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Recent development and biomedical applications of probabilistic Boolean networks
, 2013
"... Probabilistic Boolean network (PBN) modelling is a semiquantitative approach widely used for the study of the topology and dynamic aspects of biological systems. The combined use of rulebased representation and probability makes PBN appealing for largescale modelling of biological networks where ..."
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Cited by 8 (3 self)
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Probabilistic Boolean network (PBN) modelling is a semiquantitative approach widely used for the study of the topology and dynamic aspects of biological systems. The combined use of rulebased representation and probability makes PBN appealing for largescale 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 stateoftheart 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.
Selection policyinduced reduction mappings for boolean networks
 University of Southern California, Los Angles, in
, 1991
"... Abstract—Developing computational models paves the way to understanding, predicting, and influencing the longterm behavior of genomic regulatory systems. However, several major challenges have to be addressed before such models are successfully applied in practice. Their inherent high complexity re ..."
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Cited by 4 (1 self)
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Abstract—Developing computational models paves the way to understanding, predicting, and influencing the longterm behavior of genomic regulatory systems. However, several major challenges have to be addressed before such models are successfully applied in practice. Their inherent high complexity requires strategies for complexity reduction. Reducing the complexity of the model by removing genes and interpreting them as latent variables leads to the problem of selecting which states and their corresponding transitions best account for the presence of such latent variables. We use the Boolean network (BN) model to develop the general framework for selection and reduction of the model’s complexity via designating some of the model’s variables as latent ones. We also study the effects of the selection policies on the steadystate distribution and the controllability of the model. Index Terms—Compression, control, gene regulatory networks, selection policy. I.
State reduction for network intervention in probabilistic Boolean networks
 Bioinformatics
, 2010
"... Motivation: A key goal of studying biological systems is to design therapeutic intervention strategies. Probabilistic Boolean networks (PBNs) constitute a mathematical model which enables modeling, predicting and intervening in their longrun behavior using Markov chain theory. The longrun dynamics ..."
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Cited by 2 (2 self)
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Motivation: A key goal of studying biological systems is to design therapeutic intervention strategies. Probabilistic Boolean networks (PBNs) constitute a mathematical model which enables modeling, predicting and intervening in their longrun behavior using Markov chain theory. The longrun dynamics of a PBN, as represented by its steadystate distribution (SSD), can guide the design of effective intervention strategies for the modeled systems. A major obstacle for its application is the large state space of the underlying Markov chain, which poses a serious computational challenge. Hence, it is critical to reduce the model complexity of PBNs for practical applications. Results: We propose a strategy to reduce the state space of the underlying Markov chain of a PBN based on a criterion that the reduction least distorts the proportional change of stationary masses for critical states, for instance, the network attractors. In comparison
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, 2011
"... Understanding autism’s everexpanding array of behaviors, from sensation to cognition, is a major challenge. We posit that autistic and typically developing brains implement different algorithms that are better suited to learn, represent, and process different tasks; consequently, they develop diffe ..."
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Understanding autism’s everexpanding array of behaviors, from sensation to cognition, is a major challenge. We posit that autistic and typically developing brains implement different algorithms that are better suited to learn, represent, and process different tasks; consequently, they develop different interests and behaviors. Computationally, a continuum of algorithms exists, from lookup table (LUT) learning, which aims to store experiences precisely, to interpolation (INT) learning, which focuses on extracting underlying statistical structure (regularities) from experiences. We hypothesize that autistic and typical brains, respectively, are biased toward LUT and INT learning, in low and highdimensional feature spaces, possibly because of their narrow and broad tuning functions. The LUT style is good at learning relationships that are local, precise, rigid, and contain little regularity for generalization (e.g., the name–number association in a phonebook). However, it is poor at learning relationships that are context dependent, noisy, flexible, and do contain regularities for generalization (e.g., associations between gaze direction and intention, language and meaning, sensory input and interpretation, motorcontrol signal and movement, and social situation and proper response). The LUT style poorly compresses information, resulting in inefficiency, sensory overload (overwhelm), restricted interests, and
Cancer Informatics
"... This is an open access article. Unrestricted noncommercial use is permitted provided the original work is properly cited. Open Access Full open access to this and thousands of other papers at ..."
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This is an open access article. Unrestricted noncommercial use is permitted provided the original work is properly cited. Open Access Full open access to this and thousands of other papers at
Finitestate discretetime Markov chain models of gene regulatory networks
, 2014
"... In this study Markov chain models of gene regulatory networks (GRN) are developed. These models gives the ability to apply the well known theory and tools of Markov chains to GRN analysis. We introduce a new kind of the finite graph of the interactions called the combinatorial net that formally repr ..."
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In this study Markov chain models of gene regulatory networks (GRN) are developed. These models gives the ability to apply the well known theory and tools of Markov chains to GRN analysis. We introduce a new kind of the finite graph of the interactions called the combinatorial net that formally represent a GRN and the transition graphs constructed from interaction graphs. System dynamics are defined as a random walk on the transition graph that is some Markovian chain. A novel concurrent updating scheme (evolution rule) is developed to determine transitions in a transition graph. Our scheme is based on the firing of a random set of nonsteady state vertices of a combinatorial net. We demonstrate that this novel scheme gives an advance in the modeling of the asynchronicity. Also we proof the theorem that the combinatorial nets with this updating scheme can asynchronously compute a maximal independent sets of graphs. As proof of concept, we present here a number of simple combinatorial models: a discrete model of autorepression, a bistable switch, the Elowitz repressilator, a selfactivation and show that this models exhibit well known properties. 1
RESEARCH Open Access
"... A comparison study of optimal and suboptimal intervention policies for gene regulatory networks in the presence of uncertainty ..."
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A comparison study of optimal and suboptimal intervention policies for gene regulatory networks in the presence of uncertainty
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"... State reduction for network intervention in probabilistic Boolean networks ..."
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State reduction for network intervention in probabilistic Boolean networks