maya; Davidsen, Joern [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Alberta (Canada)], E-mail: aberdahl@phas.ucalgary.ca

    2009-04-15

    We clarify the effect different sampling methods and weighting schemes have on the statistics of attractors in ensembles of random Boolean networks (RBNs). We directly measure the cycle lengths of attractors and the sizes of basins of attraction in RBNs using exact enumeration of the state space. In general, the distribution of attractor lengths differs markedly from that obtained by randomly choosing an initial state and following the dynamics to reach an attractor. Our results indicate that the former distribution decays as a power law with exponent 1 for all connectivities K>1 in the infinite system size limit. In contrast, the latter distribution decays as a power law only for K=2. This is because the mean basin size grows linearly with the attractor cycle length for K>2, and is statistically independent of the cycle length for K=2. We also find that the histograms of basin sizes are strongly peaked at integer multiples of powers of two for K<3.

  11. Robust Template Decomposition without Weight Restriction for Cellular Neural Networks Implementing Arbitrary Boolean Functions Using Support Vector Classifiers

    Directory of Open Access Journals (Sweden)

    Yih-Lon Lin

    2013-01-01

    Full Text Available If the given Boolean function is linearly separable, a robust uncoupled cellular neural network can be designed as a maximal margin classifier. On the other hand, if the given Boolean function is linearly separable but has a small geometric margin or it is not linearly separable, a popular approach is to find a sequence of robust uncoupled cellular neural networks implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are restricted to assume only a given finite set of integers, and this is certainly unnecessary for the template design. In this study, we try to remove this restriction. Minterm- and maxterm-based decomposition algorithms utilizing the soft margin and maximal margin support vector classifiers are proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.

  12. Overview of methods of reverse engineering of gene regulatory networks: Boolean and Bayesian networks

    OpenAIRE

    Frolova A. O.

    2012-01-01

    Reverse engineering of gene regulatory networks is an intensively studied topic in Systems Biology as it reconstructs regulatory interactions between all genes in the genome in the most complete form. The extreme computational complexity of this problem and lack of thorough reviews on reconstruction methods of gene regulatory network is a significant obstacle to further development of this area. In this article the two most common methods for modeling gene regulatory networks are surveyed: Bo...

  13. Avalanches, branching ratios, and clustering of attractors in random Boolean networks and in the segment polarity network of Drosophila

    Energy Technology Data Exchange (ETDEWEB)

    Berdahl, Andrew; Shreim, Amer; Sood, Vishal; Davidsen, Joern; Paczuski, Maya [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4 (Canada)], E-mail: aberdahl@phas.ucalgary.ca

    2008-06-15

    We discuss basic features of emergent complexity in dynamical systems far from equilibrium by focusing on the network structure of their state space. We start by measuring the distributions of avalanche and transient times in random Boolean networks (RBNs) and in the Drosophila polarity network by exact enumeration. A transient time is the duration of the transient from a starting state to an attractor. An avalanche is a special transient which starts as a single Boolean element perturbation of an attractor state. Significant differences at short times between the avalanche and the transient times for RBNs with small connectivity K-compared to the number of elements N-indicate that attractors tend to cluster in configuration space. In addition, one bit flip has a non-negligible chance to put an attractor state directly onto another attractor. This clustering is also present in the segment polarity gene network of Drosophila melanogaster, suggesting that this may be a robust feature of biological regulatory networks. We also define and measure a branching ratio for the state space networks and find evidence for a new timescale that diverges roughly linearly with N for 2{<=}K<

  14. Boolean complexes and boolean numbers

    OpenAIRE

    Tenner, Bridget Eileen

    2017-01-01

    International audience; The Bruhat order gives a poset structure to any Coxeter group. The ideal of elements in this poset having boolean principal order ideals forms a simplicial poset. This simplicial poset defines the boolean complex for the group. In a Coxeter system of rank n, we show that the boolean complex is homotopy equivalent to a wedge of (n-1)-dimensional spheres. The number of these spheres is the boolean number, which can be computed inductively from the unlabeled Coxeter syste...

  15. Computational complexity of Boolean functions

    Energy Technology Data Exchange (ETDEWEB)

    Korshunov, Aleksei D [Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)

    2012-02-28

    Boolean functions are among the fundamental objects of discrete mathematics, especially in those of its subdisciplines which fall under mathematical logic and mathematical cybernetics. The language of Boolean functions is convenient for describing the operation of many discrete systems such as contact networks, Boolean circuits, branching programs, and some others. An important parameter of discrete systems of this kind is their complexity. This characteristic has been actively investigated starting from Shannon's works. There is a large body of scientific literature presenting many fundamental results. The purpose of this survey is to give an account of the main results over the last sixty years related to the complexity of computation (realization) of Boolean functions by contact networks, Boolean circuits, and Boolean circuits without branching. Bibliography: 165 titles.

  16. Modeling gene regulatory networks: A network simplification algorithm

    Science.gov (United States)

    Ferreira, Luiz Henrique O.; de Castro, Maria Clicia S.; da Silva, Fabricio A. B.

    2016-12-01

    Boolean networks have been used for some time to model Gene Regulatory Networks (GRNs), which describe cell functions. Those models can help biologists to make predictions, prognosis and even specialized treatment when some disturb on the GRN lead to a sick condition. However, the amount of information related to a GRN can be huge, making the task of inferring its boolean network representation quite a challenge. The method shown here takes into account information about the interactome to build a network, where each node represents a protein, and uses the entropy of each node as a key to reduce the size of the network, allowing the further inferring process to focus only on the main protein hubs, the ones with most potential to interfere in overall network behavior.

  17. Boolean Combinations of Implicit Functions for Model Clipping in Computer-Assisted Surgical Planning.

    Science.gov (United States)

    Zhan, Qiqin; Chen, Xiaojun

    2016-01-01

    This paper proposes an interactive method of model clipping for computer-assisted surgical planning. The model is separated by a data filter that is defined by the implicit function of the clipping path. Being interactive to surgeons, the clipping path that is composed of the plane widgets can be manually repositioned along the desirable presurgical path, which means that surgeons can produce any accurate shape of the clipped model. The implicit function is acquired through a recursive algorithm based on the Boolean combinations (including Boolean union and Boolean intersection) of a series of plane widgets' implicit functions. The algorithm is evaluated as highly efficient because the best time performance of the algorithm is linear, which applies to most of the cases in the computer-assisted surgical planning. Based on the above stated algorithm, a user-friendly module named SmartModelClip is developed on the basis of Slicer platform and VTK. A number of arbitrary clipping paths have been tested. Experimental results of presurgical planning for three types of Le Fort fractures and for tumor removal demonstrate the high reliability and efficiency of our recursive algorithm and robustness of the module.

  18. PARAMETER ESTIMATION IN NON-HOMOGENEOUS BOOLEAN MODELS: AN APPLICATION TO PLANT DEFENSE RESPONSE

    Directory of Open Access Journals (Sweden)

    Maria Angeles Gallego

    2014-11-01

    Full Text Available Many medical and biological problems require to extract information from microscopical images. Boolean models have been extensively used to analyze binary images of random clumps in many scientific fields. In this paper, a particular type of Boolean model with an underlying non-stationary point process is considered. The intensity of the underlying point process is formulated as a fixed function of the distance to a region of interest. A method to estimate the parameters of this Boolean model is introduced, and its performance is checked in two different settings. Firstly, a comparative study with other existent methods is done using simulated data. Secondly, the method is applied to analyze the longleaf data set, which is a very popular data set in the context of point processes included in the R package spatstat. Obtained results show that the new method provides as accurate estimates as those obtained with more complex methods developed for the general case. Finally, to illustrate the application of this model and this method, a particular type of phytopathological images are analyzed. These images show callose depositions in leaves of Arabidopsis plants. The analysis of callose depositions, is very popular in the phytopathological literature to quantify activity of plant immunity.

  19. Mathematical-logical modeling of regulations on mining safety. [Boolean algebra analysis

    Energy Technology Data Exchange (ETDEWEB)

    Fajkos, A.; Suchan, L.

    1979-09-01

    Complexity of the logical structure of mine safety regulations results from the complexity of mining problems. This complexity sometimes makes it difficult to precisely formulate mining safety regulations and to monitor their observance by the miners. It is suggested that mathematical- logical modeling can be an efficient tool in analyzing mine safety regulations. A short description of the method based on Boolean algebra, and three examples of its use in the field of mine safety regulations are presented. (2 refs.) (In Czech)

  20. Boolean Inner product Spaces and Boolean Matrices

    OpenAIRE

    Gudder, Stan; Latremoliere, Frederic

    2009-01-01

    This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and stochastic and unitary Boolean matrices are studied. A dimension theorem for orthonormal bases of a Boolean space is proven. We characterize the invariant stochastic Boolean vectors for a Boolean stochastic matrix and show that they can be used to reduce a unitary m...

  1. Monotone Boolean approximation

    Energy Technology Data Exchange (ETDEWEB)

    Hulme, B.L.

    1982-12-01

    This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application for the analysis of noncoherent fault trees and event tree sequences.

  2. Synchronization Analysis and Design of Coupled Boolean Networks Based on Periodic Switching Sequences.

    Science.gov (United States)

    Zhang, Huaguang; Tian, Hui; Wang, Zhanshan; Hou, Yanfang

    2016-12-01

    A novel synchronization analysis method is developed to solve the complete synchronization problem of many Boolean networks (BNs) coupled in the leader-follower configuration. First, an error system is constructed in terms of the algebraic representation using the semitensor product of matrices. Then, the synchronization problem of coupled BNs is converted into a problem whether all the trajectories of the error system are convergent to the zero vector. Second, according to the structure analysis of this error system, which is in the form of a switched system with leader BN states as the switching signal, a necessary and sufficient synchronization condition is derived. An algorithm is developed, which helps to determine as soon as possible whether complete synchronization among coupled BNs is achieved. Finally, a constructive design approach to follower BNs is provided. All of these follower BNs designed by our approach can completely synchronize with a given leader BN from the (Tt+1) th step at most, where Tt is the transient period of the leader BN.

  3. Determining a singleton attractor of a boolean network with nested canalyzing functions.

    Science.gov (United States)

    Akutsu, Tatsuya; Melkman, Avraham A; Tamura, Takeyuki; Yamamoto, Masaki

    2011-10-01

    In this article, we study the problem of finding a singleton attractor for several biologically important subclasses of Boolean networks (BNs). The problem of finding a singleton attractor in a BN is known to be NP-hard in general. For BNs consisting of n nested canalyzing functions, we present an O(1.799(n)) time algorithm. The core part of this development is an O(min(2(k/2) · 2(m/2), 2(k)) · poly(k, m)) time algorithm for the satisfiability problem for m nested canalyzing functions over k variables. For BNs consisting of chain functions, a subclass of nested canalyzing functions, we present an O(1.619(n)) time algorithm and show that the problem remains NP-hard, even though the satisfiability problem for m chain functions over k variables is solvable in polynomial time. Finally, we present an o(2(n)) time algorithm for bounded degree BNs consisting of canalyzing functions.

  4. Boolean Modeling Reveals the Necessity of Transcriptional Regulation for Bistability in PC12 Cell Differentiation.

    Science.gov (United States)

    Offermann, Barbara; Knauer, Steffen; Singh, Amit; Fernández-Cachón, María L; Klose, Martin; Kowar, Silke; Busch, Hauke; Boerries, Melanie

    2016-01-01

    The nerve growth factor NGF has been shown to cause cell fate decisions toward either differentiation or proliferation depending on the relative activity of downstream pERK, pAKT, or pJNK signaling. However, how these protein signals are translated into and fed back from transcriptional activity to complete cellular differentiation over a time span of hours to days is still an open question. Comparing the time-resolved transcriptome response of NGF- or EGF-stimulated PC12 cells over 24 h in combination with protein and phenotype data we inferred a dynamic Boolean model capturing the temporal sequence of protein signaling, transcriptional response and subsequent autocrine feedback. Network topology was optimized by fitting the model to time-resolved transcriptome data under MEK, PI3K, or JNK inhibition. The integrated model confirmed the parallel use of MAPK/ERK, PI3K/AKT, and JNK/JUN for PC12 cell differentiation. Redundancy of cell signaling is demonstrated from the inhibition of the different MAPK pathways. As suggested in silico and confirmed in vitro, differentiation was substantially suppressed under JNK inhibition, yet delayed only under MEK/ERK inhibition. Most importantly, we found that positive transcriptional feedback induces bistability in the cell fate switch. De novo gene expression was necessary to activate autocrine feedback that caused Urokinase-Type Plasminogen Activator (uPA) Receptor signaling to perpetuate the MAPK activity, finally resulting in the expression of late, differentiation related genes. Thus, the cellular decision toward differentiation depends on the establishment of a transcriptome-induced positive feedback between protein signaling and gene expression thereby constituting a robust control between proliferation and differentiation.

  5. Boolean ErbB network reconstructions and perturbation simulations reveal individual drug response in different breast cancer cell lines

    Science.gov (United States)

    2014-01-01

    Background Despite promising progress in targeted breast cancer therapy, drug resistance remains challenging. The monoclonal antibody drugs trastuzumab and pertuzumab as well as the small molecule inhibitor erlotinib were designed to prevent ErbB-2 and ErbB-1 receptor induced deregulated protein signalling, contributing to tumour progression. The oncogenic potential of ErbB receptors unfolds in case of overexpression or mutations. Dimerisation with other receptors allows to bypass pathway blockades. Our intention is to reconstruct the ErbB network to reveal resistance mechanisms. We used longitudinal proteomic data of ErbB receptors and downstream targets in the ErbB-2 amplified breast cancer cell lines BT474, SKBR3 and HCC1954 treated with erlotinib, trastuzumab or pertuzumab, alone or combined, up to 60 minutes and 30 hours, respectively. In a Boolean modelling approach, signalling networks were reconstructed based on these data in a cell line and time course specific manner, including prior literature knowledge. Finally, we simulated network response to inhibitor combinations to detect signalling nodes reflecting growth inhibition. Results The networks pointed to cell line specific activation patterns of the MAPK and PI3K pathway. In BT474, the PI3K signal route was favoured, while in SKBR3, novel edges highlighted MAPK signalling. In HCC1954, the inferred edges stimulated both pathways. For example, we uncovered feedback loops amplifying PI3K signalling, in line with the known trastuzumab resistance of this cell line. In the perturbation simulations on the short-term networks, we analysed ERK1/2, AKT and p70S6K. The results indicated a pathway specific drug response, driven by the type of growth factor stimulus. HCC1954 revealed an edgetic type of PIK3CA-mutation, contributing to trastuzumab inefficacy. Drug impact on the AKT and ERK1/2 signalling axes is mirrored by effects on RB and RPS6, relating to phenotypic events like cell growth or proliferation

  6. Research on Modeling of Genetic Networks Based on Information Measurement

    Institute of Scientific and Technical Information of China (English)

    ZHANG Guo-wei; SHAO Shi-huang; ZHANG Ying; LI Hai-ying

    2006-01-01

    As the basis of network of biology organism, the genetic network is concerned by many researchers.Current modeling methods to genetic network, especially the Boolean networks modeling method are analyzed. For modeling the genetic network, the information theory is proposed to mining the relations between elements in network. Through calculating the values of information entropy and mutual entropy in a case, the effectiveness of the method is verified.

  7. A Boolean delay equation model of an interdecadal Arctic climate cycle

    Energy Technology Data Exchange (ETDEWEB)

    Darby, M.S. [Univ. of Exeter (United Kingdom); Mysak, L.A. [McGill Univ., Montreal, Quebec (Canada)

    1993-05-01

    A Boolean delay equation (BDE) model is presented for the interdecadal Arctic and Greenland Sea climate cycle recently proposed by Mysak, Manak and Marsden. It is shown that 15- to 20-year oscillations can occur in the model for a variety of time delays in the BDEs. However, both the period and structure of the oscillations are sensitive to the initial conditions. In an extended model, in which the convection in the Greenland Sea is dependent upon the ice conditions during each of several previous years as well as the current year, the solution structure is more realistic, with two jumps per period of oscillation. 12 refs., 6 figs., 2 tabs.

  8. Boolean process

    Institute of Scientific and Technical Information of China (English)

    闵应骅; 李忠诚; 赵著行

    1997-01-01

    Boolean algebra successfully describes the logical behavior of a digital circuit, and has been widely used in electronic circuit design and test With the development of high speed VLSIs it is a drawback for Boolean algebra to be unable to describe circuit timing behavior. Therefore a Boolean process is defined as a family of Boolean van ables relevant to the time parameter t. A real-valued sample of a Boolean process is a waveform. Waveform functions can be manipulated formally by using mathematical tools. The distance, difference and limit of a waveform polynomial are defined, and a sufficient and necessary condition of the limit existence is presented. Based on this, the concept of sensitization is redefined precisely to demonstrate the potential and wide application possibility The new definition is very different from the traditional one, and has an impact on determining the sensitizable paths with maximum or minimum length, and false paths, and then designing and testing high performance circuits

  9. A Probabilistic Boolean Network Approach for the Analysis of Cancer-Specific Signalling: A Case Study of Deregulated PDGF Signalling in GIST.

    Directory of Open Access Journals (Sweden)

    Panuwat Trairatphisan

    Full Text Available Signal transduction networks are increasingly studied with mathematical modelling approaches while each of them is suited for a particular problem. For the contextualisation and analysis of signalling networks with steady-state protein data, we identified probabilistic Boolean network (PBN as a promising framework which could capture quantitative changes of molecular changes at steady-state with a minimal parameterisation.In our case study, we successfully applied the PBN approach to model and analyse the deregulated Platelet-Derived Growth Factor (PDGF signalling pathway in Gastrointestinal Stromal Tumour (GIST. We experimentally determined a rich and accurate dataset of steady-state profiles of selected downstream kinases of PDGF-receptor-alpha mutants in combination with inhibitor treatments. Applying the tool optPBN, we fitted a literature-derived candidate network model to the training dataset consisting of single perturbation conditions. Model analysis suggested several important crosstalk interactions. The validity of these predictions was further investigated experimentally pointing to relevant ongoing crosstalk from PI3K to MAPK signalling in tumour cells. The refined model was evaluated with a validation dataset comprising multiple perturbation conditions. The model thereby showed excellent performance allowing to quantitatively predict the combinatorial responses from the individual treatment results in this cancer setting. The established optPBN pipeline is also widely applicable to gain a better understanding of other signalling networks at steady-state in a context-specific fashion.

  10. Fixed-points in random Boolean networks: The impact of parallelism in the Barabási-Albert scale-free topology case.

    Science.gov (United States)

    Moisset de Espanés, P; Osses, A; Rapaport, I

    2016-12-01

    Fixed points are fundamental states in any dynamical system. In the case of gene regulatory networks (GRNs) they correspond to stable genes profiles associated to the various cell types. We use Kauffman's approach to model GRNs with random Boolean networks (RBNs). In this paper we explore how the topology affects the distribution of the number of fixed points in randomly generated networks. We also study the size of the basins of attraction of these fixed points if we assume the α-asynchronous dynamics (where every node is updated independently with probability 0≤α≤1). It is well-known that asynchrony avoids the cyclic attractors into which parallel dynamics tends to fall. We observe the remarkable property that, in all our simulations, if for a given RBN with Barabási-Albert topology and α-asynchronous dynamics an initial configuration reaches a fixed point, then every configuration also reaches a fixed point. By contrast, in the parallel regime, the percentage of initial configurations reaching a fixed point (for the same networks) is dramatically smaller. We contrast the results of the simulations on Barabási-Albert networks with the classical Erdös-Rényi model of random networks. Everything indicates that Barabási-Albert networks are extremely robust. Finally, we study the mean and maximum time/work needed to reach a fixed point when starting from randomly chosen initial configurations.

  11. Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators

    Science.gov (United States)

    Rosin, David P.; Rontani, Damien; Haynes, Nicholas D.; Schöll, Eckehard; Gauthier, Daniel J.

    2014-09-01

    We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast time scale of our oscillators (on the order of 100ns) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.

  12. Automatd generation of models and counterexamples and its application to open questions in Ternary Boolean algebra

    Energy Technology Data Exchange (ETDEWEB)

    Winker, S.; Wos, L.

    1978-01-01

    The purposes of this paper are to answer certain previously unanswered questions in the field of Ternary Boolean algebra; to describe the method, by use of an automated theorem-proving program as an invaluable aid, by which these answers were obtained; and to give informally the characteristics of those problems to which the method can be successfully applied. The approach under study begins with known facts in the form of axioms and lemmas of the field being investigated, finds by means of certain specified inference rules new facts, and continues to reason from the expanding set of facts until the problem at hand is solved or the procedure is interrupted. The solution often takes the form of a finite model or of a counter-example to the underlying conjecture. The model and/or counterexample is generated with the aid of an already existing automated theorem-proving procedure and without any recourse to any additional programing.

  13. Methods for Characterizing the Epigenetic Attractors Landscape Associated with Boolean Gene Regulatory Networks

    OpenAIRE

    Davila-Velderrain, Jose; Juarez-Ramiro, Luis; Martinez-Garcia, Juan C.; Alvarez-Buylla, Elena R

    2015-01-01

    Gene regulatory network (GRN) modeling is a well-established theoretical framework for the study of cell-fate specification during developmental processes. Recently, dynamical models of GRNs have been taken as a basis for formalizing the metaphorical model of Waddington's epigenetic landscape, providing a natural extension for the general protocol of GRN modeling. In this contribution we present in a coherent framework a novel implementation of two previously proposed general frameworks for m...

  14. ON THE SPECIFIC AREA OF INHOMOGENEOUS BOOLEAN MODELS. EXISTENCE RESULTS AND APPLICATIONS

    Directory of Open Access Journals (Sweden)

    Elena Villa

    2011-05-01

    Full Text Available The problem of the evaluation of the so-called specific area of a random closed set, in connection with its mean boundary measure, is mentioned in the classical book by Matheron on random closed sets (Matheron, 1975, p. 50; it is still an open problem, in general. We offer here an overview of some recent results concerning the existence of the specific area of inhomogeneous Boolean models, unifying results from geometric measure theory and from stochastic geometry. A discussion of possible applications to image analysis concerning the estimation of the mean surface density of random closed sets, and, in particular, to material science concerning birth-and-growth processes, is also provided.

  15. Use of the method of Boolean models to study different methods of drilling wells of large diameter

    Energy Technology Data Exchange (ETDEWEB)

    Selivanov, A.N.; Ryabinin, A.I.

    1981-01-01

    A description is made of the method of statistical modeling using the method of Boolean models as an example of processing and analyzing the results of drilling wells of large diameter by different methods. It is indicated that this method as compared to traditional methods of multiple-factor analysis with comparatively small volume of experimental data makes it possible to obtain a complete qualitative and quantitative characterization of the studied phenomenon.

  16. APPLICATION OF THE OVERLAY WEIGHTED MODEL AND BOOLEAN LOGIC TO DETERMINE THE BEST LOCATIONS FOR ARTIFICIAL RECHARGE OF GROUNDWATER

    Directory of Open Access Journals (Sweden)

    Peter H.S. Riad

    2011-01-01

    Full Text Available With population increase, lack of conventional fresh water resources and uncertainties due to climate change, there is growing interest in the arid and semi-arid areas to increase groundwater recharge with recycled water. Finding the best locations for artificial recharge of groundwater in such areas is one of the most crucial design steps to guarantee the long life and the sustainability of these projects. This study presents two ways to go about performing analysis; creating a suitability map to find out the suitability of every location on the map and another way is querying the created data sets to obtain a Boolean result of true or false map. These techniques have been applied on Sadat Industrial City which is located in a semi arid area in the western desert fringes of The Nile delta in the north west of Egypt. Thematic layers for number of parameters were prepared from some maps and satellite images and they have been classified, weighted and integrated in ArcGIS environment. By the means of the overlay weighted model in ArcGIS a suitability map which is classified into number of priority zones was obtained and it could be compared with the obtained true-false map of Boolean logic. Both methods suggested mostly the northern parts of the city for groundwater recharge; however the weighted model could give more accurate suitability map while Boolean logic suggested wider ranges of areas. This study recommends Boolean logic as a first estimator for locating the best locations as it is easier and not time consuming, while the overlay weighted model for more accurate results.

  17. APPLICATION OF THE OVERLAY WEIGHTED MODEL AND BOOLEAN LOGIC TO DETERMINE THE BEST LOCATIONS FOR ARTIFICIAL RECHARGE OF GROUNDWATER

    Directory of Open Access Journals (Sweden)

    Max Billib

    2011-12-01

    Full Text Available With population increase, lack of conventional fresh water resources and uncertainties due to climate change, there is growing interest in the arid and semi-arid areas to increase groundwater recharge with recycled water. Finding the best locations for artificial recharge of groundwater in such areas is one of the most crucial design steps to guarantee the long life and the sustainability of these projects. This study presents two ways to go about performing analysis; creating a suitability map to find out the suitability of every location on the map and another way is querying the created data sets to obtain a Boolean result of true or false map. These techniques have been applied on Sadat Industrial City which is located in a semi arid area in the western desert fringes of The Nile delta in the north west of Egypt. Thematic layers for number of parameters were prepared from some maps and satellite images and they have been classified, weighted and integrated in ArcGIS environment. By the means of the overlay weighted model in ArcGIS a suitability map which is classified into number of priority zones was obtained and it could be compared with the obtained true-false map of Boolean logic. Both methods suggested mostly the northern parts of the city for groundwater recharge; however the weighted model could give more accurate suitability map while Boolean logic suggested wider ranges of areas. This study recommends Boolean logic as a first estimator for locating the best locations as it is easier and not time consuming, while the overlay weighted model for more accurate results.

  18. Boolean operations of STL models based on edge-facet intersection

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    For the data processing of the Rapid Prototyping Manufacturing, Boolean operation can offer a versatile tool for editing or modifying the STL model, adding the artificial construction, and creating the complex assistant support structure to meet the special technical requests. The topological structure of STL models was built firstly in order to obtain the neighborhood relationship among the triangular facets. The intersection test between every edge of one solid and every facet of another solid Was taken to get the intersection points. According to the matching relationship of the triangle index recorded in the data structure of the intersection points, the intersection segments array and the intersection loop were traced out. Each intersected triangle was subdivided by the Constrained Delaunay Triangulations. The intersected surfaces were divided into several surface patches along the intersection loops. The inclusion prediction between the surface patch and the other solid was taken by testing whether the candidate point Was inside or outside the solid region of the slice. Detecting the loops for determination of the valid intersection lines greatly increases the efficiency and the reliability of the process.

  19. Boolean gates on actin filaments

    Science.gov (United States)

    Siccardi, Stefano; Tuszynski, Jack A.; Adamatzky, Andrew

    2016-01-01

    Actin is a globular protein which forms long polar filaments in the eukaryotic cytoskeleton. Actin networks play a key role in cell mechanics and cell motility. They have also been implicated in information transmission and processing, memory and learning in neuronal cells. The actin filaments have been shown to support propagation of voltage pulses. Here we apply a coupled nonlinear transmission line model of actin filaments to study interactions between voltage pulses. To represent digital information we assign a logical TRUTH value to the presence of a voltage pulse in a given location of the actin filament, and FALSE to the pulse's absence, so that information flows along the filament with pulse transmission. When two pulses, representing Boolean values of input variables, interact, then they can facilitate or inhibit further propagation of each other. We explore this phenomenon to construct Boolean logical gates and a one-bit half-adder with interacting voltage pulses. We discuss implications of these findings on cellular process and technological applications.

  20. Memory-Based Boolean Game and Self-Organized Phenomena on Networks

    Institute of Scientific and Technical Information of China (English)

    HUANG Zi-Gang; WU Zhi-Xi; GUAN Jian-Yue; WANG Ying-Hai

    2006-01-01

    @@ We study a memory-based Boolean game (MBBG) taking place on a regular ring, wherein each agent acts according to its local optimal states of the last M time steps recorded in memory, and the agents in the minority are rewarded. One free parameter p between 0 and 1 is introduced to denote the strength of the agent willing to make a decision according to its memory. It is found that giving proper willing strength p, the MBBG system can spontaneously evolve to a state of performance better than the random game; while for larger p, the herd behaviour emerges to reduce the system profit. By analysing the dependence of dynamics of the system on the memory capacity M, we find that a higher memory capacity favours the emergence of the better performance state, and effectively restrains the herd behaviour, thus increases the system profit. Considering the high cost of long-time memory, the enhancement of memory capacity for restraining the herd behaviour is also discussed,and M = 5 is suggested to be a good choice.

  1. Fault Tolerant Boolean Satisfiability

    CERN Document Server

    Roy, A

    2011-01-01

    A delta-model is a satisfying assignment of a Boolean formula for which any small alteration, such as a single bit flip, can be repaired by flips to some small number of other bits, yielding a new satisfying assignment. These satisfying assignments represent robust solutions to optimization problems (e.g., scheduling) where it is possible to recover from unforeseen events (e.g., a resource becoming unavailable). The concept of delta-models was introduced by Ginsberg, Parkes and Roy (AAAI 1998), where it was proved that finding delta-models for general Boolean formulas is NP-complete. In this paper, we extend that result by studying the complexity of finding delta-models for classes of Boolean formulas which are known to have polynomial time satisfiability solvers. In particular, we examine 2-SAT, Horn-SAT, Affine-SAT, dual-Horn-SAT, 0-valid and 1-valid SAT. We see a wide variation in the complexity of finding delta-models, e.g., while 2-SAT and Affine-SAT have polynomial time tests for delta-models, testing w...

  2. Symmetric Boolean Algebras

    OpenAIRE

    DÍaz, R.; Rivas, M.

    2010-01-01

    In order to study Boolean algebras in the category of vector spaces we introduce a prop whose algebras in set are Boolean algebras. A probabilistic logical interpretation for linear Boolean algebras is provided. An advantage of defining Boolean algebras in the linear category is that we are able to study its symmetric powers. We give explicit formulae for products in symmetric and cyclic Boolean algebras of various dimensions and formulate symmetric forms of the inclusion-exclusion principle.

  3. Meta-Boolean models of asymmetric division patterns in the C. elegans intestinal lineage

    Science.gov (United States)

    Pettersson, Sofia; Forchheimer, Robert; Larsson, Jan-Åke

    2013-01-01

    The intestine of Caenorhabditis elegans is derived from 20 cells that are organized into nine intestinal rings. During embryogenesis, three of the rings rotate approximately 90 degrees in a process known as intestinal twist. The underlying mechanisms for this morphological event are not fully known, but it has been demonstrated that both left-right and anterior-posterior asymmetry is required for intestinal twist to occur. We have recently presented a rule-based meta-Boolean tree model intended to describe complex lineages. In this report we apply this model to the E lineage of C. elegans, specifically targeting the asymmetric anterior-posterior division patterns within the lineage. The resulting model indicates that cells with the same factor concentration are located next to each other in the intestine regardless of lineage origin. In addition, the shift in factor concentrations coincides with the boundary for intestinal twist. When modeling lit-1 mutant data according to the same principle, the factor distributions in each cell are altered, yet the concurrence between the shift in concentration and intestinal twist remains. This pattern suggests that intestinal twist is controlled by a threshold mechanism. In the current paper we present the factor concentrations for all possible combinations of symmetric and asymmetric divisions in the E lineage and relate these to the potential threshold by studying existing data for wild-type and mutant embryos. Finally, we discuss how the resulting models can serve as a basis for experimental design in order to reveal the underlying mechanisms of intestinal twist. PMID:24058861

  4. Profiling of genetic switches using boolean implications in expression data.

    Science.gov (United States)

    Çakır, Mehmet Volkan; Binder, Hans; Wirth, Henry

    2014-01-01

    Correlation analysis assuming coexpression of the genes is a widely used method for gene expression analysis in molecular biology. Yet growing extent, quality and dimensionality of the molecular biological data permits emerging, more sophisticated approaches like Boolean implications. We present an approach which is a combination of the SOM (self organizing maps) machine learning method and Boolean implication analysis to identify relations between genes, metagenes and similarly behaving metagene groups (spots). Our method provides a way to assign Boolean states to genes/metagenes/spots and offers a functional view over significantly variant elements of gene expression data on these three different levels. While being able to cover relations between weakly correlated entities Boolean implication method also decomposes these relations into six implication classes. Our method allows one to validate or identify potential relationships between genes and functional modules of interest and to assess their switching behaviour. Furthermore the output of the method renders it possible to construct and study the network of genes. By providing logical implications as updating rules for the network it can also serve to aid modelling approaches.

  5. Understanding the sequential activation of Type III and Type VI Secretion Systems in Salmonella typhimurium using Boolean modeling

    Science.gov (United States)

    2013-01-01

    Background Three pathogenicity islands, viz. SPI-1 (Salmonella pathogenicity island 1), SPI-2 (Salmonella pathogenicity island 2) and T6SS (Type VI Secretion System), present in the genome of Salmonella typhimurium have been implicated in the virulence of the pathogen. While the regulation of SPI-1 and SPI-2 (both encoding components of the Type III Secretion System - T3SS) are well understood, T6SS regulation is comparatively less studied. Interestingly, inter-connections among the regulatory elements of these three virulence determinants have also been suggested to be essential for successful infection. However, till date, an integrated view of gene regulation involving the regulators of these three secretion systems and their cross-talk is not available. Results In the current study, relevant regulatory information available from literature have been integrated into a single Boolean network, which portrays the dynamics of T3SS (SPI-1 and SPI-2) and T6SS mediated virulence. Some additional regulatory interactions involving a two-component system response regulator YfhA have also been predicted and included in the Boolean network. These predictions are aimed at deciphering the effects of osmolarity on T6SS regulation, an aspect that has been suggested in earlier studies, but the mechanism of which was hitherto unknown. Simulation of the regulatory network was able to recreate in silico the experimentally observed sequential activation of SPI-1, SPI-2 and T6SS. Conclusions The present study integrates relevant gene regulatory data (from literature and our prediction) into a single network, representing the cross-communication between T3SS (SPI-1 and SPI-2) and T6SS. This holistic view of regulatory interactions is expected to improve the current understanding of pathogenesis of S. typhimurium. PMID:24079299

  6. Controllability and observability of Boolean control networks%布尔控制网络的能控性与能观性

    Institute of Scientific and Technical Information of China (English)

    李志强; 宋金利

    2013-01-01

    Using the semi-tensor product,we convert the Boolean control network to its algebraic form.From the structure matrix of Boolean control network,the controllability and observability of the Boolean control network are discussed.A novel necessary and sufficient condition for controllability,which improves the recent results,is given.The new controllability condition eliminates the redundant computation of controllability matrix.The highest power of matrix is reduced from 2m+n to 2 n.Also,a sufficient condition for observability is obtained,which can be computed easily.A numerical example is presented to show the applicability of our controllability and observability condition.%利用矩阵的半张量积,布尔控制网络被转化为离散时间系统.本文从离散时间系统的结构矩阵出发,讨论了逻辑控制系统的能控能观性条件,得到了一个新的能控性条件.新的条件简化了原有能控性矩阵的计算复杂性,矩阵的最高阶数由原来的2m+n降到了2n.另外,还得到了检验布尔控制网络能观性的条件.与原有条件相比,新的条件更容易计算检验.最后,给出一个实例,检验给出的能控能观性判断条件的正确性.

  7. Free Boolean Topological Groups

    Directory of Open Access Journals (Sweden)

    Ol’ga Sipacheva

    2015-11-01

    Full Text Available Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups.

  8. On Boolean Stable Laws

    CERN Document Server

    Arizmendi, Octavio

    2012-01-01

    We determine which Boolean stable law is freely infinitely divisible and which is not. Some positive Boolean stable laws and a mixture of them have completely monotonic densities and they are both freely and classically infinitely divisible. Freely infinitely divisible Boolean stable laws and the corresponding free stable laws are non trivial examples whose free divisibility indicators are infinity.

  9. Boolean reasoning the logic of boolean equations

    CERN Document Server

    Brown, Frank Markham

    2012-01-01

    A systematic treatment of Boolean reasoning, this concise, newly revised edition combines the works of early logicians with recent investigations, including previously unpublished research results. Brown begins with an overview of elementary mathematical concepts and outlines the theory of Boolean algebras. Two concluding chapters deal with applications. 1990 edition.

  10. Boolean algebra essentials

    CERN Document Server

    Solomon, Alan D

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean

  11. Sublogarithmic uniform Boolean proof nets

    CERN Document Server

    Aubert, Clément

    2012-01-01

    Using a proofs-as-programs correspondence, Terui was able to compare two models of parallel computation: Boolean circuits and proof nets for multiplicative linear logic. Mogbil et. al. gave a logspace translation allowing us to compare their computational power as uniform complexity classes. This paper presents a novel translation in AC0 and focuses on a simpler restricted notion of uniform Boolean proof nets. We can then encode constant-depth circuits and compare complexity classes below logspace, which were out of reach with the previous translations.

  12. A Boolean action of C(M,U(1)) without a spatial model

    CERN Document Server

    Moore, Justin Tatch

    2012-01-01

    We will demonstrate that if M is an uncountable compact metric space, then there is an action of the Polish group of all continuous functions from M to U(1) on a separable probability algebra which preserves the measure and yet does not admit a point realization (in a standard probability space) in the sense of Mackey. This contrasts Mackey's point realization theorem for locally compact, second countable groups which asserts that any measure preserving Boolean action of a locally compact, second countable group on a separable probability algebra can be realized as an action on the points of a standard probability space.

  13. Optimal finite horizon control in gene regulatory networks

    Science.gov (United States)

    Liu, Qiuli

    2013-06-01

    As a paradigm for modeling gene regulatory networks, probabilistic Boolean networks (PBNs) form a subclass of Markov genetic regulatory networks. To date, many different stochastic optimal control approaches have been developed to find therapeutic intervention strategies for PBNs. A PBN is essentially a collection of constituent Boolean networks via a probability structure. Most of the existing works assume that the probability structure for Boolean networks selection is known. Such an assumption cannot be satisfied in practice since the presence of noise prevents the probability structure from being accurately determined. In this paper, we treat a case in which we lack the governing probability structure for Boolean network selection. Specifically, in the framework of PBNs, the theory of finite horizon Markov decision process is employed to find optimal constituent Boolean networks with respect to the defined objective functions. In order to illustrate the validity of our proposed approach, an example is also displayed.

  14. Boolean metric spaces and Boolean algebraic varieties

    OpenAIRE

    Avilés, Antonio

    2009-01-01

    The concepts of Boolean metric space and convex combination are used to characterize polynomial maps in a class of commutative Von Neumann regular rings including Boolean rings and p-rings, that we have called CFG-rings. In those rings, the study of the category of algebraic varieties (i.e. sets of solutions to a finite number of polynomial equations with polynomial maps as morphisms) is equivalent to the study of a class of Boolean metric spaces, that we call here CFG-spaces.

  15. Analysis and Control of Boolean Networks:A Semi-tensor Product Approach%布尔网络的分析与控制-矩阵半张量积方法

    Institute of Scientific and Technical Information of China (English)

    程代展; 齐洪胜; 赵寅

    2011-01-01

    布尔网络是描述基因调控网络的一个有力工具.由于系统生物学的发展,布尔网络的分析与控制成为生物学与系统控制学科的交叉热点.本文综述作者用其原创的矩阵半张量积方法在布尔网络的分析与控制中得到的一系列结果.内容包括:布尔网络的拓扑结构,布尔控制网络的能控、能观性与实现,布尔网络的稳定性和布尔控制网络的镇定,布尔控制网络的干扰解耦,布尔(控制)网络的辨识,以及布尔网络的最优控制等.%Boolean network is a powerful tool for describing gene regulatory network. With the development of the systems biology, the analysis and control of Boolean networks become a hot topic for multidisciplinary research. This paper surveys some recent results obtained in the analysis and control of Boolean networks using semi-tensor product of matrices. The contents of this paper include the topological structure of Boolean networks, the controllability and observability, realization, stability and stabilization, disturbance decoupling, identification, and optimal control of Boolean (control) networks.

  16. Maximum-Likelihood Adaptive Filter for Partially Observed Boolean Dynamical Systems

    Science.gov (United States)

    Imani, Mahdi; Braga-Neto, Ulisses M.

    2017-01-01

    Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear models with application in estimation and control of Boolean processes based on noisy and incomplete measurements. The optimal minimum mean square error (MMSE) algorithms for POBDS state estimation, namely, the Boolean Kalman filter (BKF) and Boolean Kalman smoother (BKS), are intractable in the case of large systems, due to computational and memory requirements. To address this, we propose approximate MMSE filtering and smoothing algorithms based on the auxiliary particle filter (APF) method from sequential Monte-Carlo theory. These algorithms are used jointly with maximum-likelihood (ML) methods for simultaneous state and parameter estimation in POBDS models. In the presence of continuous parameters, ML estimation is performed using the expectation-maximization (EM) algorithm; we develop for this purpose a special smoother which reduces the computational complexity of the EM algorithm. The resulting particle-based adaptive filter is applied to a POBDS model of Boolean gene regulatory networks observed through noisy RNA-Seq time series data, and performance is assessed through a series of numerical experiments using the well-known cell cycle gene regulatory model.

  17. Synchronization of coupled Boolean phase oscillators

    Science.gov (United States)

    Rosin, David P.; Rontani, Damien; Gauthier, Daniel J.

    2014-04-01

    We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged. Specifically, increasing the coupling strength via the range of state-dependent delay leads to larger locking ranges in uni- and bidirectional coupling of oscillators in both experiment and numerical simulation with a piecewise switching model. In the unidirectional coupling scheme, we unveil asymmetric triangular-shaped locking regions (Arnold tongues) that appear at multiples of the natural frequency of the oscillators. This extends observations of a single locking region reported in previous studies. In the bidirectional coupling scheme, we map out a symmetric locking region in the parameter space of frequency detuning and coupling strength. Because of the large scalability of our setup, our observations constitute a first step towards realizing large-scale networks of coupled oscillators to address fundamental questions on the dynamical properties of networks in a new experimental setting.

  18. Non-Boolean probabilities and quantum measurement

    Energy Technology Data Exchange (ETDEWEB)

    Niestegge, Gerd

    2001-08-03

    A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum mechanical Hilbert space formalism and exhibits a particular phenomenon (state-independent conditional probabilities) which may provide new opportunities for an understanding of the quantum measurement process. Examples of the proposed model are provided, using Jordan operator algebras. (author)

  19. On Validating Boolean Optimizers

    CERN Document Server

    Morgado, Antonio

    2011-01-01

    Boolean optimization finds a wide range of application domains, that motivated a number of different organizations of Boolean optimizers since the mid 90s. Some of the most successful approaches are based on iterative calls to an NP oracle, using either linear search, binary search or the identification of unsatisfiable sub-formulas. The increasing use of Boolean optimizers in practical settings raises the question of confidence in computed results. For example, the issue of confidence is paramount in safety critical settings. One way of increasing the confidence of the results computed by Boolean optimizers is to develop techniques for validating the results. Recent work studied the validation of Boolean optimizers based on branch-and-bound search. This paper complements existing work, and develops methods for validating Boolean optimizers that are based on iterative calls to an NP oracle. This entails implementing solutions for validating both satisfiable and unsatisfiable answers from the NP oracle. The wo...

  20. INCLUSION RATIO BASED ESTIMATOR FOR THE MEAN LENGTH OF THE BOOLEAN LINE SEGMENT MODEL WITH AN APPLICATION TO NANOCRYSTALLINE CELLULOSE

    Directory of Open Access Journals (Sweden)

    Mikko Niilo-Rämä

    2014-06-01

    Full Text Available A novel estimator for estimating the mean length of fibres is proposed for censored data observed in square shaped windows. Instead of observing the fibre lengths, we observe the ratio between the intensity estimates of minus-sampling and plus-sampling. It is well-known that both intensity estimators are biased. In the current work, we derive the ratio of these biases as a function of the mean length assuming a Boolean line segment model with exponentially distributed lengths and uniformly distributed directions. Having the observed ratio of the intensity estimators, the inverse of the derived function is suggested as a new estimator for the mean length. For this estimator, an approximation of its variance is derived. The accuracies of the approximations are evaluated by means of simulation experiments. The novel method is compared to other methods and applied to real-world industrial data from nanocellulose crystalline.

  1. Boolean integral calculus

    Science.gov (United States)

    Tucker, Jerry H.; Tapia, Moiez A.; Bennett, A. Wayne

    1988-01-01

    The concept of Boolean integration is developed, and different Boolean integral operators are introduced. Given the changes in a desired function in terms of the changes in its arguments, the ways of 'integrating' (i.e. realizing) such a function, if it exists, are presented. The necessary and sufficient conditions for integrating, in different senses, the expression specifying the changes are obtained. Boolean calculus has applications in the design of logic circuits and in fault analysis.

  2. Monotone Boolean functions

    Energy Technology Data Exchange (ETDEWEB)

    Korshunov, A D [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)

    2003-10-31

    Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published. However, until now there has been no sufficiently complete monograph or survey of results of investigations concerning monotone Boolean functions. The object of this survey is to present the main results on monotone Boolean functions obtained during the last 50 years.

  3. Random Boolean expressions

    OpenAIRE

    Gardy, Danièle

    2005-01-01

    International audience; We examine how we can define several probability distributions on the set of Boolean functions on a fixed number of variables, starting from a representation of Boolean expressions by trees. Analytic tools give us a systematic way to prove the existence of probability distributions, the main challenge being the actual computation of the distributions. We finally consider the relations between the probability of a Boolean function and its complexity.

  4. Boolean Operator Fuzzy Logic

    Institute of Scientific and Technical Information of China (English)

    刘叙华; 邓安生

    1994-01-01

    A new approach of operator fuzzy logic, Boolean operator fuzzy logic (BOFL) based on Boolean algebra, is presented. The resolution principle is also introduced into BOFL. BOFL is a natural generalization of classical logic and can be applied to the qualitative description of fuzzy knowledge.

  5. Boolean Expression Diagrams

    DEFF Research Database (Denmark)

    Andersen, Henrik Reif; Hulgaard, Henrik

    2002-01-01

    This paper presents a new data structure called boolean expression diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of binary decision diagrams (BDDs) which can represent any Boolean circuit in linear space. Two algorithms are described for transforming...... a BED into a reduced ordered BDD. One is a generalized version of the BDD apply-operator while the other can exploit the structural information of the Boolean expression. This ability is demonstrated by verifying that two different circuit implementations of a 16-bit multiplier implement the same...... Boolean function. Using BEDs, this verification problem is solved efficiently, while using standard BDD techniques this problem is infeasible. Generally, BEDs are useful in applications, for example tautology checking, where the end-result as a reduced ordered BDD is small. Moreover, using operators...

  6. Boolean Expression Diagrams

    DEFF Research Database (Denmark)

    Andersen, Henrik Reif; Hulgaard, Henrik

    1997-01-01

    This paper presents a new data structure called Boolean Expression Diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) which can represent any Boolean circuit in linear space and still maintain many of the desirable...... properties of BDDs. Two algorithms are described for transforming a BED into a reduced ordered BDD. One closely mimics the BDD apply-operator while the other can exploit the structural information of the Boolean expression. The efficacy of the BED representation is demonstrated by verifying...... that the redundant and non-redundant versions of the ISCAS 85 benchmark circuits are identical. In particular, it is verified that the two 16-bit multiplication circuits (c6288 and c6288nr) implement the same Boolean functions. Using BEDs, this verification problem is solved in less than a second, while using...

  7. 广义Boolean-like环%Generalized Boolean-like Rings

    Institute of Scientific and Technical Information of China (English)

    秦蕊

    2013-01-01

    广义Boolean-like环是Boolean-like环的一个推广,文章主要介绍了广义Boolean-like环的构建,从而列举了若干广义Boolean-like环的相关例子及基本性质.并且,考虑了广义Boolean-like环的部分扩张,如上三角矩阵环.

  8. A new formalism that combines advantages of fault-trees and Markov models: Boolean logic driven Markov processes

    Energy Technology Data Exchange (ETDEWEB)

    Bouissou, Marc; Bon, Jean-Louis

    2003-11-01

    This paper introduces a modeling formalism that enables the analyst to combine concepts inherited from fault trees and Markov models in a new way. We call this formalism Boolean logic Driven Markov Processes (BDMP). It has two advantages over conventional models used in dependability assessment: it allows the definition of complex dynamic models while remaining nearly as readable and easy to build as fault-trees, and it offers interesting mathematical properties, which enable an efficient processing for BDMP that are equivalent to Markov processes with huge state spaces. We give a mathematical definition of BDMP, the demonstration of their properties, and several examples to illustrate how powerful and easy to use they are. From a mathematical point of view, a BDMP is nothing more than a certain way to define a global Markov process, as the result of several elementary processes which can interact in a given manner. An extreme case is when the processes are independent. Then we simply have a fault-tree, the leaves of which are associated to independent Markov processes.

  9. On pseudo-Boolean polynomials

    Science.gov (United States)

    Leont'ev, V. K.

    2015-11-01

    A pseudo-Boolean function is an arbitrary mapping of the set of binary n-tuples to the real line. Such functions are a natural generalization of classical Boolean functions and find numerous applications in various applied studies. Specifically, the Fourier transform of a Boolean function is a pseudo-Boolean function. A number of facts associated with pseudo-Boolean polynomials are presented, and their applications to well-known discrete optimization problems are described.

  10. Boolean differential equations

    CERN Document Server

    Steinbach, Bernd

    2013-01-01

    The Boolean Differential Calculus (BDC) is a very powerful theory that extends the structure of a Boolean Algebra significantly. Based on a small number of definitions, many theorems have been proven. The available operations have been efficiently implemented in several software packages. There is a very wide field of applications. While a Boolean Algebra is focused on values of logic functions, the BDC allows the evaluation of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. Due to the same basic data structures, the BDC can

  11. Dynamic Boolean Mathematics

    Science.gov (United States)

    Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen

    2016-01-01

    Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…

  12. Clustering Boolean Tensors

    OpenAIRE

    Metzler, S; Miettinen, P

    2015-01-01

    Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required to be binary and we use Boolean algebra -- much of that hardness comes from the possibility of overlapping components. Yet, in many applications we are perfectly happy to partition at least one of the modes. In this paper we investigate what consequences doe...

  13. Symmetric Boolean functions

    OpenAIRE

    Canteaut, Anne; Videau, Marion

    2005-01-01

    http://www.ieee.org/; We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. Our main result establishes the link between the periodicity of the simplified value vector of a symmetric Boolean function and its degree. Besides the reduction of the amount of memory required for representing a symmetric function, this property has some consequences from a cryptographic point of view. For instance, it leads to a new general bound on the order of...

  14. Nearly projective Boolean algebras

    CERN Document Server

    Heindorf, Lutz; Shapiro, Leonid B

    1994-01-01

    The book is a fairly complete and up-to-date survey of projectivity and its generalizations in the class of Boolean algebras. Although algebra adds its own methods and questions, many of the results presented were first proved by topologists in the more general setting of (not necessarily zero-dimensional) compact spaces. An appendix demonstrates the application of advanced set-theoretic methods to the field. The intended readers are Boolean and universal algebraists. The book will also be useful for general topologists wanting to learn about kappa-metrizable spaces and related classes. The text is practically self-contained but assumes experience with the basic concepts and techniques of Boolean algebras.

  15. The Boolean Isomorphism problem

    Energy Technology Data Exchange (ETDEWEB)

    Agrawal, M. [Indian Institute of Technology, Kanpur (India); Thierauf, T. [Universitaet Ulm (Germany)

    1996-12-31

    We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a one-round interactive proof for BI, where the verifier has access to an NP oracle. To obtain this, we use a recent result from learning theory by Bshouty et.al. that Boolean formulas can be learned probabilistically with equivalence queries and access to an NP oracle. As a consequence, BI cannot be {sigma}{sup p}{sub 2} complete unless the Polynomial Hierarchy collapses. This solves an open problem posed in [BRS95]. Further properties of BI are shown: BI has And- and Or-functions, the counting version, No. BI, can be computed in polynomial time relative to BI, and BI is self-reducible.

  16. A network model for plant-pollinator community assembly.

    Science.gov (United States)

    Campbell, Colin; Yang, Suann; Albert, Réka; Shea, Katriona

    2011-01-04

    Community assembly models, usually constructed for food webs, are an important component of our understanding of how ecological communities are formed. However, models for mutualistic community assembly are still needed, especially because these communities are experiencing significant anthropogenic disturbances that affect their biodiversity. Here, we present a unique network model that simulates the colonization and extinction process of mutualistic community assembly. We generate regional source pools of species interaction networks on the basis of statistical properties reported in the literature. We develop a dynamic synchronous Boolean framework to simulate, with few free parameters, the dynamics of new mutualistic community formation from the regional source pool. This approach allows us to deterministically map out every possible trajectory of community formation. This level of detail is rarely observed in other analytic approaches and allows for thorough analysis of the dynamical properties of community formation. As for food web assembly, we find that the number of stable communities is quite low, and the composition of the source pool influences the abundance and nature of community outcomes. However, in contrast to food web assembly, stable mutualistic communities form rapidly. Small communities with minor fluctuations in species presence/absence (self-similar limit cycles) are the most common community outcome. The unique application of this Boolean network approach to the study of mutualistic community assembly offers a great opportunity to improve our understanding of these critical communities.

  17. Quantum Boolean image denoising

    Science.gov (United States)

    Mastriani, Mario

    2015-05-01

    A quantum Boolean image processing methodology is presented in this work, with special emphasis in image denoising. A new approach for internal image representation is outlined together with two new interfaces: classical to quantum and quantum to classical. The new quantum Boolean image denoising called quantum Boolean mean filter works with computational basis states (CBS), exclusively. To achieve this, we first decompose the image into its three color components, i.e., red, green and blue. Then, we get the bitplanes for each color, e.g., 8 bits per pixel, i.e., 8 bitplanes per color. From now on, we will work with the bitplane corresponding to the most significant bit (MSB) of each color, exclusive manner. After a classical-to-quantum interface (which includes a classical inverter), we have a quantum Boolean version of the image within the quantum machine. This methodology allows us to avoid the problem of quantum measurement, which alters the results of the measured except in the case of CBS. Said so far is extended to quantum algorithms outside image processing too. After filtering of the inverted version of MSB (inside quantum machine), the result passes through a quantum-classical interface (which involves another classical inverter) and then proceeds to reassemble each color component and finally the ending filtered image. Finally, we discuss the more appropriate metrics for image denoising in a set of experimental results.

  18. Algebraic partial Boolean algebras

    Energy Technology Data Exchange (ETDEWEB)

    Smith, Derek [Math Department, Lafayette College, Easton, PA 18042 (United States)

    2003-04-04

    Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A{sub 5} sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E{sub 8}.

  19. Inference in hybrid Bayesian networks

    DEFF Research Database (Denmark)

    Lanseth, Helge; Nielsen, Thomas Dyhre; Rumí, Rafael

    2009-01-01

    Since the 1980s, Bayesian Networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability-techniques (like fault trees...... decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability....

  20. Dynamic Network Models

    CERN Document Server

    Armbruster, Benjamin

    2011-01-01

    We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which has relevance for connectivity and the spread of infections. Second, we analyze the effect of node turnover, when nodes enter and leave the network, which has relevance for network models incorporating births, deaths, aging, and other demographic factors.

  1. Summing Boolean Algebras

    Institute of Scientific and Technical Information of China (English)

    Antonio AIZPURU; Antonio GUTI(E)RREZ-D(A)VILA

    2004-01-01

    In this paper we will study some families and subalgebras ( ) of ( )(N) that let us characterize the unconditional convergence of series through the weak convergence of subseries ∑i∈A xi, A ∈ ( ).As a consequence, we obtain a new version of the Orlicz-Pettis theorem, for Banach spaces. We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces.

  2. 基于布尔语义的Gentzen推导模型%Gentzen Deduction Model Based on Boolean Logic Semantics

    Institute of Scientific and Technical Information of China (English)

    陈博; 眭跃飞

    2015-01-01

    Deduction systems are important arts of searching technology. This paper gives a new correspondence between the propositional logic and Boolean algebra, where an inequation is corresponding to a Gentzen sequent, so that the inequation is true in every Boolean algebra if and only if the Gentzen sequent is provable. In information retrieval, the information inference can effectively turn into the operation on poset. Precisely, the logical language for the propositional logic contains operators Ø'Ù'Ú;the terms instead of formulas are defined (a|Øt|t1 Ù t2|t1 Ú t2 , where a is an element) and used to represent elements in Boolean algebra. This paper defines an assignment v using Boolean algebra as its domain, and assigns the terms to be the element in Boolean algebra. The sequence ΓÞΔ is satisfied if tv £tv. Finally, this paper gives a Gentzen system to prove the soundness and completeness theorem.%布尔模型是信息检索系统的一种基础模型。给出了命题逻辑和布尔代数间的一种新的对应关系,其中布尔代数中的不等式对应Gentzen系统中的矢列式,使得当一个不等式在任意布尔代数中为真,当且仅当它所对应的矢列式是可证的。并且使得在信息检索中,针对信息的推理可以有效地转为偏序集上的运算。讨论的命题逻辑语言的运算符为Ø、Ù、Ú;并且定义了项(a|Øt|t1Ù t2|t1Ú t2'其中a是一个元素)来替代原先的公式和表示布尔代数中的元素。此外,定义了以布尔代数为论域的赋值v,将命题逻辑中的项赋值为布尔代数中的元素,并且如果tv £t v ,则矢列式ΓÞ D为真。最后给出了Gentzen系统下的可靠性和完备性定理的证明。tÎΓtÎΔ

  3. Mining, modeling, and evaluation of subnetworks from large biomolecular networks and its comparison study.

    Science.gov (United States)

    Hu, Xiaohua; Ng, Michael; Wu, Fang-Xiang; Sokhansanj, Bahrad A

    2009-03-01

    In this paper, we present a novel method to mine, model, and evaluate a regulatory system executing cellular functions that can be represented as a biomolecular network. Our method consists of two steps. First, a novel scale-free network clustering approach is applied to such a biomolecular network to obtain various subnetworks. Second, computational models are generated for the subnetworks and simulated to predict their behavior in the cellular context. We discuss and evaluate some of the advanced computational modeling approaches, in particular, state-space modeling, probabilistic Boolean network modeling, and fuzzy logic modeling. The modeling and simulation results represent hypotheses that are tested against high-throughput biological datasets (microarrays and/or genetic screens) under normal and perturbation conditions. Experimental results on time-series gene expression data for the human cell cycle indicate that our approach is promising for subnetwork mining and simulation from large biomolecular networks.

  4. Modeling worldwide highway networks

    Science.gov (United States)

    Villas Boas, Paulino R.; Rodrigues, Francisco A.; da F. Costa, Luciano

    2009-12-01

    This Letter addresses the problem of modeling the highway systems of different countries by using complex networks formalism. More specifically, we compare two traditional geographical models with a modified geometrical network model where paths, rather than edges, are incorporated at each step between the origin and the destination vertices. Optimal configurations of parameters are obtained for each model and used for the comparison. The highway networks of Australia, Brazil, India, and Romania are considered and shown to be properly modeled by the modified geographical model.

  5. Brain Network Modelling

    DEFF Research Database (Denmark)

    Andersen, Kasper Winther

    Three main topics are presented in this thesis. The first and largest topic concerns network modelling of functional Magnetic Resonance Imaging (fMRI) and Diffusion Weighted Imaging (DWI). In particular nonparametric Bayesian methods are used to model brain networks derived from resting state f...... for their ability to reproduce node clustering and predict unseen data. Comparing the models on whole brain networks, BCD and IRM showed better reproducibility and predictability than IDM, suggesting that resting state networks exhibit community structure. This also points to the importance of using models, which...... allow for complex interactions between all pairs of clusters. In addition, it is demonstrated how the IRM can be used for segmenting brain structures into functionally coherent clusters. A new nonparametric Bayesian network model is presented. The model builds upon the IRM and can be used to infer...

  6. J-Boolean like环%J-Boolean Like Ring

    Institute of Scientific and Technical Information of China (English)

    秦蕊

    2013-01-01

    本文首先引进了Boolean-like环的一类新的扩张J-Boolean like环,即对任意环R中元素a,b都有(a-a2)(b-b2)∈J(R),这里J(R)为环R的Jacobson根,则环R称为J-Boolean like环.证明了两个定理分别为(1)设D是一个环,C是D的一个子环,R[D,C]是一个J-Boolean like环(=)(a)C,D是J-Boolean like环,(b)J2(C)(∈)J(D).(2)如果B/J(B)是Boolean环,并且B[i]={a+bi| i2=ui+η,a,b,u,η∈B},那么B[i]是J-Booleanlike环当且仅当uη∈J(B).

  7. Adjunctions between Boolean spaces and skew Boolean algebras

    CERN Document Server

    Kudryavtseva, Ganna

    2011-01-01

    We apply the representation theory of left-handed skew Boolean algebras by sections of their dual \\'{e}tale spaces, given in \\cite{K}, to construct a series of dual adjunctions between the categories of locally compact Boolean spaces and left-handed skew Boolean algebras by means of extensions of certain enriched $\\Hom$-set functors induced by objects sitting in two categories. The constructed adjunctions are "deformations" of Stone duality obtained by the replacement in the latter of the category of Boolean algebras by the category of left-handed skew Boolean algebras. The constructions provide natural settings for the $\\omega$-functor constructed in \\cite{LS} and its left adjoint functor.

  8. Modeling Epidemic Network Failures

    DEFF Research Database (Denmark)

    Ruepp, Sarah Renée; Fagertun, Anna Manolova

    2013-01-01

    This paper presents the implementation of a failure propagation model for transport networks when multiple failures occur resulting in an epidemic. We model the Susceptible Infected Disabled (SID) epidemic model and validate it by comparing it to analytical solutions. Furthermore, we evaluate...... the SID model’s behavior and impact on the network performance, as well as the severity of the infection spreading. The simulations are carried out in OPNET Modeler. The model provides an important input to epidemic connection recovery mechanisms, and can due to its flexibility and versatility be used...... to evaluate multiple epidemic scenarios in various network types....

  9. Approximate Reasoning with Fuzzy Booleans

    NARCIS (Netherlands)

    Broek, van den P.M.; Noppen, J.A.R.

    2004-01-01

    This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante

  10. Artificial neural network modelling

    CERN Document Server

    Samarasinghe, Sandhya

    2016-01-01

    This book covers theoretical aspects as well as recent innovative applications of Artificial Neural networks (ANNs) in natural, environmental, biological, social, industrial and automated systems. It presents recent results of ANNs in modelling small, large and complex systems under three categories, namely, 1) Networks, Structure Optimisation, Robustness and Stochasticity 2) Advances in Modelling Biological and Environmental Systems and 3) Advances in Modelling Social and Economic Systems. The book aims at serving undergraduates, postgraduates and researchers in ANN computational modelling. .

  11. On Kolmogorov's superpositions and Boolean functions

    Energy Technology Data Exchange (ETDEWEB)

    Beiu, V.

    1998-12-31

    The paper overviews results dealing with the approximation capabilities of neural networks, as well as bounds on the size of threshold gate circuits. Based on an explicit numerical (i.e., constructive) algorithm for Kolmogorov's superpositions they will show that for obtaining minimum size neutral networks for implementing any Boolean function, the activation function of the neurons is the identity function. Because classical AND-OR implementations, as well as threshold gate implementations require exponential size (in the worst case), it will follow that size-optimal solutions for implementing arbitrary Boolean functions require analog circuitry. Conclusions and several comments on the required precision are ending the paper.

  12. Cardinal invariants on Boolean algebras

    CERN Document Server

    Monk, J Donald

    2014-01-01

    This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the...

  13. Cryptographic Boolean functions and applications

    CERN Document Server

    Cusick, Thomas W

    2009-01-01

    Boolean functions are the building blocks of symmetric cryptographic systems. Symmetrical cryptographic algorithms are fundamental tools in the design of all types of digital security systems (i.e. communications, financial and e-commerce).Cryptographic Boolean Functions and Applications is a concise reference that shows how Boolean functions are used in cryptography. Currently, practitioners who need to apply Boolean functions in the design of cryptographic algorithms and protocols need to patch together needed information from a variety of resources (books, journal articles and other sources). This book compiles the key essential information in one easy to use, step-by-step reference. Beginning with the basics of the necessary theory the book goes on to examine more technical topics, some of which are at the frontier of current research.-Serves as a complete resource for the successful design or implementation of cryptographic algorithms or protocols using Boolean functions -Provides engineers and scient...

  14. Quantum algorithms for testing Boolean functions

    OpenAIRE

    Erika Andersson; Floess, Dominik F.; Mark Hillery

    2010-01-01

    We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same quantum algorithm can also be used to learn which input variables other types of Boolean functions...

  15. 基于布尔感知模型的边界线多重覆盖算法%Boundary Line Algorithm Multiple Coverage Based on Boolean Perception Model

    Institute of Scientific and Technical Information of China (English)

    薛兴亮; 孙荣凯; 高玉章

    2013-01-01

    无线传感器网络监视预警系统的区域边界具有特殊重要性,针对节点的布尔感知模型,根据节点感知圆盘的相互关系,可将整条边界线划分为不可再分割的可数个最小曲线段,利用改进的贪婪式算法研究了集中式多重覆盖算法和分布式多重覆盖算法,通过仿真实验,验证了多重覆盖带来的高检测概率以及高覆盖概率。%As the special importance of boundary area in wireless sensor network monitoring and warn-ing system, for the perception of the node boolean perception model, the entire boundary line can be divided into countable smallest curve segments based on the relationship between the node sens-ing disc. Then the centralized multiple coverage and the distributed multiple coverage were studied by using an improved greedy algorithm. At last, the high probability of detection and high coverage was verified probability in multiple coverage by means of simulation results.

  16. Modeling Evolving Innovation Networks

    OpenAIRE

    Koenig, Michael D.; Battiston, Stefano; Schweitzer, Frank

    2007-01-01

    We develop a new framework for modeling innovation networks which evolve over time. The nodes in the network represent firms, whereas the directed links represent unilateral interactions between the firms. Both nodes and links evolve according to their own dynamics and on different time scales. The model assumes that firms produce knowledge based on the knowledge exchange with other firms, which involves both costs and benefits for the participating firms. In order to increase their knowledge...

  17. Combinatorial optimization with Boolean constraints

    Energy Technology Data Exchange (ETDEWEB)

    Hulme, B.L.; Worrell, R.B.

    1983-02-01

    This report shows how Boolean algebraic formula manipulation can be used to solve certain kinds of optimization problems. If the problem can be formulated in terms of 0 to 1 variables and if the feasible solutions can be described by a Boolean equation, then the method of this report can be used. The method generates feasible solutions algebraically as terms of a disjunctive normal form of a Boolean function. Many small sample problems are solved to illustrate the method and the practical situations in which these optimization problems arise.

  18. Network dynamics and systems biology

    Science.gov (United States)

    Norrell, Johannes A.

    The physics of complex systems has grown considerably as a field in recent decades, largely due to improved computational technology and increased availability of systems level data. One area in which physics is of growing relevance is molecular biology. A new field, systems biology, investigates features of biological systems as a whole, a strategy of particular importance for understanding emergent properties that result from a complex network of interactions. Due to the complicated nature of the systems under study, the physics of complex systems has a significant role to play in elucidating the collective behavior. In this dissertation, we explore three problems in the physics of complex systems, motivated in part by systems biology. The first of these concerns the applicability of Boolean models as an approximation of continuous systems. Studies of gene regulatory networks have employed both continuous and Boolean models to analyze the system dynamics, and the two have been found produce similar results in the cases analyzed. We ask whether or not Boolean models can generically reproduce the qualitative attractor dynamics of networks of continuously valued elements. Using a combination of analytical techniques and numerical simulations, we find that continuous networks exhibit two effects---an asymmetry between on and off states, and a decaying memory of events in each element's inputs---that are absent from synchronously updated Boolean models. We show that in simple loops these effects produce exactly the attractors that one would predict with an analysis of the stability of Boolean attractors, but in slightly more complicated topologies, they can destabilize solutions that are stable in the Boolean approximation, and can stabilize new attractors. Second, we investigate ensembles of large, random networks. Of particular interest is the transition between ordered and disordered dynamics, which is well characterized in Boolean systems. Networks at the

  19. Odefy -- From discrete to continuous models

    Directory of Open Access Journals (Sweden)

    Wittmann Dominik M

    2010-05-01

    Full Text Available Abstract Background Phenomenological information about regulatory interactions is frequently available and can be readily converted to Boolean models. Fully quantitative models, on the other hand, provide detailed insights into the precise dynamics of the underlying system. In order to connect discrete and continuous modeling approaches, methods for the conversion of Boolean systems into systems of ordinary differential equations have been developed recently. As biological interaction networks have steadily grown in size and complexity, a fully automated framework for the conversion process is desirable. Results We present Odefy, a MATLAB- and Octave-compatible toolbox for the automated transformation of Boolean models into systems of ordinary differential equations. Models can be created from sets of Boolean equations or graph representations of Boolean networks. Alternatively, the user can import Boolean models from the CellNetAnalyzer toolbox, GINSim and the PBN toolbox. The Boolean models are transformed to systems of ordinary differential equations by multivariate polynomial interpolation and optional application of sigmoidal Hill functions. Our toolbox contains basic simulation and visualization functionalities for both, the Boolean as well as the continuous models. For further analyses, models can be exported to SQUAD, GNA, MATLAB script files, the SB toolbox, SBML and R script files. Odefy contains a user-friendly graphical user interface for convenient access to the simulation and exporting functionalities. We illustrate the validity of our transformation approach as well as the usage and benefit of the Odefy toolbox for two biological systems: a mutual inhibitory switch known from stem cell differentiation and a regulatory network giving rise to a specific spatial expression pattern at the mid-hindbrain boundary. Conclusions Odefy provides an easy-to-use toolbox for the automatic conversion of Boolean models to systems of ordinary

  20. Boolean algebraic analysis of fire protection

    Energy Technology Data Exchange (ETDEWEB)

    Hulme, B.L.; Shiver, A.W.; Slater, P.J.

    1982-01-01

    This paper describes a computational procedure which can be used to find minimum cost ways to protect the critical combinations of equipment from a single-source fire by protecting certain areas and strengthening certain barriers against fire. The procedure yields a complete set of optimum solutions by iteratively computing upper and lower bounds on the minimum cost. The fire protection sets evolve from Boolean algebraic computations which obtain minimum cost blocking sets associated with the lower bounds while the upper bounds are producd by maxflow-mincut calculations in a network.

  1. Construction of cell type-specific logic models of signaling networks using CellNOpt.

    Science.gov (United States)

    Morris, Melody K; Melas, Ioannis; Saez-Rodriguez, Julio

    2013-01-01

    Mathematical models are useful tools for understanding protein signaling networks because they provide an integrated view of pharmacological and toxicological processes at the molecular level. Here we describe an approach previously introduced based on logic modeling to generate cell-specific, mechanistic and predictive models of signal transduction. Models are derived from a network encoding prior knowledge that is trained to signaling data, and can be either binary (based on Boolean logic) or quantitative (using a recently developed formalism, constrained fuzzy logic). The approach is implemented in the freely available tool CellNetOptimizer (CellNOpt). We explain the process CellNOpt uses to train a prior knowledge network to data and illustrate its application with a toy example as well as a realistic case describing signaling networks in the HepG2 liver cancer cell line.

  2. A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks

    Science.gov (United States)

    Laomettachit, Teeraphan; Chen, Katherine C.; Baumann, William T.

    2016-01-01

    To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a “standard component” modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with “standard components” can capture in quantitative detail many essential properties of cell cycle control in budding yeast. PMID:27187804

  3. Modeling of the hypothalamic-pituitary-adrenal axis-mediated interaction between the serotonin regulation pathway and the stress response using a Boolean approximation: a novel study of depression

    Science.gov (United States)

    2013-01-01

    Major depressive disorder (MDD) is a multifactorial disorder known to be influenced by both genetic and environmental factors. MDD presents a heritability of 37%, and a genetic contribution has also been observed in studies of family members of individuals with MDD that imply that the probability of suffering the disorder is approximately three times higher if a first-degree family member is affected. Childhood maltreatment and stressful life events (SLEs) have been established as critical environmental factors that profoundly influence the onset of MDD. The serotonin pathway has been a strong candidate for genetic studies, but it only explains a small proportion of the heritability of the disorder, which implies the involvement of other pathways. The serotonin (5-HT) pathway interacts with the stress response pathway in a manner mediated by the hypothalamic-pituitary-adrenal (HPA) axis. To analyze the interaction between the pathways, we propose the use of a synchronous Boolean network (SBN) approximation. The principal aim of this work was to model the interaction between these pathways, taking into consideration the presence of selective serotonin reuptake inhibitors (SSRIs), in order to observe how the pathways interact and to examine if the system is stable. Additionally, we wanted to study which genes or metabolites have the greatest impact on model stability when knocked out in silico. We observed that the biological model generated predicts steady states (attractors) for each of the different runs performed, thereby proving that the system is stable. These attractors changed in shape, especially when anti-depressive drugs were also included in the simulation. This work also predicted that the genes with the greatest impact on model stability were those involved in the neurotrophin pathway, such as CREB, BDNF (which has been associated with major depressive disorder in a variety of studies) and TRkB, followed by genes and metabolites related to 5-HT

  4. Structured scale dependence in the Lyapunov exponent of a Boolean chaotic map.

    Science.gov (United States)

    Cohen, Seth D

    2015-04-01

    We report on structures in a scale-dependent Lyapunov exponent of an experimental chaotic map that arise due to discontinuities in the map. The chaos is realized in an autonomous Boolean network, which is constructed using asynchronous logic gates to form a map operator that outputs an unclocked pulse-train of varying widths. The map operator executes pulse-width stretching and folding and the operator's output is fed back to its input to continuously iterate the map. Using a simple model, we show that the structured scale-dependence in the system's Lyapunov exponent is the result of the discrete logic elements in the map operator's stretching function.

  5. Modeling Nuclear Receptor-Mediated Activity and Hepatotoxicity with Boolean Networks

    Science.gov (United States)

    Predicting the human health risk of chronic exposure to environmental contaminants remains an open problem. Chronic exposure to a wide array of chemicals – e.g., conazoles, perfluourinated chemicals and phthalates – has been associated with a range of hepatic lesions in rodents t...

  6. A Boolean Network Model of Nuclear Receptor Mediated Cell Cycle Progression (S)

    Science.gov (United States)

    Nuclear receptors (NRs) are ligand-activated transcription factors that regulate a broad range of cellular processes. Hormones, lipids and xenobiotics have been shown to activate NRs with a range of consequences on development, metabolism, oxidative stress, apoptosis, and prolif...

  7. A Boolean Network Model of Nuclear Receptor Mediated Cell Cycle Progression

    Science.gov (United States)

    Nuclear receptors (NRs) are ligand-activated transcription factors that regulate a broad range of cellular processes. Hormones, lipids and xenobiotics have been shown to activate NRs with a range of consequences on development, metabolism, oxidative stress, apoptosis, and prolif...

  8. Models of educational institutions' networking

    OpenAIRE

    Shilova Olga Nikolaevna

    2015-01-01

    The importance of educational institutions' networking in modern sociocultural conditions and a definition of networking in education are presented in the article. The results of research levels, methods and models of educational institutions' networking are presented and substantially disclosed.

  9. Boolean Searches--A Life Skill.

    Science.gov (United States)

    Ala, Judy; Cerabona, Kathy

    1992-01-01

    Discusses the importance of Boolean searching as a skill that students will need in the future. Methods for teaching Boolean searching are described, and the value of truncation as an online searching aid is considered. (MES)

  10. Generalized periodic and generalized Boolean rings

    Directory of Open Access Journals (Sweden)

    Howard E. Bell

    2001-01-01

    Full Text Available We prove that a generalized periodic, as well as a generalized Boolean, ring is either commutative or periodic. We also prove that a generalized Boolean ring with central idempotents must be nil or commutative. We further consider conditions which imply the commutativity of a generalized periodic, or a generalized Boolean, ring.

  11. Duality methods in networks, computer science models, and disordered condensed matter systems

    Science.gov (United States)

    Mitchell, Joseph Dan

    In this thesis, I explore lattice independent duality and systems to which it can be applied. I first demonstrate classical duality on models in an external field, including the Ising, Potts, and x -- y models, showing in particular how this modifies duality to be lattice independent and applicable to networks. I then present a novel application of duality on the boolean satsifiability problem, one of the most important problems in computational complexity, through mapping to a low temperature Ising model. This establishes the equivalence between boolean satisfiability and a problem of enumerating the positive solutions to a Diophantine system of equations. I continue by combining duality with a prominent tool for models on networks, belief propagation, deriving a new message passing procedure, dual belief propagation. In the final part of my thesis, I shift to propose and examine a semiclassical model, the two-component Coulomb glass model, which can explain the giant magnetoresistance peak present in disordered films near a superconductor-insulator transition as the effect of competition between single particle and localized pair transport. I numerically analyze the density of states and transport properties of this model.

  12. Exploiting Surroundedness for Saliency Detection: A Boolean Map Approach.

    Science.gov (United States)

    Zhang, Jianming; Sclaroff, Stan

    2016-05-01

    We demonstrate the usefulness of surroundedness for eye fixation prediction by proposing a Boolean Map based Saliency model (BMS). In our formulation, an image is characterized by a set of binary images, which are generated by randomly thresholding the image's feature maps in a whitened feature space. Based on a Gestalt principle of figure-ground segregation, BMS computes a saliency map by discovering surrounded regions via topological analysis of Boolean maps. Furthermore, we draw a connection between BMS and the Minimum Barrier Distance to provide insight into why and how BMS can properly captures the surroundedness cue via Boolean maps. The strength of BMS is verified by its simplicity, efficiency and superior performance compared with 10 state-of-the-art methods on seven eye tracking benchmark datasets.

  13. Geometric Operators on Boolean Functions

    DEFF Research Database (Denmark)

    Frisvad, Jeppe Revall; Falster, Peter

    function. With this image of a Boolean function corresponding to a propositional formula, we prove that the orthogonal projection operator leads to a theorem describing all rules of inference in propositional reasoning. In other words, we can capture all kinds of inference in propositional logic by means...... independent of representation such that we no longer need to be much concerned with the form of the Boolean functions. Knowing that the operators can easily be implemented (as they have been in array-based logic), shows the advantage they give with respect to automated reasoning....

  14. Boolean Operations on Conic Polygons

    Institute of Scientific and Technical Information of China (English)

    Yong-Xi Gong; Yu Liu; Lun Wu; Yu-Bo Xie

    2009-01-01

    An algorithm for Boolean operations on conic polygons is proposed. Conic polygons are polygons consisting of conic segments or bounded conics with directions. Preliminaries of Boolean operations on general polygons are presented. In our algorithm, the intersection points and the topological relationships between two conic polygons are computed. Boundaries are obtained by tracking path and selecting uncrossed boundaries following rule tables to build resulting conic polygons.We define a set of rules for the intersection, union, and subtraction operations on conic polygons. The algorithm considers degeneration cases such as homology, complement, interior, and exterior. The algorithm is also evaluated and implemented.

  15. On the robustness of random Boolean formulae

    Energy Technology Data Exchange (ETDEWEB)

    Mozeika, Alexander; Saad, David [Non-linearity and Complexity Research Group, Aston University, Birmingham B4 7ET (United Kingdom); Raymond, Jack, E-mail: a.s.mozeika@aston.ac.u, E-mail: d.saad@aston.ac.u [Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay (Hong Kong)

    2010-06-01

    Random Boolean formulae, generated by a growth process of noisy logical gates are analyzed using the generating functional methodology of statistical physics. We study the type of functions generated for different input distributions, their robustness for a given level of gate error and its dependence on the formulae depth and complexity and the gates used. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding typical-case phase transitions. Results for error-rates, function-depth and sensitivity of the generated functions are obtained for various gate-type and noise models.

  16. Coevolutionary modeling in network formation

    KAUST Repository

    Al-Shyoukh, Ibrahim

    2014-12-03

    Network coevolution, the process of network topology evolution in feedback with dynamical processes over the network nodes, is a common feature of many engineered and natural networks. In such settings, the change in network topology occurs at a comparable time scale to nodal dynamics. Coevolutionary modeling offers the possibility to better understand how and why network structures emerge. For example, social networks can exhibit a variety of structures, ranging from almost uniform to scale-free degree distributions. While current models of network formation can reproduce these structures, coevolutionary modeling can offer a better understanding of the underlying dynamics. This paper presents an overview of recent work on coevolutionary models of network formation, with an emphasis on the following three settings: (i) dynamic flow of benefits and costs, (ii) transient link establishment costs, and (iii) latent preferential attachment.

  17. Modular Decomposition of Boolean Functions

    NARCIS (Netherlands)

    J.C. Bioch (Cor)

    2002-01-01

    textabstractModular decomposition is a thoroughly investigated topic in many areas such as switching theory, reliability theory, game theory and graph theory. Most appli- cations can be formulated in the framework of Boolean functions. In this paper we give a uni_ed treatment of modular decompositio

  18. Evolutionary Design of Boolean Functions

    Institute of Scientific and Technical Information of China (English)

    WANG Zhang-yi; ZHANG Huan-guo; QIN Zhong-ping; MENG Qing-shu

    2005-01-01

    We use evolutionary computing to synthesize Boolean functions randomly. By using specific crossover and mutation operator in evolving process and modifying search space and fitness function, we get some high non-linearity functions which have other good cryptography characteristics such as autocorrelation etc. Comparing to other heuristic search techniques, evolutionary computing approach is more effective because of global search strategy and implicit parallelism.

  19. Construction of optimized Boolean functions

    Institute of Scientific and Technical Information of China (English)

    CHEN Wei; YANG Yi-xian; NIU Xin-xin

    2006-01-01

    Considering connections of characteristics,this paper is aimed at the construction of optimized Boolean functions.A new method based on the Bent function,discrete Walsh spectrum and characteristics matrices are presented by concatenating,breaking,and revising output sequences conditionally.This new construction can be used to construct different kinds of functions satisfying different design criteria.

  20. Model Diagnostics for Bayesian Networks

    Science.gov (United States)

    Sinharay, Sandip

    2006-01-01

    Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…

  1. Mining and modeling character networks

    CERN Document Server

    Bonato, Anthony; Elenberg, Ethan R; Gleich, David F; Hou, Yangyang

    2016-01-01

    We investigate social networks of characters found in cultural works such as novels and films. These character networks exhibit many of the properties of complex networks such as skewed degree distribution and community structure, but may be of relatively small order with a high multiplicity of edges. Building on recent work of beveridge, we consider graph extraction, visualization, and network statistics for three novels: Twilight by Stephanie Meyer, Steven King's The Stand, and J.K. Rowling's Harry Potter and the Goblet of Fire. Coupling with 800 character networks from films found in the http://moviegalaxies.com/ database, we compare the data sets to simulations from various stochastic complex networks models including random graphs with given expected degrees (also known as the Chung-Lu model), the configuration model, and the preferential attachment model. Using machine learning techniques based on motif (or small subgraph) counts, we determine that the Chung-Lu model best fits character networks and we ...

  2. Boolean logic in artificial intelligence and Turing degrees of Boolean-valued sets

    Energy Technology Data Exchange (ETDEWEB)

    Cai, Maohua.

    1989-01-01

    Over the years a number of generalizations of recursion theory have been introduced and studied. In this dissertation the author presents yet another such generalization. Based on the concept of a weakly recursively presented Boolean algebra, he defines Boolean-valued sets, Boolean-valued recursive sets, and Boolean-valued recursively enumerable sets and discuss the basic relationships between a Boolean-valued set, its principal part, and its support. Then he generalizes many elementary concepts and results about recursive and recursively enumerable sets such as the s-m-n theorem, the recursion theorem, and the projection theorem, etc. to Boolean valued sets. By using finite and infinite injury arguments, he generalizes the Friedberg-Muchnik theorem, the theorem about nonrecursive low r.e. sets, the minimal pair theorem, and other results. Finally, he discusses the possible application of Boolean-valued logic in artificial intelligence, and gives an implementation of a parser for the four-valued Boolean logic.

  3. Quantum algorithms for testing Boolean functions

    Directory of Open Access Journals (Sweden)

    Erika Andersson

    2010-06-01

    Full Text Available We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same quantum algorithm can also be used to learn which input variables other types of Boolean functions depend on, with a success probability that depends on the form of the Boolean function that is tested, but does not depend on the total number of input variables. We also outline a procedure to futher amplify the success probability, based on another quantum algorithm, the Grover search.

  4. On the Link Between Strongly Connected Iteration Graphs and Chaotic Boolean Discrete-Time Dynamical Systems

    CERN Document Server

    Bahi, J M; Guyeux, C; Richard, A

    2011-01-01

    Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a continuous function, whose discrete-time iterations are chaotic if and only if the iteration graph of the Boolean network is strongly connected. Then, sufficient conditions for this strong connectivity are expressed on the interaction graph of this network, leading to a constructive method of chaotic function computation. The whole approach is evaluated in the chaos-based pseudo-random number generation context.

  5. Polynomial threshold functions and Boolean threshold circuits

    DEFF Research Database (Denmark)

    Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.

    2013-01-01

    We study the complexity of computing Boolean functions on general Boolean domains by polynomial threshold functions (PTFs). A typical example of a general Boolean domain is 12n . We are mainly interested in the length (the number of monomials) of PTFs, with their degree and weight being...... of secondary interest. We show that PTFs on general Boolean domains are tightly connected to depth two threshold circuits. Our main results in regard to this connection are: PTFs of polynomial length and polynomial degree compute exactly the functions computed by THRMAJ circuits. An exponential length lower...

  6. Rational Verification in Iterated Electric Boolean Games

    Directory of Open Access Journals (Sweden)

    Youssouf Oualhadj

    2016-07-01

    Full Text Available Electric boolean games are compact representations of games where the players have qualitative objectives described by LTL formulae and have limited resources. We study the complexity of several decision problems related to the analysis of rationality in electric boolean games with LTL objectives. In particular, we report that the problem of deciding whether a profile is a Nash equilibrium in an iterated electric boolean game is no harder than in iterated boolean games without resource bounds. We show that it is a PSPACE-complete problem. As a corollary, we obtain that both rational elimination and rational construction of Nash equilibria by a supervising authority are PSPACE-complete problems.

  7. Progress in Applications of Boolean Functions

    CERN Document Server

    Sasao, Tsutomu

    2010-01-01

    This book brings together five topics on the application of Boolean functions. They are 1. Equivalence classes of Boolean functions: The number of n-variable functions is large, even for values as small as n = 6, and there has been much research on classifying functions. There are many classifications, each with their own distinct merit. 2. Boolean functions for cryptography: The process of encrypting/decrypting plain text messages often depends on Boolean functions with specific properties. For example, highly nonlinear functions are valued because they are less susceptible to linear attacks.

  8. Boolean Factor Congruences and Property (*)

    CERN Document Server

    Terraf, Pedro Sánchez

    2008-01-01

    A variety V has Boolean factor congruences (BFC) if the set of factor congruences of every algebra in V is a distributive sublattice of its congruence lattice; this property holds in rings with unit and in every variety which has a semilattice operation. BFC has a prominent role in the study of uniqueness of direct product representations of algebras, since it is a strengthening of the refinement property. We provide an explicit Mal'cev condition for BFC. With the aid of this condition, it is shown that BFC is equivalent to a variant of the definability property (*), an open problem in R. Willard's work ("Varieties Having Boolean Factor Congruences," J. Algebra, 132 (1990)).

  9. Generalizing Boolean Satisfiability III: Implementation

    CERN Document Server

    Dixon, H E; Hofer, D; Luks, E M; Parkes, A J; 10.1613/jair.1656

    2011-01-01

    This is the third of three papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal has been to define a representation in which this structure is apparent and can be exploited to improve computational performance. The first paper surveyed existing work that (knowingly or not) exploited problem structure to improve the performance of satisfiability engines, and the second paper showed that this structure could be understood in terms of groups of permutations acting on individual clauses in any particular Boolean theory. We conclude the series by discussing the techniques needed to implement our ideas, and by reporting on their performance on a variety of problem instances.

  10. Constructive version of Boolean algebra

    CERN Document Server

    Ciraulo, Francesco; Toto, Paola

    2012-01-01

    The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we first show some properties concerning overlap algebras: we prove that the notion of overlap morphism corresponds classically to that of map preserving arbitrary joins; we provide a description of atomic set-based overlap algebras in the language of formal topology, thus giving a predicative characterization of discrete locales; we show that the power-collection of a set is the free overlap algebra join-generated from the set. Then, we generalize the concept of overlap algebra and overlap morphism in various ways to provide constructive versions of the category of Boolean algebras with maps preserving arbitrary existing joins.

  11. Single axioms for Boolean algebra.

    Energy Technology Data Exchange (ETDEWEB)

    McCune, W.

    2000-06-30

    Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction techniques were applied to find axioms of lengths 105, 131, 111, and 127, respectively, each with six variables.

  12. Difference equation for tracking perturbations in systems of Boolean nested canalyzing functions.

    Science.gov (United States)

    Dimitrova, Elena S; Yordanov, Oleg I; Matache, Mihaela T

    2015-06-01

    This paper studies the spread of perturbations through networks composed of Boolean functions with special canalyzing properties. Canalyzing functions have the property that at least for one value of one of the inputs the output is fixed, irrespective of the values of the other inputs. In this paper the focus is on partially nested canalyzing functions, in which multiple, but not all inputs have this property in a cascading fashion. They naturally describe many relationships in real networks. For example, in a gene regulatory network, the statement "if gene A is expressed, then gene B is not expressed regardless of the states of other genes" implies that A is canalyzing. On the other hand, the additional statement "if gene A is not expressed, and gene C is expressed, then gene B is automatically expressed; otherwise gene B's state is determined by some other type of rule" implies that gene B is expressed by a partially nested canalyzing function with more than two variables, but with two canalyzing variables. In this paper a difference equation model of the probability that a network node's value is affected by an initial perturbation over time is developed, analyzed, and validated numerically. It is shown that the effect of a perturbation decreases towards zero over time if the Boolean functions are canalyzing in sufficiently many variables. The maximum dynamical impact of a perturbation is shown to be comparable to the average impact for a wide range of values of the average sensitivity of the network. Percolation limits are also explored; these are parameter values which generate a transition of the expected perturbation effect to zero as other parameters are varied, so that the initial perturbation does not scale up with the parameters once the percolation limits are reached.

  13. THE INVERSE PROBLEM FOR BOOLEAN EQUATIONS

    Directory of Open Access Journals (Sweden)

    Hussain Mobarak Albarakati

    2012-01-01

    Full Text Available The Forward Problem (FB of Boolean equations consists of finding solutions of a system of Boolean equations, or equivalently, a single Boolean equation of the form f(X = 0 where f(X: Bn → B and B is an arbitrary Boolean algebra. By contrast, the Inverse Problem (IB of Boolean equations aims to reconstruct the equation f (X = 0 given the set of solutions and hence to verify the correctness of this set. This study derives methods that handle this inverse problem for the main types of solutions of Boolean equations. These include: (a Subsumptive general solutions, in which each of the variables is expressed as an interval by deriving successive conjunctive or disjunctive eliminants of the original function, (b Parametric general solutions, in which each of the variables is expressed via arbitrary parameters which are freely chosen elements of the underlying Boolean algebra and (c Particular solutions, each of which is an assignment from the underlying Boolean algebra to every pertinent variable that makes the Boolean equation an identity. The reconstructed function f(X in every case is set in a canonical form, such as the complete-sum form, to facilitate proving its equivalence to the original function. The methods presented herein are demonstrated with carefully-chosen illustrative examples over big Boolean algebras of various sizes. Among the methods utilized in handling the inverse problem for Boolean equations, the ones utilizing the variable-entered Karnaugh map offered pictorial insight and exhibited an efficient divide-and-conquer strategy.

  14. Modelling Vocabulary Loss

    Science.gov (United States)

    Meara, Paul

    2004-01-01

    This paper describes some simple simulation models of vocabulary attrition. The attrition process is modelled using a random autonomous Boolean network model, and some parallels with real attrition data are drawn. The paper argues that applying a complex systems approach to attrition can provide some important insights, which suggest that real…

  15. Internet Network Resource Information Model

    Institute of Scientific and Technical Information of China (English)

    陈传峰; 李增智; 唐亚哲; 刘康平

    2002-01-01

    The foundation of any network management systens is a database that con-tains information about the network resources relevant to the management tasks. A networkinformation model is an abstraction of network resources, including both managed resources andmanaging resources. In the SNMP-based management framework, management information isdefined almost exclusively from a "device" viewpoint, namely, managing a network is equiva-lent to managing a collection of individual nodes. Aiming at making use of recent advances indistributed computing and in object-oriented analysis and design, the Internet management ar-chitecture can also be based on the Open Distributed Processing Reference Model (RM-ODP).The purpose of this article is to provide an Internet Network Resource Information Model.First, a layered management information architecture will be discussed. Then the Internetnetwork resource information model is presented. The information model is specified usingObject-Z.

  16. Complex Networks in Psychological Models

    Science.gov (United States)

    Wedemann, R. S.; Carvalho, L. S. A. V. D.; Donangelo, R.

    We develop schematic, self-organizing, neural-network models to describe mechanisms associated with mental processes, by a neurocomputational substrate. These models are examples of real world complex networks with interesting general topological structures. Considering dopaminergic signal-to-noise neuronal modulation in the central nervous system, we propose neural network models to explain development of cortical map structure and dynamics of memory access, and unify different mental processes into a single neurocomputational substrate. Based on our neural network models, neurotic behavior may be understood as an associative memory process in the brain, and the linguistic, symbolic associative process involved in psychoanalytic working-through can be mapped onto a corresponding process of reconfiguration of the neural network. The models are illustrated through computer simulations, where we varied dopaminergic modulation and observed the self-organizing emergent patterns at the resulting semantic map, interpreting them as different manifestations of mental functioning, from psychotic through to normal and neurotic behavior, and creativity.

  17. Developing Personal Network Business Models

    DEFF Research Database (Denmark)

    Saugstrup, Dan; Henten, Anders

    2006-01-01

    on the 'state of the art' in the field of business modeling. Furthermore, the paper suggests three generic business models for PNs: a service oriented model, a self-organized model, and a combination model. Finally, examples of relevant services and applications in relation to three different cases......The aim of the paper is to examine the issue of business modeling in relation to personal networks, PNs. The paper builds on research performed on business models in the EU 1ST MAGNET1 project (My personal Adaptive Global NET). The paper presents the Personal Network concept and briefly reports...... are presented and analyzed in light of business modeling of PN....

  18. Network Simulation Models

    Science.gov (United States)

    2008-12-01

    well, then a Euclidean distance would be appropriate. The quadratic assignment procedure ( QAP ) (Krackhardt, 1987) could be used to compare the...Networks. Journal of Applied Psychology, 71(1): 50-55. Krackhardt, D. (1987). QAP Partialling as a Test of Spuriousness. Social Networks, 9, 171-186

  19. Version Spaces and Generalized Monotone Boolean Functions

    NARCIS (Netherlands)

    J.C. Bioch (Cor); T. Ibaraki

    2002-01-01

    textabstractWe consider generalized monotone functions f: X --> {0,1} defined for an arbitrary binary relation <= on X by the property x <= y implies f(x) <= f(y). These include the standard monotone (or positive) Boolean functions, regular Boolean functions and other interesting functions as speci

  20. A Note on Boolean Stochastic Processes

    Science.gov (United States)

    Fidaleo, Francesco

    2015-03-01

    For the quantum stochastic processes generated by the Boolean commutation relations, we prove the following version of De Finetti Theorem: each of such Boolean processes is exchangeable if and only if it is independent and identically distributed with respect to the tail algebra.

  1. Boolean Search: Current State and Perspectives.

    Science.gov (United States)

    Frants, Valery I.; Shapiro, Jacob; Taksa, Isak; Voiskunskii, Vladimir G.

    1999-01-01

    Discusses the use of Boolean logic in information-retrieval systems and analyzes existing criticisms of operational systems. Considers users' ability to use and understand Boolean operators, ranking, the quality of query formulations, and negative effects of criticism; and concludes that criticism is directed at the methodology employed in…

  2. Kazhdan-Lusztig polynomials of boolean elements

    CERN Document Server

    Mongelli, Pietro

    2011-01-01

    We give closed combinatorial product formulas for Kazhdan-Lusztig poynomials and their parabolic analogue of type q in the case of boolean elements, introduced in [M. Marietti, Boolean elements in Kazhdan-Lusztig theory, J. Algebra 295 (2006)], in Coxeter groups whose Coxeter graph is a tree.

  3. Boolean analysis of addition and multiplication

    Energy Technology Data Exchange (ETDEWEB)

    Faltin, F. (Cornell Univ., Ithaca, NY); Metropolis, N.; Ross, B.; Rota, G.-C.

    1977-01-01

    The notions of binary string and binary symmetric function are introduced, and basic results presented. Boolean algorithms are given for binary addition and multiplication. An analysis of the redundancies involved is straightforward. The examination of carry propagation which arises in the Boolean analysis of functions may lead to a new interpretation of the notion of computational complexity.

  4. Boolean integral calculus for digital systems

    Science.gov (United States)

    Tucker, J. H.; Tapia, M. A.; Bennett, A. W.

    1985-01-01

    The concept of Boolean integration is introduced and developed. When the changes in a desired function are specified in terms of changes in its arguments, then ways of 'integrating' (i.e., realizing) the function, if it exists, are presented. Boolean integral calculus has applications in design of logic circuits.

  5. Modeling regulatory cascades using Artificial Neural Networks: the case of transcriptional regulatory networks shaped during the yeast stress response.

    Science.gov (United States)

    Manioudaki, Maria E; Poirazi, Panayiota

    2013-01-01

    Over the last decade, numerous computational methods have been developed in order to infer and model biological networks. Transcriptional networks in particular have attracted significant attention due to their critical role in cell survival. The majority of network inference methods use genome-wide experimental data to search for modules of genes with coherent expression profiles and common regulators, often ignoring the multi-layer structure of transcriptional cascades. Modeling methodologies on the other hand assume a given network structure and vary significantly in their algorithmic approach, ranging from over-simplified representations (e.g., Boolean networks) to detailed -but computationally expensive-network simulations (e.g., with differential equations). In this work we use Artificial Neural Networks (ANNs) to model transcriptional regulatory cascades that emerge during the stress response in Saccharomyces cerevisiae and extend in three layers. We confine the structure of the ANNs to match the structure of the biological networks as determined by gene expression, DNA-protein interaction and experimental evidence provided in publicly available databases. Trained ANNs are able to predict the expression profile of 11 target genes across multiple experimental conditions with a correlation coefficient >0.7. When time-dependent interactions between upstream transcription factors (TFs) and their indirect targets are also included in the ANNs, accurate predictions are achieved for 30/34 target genes. Moreover, heterodimer formation is taken into account. We show that ANNs can be used to (1) accurately predict the expression of downstream genes in a 3-layer transcriptional cascade based on the expression of their indirect regulators and (2) infer the condition- and time-dependent activity of various TFs as well as during heterodimer formation. We show that a three-layer regulatory cascade whose structure is determined by co-expressed gene modules and their

  6. Network models in anatomical systems.

    Science.gov (United States)

    Esteve-Altava, Borja; Marugán-Lobón, Jesús; Botella, Héctor; Rasskin-Gutman, Diego

    2011-01-01

    Network theory has been extensively used to model the underlying structure of biological processes. From genetics to ecology, network thinking is changing our understanding of complex systems, specifically how their internal structure determines their overall behavior. Concepts such as hubs, scale-free or small-world networks, common in the complexity literature, are now used more and more in sociology, neurosciences, as well as other anthropological fields. Even though the use of network models is nowadays so widely applied, few attempts have been carried out to enrich our understanding in the classical morphological sciences such as in comparative anatomy or physical anthropology. The purpose of this article is to introduce the usage of network tools in morphology; specifically by building anatomical networks, dealing with the most common analyses and problems, and interpreting their outcome.

  7. Telecommunications network modelling, planning and design

    CERN Document Server

    Evans, Sharon

    2003-01-01

    Telecommunication Network Modelling, Planning and Design addresses sophisticated modelling techniques from the perspective of the communications industry and covers some of the major issues facing telecommunications network engineers and managers today. Topics covered include network planning for transmission systems, modelling of SDH transport network structures and telecommunications network design and performance modelling, as well as network costs and ROI modelling and QoS in 3G networks.

  8. On the parity complexity measures of Boolean functions

    OpenAIRE

    Zhang,Zhiqiang; Shi, Yaoyun

    2010-01-01

    The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to the non-deterministic complexity of the function or its complement. We also show that they are polynomially related to an analogue of the block sensitivity. We further study parity decision trees in their relations with an intermediate variant of the decisi...

  9. Multipath Detection Using Boolean Satisfiability Techniques

    Directory of Open Access Journals (Sweden)

    Fadi A. Aloul

    2011-01-01

    Full Text Available A new technique for multipath detection in wideband mobile radio systems is presented. The proposed scheme is based on an intelligent search algorithm using Boolean Satisfiability (SAT techniques to search through the uncertainty region of the multipath delays. The SAT-based scheme utilizes the known structure of the transmitted wideband signal, for example, pseudo-random (PN code, to effectively search through the entire space by eliminating subspaces that do not contain a possible solution. The paper presents a framework for modeling the multipath detection problem as a SAT application. It also provides simulation results that demonstrate the effectiveness of the proposed scheme in detecting the multipath components in frequency-selective Rayleigh fading channels.

  10. Boolean-Lie algebras and the Leibniz rule

    Energy Technology Data Exchange (ETDEWEB)

    Bazso, Fueloep [KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, PO Box 49, H-1525 Budapest (Hungary); Labos, Elemer [Neurobiology Research Group, United Research Organization of the Hungarian Academy of Sciences and Semmelweis University, H-1450 Budapest, PO Box 95 (Hungary)

    2006-06-02

    Using internal negations acting on Boolean functions, the notion of Boolean-Lie algebra is introduced. The underlying Lie product is the Boolean analogue of the Poisson bracket. The structure of a Boolean-Lie algebra is determined; it turns out to be solvable, but not nilpotent. We prove that the adjoint representation of an element of the Boolean-Lie algebra acts as a derivative operator on the space of Boolean functions. The adjoint representation is related to the previously known concept of the sensitivity function. Using the notion of adjoint representation we give the definition of a temporal derivative applicable to iterative dynamics of Boolean mappings.

  11. Campus network security model study

    Science.gov (United States)

    Zhang, Yong-ku; Song, Li-ren

    2011-12-01

    Campus network security is growing importance, Design a very effective defense hacker attacks, viruses, data theft, and internal defense system, is the focus of the study in this paper. This paper compared the firewall; IDS based on the integrated, then design of a campus network security model, and detail the specific implementation principle.

  12. Neural network modeling of emotion

    Science.gov (United States)

    Levine, Daniel S.

    2007-03-01

    This article reviews the history and development of computational neural network modeling of cognitive and behavioral processes that involve emotion. The exposition starts with models of classical conditioning dating from the early 1970s. Then it proceeds toward models of interactions between emotion and attention. Then models of emotional influences on decision making are reviewed, including some speculative (not and not yet simulated) models of the evolution of decision rules. Through the late 1980s, the neural networks developed to model emotional processes were mainly embodiments of significant functional principles motivated by psychological data. In the last two decades, network models of these processes have become much more detailed in their incorporation of known physiological properties of specific brain regions, while preserving many of the psychological principles from the earlier models. Most network models of emotional processes so far have dealt with positive and negative emotion in general, rather than specific emotions such as fear, joy, sadness, and anger. But a later section of this article reviews a few models relevant to specific emotions: one family of models of auditory fear conditioning in rats, and one model of induced pleasure enhancing creativity in humans. Then models of emotional disorders are reviewed. The article concludes with philosophical statements about the essential contributions of emotion to intelligent behavior and the importance of quantitative theories and models to the interdisciplinary enterprise of understanding the interactions of emotion, cognition, and behavior.

  13. The combination of the functionalities of feedback circuits is determinant for the attractors' number and size in pathway-like Boolean networks.

    Science.gov (United States)

    Azpeitia, Eugenio; Muñoz, Stalin; González-Tokman, Daniel; Martínez-Sánchez, Mariana Esther; Weinstein, Nathan; Naldi, Aurélien; Álvarez-Buylla, Elena R; Rosenblueth, David A; Mendoza, Luis

    2017-02-10

    Molecular regulation was initially assumed to follow both a unidirectional and a hierarchical organization forming pathways. Regulatory processes, however, form highly interlinked networks with non-hierarchical and non-unidirectional structures that contain statistically overrepresented circuits or motifs. Here, we analyze the behavior of pathways containing non-unidirectional (i.e. bidirectional) and non-hierarchical interactions that create motifs. In comparison with unidirectional and hierarchical pathways, our pathways have a high diversity of behaviors, characterized by the size and number of attractors. Motifs have been studied individually showing that feedback circuit motifs regulate the number and size of attractors. It is less clear what happens in molecular networks that usually contain multiple feedbacks. Here, we find that the way feedback circuits couple to each other (i.e., the combination of the functionalities of feedback circuits) regulate both the number and size of the attractors. We show that the different expected results of epistasis analysis (a method to infer regulatory interactions) are produced by many non-hierarchical and non-unidirectional structures. Thus, these structures cannot be correctly inferred by epistasis analysis. Finally, we show that the combinations of functionalities, combined with other network properties, allow for a better characterization of regulatory structures.

  14. The combination of the functionalities of feedback circuits is determinant for the attractors’ number and size in pathway-like Boolean networks

    Science.gov (United States)

    Azpeitia, Eugenio; Muñoz, Stalin; González-Tokman, Daniel; Martínez-Sánchez, Mariana Esther; Weinstein, Nathan; Naldi, Aurélien; Álvarez-Buylla, Elena R.; Rosenblueth, David A.; Mendoza, Luis

    2017-01-01

    Molecular regulation was initially assumed to follow both a unidirectional and a hierarchical organization forming pathways. Regulatory processes, however, form highly interlinked networks with non-hierarchical and non-unidirectional structures that contain statistically overrepresented circuits or motifs. Here, we analyze the behavior of pathways containing non-unidirectional (i.e. bidirectional) and non-hierarchical interactions that create motifs. In comparison with unidirectional and hierarchical pathways, our pathways have a high diversity of behaviors, characterized by the size and number of attractors. Motifs have been studied individually showing that feedback circuit motifs regulate the number and size of attractors. It is less clear what happens in molecular networks that usually contain multiple feedbacks. Here, we find that the way feedback circuits couple to each other (i.e., the combination of the functionalities of feedback circuits) regulate both the number and size of the attractors. We show that the different expected results of epistasis analysis (a method to infer regulatory interactions) are produced by many non-hierarchical and non-unidirectional structures. Thus, these structures cannot be correctly inferred by epistasis analysis. Finally, we show that the combinations of functionalities, combined with other network properties, allow for a better characterization of regulatory structures. PMID:28186191

  15. Nonequilibrium model on Apollonian networks.

    Science.gov (United States)

    Lima, F W S; Moreira, André A; Araújo, Ascânio D

    2012-11-01

    We investigate the majority-vote model with two states (-1,+1) and a noise parameter q on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter q. Previous results on the Ising model in Apollonian networks have reported no presence of a phase transition. We also studied the effect of redirecting a fraction p of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio γ/ν, β/ν, and 1/ν for several values of rewiring probability p. The critical noise q{c} and U were also calculated. Therefore, the results presented here demonstrate that the majority-vote model belongs to a different universality class than equilibrium Ising model on Apollonian network.

  16. Kramers-Wannier duality applied to the boolean satifiability problem

    Science.gov (United States)

    Mitchell, Joe; Hsu, Benjamin; Galitski, Victor

    2014-03-01

    Kramers-Wannier duality, first considered in 1941, is an exact technique used in statistical mechanics to relate two models together through an order-disorder transformation, and thereby study their structure and critical phenomena. The boolean satisfiability problem is one of the most important problems in computer science, specifically complexity theory; it is the first proven NP-complete problem. Using a mapping to a multi-spin Ising model in the limit of zero temperature, we present an application of Kramers-Wannier duality to this problem. This results in a novel relationship between solving the boolean satisfiability counting problem and a different computational problem: listing the non-negative solutions to a particular system of linear integer equations. This mapping relates the complexity of the two problems. We discuss the generality of Kramers-Wannier duality and its possible application to other computational problems. This research was supported by NSF-CAREER award No. DMR-0847224 and Simons Foundation.

  17. Algebraic Statistics for Network Models

    Science.gov (United States)

    2014-02-19

    AFRL-OSR-VA-TR-2014-0070 (DARPA) Algebraic Statistics for Network Models SONJA PETROVIC PENNSYLVANIA STATE UNIVERSITY 02/19/2014 Final Report...DARPA GRAPHS Phase I Algebraic Statistics for Network Models FA9550-12-1-0392 Sonja Petrović petrovic@psu.edu1 Department of Statistics Pennsylvania...Department of Statistics, Heinz College , Machine Learning Department, Cylab Carnegie Mellon University 1. Abstract This project focused on the family of

  18. Mining TCGA data using Boolean implications.

    Science.gov (United States)

    Sinha, Subarna; Tsang, Emily K; Zeng, Haoyang; Meister, Michela; Dill, David L

    2014-01-01

    Boolean implications (if-then rules) provide a conceptually simple, uniform and highly scalable way to find associations between pairs of random variables. In this paper, we propose to use Boolean implications to find relationships between variables of different data types (mutation, copy number alteration, DNA methylation and gene expression) from the glioblastoma (GBM) and ovarian serous cystadenoma (OV) data sets from The Cancer Genome Atlas (TCGA). We find hundreds of thousands of Boolean implications from these data sets. A direct comparison of the relationships found by Boolean implications and those found by commonly used methods for mining associations show that existing methods would miss relationships found by Boolean implications. Furthermore, many relationships exposed by Boolean implications reflect important aspects of cancer biology. Examples of our findings include cis relationships between copy number alteration, DNA methylation and expression of genes, a new hierarchy of mutations and recurrent copy number alterations, loss-of-heterozygosity of well-known tumor suppressors, and the hypermethylation phenotype associated with IDH1 mutations in GBM. The Boolean implication results used in the paper can be accessed at http://crookneck.stanford.edu/microarray/TCGANetworks/.

  19. Mining TCGA Data Using Boolean Implications

    Science.gov (United States)

    Sinha, Subarna; Tsang, Emily K.; Zeng, Haoyang; Meister, Michela; Dill, David L.

    2014-01-01

    Boolean implications (if-then rules) provide a conceptually simple, uniform and highly scalable way to find associations between pairs of random variables. In this paper, we propose to use Boolean implications to find relationships between variables of different data types (mutation, copy number alteration, DNA methylation and gene expression) from the glioblastoma (GBM) and ovarian serous cystadenoma (OV) data sets from The Cancer Genome Atlas (TCGA). We find hundreds of thousands of Boolean implications from these data sets. A direct comparison of the relationships found by Boolean implications and those found by commonly used methods for mining associations show that existing methods would miss relationships found by Boolean implications. Furthermore, many relationships exposed by Boolean implications reflect important aspects of cancer biology. Examples of our findings include cis relationships between copy number alteration, DNA methylation and expression of genes, a new hierarchy of mutations and recurrent copy number alterations, loss-of-heterozygosity of well-known tumor suppressors, and the hypermethylation phenotype associated with IDH1 mutations in GBM. The Boolean implication results used in the paper can be accessed at http://crookneck.stanford.edu/microarray/TCGANetworks/. PMID:25054200

  20. Mining TCGA data using Boolean implications.

    Directory of Open Access Journals (Sweden)

    Subarna Sinha

    Full Text Available Boolean implications (if-then rules provide a conceptually simple, uniform and highly scalable way to find associations between pairs of random variables. In this paper, we propose to use Boolean implications to find relationships between variables of different data types (mutation, copy number alteration, DNA methylation and gene expression from the glioblastoma (GBM and ovarian serous cystadenoma (OV data sets from The Cancer Genome Atlas (TCGA. We find hundreds of thousands of Boolean implications from these data sets. A direct comparison of the relationships found by Boolean implications and those found by commonly used methods for mining associations show that existing methods would miss relationships found by Boolean implications. Furthermore, many relationships exposed by Boolean implications reflect important aspects of cancer biology. Examples of our findings include cis relationships between copy number alteration, DNA methylation and expression of genes, a new hierarchy of mutations and recurrent copy number alterations, loss-of-heterozygosity of well-known tumor suppressors, and the hypermethylation phenotype associated with IDH1 mutations in GBM. The Boolean implication results used in the paper can be accessed at http://crookneck.stanford.edu/microarray/TCGANetworks/.

  1. In silico design and in vivo implementation of yeast gene Boolean gates.

    Science.gov (United States)

    Marchisio, Mario A

    2014-01-01

    In our previous computational work, we showed that gene digital circuits can be automatically designed in an electronic fashion. This demands, first, a conversion of the truth table into Boolean formulas with the Karnaugh map method and, then, the translation of the Boolean formulas into circuit schemes organized into layers of Boolean gates and Pools of signal carriers. In our framework, gene digital circuits that take up to three different input signals (chemicals) arise from the composition of three kinds of basic Boolean gates, namely YES, NOT, and AND. Here we present a library of YES, NOT, and AND gates realized via plasmidic DNA integration into the yeast genome. Boolean behavior is reproduced via the transcriptional control of a synthetic bipartite promoter that contains sequences of the yeast VPH1 and minimal CYC1 promoters together with operator binding sites for bacterial (i.e. orthogonal) repressor proteins. Moreover, model-driven considerations permitted us to pinpoint a strategy for re-designing gates when a better digital performance is required. Our library of well-characterized Boolean gates is the basis for the assembly of more complex gene digital circuits. As a proof of concepts, we engineered two 2-input OR gates, designed by our software, by combining YES and NOT gates present in our library.

  2. In silico design and in vivo implementation of yeast gene Boolean gates

    Science.gov (United States)

    2014-01-01

    In our previous computational work, we showed that gene digital circuits can be automatically designed in an electronic fashion. This demands, first, a conversion of the truth table into Boolean formulas with the Karnaugh map method and, then, the translation of the Boolean formulas into circuit schemes organized into layers of Boolean gates and Pools of signal carriers. In our framework, gene digital circuits that take up to three different input signals (chemicals) arise from the composition of three kinds of basic Boolean gates, namely YES, NOT, and AND. Here we present a library of YES, NOT, and AND gates realized via plasmidic DNA integration into the yeast genome. Boolean behavior is reproduced via the transcriptional control of a synthetic bipartite promoter that contains sequences of the yeast VPH1 and minimal CYC1 promoters together with operator binding sites for bacterial (i.e. orthogonal) repressor proteins. Moreover, model-driven considerations permitted us to pinpoint a strategy for re-designing gates when a better digital performance is required. Our library of well-characterized Boolean gates is the basis for the assembly of more complex gene digital circuits. As a proof of concepts, we engineered two 2-input OR gates, designed by our software, by combining YES and NOT gates present in our library. PMID:24485181

  3. Boolean Algebra of C-Algebras

    Directory of Open Access Journals (Sweden)

    G.C. Rao

    2012-11-01

    Full Text Available A C- algebra is the algebraic form of the 3-valued conditional logic, which was introduced by F. Guzman and C. C. Squier in 1990. In this paper, some equivalent conditions for a C- algebra to become a boolean algebra in terms of congruences are given. It is proved that the set of all central elements B(A is isomorphic to the Boolean algebra of all C-algebras Sa, where a B(A. It is also proved that B(A is isomorphic to the Boolean algebra of all C-algebras Aa, where a B(A.

  4. Flexible method for Boolean information retrieval

    Energy Technology Data Exchange (ETDEWEB)

    Salton, G.; Wu, H.

    1983-01-01

    A new flexible retrieval system is described which makes it possible to relax the strict conditions of Boolean query logic thereby retrieving useful items that are rejected in a conventional retrieval situation. The query structure inherent in the Boolean system is preserved, while at the same time weighted terms may be incorporated into both queries and stored documents; the retrieved output can also be ranked in strict similarity order with the user queries. A conventional retrieval system can be modified to make use of the flexible metric system. Laboratory tests indicate that the extended system produces better retrieval output than either the Boolean or the vector processing systems. 11 references.

  5. A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle

    Science.gov (United States)

    Ortiz-Gutiérrez, Elizabeth; García-Cruz, Karla; Azpeitia, Eugenio; Castillo, Aaron; Sánchez, María de la Paz; Álvarez-Buylla, Elena R.

    2015-01-01

    Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular components and other regulators considered here. We validate the model by comparing our in silico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recovered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent consequence of the inherent characteristics of the regulatory logic proposed here. This dynamical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes. PMID:26340681

  6. Advances in theoretical models of network science

    Institute of Scientific and Technical Information of China (English)

    FANG Jin-qing; BI Qiao; LI Yong

    2007-01-01

    In this review article, we will summarize the main advances in network science investigated by the CIAE Group of Complex Network in this field. Several theoretical models of network science were proposed and their topological and dynamical properties are reviewed and compared with the other models. Our models mainly include a harmonious unifying hybrid preferential model, a large unifying hybrid network model, a quantum interference network, a hexagonal nanowire network, and a small-world network with the same degree. The models above reveal some new phenomena and findings, which are useful for deeply understanding and investigating complex networks and their applications.

  7. Comparing signaling networks between normal and transformed hepatocytes using discrete logical models.

    Science.gov (United States)

    Saez-Rodriguez, Julio; Alexopoulos, Leonidas G; Zhang, Mingsheng; Morris, Melody K; Lauffenburger, Douglas A; Sorger, Peter K

    2011-08-15

    Substantial effort in recent years has been devoted to constructing and analyzing large-scale gene and protein networks on the basis of "omic" data and literature mining. These interaction graphs provide valuable insight into the topologies of complex biological networks but are rarely context specific and cannot be used to predict the responses of cell signaling proteins to specific ligands or drugs. Conversely, traditional approaches to analyzing cell signaling are narrow in scope and cannot easily make use of network-level data. Here, we combine network analysis and functional experimentation by using a hybrid approach in which graphs are converted into simple mathematical models that can be trained against biochemical data. Specifically, we created Boolean logic models of immediate-early signaling in liver cells by training a literature-based prior knowledge network against biochemical data obtained from primary human hepatocytes and 4 hepatocellular carcinoma cell lines exposed to combinations of cytokines and small-molecule kinase inhibitors. Distinct families of models were recovered for each cell type, and these families clustered topologically into normal and diseased sets.

  8. Current approaches to gene regulatory network modelling

    Directory of Open Access Journals (Sweden)

    Brazma Alvis

    2007-09-01

    Full Text Available Abstract Many different approaches have been developed to model and simulate gene regulatory networks. We proposed the following categories for gene regulatory network models: network parts lists, network topology models, network control logic models, and dynamic models. Here we will describe some examples for each of these categories. We will study the topology of gene regulatory networks in yeast in more detail, comparing a direct network derived from transcription factor binding data and an indirect network derived from genome-wide expression data in mutants. Regarding the network dynamics we briefly describe discrete and continuous approaches to network modelling, then describe a hybrid model called Finite State Linear Model and demonstrate that some simple network dynamics can be simulated in this model.

  9. Structure learning for Bayesian networks as models of biological networks.

    Science.gov (United States)

    Larjo, Antti; Shmulevich, Ilya; Lähdesmäki, Harri

    2013-01-01

    Bayesian networks are probabilistic graphical models suitable for modeling several kinds of biological systems. In many cases, the structure of a Bayesian network represents causal molecular mechanisms or statistical associations of the underlying system. Bayesian networks have been applied, for example, for inferring the structure of many biological networks from experimental data. We present some recent progress in learning the structure of static and dynamic Bayesian networks from data.

  10. Detecting Emergent Behaviors with Semi-Boolean Algebra

    Energy Technology Data Exchange (ETDEWEB)

    Haglich, Peter [Lockheed Martin Corporation; Rouff, Christopher [Lockheed Martin Corporation; Pullum, Laura L [ORNL

    2010-01-01

    As systems continue to be interconnected, their collective behavior becomes increasingly difficult to predict. The emergent properties of systems of systems make them powerful, but at the same time make them more difficult to design, assure proper behaviors emerge, operate correctly, and have no new security holes. Learning and adaptation cause additional concerns because emergent behavior patterns simply cannot be fully predicted through the use of traditional system development methods, such as testing and model checking. In addition, self-organization can occur as the individual systems optimize to address inefficiencies in the larger system. Designing for and detecting emergent behavior is something that has not been addressed in current systems development methodologies. This paper gives background on approaches for modeling and verifying emergent behavior and then discusses the use of semi-Boolean algebra as a means for detecting emergence in combined behaviors. Semi-Boolean algebra is a generalization of the Boolean algebra concept obtained by weakening the requirement that any two elements have a common upper bound. An example is given and several ways are described that allow emergent behavior to be detected with this technique.

  11. Network model of security system

    Directory of Open Access Journals (Sweden)

    Adamczyk Piotr

    2016-01-01

    Full Text Available The article presents the concept of building a network security model and its application in the process of risk analysis. It indicates the possibility of a new definition of the role of the network models in the safety analysis. Special attention was paid to the development of the use of an algorithm describing the process of identifying the assets, vulnerability and threats in a given context. The aim of the article is to present how this algorithm reduced the complexity of the problem by eliminating from the base model these components that have no links with others component and as a result and it was possible to build a real network model corresponding to reality.

  12. A new transient network model for associative polymer networks

    NARCIS (Netherlands)

    Wientjes, R.H.W.; Jongschaap, R.J.J.; Duits, M.H.G.; Mellema, J.

    1999-01-01

    A new model for the linear viscoelastic behavior of polymer networks is developed. In this model the polymer system is described as a network of spring segments connected via sticky points (as in the Lodge model). [Lodge, A. S., “A network theory of flow birefringence and stress in concentrated poly

  13. Adiabatic quantum gates and Boolean functions

    Energy Technology Data Exchange (ETDEWEB)

    Andrecut, M; Ali, M K [Department of Physics, University of Lethbridge, Lethbridge, AB, T1K 3M4 (Canada)

    2004-06-25

    We discuss the logical implementation of quantum gates and Boolean functions in the framework of quantum adiabatic method, which uses the language of ground states, spectral gaps and Hamiltonians instead of the standard unitary transformation language. (letter to the editor)

  14. Understanding the Complexity of Terrorist Networks

    CERN Document Server

    Fellman, Philip V

    2009-01-01

    Complexity science affords a number of novel tools for examining terrorism, particularly network analysis and NK-Boolean fitness landscapes. The following paper explores various aspects of terrorist networks which can be illuminated through applications of non-linear dynamical systems modeling to terrorist network structures. Of particular interest are some of the emergent properties of terrorist networks as typified by the 9-11 hijackers network, properties of centrality, hierarchy and distance, as well as ways in which attempts to disrupt the transmission of information through terrorist networks may be expected to produce greater or lesser levels of fitness in those organizations.

  15. Generalizing Boolean Satisfiability II: Theory

    CERN Document Server

    Dixon, H E; Luks, E M; Parkes, A J; 10.1613/jair.1555

    2011-01-01

    This is the second of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper presents the theoretical basis for the ideas underlying ZAP, arguing that existing ideas in this area exploit a single, recurring structure in that multiple database axioms can be obtained by operating on a single axiom using a subgroup of the group of permutations on the literals in the problem. We argue that the group structure precisely captures the general structure at which earlier approaches hinted, and give numerous examples of its use. We go on to extend the Davis-Putnam-Logemann-...

  16. Local Correction of Boolean Functions

    CERN Document Server

    Alon, Noga

    2011-01-01

    A Boolean function f over n variables is said to be q-locally correctable if, given a black-box access to a function g which is "close" to an isomorphism f_sigma of f, we can compute f_sigma(x) for any x in Z_2^n with good probability using q queries to g. We observe that any k-junta, that is, any function which depends only on k of its input variables, is O(2^k)-locally correctable. Moreover, we show that there are examples where this is essentially best possible, and locally correcting some k-juntas requires a number of queries which is exponential in k. These examples, however, are far from being typical, and indeed we prove that for almost every k-junta, O(k log k) queries suffice.

  17. Boolean computation of optimum hitting sets

    Energy Technology Data Exchange (ETDEWEB)

    Hulme, B.L.; Baca, L.S.; Shiver, A.W.; Worrell, R.B.

    1984-04-01

    This report presents the results of computational experience in solving weighted hitting set problems by Boolean algebraic methods. The feasible solutions are obtained by Boolean formula manipulations, and the optimum solutions are obtained by comparing the weight sums of the feasible solutions. Both the algebra and the optimization can be accomplished using the SETS language. One application is to physical protection problems. 8 references, 2 tables.

  18. On Boolean matrices with full factor rank

    Energy Technology Data Exchange (ETDEWEB)

    Shitov, Ya [National Research University " Higher School of Economics" , Moscow (Russian Federation)

    2013-11-30

    It is demonstrated that every (0,1)-matrix of size n×m having Boolean rank n contains a column with at least √n/2−1 zero entries. This bound is shown to be asymptotically optimal. As a corollary, it is established that the size of a full-rank Boolean matrix is bounded from above by a function of its tropical and determinantal ranks. Bibliography: 16 titles.

  19. Testing Booleanity and the Uncertainty Principle

    CERN Document Server

    Gur, Tom

    2012-01-01

    Let f:{-1,1}^n -> R be a real function on the hypercube, given by its discrete Fourier expansion, or, equivalently, represented as a multilinear polynomial. We say that it is Boolean if its image is in {-1,1}. We show that every function on the hypercube with a sparse Fourier expansion must either be Boolean or far from Boolean. In particular, we show that a multilinear polynomial with at most k terms must either be Boolean, or output values different than -1 or 1 for a fraction of at least 2/(k+2)^2 of its domain. It follows that given black box access to f, together with the guarantee that its representation as a multilinear polynomial has at most k terms, one can test Booleanity using O(k^2) queries. We show an Omega(k) queries lower bound for this problem. We also consider the problem of deciding if a function is Boolean, given its explicit representation as a k term multilinear polynomial. The naive approach of evaluating it at every input has O(kn2^n) time complexity. For large k (i.e, exponential) we p...

  20. Target-Centric Network Modeling

    DEFF Research Database (Denmark)

    Mitchell, Dr. William L.; Clark, Dr. Robert M.

    In Target-Centric Network Modeling: Case Studies in Analyzing Complex Intelligence Issues, authors Robert Clark and William Mitchell take an entirely new approach to teaching intelligence analysis. Unlike any other book on the market, it offers case study scenarios using actual intelligence repor....... Working through these cases, students will learn to manage and evaluate realistic intelligence accounts.......In Target-Centric Network Modeling: Case Studies in Analyzing Complex Intelligence Issues, authors Robert Clark and William Mitchell take an entirely new approach to teaching intelligence analysis. Unlike any other book on the market, it offers case study scenarios using actual intelligence......, and collaborative sharing in the process of creating a high-quality, actionable intelligence product. The case studies reflect the complexity of twenty-first century intelligence issues by dealing with multi-layered target networks that cut across political, economic, social, technological, and military issues...

  1. On the average sensitivity of laced Boolean functions

    CERN Document Server

    jiyou, Li

    2011-01-01

    In this paper we obtain the average sensitivity of the laced Boolean functions. This confirms a conjecture of Shparlinski. We also compute the weights of the laced Boolean functions and show that they are almost balanced.

  2. CNEM: Cluster Based Network Evolution Model

    Directory of Open Access Journals (Sweden)

    Sarwat Nizamani

    2015-01-01

    Full Text Available This paper presents a network evolution model, which is based on the clustering approach. The proposed approach depicts the network evolution, which demonstrates the network formation from individual nodes to fully evolved network. An agglomerative hierarchical clustering method is applied for the evolution of network. In the paper, we present three case studies which show the evolution of the networks from the scratch. These case studies include: terrorist network of 9/11 incidents, terrorist network of WMD (Weapons Mass Destruction plot against France and a network of tweets discussing a topic. The network of 9/11 is also used for evaluation, using other social network analysis methods which show that the clusters created using the proposed model of network evolution are of good quality, thus the proposed method can be used by law enforcement agencies in order to further investigate the criminal networks

  3. Biological transportation networks: Modeling and simulation

    KAUST Repository

    Albi, Giacomo

    2015-09-15

    We present a model for biological network formation originally introduced by Cai and Hu [Adaptation and optimization of biological transport networks, Phys. Rev. Lett. 111 (2013) 138701]. The modeling of fluid transportation (e.g., leaf venation and angiogenesis) and ion transportation networks (e.g., neural networks) is explained in detail and basic analytical features like the gradient flow structure of the fluid transportation network model and the impact of the model parameters on the geometry and topology of network formation are analyzed. We also present a numerical finite-element based discretization scheme and discuss sample cases of network formation simulations.

  4. Ising model for distribution networks

    CERN Document Server

    Hooyberghs, H; Giuraniuc, C; Van Schaeybroeck, B; Indekeu, J O

    2012-01-01

    An elementary Ising spin model is proposed for demonstrating cascading failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidary environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of t...

  5. Boolean integration. [applied to switching network synthesis

    Science.gov (United States)

    Tucker, J. H.; Tapia, M. A.; Bennett, A. W.

    1976-01-01

    This paper presents the necessary and sufficient conditions for a given differential expression to be compatibly integrable and it presents the necessary and sufficient conditions for a given expression to be exactly integrable. Methods are given for integrating a differential expression when it is exactly integrable and when it is compatibly integrable. The physical interpretation is given of the integral of order k, of a differential expression, and it is shown that any differential expression of the proper form is integrable by parts.

  6. Nonparametric Bayesian Modeling of Complex Networks

    DEFF Research Database (Denmark)

    Schmidt, Mikkel Nørgaard; Mørup, Morten

    2013-01-01

    Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using...... for complex networks can be derived and point out relevant literature....

  7. Simulating Boolean circuits on a DNA computer

    Energy Technology Data Exchange (ETDEWEB)

    Ogihara, Mitsunori; Ray, A. [Univ. of Rochester, NY (United States)

    1997-12-01

    We demonstrate that DNA computers can simulate Boolean circuits with a small overhead. Boolean circuits embody the notion of massively parallel signal processing and are frequently encountered in many parallel algorithms. Many important problems such as sorting, integer arithmetic, and matrix multiplication are known to be computable by small size Boolean circuits much faster than by ordinary sequential digital computers. This paper shows that DNA chemistry allows one to simulate large semi-unbounded fan-in Boolean circuits with a logarithmic slowdown in computation time. Also, for the class NC{sup 1}, the slowdown can be reduced to a constant. In this algorithm we have encoded the inputs, the Boolean AND gates, and the OR gates to DNA oligonucleotide sequences. We operate on the gates and the inputs by standard molecular techniques of sequence-specific annealing, ligation, separation by size, amplification, sequence-specific cleavage, and detection by size. Additional steps of amplification are not necessary for NC{sup 1} circuits. Preliminary biochemical experiments on a small test circuit have produced encouraging results. Further confirmatory experiments are in progress. 19 refs., 3 figs., 1 tab.

  8. A Simple Blueprint for Automatic Boolean Query Processing.

    Science.gov (United States)

    Salton, G.

    1988-01-01

    Describes a new Boolean retrieval environment in which an extended soft Boolean logic is used to automatically construct queries from original natural language formulations provided by users. Experimental results that compare the retrieval effectiveness of this method to conventional Boolean and vector processing are discussed. (27 references)…

  9. TIGER: Toolbox for integrating genome-scale metabolic models, expression data, and transcriptional regulatory networks

    Directory of Open Access Journals (Sweden)

    Jensen Paul A

    2011-09-01

    Full Text Available Abstract Background Several methods have been developed for analyzing genome-scale models of metabolism and transcriptional regulation. Many of these methods, such as Flux Balance Analysis, use constrained optimization to predict relationships between metabolic flux and the genes that encode and regulate enzyme activity. Recently, mixed integer programming has been used to encode these gene-protein-reaction (GPR relationships into a single optimization problem, but these techniques are often of limited generality and lack a tool for automating the conversion of rules to a coupled regulatory/metabolic model. Results We present TIGER, a Toolbox for Integrating Genome-scale Metabolism, Expression, and Regulation. TIGER converts a series of generalized, Boolean or multilevel rules into a set of mixed integer inequalities. The package also includes implementations of existing algorithms to integrate high-throughput expression data with genome-scale models of metabolism and transcriptional regulation. We demonstrate how TIGER automates the coupling of a genome-scale metabolic model with GPR logic and models of transcriptional regulation, thereby serving as a platform for algorithm development and large-scale metabolic analysis. Additionally, we demonstrate how TIGER's algorithms can be used to identify inconsistencies and improve existing models of transcriptional regulation with examples from the reconstructed transcriptional regulatory network of Saccharomyces cerevisiae. Conclusion The TIGER package provides a consistent platform for algorithm development and extending existing genome-scale metabolic models with regulatory networks and high-throughput data.

  10. Mathematical Modelling Plant Signalling Networks

    KAUST Repository

    Muraro, D.

    2013-01-01

    During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.

  11. On the parity complexity measures of Boolean functions

    CERN Document Server

    Zhang, Zhiqiang; 10.1016/j.tcs.2010.03.027

    2010-01-01

    The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to the non-deterministic complexity of the function or its complement. We also show that they are polynomially related to an analogue of the block sensitivity. We further study parity decision trees in their relations with an intermediate variant of the decision trees, as well as with communication complexity.

  12. Generalization performance of regularized neural network models

    DEFF Research Database (Denmark)

    Larsen, Jan; Hansen, Lars Kai

    1994-01-01

    Architecture optimization is a fundamental problem of neural network modeling. The optimal architecture is defined as the one which minimizes the generalization error. This paper addresses estimation of the generalization performance of regularized, complete neural network models. Regularization...

  13. Plant Growth Models Using Artificial Neural Networks

    Science.gov (United States)

    Bubenheim, David

    1997-01-01

    In this paper, we descrive our motivation and approach to devloping models and the neural network architecture. Initial use of the artificial neural network for modeling the single plant process of transpiration is presented.

  14. Duality theories for Boolean algebras with operators

    CERN Document Server

    Givant, Steven

    2014-01-01

    In this new text, Steven Givant—the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski—develops three theories of duality for Boolean algebras with operators. Givant addresses the two most recognized dualities (one algebraic and the other topological) and introduces a third duality, best understood as a hybrid of the first two. This text will be of interest to graduate students and researchers in the fields of mathematics, computer science, logic, and philosophy who are interested in exploring special or general classes of Boolean algebras with operators. Readers should be familiar with the basic arithmetic and theory of Boolean algebras, as well as the fundamentals of point-set topology.

  15. Scalable Capacity Bounding Models for Wireless Networks

    OpenAIRE

    Du, Jinfeng; Medard, Muriel; Xiao, Ming; Skoglund, Mikael

    2014-01-01

    The framework of network equivalence theory developed by Koetter et al. introduces a notion of channel emulation to construct noiseless networks as upper (resp. lower) bounding models, which can be used to calculate the outer (resp. inner) bounds for the capacity region of the original noisy network. Based on the network equivalence framework, this paper presents scalable upper and lower bounding models for wireless networks with potentially many nodes. A channel decoupling method is proposed...

  16. Linear fuzzy gene network models obtained from microarray data by exhaustive search

    Directory of Open Access Journals (Sweden)

    Quong Judy N

    2004-08-01

    Full Text Available Abstract Background Recent technological advances in high-throughput data collection allow for experimental study of increasingly complex systems on the scale of the whole cellular genome and proteome. Gene network models are needed to interpret the resulting large and complex data sets. Rationally designed perturbations (e.g., gene knock-outs can be used to iteratively refine hypothetical models, suggesting an approach for high-throughput biological system analysis. We introduce an approach to gene network modeling based on a scalable linear variant of fuzzy logic: a framework with greater resolution than Boolean logic models, but which, while still semi-quantitative, does not require the precise parameter measurement needed for chemical kinetics-based modeling. Results We demonstrated our approach with exhaustive search for fuzzy gene interaction models that best fit transcription measurements by microarray of twelve selected genes regulating the yeast cell cycle. Applying an efficient, universally applicable data normalization and fuzzification scheme, the search converged to a small number of models that individually predict experimental data within an error tolerance. Because only gene transcription levels are used to develop the models, they include both direct and indirect regulation of genes. Conclusion Biological relationships in the best-fitting fuzzy gene network models successfully recover direct and indirect interactions predicted from previous knowledge to result in transcriptional correlation. Fuzzy models fit on one yeast cell cycle data set robustly predict another experimental data set for the same system. Linear fuzzy gene networks and exhaustive rule search are the first steps towards a framework for an integrated modeling and experiment approach to high-throughput "reverse engineering" of complex biological systems.

  17. Brand Marketing Model on Social Networks

    Directory of Open Access Journals (Sweden)

    Jolita Jezukevičiūtė

    2014-04-01

    Full Text Available The paper analyzes the brand and its marketing solutions onsocial networks. This analysis led to the creation of improvedbrand marketing model on social networks, which will contributeto the rapid and cheap organization brand recognition, increasecompetitive advantage and enhance consumer loyalty. Therefore,the brand and a variety of social networks are becoming a hotresearch area for brand marketing model on social networks.The world‘s most successful brand marketing models exploratoryanalysis of a single case study revealed a brand marketingsocial networking tools that affect consumers the most. Basedon information analysis and methodological studies, develop abrand marketing model on social networks.

  18. Boolean differentiation and integration using Karnaugh maps

    Science.gov (United States)

    Tucker, J. H.; Tapia, M. A.; Bennett, A. W.

    1977-01-01

    Algorithms are presented for differentiation and integration of Boolean functions by means of Karnaugh maps. The algorithms are considered simple when the number of variables is six or less; in this case Boolean differentiation and integration is said to be as easy as the Karnaugh map method of simplifying switching functions. It is suggested that the algorithms would be useful in the analysis of faults in combinational systems and in the synthesis of asynchronous sequential systems which utilize edge-sensitive flip-flops.

  19. Coherent spaces, Boolean rings and quantum gates

    Science.gov (United States)

    Vourdas, A.

    2016-10-01

    Coherent spaces spanned by a finite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they transform into projectors of the same type, under displacement transformations, and also under time evolution. The set of these spaces, with the logical OR and AND operations is a distributive lattice, and with the logical XOR and AND operations is a Boolean ring (Stone's formalism). Applications of this Boolean ring into classical CNOT gates with n-ary variables, and also quantum CNOT gates with coherent states, are discussed.

  20. Information encryption systems based on Boolean functions

    Directory of Open Access Journals (Sweden)

    Aureliu Zgureanu

    2011-02-01

    Full Text Available An information encryption system based on Boolean functions is proposed. Information processing is done using multidimensional matrices, performing logical operations with these matrices. At the basis of ensuring high level security of the system the complexity of solving the problem of building systems of Boolean functions that depend on many variables (tens and hundreds is set. Such systems represent the private key. It varies both during the encryption and decryption of information, and during the transition from one message to another.

  1. Analysis of affinely equivalent Boolean functions

    Institute of Scientific and Technical Information of China (English)

    MENG QingShu; ZHANG HuanGuo; YANG Min; WANG ZhangYi

    2007-01-01

    By some basic transforms and invariant theory, we give two results: 1) an algorithm,which can be used to judge if two Boolean functions are affinely equivalent and to obtain the equivalence relationship if they are equivalent. This is useful in studying Boolean functions and in engineering. For example, we classify all 8-variable homogeneous bent functions of degree 3 into two classes; 2) Reed-Muller codes R(4,6)/R(1,6), R(3,7)/R(1,7) are classified efficiently.

  2. Hybrid modeling of the crosstalk between signaling and transcriptional networks using ordinary differential equations and multi-valued logic.

    Science.gov (United States)

    Khan, Faiz M; Schmitz, Ulf; Nikolov, Svetoslav; Engelmann, David; Pützer, Brigitte M; Wolkenhauer, Olaf; Vera, Julio

    2014-01-01

    A decade of successful results indicates that systems biology is the appropriate approach to investigate the regulation of complex biochemical networks involving transcriptional and post-transcriptional regulations. It becomes mandatory when dealing with highly interconnected biochemical networks, composed of hundreds of compounds, or when networks are enriched in non-linear motifs like feedback and feedforward loops. An emerging dilemma is to conciliate models of massive networks and the adequate description of non-linear dynamics in a suitable modeling framework. Boolean networks are an ideal representation of massive networks that are humble in terms of computational complexity and data demand. However, they are inappropriate when dealing with nested feedback/feedforward loops, structural motifs common in biochemical networks. On the other hand, models of ordinary differential equations (ODEs) cope well with these loops, but they require enormous amounts of quantitative data for a full characterization of the model. Here we propose hybrid models, composed of ODE and logical sub-modules, as a strategy to handle large scale, non-linear biochemical networks that include transcriptional and post-transcriptional regulations. We illustrate the construction of this kind of models using as example a regulatory network centered on E2F1, a transcription factor involved in cancer. The hybrid modeling approach proposed is a good compromise between quantitative/qualitative accuracy and scalability when considering large biochemical networks with a small highly interconnected core, and module of transcriptionally regulated genes that are not part of critical regulatory loops. This article is part of a Special Issue entitled: Computational Proteomics, Systems Biology & Clinical Implications. Guest Editor: Yudong Cai.

  3. Compensatory interactions to stabilize multiple steady states or mitigate the effects of multiple deregulations in biological networks

    Science.gov (United States)

    Yang, Gang; Campbell, Colin; Albert, Réka

    2016-12-01

    Complex diseases can be modeled as damage to intracellular networks that results in abnormal cell behaviors. Network-based dynamic models such as Boolean models have been employed to model a variety of biological systems including those corresponding to disease. Previous work designed compensatory interactions to stabilize an attractor of a Boolean network after single node damage. We generalize this method to a multinode damage scenario and to the simultaneous stabilization of multiple steady state attractors. We classify the emergent situations, with a special focus on combinatorial effects, and characterize each class through simulation. We explore how the structural and functional properties of the network affect its resilience and its possible repair scenarios. We demonstrate the method's applicability to two intracellular network models relevant to cancer. This work has implications in designing prevention strategies for complex disease.

  4. The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks

    OpenAIRE

    Greenbury, Sam F.; Johnston, Iain G.; Matthew A Smith; Doye, Jonathan P. K.; Louis, Ard A.

    2010-01-01

    Abstract We investigate how scale-free (SF) and Erdos-Renyi (ER) topologies affect the interplay between evolvability and robustness of model gene regulatory networks with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006) we find that networks with SFin topologies, that is SF topology for incoming nodes and ER topology for outgoing nodes, are significantly more evolvable towards specific oscillatory targets than networks with ER topology for both incoming an...

  5. Soft Boolean algebra%软布尔代数

    Institute of Scientific and Technical Information of China (English)

    刘卫锋

    2013-01-01

    将软集理论应用到布尔代数中,提出了软布尔代数、软布尔子代数、软布尔代数的软理想、软理想布尔代数等概念,研究了它们的相关性质,并初步讨论了软布尔代数与几类布尔代数的模糊子代数的关系。%The soft set theory is applied to the Boolean algebra.The concepts of soft Boolean algebra, soft Boolean sub-algebra, soft ideal of soft Boolean algebra and idealistic soft Boolean algebra are presented and some related algebraic properties are discussed.The relations between soft Boolean algebra and several kinds of fuzzy subalgebras of Boolean algebra are preliminarily investigated.

  6. Network Bandwidth Utilization Forecast Model on High Bandwidth Network

    Energy Technology Data Exchange (ETDEWEB)

    Yoo, Wucherl; Sim, Alex

    2014-07-07

    With the increasing number of geographically distributed scientific collaborations and the scale of the data size growth, it has become more challenging for users to achieve the best possible network performance on a shared network. We have developed a forecast model to predict expected bandwidth utilization for high-bandwidth wide area network. The forecast model can improve the efficiency of resource utilization and scheduling data movements on high-bandwidth network to accommodate ever increasing data volume for large-scale scientific data applications. Univariate model is developed with STL and ARIMA on SNMP path utilization data. Compared with traditional approach such as Box-Jenkins methodology, our forecast model reduces computation time by 83.2percent. It also shows resilience against abrupt network usage change. The accuracy of the forecast model is within the standard deviation of the monitored measurements.

  7. An acoustical model based monitoring network

    NARCIS (Netherlands)

    Wessels, P.W.; Basten, T.G.H.; Eerden, F.J.M. van der

    2010-01-01

    In this paper the approach for an acoustical model based monitoring network is demonstrated. This network is capable of reconstructing a noise map, based on the combination of measured sound levels and an acoustic model of the area. By pre-calculating the sound attenuation within the network the noi

  8. A system dynamics model for communications networks

    Science.gov (United States)

    Awcock, A. J.; King, T. E. G.

    1985-09-01

    An abstract model of a communications network in system dynamics terminology is developed as implementation of this model by a FORTRAN program package developed at RSRE is discussed. The result of this work is a high-level simulation package in which the performance of adaptive routing algorithms and other network controls may be assessed for a network of arbitrary topology.

  9. Modelling delay propagation within an airport network

    NARCIS (Netherlands)

    Pyrgiotis, N.; Malone, K.M.; Odoni, A.

    2013-01-01

    We describe an analytical queuing and network decomposition model developed to study the complex phenomenon of the propagation of delays within a large network of major airports. The Approximate Network Delays (AND) model computes the delays due to local congestion at individual airports and capture

  10. Competitive learning of monotone Boolean functions

    OpenAIRE

    2014-01-01

    We apply competitive analysis onto the problem of minimizing the number of queries to an oracle to completely reconstruct a given monotone Boolean function. Besides lower and upper bounds on the competitivity we determine optimal deterministic online algorithms for the smallest problem instances.

  11. Demonstrating Boolean Logic Using Simple Electrical Circuits

    Science.gov (United States)

    McElhaney, Kevin W.

    2004-01-01

    While exploring the subject of geometric proofs, boolean logic operators AND and OR can be used to allow students to visualize their true-or-false patterns. An activity in the form of constructing electrical circuits is illustrated to explain the concept.

  12. A Boolean Map Theory of Visual Attention

    Science.gov (United States)

    Huang, Liqiang; Pashler, Harold

    2007-01-01

    A theory is presented that attempts to answer two questions. What visual contents can an observer consciously access at one moment? Answer: only one feature value (e.g., green) per dimension, but those feature values can be associated (as a group) with multiple spatially precise locations (comprising a single labeled Boolean map). How can an…

  13. Short single axioms for boolean algebra.

    Energy Technology Data Exchange (ETDEWEB)

    McCune, W.; Veroff, R.; Fitelson, B.; Harris, K.; Feist, A.; Wos, L.; Mathematics and Computer Science; Univ. of New Mexico; Univ. of Wisconsin at Madison; Duke Univ.

    2002-01-01

    We present short single equational axioms for Boolean algebra in terms of disjunction and negation and in terms of the Sheffer stroke. Previously known single axioms for these theories are much longer than the ones we present. We show that there is no shorter axiom in terms of the Sheffer stroke. Automated deduction techniques were used in several parts of the work.

  14. A Short Sheffer axiom for Boolean algebra.

    Energy Technology Data Exchange (ETDEWEB)

    Veroff, R.; McCune, W.

    2000-06-30

    A short Sheffer stroke identity is shown to be a single axiom for Boolean algebra. The axiom has length 15 and 3 variables. The proof shows that it is equivalent to Sheffer's original 3-basis for the theory. Automated deduction techniques were used to find the proof. The shortest single axiom previously known to us has length 105 and 6 variables.

  15. Quantum walks outside of boolean domain as a gate for one, two, or three qubits

    Science.gov (United States)

    Cavin, Thomas; Solenov, Dmitry

    Quantum computing needs entangling quantum gates to perform computation and error correction. We will discuss a novel way to implement quantum gates, such as CNOT, using quantum walks that are directed through a network of states outside of the boolean domain. In such implementations it is important to investigate walks on networks of different connectivities. Specifically, we will discuss solutions to non-symmetric linear chain networks and demonstrate how solutions to more complex networks that have branching, such as cubes, can be expressed in terms of linear chain solutions. We then show examples of implementing single qubit and two-qubit entangling gates.

  16. Eight challenges for network epidemic models

    Directory of Open Access Journals (Sweden)

    Lorenzo Pellis

    2015-03-01

    Full Text Available Networks offer a fertile framework for studying the spread of infection in human and animal populations. However, owing to the inherent high-dimensionality of networks themselves, modelling transmission through networks is mathematically and computationally challenging. Even the simplest network epidemic models present unanswered questions. Attempts to improve the practical usefulness of network models by including realistic features of contact networks and of host–pathogen biology (e.g. waning immunity have made some progress, but robust analytical results remain scarce. A more general theory is needed to understand the impact of network structure on the dynamics and control of infection. Here we identify a set of challenges that provide scope for active research in the field of network epidemic models.

  17. An evolutionary model of social networks

    Science.gov (United States)

    Ludwig, M.; Abell, P.

    2007-07-01

    Social networks in communities, markets, and societies self-organise through the interactions of many individuals. In this paper we use a well-known mechanism of social interactions — the balance of sentiment in triadic relations — to describe the development of social networks. Our model contrasts with many existing network models, in that people not only establish but also break up relations whilst the network evolves. The procedure generates several interesting network features such as a variety of degree distributions and degree correlations. The resulting network converges under certain conditions to a steady critical state where temporal disruptions in triangles follow a power-law distribution.

  18. The model of social crypto-network

    Directory of Open Access Journals (Sweden)

    Марк Миколайович Орел

    2015-06-01

    Full Text Available The article presents the theoretical model of social network with the enhanced mechanism of privacy policy. It covers the problems arising in the process of implementing the mentioned type of network. There are presented the methods of solving problems arising in the process of building the social network with privacy policy. It was built a theoretical model of social networks with enhanced information protection methods based on information and communication blocks

  19. Modeling Diagnostic Assessments with Bayesian Networks

    Science.gov (United States)

    Almond, Russell G.; DiBello, Louis V.; Moulder, Brad; Zapata-Rivera, Juan-Diego

    2007-01-01

    This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models…

  20. A dynamic network model for interbank market

    Science.gov (United States)

    Xu, Tao; He, Jianmin; Li, Shouwei

    2016-12-01

    In this paper, a dynamic network model based on agent behavior is introduced to explain the formation mechanism of interbank market network. We investigate the impact of credit lending preference on interbank market network topology, the evolution of interbank market network and stability of interbank market. Experimental results demonstrate that interbank market network is a small-world network and cumulative degree follows the power-law distribution. We find that the interbank network structure keeps dynamic stability in the network evolution process. With the increase of bank credit lending preference, network clustering coefficient increases and average shortest path length decreases monotonously, which improves the stability of the network structure. External shocks are main threats for the interbank market and the reduction of bank external investment yield rate and deposits fluctuations contribute to improve the resilience of the banking system.

  1. An approach to 3D NURBS modeling of complex fault network considering its historic tectonics

    Institute of Scientific and Technical Information of China (English)

    ZHONG Denghua; LIU Jie; LI Mingchao

    2006-01-01

    Fault disposal is a research area that presents difficulties in 3D geological modeling and visualization. In this paper, we propose an integrated approach to reconstructing a complex fault network (CFN). Based on the non-uniform rational B-spline (NURBS)techniques, fault surface was constructed, reflecting the regulation of its spatial tendency, and correlative surfaces were enclosed to form a fault body model. Based on these models and considering their historic tectonics, a method was put forward to settle the 3D modeling problem when the intersection of two faults in CFN induced the change of their relative positions. First, according to the relationships of intersection obtained from geological interpretation, we introduced the topological sort to determine the order of fault body construction and rebuilt fault bodies in terms of the order; then, with the disposal method of two intersectant faults in 3D modeling and applying the Boolean operation, we investigated the characteristic of faults at the intersectant part. An example of its application in hydropower engineering project was proposed. Its results show that this modeling approach can increase the computing efficiency while less computer memory is required, and it can also factually and objectively reproduce the CFN in the engineering region, which establishes a theoretical basis for 3D modeling and analysis of complex engineering geology.

  2. Reconfigurable Boolean Logic Using Magnetic Single-Electron Transistors

    Science.gov (United States)

    Gonzalez-Zalba, M. Fernando; Ciccarelli, Chiara; Zarbo, Liviu P.; Irvine, Andrew C.; Campion, Richard C.; Gallagher, Bryan L.; Jungwirth, Tomas; Ferguson, Andrew J.; Wunderlich, Joerg

    2015-01-01

    We propose a novel hybrid single-electron device for reprogrammable low-power logic operations, the magnetic single-electron transistor (MSET). The device consists of an aluminium single-electron transistor with a GaMnAs magnetic back-gate. Changing between different logic gate functions is realized by reorienting the magnetic moments of the magnetic layer, which induces a voltage shift on the Coulomb blockade oscillations of the MSET. We show that we can arbitrarily reprogram the function of the device from an n-type SET for in-plane magnetization of the GaMnAs layer to p-type SET for out-of-plane magnetization orientation. Moreover, we demonstrate a set of reprogrammable Boolean gates and its logical complement at the single device level. Finally, we propose two sets of reconfigurable binary gates using combinations of two MSETs in a pull-down network. PMID:25923789

  3. Bayesian estimation of the network autocorrelation model

    NARCIS (Netherlands)

    Dittrich, D.; Leenders, R.T.A.J.; Mulder, J.

    2017-01-01

    The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of

  4. Object Oriented Modeling Of Social Networks

    NARCIS (Netherlands)

    Zeggelink, Evelien P.H.; Oosten, Reinier van; Stokman, Frans N.

    1996-01-01

    The aim of this paper is to explain principles of object oriented modeling in the scope of modeling dynamic social networks. As such, the approach of object oriented modeling is advocated within the field of organizational research that focuses on networks. We provide a brief introduction into the f

  5. Social insect colony as a biological regulatory system: modelling information flow in dominance networks.

    Science.gov (United States)

    Nandi, Anjan K; Sumana, Annagiri; Bhattacharya, Kunal

    2014-12-06

    Social insects provide an excellent platform to investigate flow of information in regulatory systems since their successful social organization is essentially achieved by effective information transfer through complex connectivity patterns among the colony members. Network representation of such behavioural interactions offers a powerful tool for structural as well as dynamical analysis of the underlying regulatory systems. In this paper, we focus on the dominance interaction networks in the tropical social wasp Ropalidia marginata-a species where behavioural observations indicate that such interactions are principally responsible for the transfer of information between individuals about their colony needs, resulting in a regulation of their own activities. Our research reveals that the dominance networks of R. marginata are structurally similar to a class of naturally evolved information processing networks, a fact confirmed also by the predominance of a specific substructure-the 'feed-forward loop'-a key functional component in many other information transfer networks. The dynamical analysis through Boolean modelling confirms that the networks are sufficiently stable under small fluctuations and yet capable of more efficient information transfer compared to their randomized counterparts. Our results suggest the involvement of a common structural design principle in different biological regulatory systems and a possible similarity with respect to the effect of selection on the organization levels of such systems. The findings are also consistent with the hypothesis that dominance behaviour has been shaped by natural selection to co-opt the information transfer process in such social insect species, in addition to its primal function of mediation of reproductive competition in the colony.

  6. Agent-based modeling and network dynamics

    CERN Document Server

    Namatame, Akira

    2016-01-01

    The book integrates agent-based modeling and network science. It is divided into three parts, namely, foundations, primary dynamics on and of social networks, and applications. The book begins with the network origin of agent-based models, known as cellular automata, and introduce a number of classic models, such as Schelling’s segregation model and Axelrod’s spatial game. The essence of the foundation part is the network-based agent-based models in which agents follow network-based decision rules. Under the influence of the substantial progress in network science in late 1990s, these models have been extended from using lattices into using small-world networks, scale-free networks, etc. The book also shows that the modern network science mainly driven by game-theorists and sociophysicists has inspired agent-based social scientists to develop alternative formation algorithms, known as agent-based social networks. The book reviews a number of pioneering and representative models in this family. Upon the gi...

  7. Boolean and brain-inspired computing using spin-transfer torque devices

    Science.gov (United States)

    Fan, Deliang

    Several completely new approaches (such as spintronic, carbon nanotube, graphene, TFETs, etc.) to information processing and data storage technologies are emerging to address the time frame beyond current Complementary Metal-Oxide-Semiconductor (CMOS) roadmap. The high speed magnetization switching of a nano-magnet due to current induced spin-transfer torque (STT) have been demonstrated in recent experiments. Such STT devices can be explored in compact, low power memory and logic design. In order to truly leverage STT devices based computing, researchers require a re-think of circuit, architecture, and computing model, since the STT devices are unlikely to be drop-in replacements for CMOS. The potential of STT devices based computing will be best realized by considering new computing models that are inherently suited to the characteristics of STT devices, and new applications that are enabled by their unique capabilities, thereby attaining performance that CMOS cannot achieve. The goal of this research is to conduct synergistic exploration in architecture, circuit and device levels for Boolean and brain-inspired computing using nanoscale STT devices. Specifically, we first show that the non-volatile STT devices can be used in designing configurable Boolean logic blocks. We propose a spin-memristor threshold logic (SMTL) gate design, where memristive cross-bar array is used to perform current mode summation of binary inputs and the low power current mode spintronic threshold device carries out the energy efficient threshold operation. Next, for brain-inspired computing, we have exploited different spin-transfer torque device structures that can implement the hard-limiting and soft-limiting artificial neuron transfer functions respectively. We apply such STT based neuron (or 'spin-neuron') in various neural network architectures, such as hierarchical temporal memory and feed-forward neural network, for performing "human-like" cognitive computing, which show more than

  8. Edge exchangeable models for network data

    CERN Document Server

    Crane, Harry

    2016-01-01

    Exchangeable models for vertex labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distributions observed in many network datasets. Out of this mathematical impossibility emerges the question of how network data can be modeled in a way that reflects known empirical behaviors and respects basic statistical principles. We address this question by observing that edges, not vertices, act as the statistical units in most network datasets, making a theory of edge labeled networks more natural for most applications. Within this context we introduce the new invariance principle of {\\em edge exchangeability}, which unlike its vertex exchangeable counterpart can produce networks with sparse and/or power law structure. We characterize the class of all edge exchangeable network models and identify a particular two parameter family of models with suitable theoretical properties for statistical inference. We discuss issues of estimation from edge exchangeable models and compare our a...

  9. Network class superposition analyses.

    Directory of Open Access Journals (Sweden)

    Carl A B Pearson

    Full Text Available Networks are often used to understand a whole system by modeling the interactions among its pieces. Examples include biomolecules in a cell interacting to provide some primary function, or species in an environment forming a stable community. However, these interactions are often unknown; instead, the pieces' dynamic states are known, and network structure must be inferred. Because observed function may be explained by many different networks (e.g., ≈ 10(30 for the yeast cell cycle process, considering dynamics beyond this primary function means picking a single network or suitable sample: measuring over all networks exhibiting the primary function is computationally infeasible. We circumvent that obstacle by calculating the network class ensemble. We represent the ensemble by a stochastic matrix T, which is a transition-by-transition superposition of the system dynamics for each member of the class. We present concrete results for T derived from boolean time series dynamics on networks obeying the Strong Inhibition rule, by applying T to several traditional questions about network dynamics. We show that the distribution of the number of point attractors can be accurately estimated with T. We show how to generate Derrida plots based on T. We show that T-based Shannon entropy outperforms other methods at selecting experiments to further narrow the network structure. We also outline an experimental test of predictions based on T. We motivate all of these results in terms of a popular molecular biology boolean network model for the yeast cell cycle, but the methods and analyses we introduce are general. We conclude with open questions for T, for example, application to other models, computational considerations when scaling up to larger systems, and other potential analyses.

  10. Exact and heuristic methods for solving Boolean games

    OpenAIRE

    DE CLERCQ, Sofie; Bauters, Kim; Schockaert, Steven; Mihaylov, Mihail; Nowé, Ann; De Cock, Martine

    2015-01-01

    Boolean games are a framework for reasoning about the rational behavior of agents whose goals are formalized using propositional formulas. Compared to normal form games, a well-studied and related game framework, Boolean games allow for an intuitive and more compact representation of the agents’ goals. So far, Boolean games have been mainly studied in the literature from the Knowledge Representation perspective, and less attention has been paid on the algorithmic issues underlying the computa...

  11. Evolutionary Phylogenetic Networks: Models and Issues

    Science.gov (United States)

    Nakhleh, Luay

    Phylogenetic networks are special graphs that generalize phylogenetic trees to allow for modeling of non-treelike evolutionary histories. The ability to sequence multiple genetic markers from a set of organisms and the conflicting evolutionary signals that these markers provide in many cases, have propelled research and interest in phylogenetic networks to the forefront in computational phylogenetics. Nonetheless, the term 'phylogenetic network' has been generically used to refer to a class of models whose core shared property is tree generalization. Several excellent surveys of the different flavors of phylogenetic networks and methods for their reconstruction have been written recently. However, unlike these surveys, this chapte focuses specifically on one type of phylogenetic networks, namely evolutionary phylogenetic networks, which explicitly model reticulate evolutionary events. Further, this chapter focuses less on surveying existing tools, and addresses in more detail issues that are central to the accurate reconstruction of phylogenetic networks.

  12. Modeling Network Evolution Using Graph Motifs

    CERN Document Server

    Conway, Drew

    2011-01-01

    Network structures are extremely important to the study of political science. Much of the data in its subfields are naturally represented as networks. This includes trade, diplomatic and conflict relationships. The social structure of several organization is also of interest to many researchers, such as the affiliations of legislators or the relationships among terrorist. A key aspect of studying social networks is understanding the evolutionary dynamics and the mechanism by which these structures grow and change over time. While current methods are well suited to describe static features of networks, they are less capable of specifying models of change and simulating network evolution. In the following paper I present a new method for modeling network growth and evolution. This method relies on graph motifs to generate simulated network data with particular structural characteristic. This technique departs notably from current methods both in form and function. Rather than a closed-form model, or stochastic ...

  13. Logical Attractors: a Boolean Approach to the Dynamics of Psychosis

    Science.gov (United States)

    Kupper, Z.; Hoffmann, H.

    A Boolean modeling approach to attractors in the dynamics of psychosis is presented: Kinetic Logic, originating from R. Thomas, describes systems on an intermediate level between a purely verbal, qualitative description and a description using nonlinear differential equations. With this method we may model impact, feedback and temporal evolution, as well as analyze the resulting attractors. In our previous research the method has been applied to general and more specific questions in the dynamics of psychotic disorders. In this paper a model is introduced that describes different dynamical patterns of chronic psychosis in the context of vocational rehabilitation. It also shows to be useful in formulating and exploring possible treatment strategies. Finally, some of the limitations and benefits of Kinetic Logic as a modeling tool for psychology and psychiatry are discussed.

  14. A Generalization of J-Boolean Like Rings%J-Boolean like 环的扩张

    Institute of Scientific and Technical Information of China (English)

    秦蕊

    2014-01-01

    对 J-Boolean like环进行了扩张,并且将 J-Boolean like环与广义矩阵环和Morita Context环联系起来,进而探索了部分环为 J-Boolean like环时应具备的条件,且给出若干相关例子。%The paper mainly explored the generalization of J-Boolean like rings ,and connected J-Boolean like rings with generalized matrix rings and Morita Context rings ,then studied the conditions when a part of other rings became J-Boolean like rings ,and listed some examples .

  15. Combinational Logic-Level Verification using Boolean Expression Diagrams

    DEFF Research Database (Denmark)

    Hulgaard, Henrik; Williams, Poul Frederick; Andersen, Henrik Reif

    1997-01-01

    Boolean Expression Diagrams (BEDs) is a new data structure for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) that are capable of representing any Boolean circuit in linear space and still maintain many of the desirable properties...... of BDDs. This paper demonstrates that BEDs are well suited for solving the combinational logic-level verification problem which is, given two combinational circuits, to determine whether they implement the same Boolean functions. Based on all combinational circuits in the ISCAS 85 and LGSynth 91...

  16. The Number of Monotone and Self-Dual Boolean Functions

    Directory of Open Access Journals (Sweden)

    Haviarova L.

    2014-12-01

    Full Text Available In the present paper we study properties of pre-complete class of Boolean functions - monotone Boolean functions. We discuss interval graph, the abbreviated d.n.f., a minimal d.n.f. and a shortest d.n.f. of this function. Then we present a d.n.f. with the highest number of conjunctionsand we determinate the exact number of them. We count the number of monotone Boolean functions with some special properties. In the end we estimate the number of Boolean functionthat are monotone and self-dual at the same time.

  17. Boolean Differentiation Equations Applicable in Reconfigurable Computational Medium

    Directory of Open Access Journals (Sweden)

    Shidlovskiy Stanislav

    2016-01-01

    Full Text Available High performance computing environment synthesis with parallel architecture reconstructing throughout the process itself is described. Synthesized computational medium involving Boolean differential equation calculations so as to function in real-time image processing. Automaton imaging was illustrated involving the rearrangement of every processing medium element to calculate the partial differentials of n-th order in respect to Boolean function variables. The method of obtaining setting codes for each element was also described. An example in calculating 2nd -order Boolean derivative to two differentials in respect to Boolean functions, depending on three arguments within the reconstructible computational medium of 8×8 processing elements was given.

  18. Totally optimal decision trees for Boolean functions

    KAUST Repository

    Chikalov, Igor

    2016-07-28

    We study decision trees which are totally optimal relative to different sets of complexity parameters for Boolean functions. A totally optimal tree is an optimal tree relative to each parameter from the set simultaneously. We consider the parameters characterizing both time (in the worst- and average-case) and space complexity of decision trees, i.e., depth, total path length (average depth), and number of nodes. We have created tools based on extensions of dynamic programming to study totally optimal trees. These tools are applicable to both exact and approximate decision trees, and allow us to make multi-stage optimization of decision trees relative to different parameters and to count the number of optimal trees. Based on the experimental results we have formulated the following hypotheses (and subsequently proved): for almost all Boolean functions there exist totally optimal decision trees (i) relative to the depth and number of nodes, and (ii) relative to the depth and average depth.

  19. Fast Vertical Mining Using Boolean Algebra

    Directory of Open Access Journals (Sweden)

    Hosny M. Ibrahim

    2015-01-01

    Full Text Available The vertical association rules mining algorithm is an efficient mining method, which makes use of support sets of frequent itemsets to calculate the support of candidate itemsets. It overcomes the disadvantage of scanning database many times like Apriori algorithm. In vertical mining, frequent itemsets can be represented as a set of bit vectors in memory, which enables for fast computation. The sizes of bit vectors for itemsets are the main space expense of the algorithm that restricts its expansibility. Therefore, in this paper, a proposed algorithm that compresses the bit vectors of frequent itemsets will be presented. The new bit vector schema presented here depends on Boolean algebra rules to compute the intersection of two compressed bit vectors without making any costly decompression operation. The experimental results show that the proposed algorithm, Vertical Boolean Mining (VBM algorithm is better than both Apriori algorithm and the classical vertical association rule mining algorithm in the mining time and the memory usage.

  20. Classical Boolean logic gates with quantum systems

    Energy Technology Data Exchange (ETDEWEB)

    Renaud, N; Joachim, C, E-mail: n-renaud@northwestern.edu [Nanoscience Group and MANA Satellite CEMES/CNRS, 29 rue J Marvig, BP 94347, 31055 Toulouse Cedex (France)

    2011-04-15

    An analytical method is proposed to implement any classical Boolean function in a small quantum system by taking the advantage of its electronic transport properties. The logical input, {alpha} = {l_brace}{alpha}{sub 1}, ..., {alpha}{sub N}{r_brace}, is used to control well-identified parameters of the Hamiltonian of the system noted H{sub 0}({alpha}). The logical output is encoded in the tunneling current intensity passing through the quantum system when connected to conducting electrodes. It is demonstrated how to implement the six symmetric two-input/one-output Boolean functions in a quantum system. This system can be switched from one logic function to another by changing its structural parameters. The stability of the logic gates is discussed, perturbing the Hamiltonian with noise sources and studying the effect of decoherence.

  1. Boolean representations of simplicial complexes and matroids

    CERN Document Server

    Rhodes, John

    2015-01-01

    This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context.   Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean represent...

  2. Random graph models for dynamic networks

    CERN Document Server

    Zhang, Xiao; Newman, M E J

    2016-01-01

    We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of edges are governed by continuous-time Markov processes with rate parameters that can depend on properties of the nodes. In addition to computing equilibrium properties of these models, we demonstrate their use in data analysis and statistical inference, giving efficient algorithms for fitting them to observed network data. This allows us, for instance, to estimate the time constants of network evolution or infer community structure from temporal network data using cues embedded both in the probabilities over time that node pairs are connected by edges and in the characteristic dynamics of edge appearance and disappearance. We illustrate our methods with a selection of applications, both to computer-generated test networks and real-world examples.

  3. Boolean methods of optimization over independence systems

    Energy Technology Data Exchange (ETDEWEB)

    Hulme, B.L.

    1983-01-01

    This paper presents both a direct and an iterative method of solving the combinatorial optimization problem associated with any independence system. The methods use Boolean algebraic computations to produce solutions. In addition, the iterative method employs a version of the greedy algorithm both to compute upper bounds on the optimum value and to produce the additional circuits needed at every stage. The methods are extensions of those used to solve a problem of fire protection at nuclear reactor power plants.

  4. Boolean approach to common event analysis

    Energy Technology Data Exchange (ETDEWEB)

    Worrell, R.B.; Stack, D.W.

    1980-01-01

    Although different phenomena may be involved, the problem that must be solved for each kind of common event analysis is essentially the same: to determine the effect of common events on the behavior of a system. A Boolean approach to the problem is set forth. Because of the large equations that arise, processing must be done by computers. Vital location analysis is a particular kind of common event analysis that is used to study ways to prevent the sabotage of nuclear reactors. (RWR)

  5. GBL-2D Version 1.0: a 2D geometry boolean library.

    Energy Technology Data Exchange (ETDEWEB)

    McBride, Cory L. (Elemental Technologies, American Fort, UT); Schmidt, Rodney Cannon; Yarberry, Victor R.; Meyers, Ray J. (Elemental Technologies, American Fort, UT)

    2006-11-01

    This report describes version 1.0 of GBL-2D, a geometric Boolean library for 2D objects. The library is written in C++ and consists of a set of classes and routines. The classes primarily represent geometric data and relationships. Classes are provided for 2D points, lines, arcs, edge uses, loops, surfaces and mask sets. The routines contain algorithms for geometric Boolean operations and utility functions. Routines are provided that incorporate the Boolean operations: Union(OR), XOR, Intersection and Difference. A variety of additional analytical geometry routines and routines for importing and exporting the data in various file formats are also provided. The GBL-2D library was originally developed as a geometric modeling engine for use with a separate software tool, called SummitView [1], that manipulates the 2D mask sets created by designers of Micro-Electro-Mechanical Systems (MEMS). However, many other practical applications for this type of software can be envisioned because the need to perform 2D Boolean operations can arise in many contexts.

  6. Modelling the structure of complex networks

    DEFF Research Database (Denmark)

    Herlau, Tue

    networks has been independently studied as mathematical objects in their own right. As such, there has been both an increased demand for statistical methods for complex networks as well as a quickly growing mathematical literature on the subject. In this dissertation we explore aspects of modelling complex....... The next chapters will treat some of the various symmetries, representer theorems and probabilistic structures often deployed in the modelling complex networks, the construction of sampling methods and various network models. The introductory chapters will serve to provide context for the included written...

  7. Biodiversity: modelling angiosperms as networks.

    Science.gov (United States)

    Gottlieb, O R; Borin, M R

    2000-11-01

    In the neotropics, one of the last biological frontiers, the major ecological concern should not involve local strategies, but global effects often responsible for irreparable damage. For a holistic approach, angiosperms are ideal model systems dominating most land areas of the present world in an astonishing variety of form and function. Recognition of biogeographical patterns requires new methodologies and entails several questions, such as their nature, dynamics and mechanism. Demographical patterns of families, modelled via species dominance, reveal the existence of South American angiosperm networks converging at the central Brazilian plateau. Biodiversity of habitats, measured via taxonomic uniqueness, reveal higher creative power at this point of convergence than in more peripheral regions. Compositional affinities of habitats, measured via bioconnectivity, reveal the decisive role of ecotones in the exchange or redistribution of information, energy and organisms among the ecosystems. Forming dynamic boundaries, ecotones generate and relay evolutionary novelty, and integrate all neotropical ecosystems into a single vegetation net. Connectivity in such plant webs may depend on mycorrhizal links. If sufficiently general such means of metabolic transfer will require revision of the chemical composition of many plants.

  8. Bernstein copula approach to model direction-length dependency for 2D discrete fracture network simulation

    Science.gov (United States)

    Mendoza-Torres, F.; Diaz-Viera, M. A.

    2015-12-01

    In many natural fractured porous media, such as aquifers, soils, oil and geothermal reservoirs, fractures play a crucial role in their flow and transport properties. An approach that has recently gained popularity for modeling fracture systems is the Discrete Fracture Network (DFN) model. This approach consists in applying a stochastic boolean simulation method, also known as object simulation method, where fractures are represented as simplified geometric objects (line segments in 2D and polygons in 3D). One of the shortcomings of this approach is that it usually does not consider the dependency relationships that may exist between the geometric properties of fractures (direction, length, aperture, etc), that is, each property is simulated independently. In this work a method for modeling such dependencies by copula theory is introduced. In particular, a nonparametric model using Bernstein copulas for direction-length fracture dependency in 2D is presented. The application of this method is illustrated in a case study for a fractured rock sample from a carbonate reservoir outcrop.

  9. Modeling of hysteresis in gene regulatory networks.

    Science.gov (United States)

    Hu, J; Qin, K R; Xiang, C; Lee, T H

    2012-08-01

    Hysteresis, observed in many gene regulatory networks, has a pivotal impact on biological systems, which enhances the robustness of cell functions. In this paper, a general model is proposed to describe the hysteretic gene regulatory network by combining the hysteresis component and the transient dynamics. The Bouc-Wen hysteresis model is modified to describe the hysteresis component in the mammalian gene regulatory networks. Rigorous mathematical analysis on the dynamical properties of the model is presented to ensure the bounded-input-bounded-output (BIBO) stability and demonstrates that the original Bouc-Wen model can only generate a clockwise hysteresis loop while the modified model can describe both clockwise and counter clockwise hysteresis loops. Simulation studies have shown that the hysteresis loops from our model are consistent with the experimental observations in three mammalian gene regulatory networks and two E.coli gene regulatory networks, which demonstrate the ability and accuracy of the mathematical model to emulate natural gene expression behavior with hysteresis. A comparison study has also been conducted to show that this model fits the experiment data significantly better than previous ones in the literature. The successful modeling of the hysteresis in all the five hysteretic gene regulatory networks suggests that the new model has the potential to be a unified framework for modeling hysteresis in gene regulatory networks and provide better understanding of the general mechanism that drives the hysteretic function.

  10. Complete Boolean Satisfiability Solving Algorithms Based on Local Search

    Institute of Scientific and Technical Information of China (English)

    Wen-Sheng Guo; Guo-Wu Yang; William N.N.Hung; Xiaoyu Song

    2013-01-01

    Boolean satisfiability (SAT) is a well-known problem in computer science,artificial intelligence,and operations research.This paper focuses on the satisfiability problem of Model RB structure that is similar to graph coloring problems and others.We propose a translation method and three effective complete SAT solving algorithms based on the characterization of Model RB structure.We translate clauses into a graph with exclusive sets and relative sets.In order to reduce search depth,we determine search order using vertex weights and clique in the graph.The results show that our algorithms are much more effective than the best SAT solvers in numerous Model RB benchmarks,especially in those large benchmark instances.

  11. Nonconsensus opinion model on directed networks

    NARCIS (Netherlands)

    Qu, B.; Li, Q.; Havlin, S.; Stanley, E.; Wang, H.

    2014-01-01

    Dynamic social opinion models have been widely studied on undirected networks, and most of them are based on spin interaction models that produce a consensus. In reality, however, many networks such as Twitter and the World Wide Web are directed and are composed of both unidirectional and bidirectio

  12. Radio channel modeling in body area networks

    NARCIS (Netherlands)

    An, L.; Bentum, M.J.; Meijerink, A.; Scanlon, W.G.

    2010-01-01

    A body area network (BAN) is a network of bodyworn or implanted electronic devices, including wireless sensors which can monitor body parameters or to detect movements. One of the big challenges in BANs is the propagation channel modeling. Channel models can be used to understand wave propagation in

  13. Radio channel modeling in body area networks

    NARCIS (Netherlands)

    An, L.; Bentum, M.J.; Meijerink, A.; Scanlon, W.G.

    2009-01-01

    A body area network (BAN) is a network of bodyworn or implanted electronic devices, including wireless sensors which can monitor body parameters or to de- tect movements. One of the big challenges in BANs is the propagation channel modeling. Channel models can be used to understand wave propagation

  14. Computer-aided design of modular protein devices: Boolean AND gene activation

    Science.gov (United States)

    Salis, H.; Kaznessis, Y. N.

    2006-12-01

    Many potentially useful synthetic gene networks require the expression of an engineered gene if and only if two different DNA-binding proteins exist in sufficient concentration. While some natural and engineered systems activate gene expression according to a logical AND-like behavior, they often utilize allosteric or cooperative protein-protein interactions, rendering their components unsuitable for a toolbox of modular parts for use in multiple applications. Here, we develop a quantitative model to demonstrate that a small system of interacting fusion proteins, called a protein device, can activate an engineered gene according to the Boolean AND behavior while using only modular protein domains and DNA sites. The fusion proteins are created from transactivating, DNA-binding, non-DNA binding, and protein-protein interaction domains along with the corresponding peptide ligands. Using a combined kinetic and thermodynamic model, we identify the characteristics of the molecular components and their rates of constitutive production that maximize the fidelity of AND behavior. These AND protein devices facilitate the creation of complex genetic programs and may be used to create gene therapies, biosensors and other biomedical and biotechnological applications that turn on gene expression only when multiple DNA-binding proteins are simultaneously present.

  15. Optimizing tridiagonal solvers for alternating direction methods on Boolean cube multiprocessors

    Energy Technology Data Exchange (ETDEWEB)

    Ho, C.T. (IBM Almaden Research Center, San Jose, CA (US)); Johnsson, S.L. (Dept. of Computer Science and Electrical Engineering, Yale Univ., New Haven, CT (US))

    1990-05-01

    Sets of tridiagonal systems occur in many applications. Fast Poisson solvers and Alternate Direction Methods make use of tridiagonal system solvers. Network-based multiprocessors provide a cost-effective alternative to traditional supercomputer architectures. The complexity of concurrent algorithms for the solution of multiple tridiagonal systems on Boolean-cube-configured multiprocessors with distributed memory are investigated. Variations of odd-even cyclic reduction, parallel cyclic reduction, and algorithms making use of data transposition with or without substructuring and local elimination, or pipelined elimination, are considered. A simple performance model is used for algorithm comparison, and the validity of the model is verified on an Intel iPSC/1. For many combinations of machine and system parameters, pipelined elimination, or equation transposition with or without substructuring is optimum. Hybrid algorithms that at any stage choose the best algorithm among the considered ones for the remainder of the problem are presented. It is shown that the optimum partitioning of a set of independent tridiagonal systems among a set of processors yields the embarrassingly parallel case.

  16. Unified Hybrid Network Theoretical Model Trilogy

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    The first of the unified hybrid network theoretical model trilogy (UHNTF) is the harmonious unification hybrid preferential model (HUHPM), seen in the inner loop of Fig. 1, the unified hybrid ratio is defined.

  17. Network models in economics and finance

    CERN Document Server

    Pardalos, Panos; Rassias, Themistocles

    2014-01-01

    Using network models to investigate the interconnectivity in modern economic systems allows researchers to better understand and explain some economic phenomena. This volume presents contributions by known experts and active researchers in economic and financial network modeling. Readers are provided with an understanding of the latest advances in network analysis as applied to economics, finance, corporate governance, and investments. Moreover, recent advances in market network analysis  that focus on influential techniques for market graph analysis are also examined. Young researchers will find this volume particularly useful in facilitating their introduction to this new and fascinating field. Professionals in economics, financial management, various technologies, and network analysis, will find the network models presented in this book beneficial in analyzing the interconnectivity in modern economic systems.

  18. A Network Formation Model Based on Subgraphs

    CERN Document Server

    Chandrasekhar, Arun

    2016-01-01

    We develop a new class of random-graph models for the statistical estimation of network formation that allow for substantial correlation in links. Various subgraphs (e.g., links, triangles, cliques, stars) are generated and their union results in a network. We provide estimation techniques for recovering the rates at which the underlying subgraphs were formed. We illustrate the models via a series of applications including testing for incentives to form cross-caste relationships in rural India, testing to see whether network structure is used to enforce risk-sharing, testing as to whether networks change in response to a community's exposure to microcredit, and show that these models significantly outperform stochastic block models in matching observed network characteristics. We also establish asymptotic properties of the models and various estimators, which requires proving a new Central Limit Theorem for correlated random variables.

  19. Strategic games on a hierarchical network model

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Among complex network models, the hierarchical network model is the one most close to such real networks as world trade web, metabolic network, WWW, actor network, and so on. It has not only the property of power-law degree distribution, but growth based on growth and preferential attachment, showing the scale-free degree distribution property. In this paper, we study the evolution of cooperation on a hierarchical network model, adopting the prisoner's dilemma (PD) game and snowdrift game (SG) as metaphors of the interplay between connected nodes. BA model provides a unifying framework for the emergence of cooperation. But interestingly, we found that on hierarchical model, there is no sign of cooperation for PD game, while the frequency of cooperation decreases as the common benefit decreases for SG. By comparing the scaling clustering coefficient properties of the hierarchical network model with that of BA model, we found that the former amplifies the effect of hubs. Considering different performances of PD game and SG on complex network, we also found that common benefit leads to cooperation in the evolution. Thus our study may shed light on the emergence of cooperation in both natural and social environments.

  20. Gossip spread in social network Models

    Science.gov (United States)

    Johansson, Tobias

    2017-04-01

    Gossip almost inevitably arises in real social networks. In this article we investigate the relationship between the number of friends of a person and limits on how far gossip about that person can spread in the network. How far gossip travels in a network depends on two sets of factors: (a) factors determining gossip transmission from one person to the next and (b) factors determining network topology. For a simple model where gossip is spread among people who know the victim it is known that a standard scale-free network model produces a non-monotonic relationship between number of friends and expected relative spread of gossip, a pattern that is also observed in real networks (Lind et al., 2007). Here, we study gossip spread in two social network models (Toivonen et al., 2006; Vázquez, 2003) by exploring the parameter space of both models and fitting them to a real Facebook data set. Both models can produce the non-monotonic relationship of real networks more accurately than a standard scale-free model while also exhibiting more realistic variability in gossip spread. Of the two models, the one given in Vázquez (2003) best captures both the expected values and variability of gossip spread.