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Full-Text Articles in Physical Sciences and Mathematics
Entropy Analysis Of Boolean Network Reduction According To The Determinative Power Of Nodes, Matthew J. Pelz, Mihaela T. Velcsov
Entropy Analysis Of Boolean Network Reduction According To The Determinative Power Of Nodes, Matthew J. Pelz, Mihaela T. Velcsov
Mathematics Faculty Publications
Boolean networks are utilized to model systems in a variety of disciplines. The complexity of the systems under exploration often necessitates the construction of model networks with large numbers of nodes and unwieldy state spaces. A recently developed, entropy-based method for measuring the determinative power of each node offers a new method for identifying the most relevant nodes to include in subnetworks that may facilitate analysis of the parent network. We develop a determinative-power-based reduction algorithm and deploy it on 36 network types constructed through various combinations of settings with regards to the connectivity, topology, and functionality of networks. We …
Identification Of Biologically Essential Nodes Via Determinative Power In Logical Models Of Cellular Processes, Trevor Pentzien, Bhanwar L. Puniya, Tomáš Helikar, Mihaela Teodora Matache
Identification Of Biologically Essential Nodes Via Determinative Power In Logical Models Of Cellular Processes, Trevor Pentzien, Bhanwar L. Puniya, Tomáš Helikar, Mihaela Teodora Matache
Mathematics Faculty Publications
A variety of biological networks can bemodeled as logical or Boolean networks. However, a simplification of the reality to binary states of the nodes does not ease the difficulty of analyzing the dynamics of large, complex networks, such as signal transduction networks, due to the exponential dependence of the state space on the number of nodes. This paper considers a recently introduced method for finding a fairly small subnetwork, representing a collection of nodes that determine the states of most other nodes with a reasonable level of entropy. The subnetwork contains the most determinative nodes that yield the highest information …
Estimating Propensity Parameters Using Google Pagerank And Genetic Algorithms, David Murrugarra, Jacob Miller, Alex N. Mueller
Estimating Propensity Parameters Using Google Pagerank And Genetic Algorithms, David Murrugarra, Jacob Miller, Alex N. Mueller
Mathematics Faculty Publications
Stochastic Boolean networks, or more generally, stochastic discrete networks, are an important class of computational models for molecular interaction networks. The stochasticity stems from the updating schedule. Standard updating schedules include the synchronous update, where all the nodes are updated at the same time, and the asynchronous update where a random node is updated at each time step. The former produces a deterministic dynamics while the latter a stochastic dynamics. A more general stochastic setting considers propensity parameters for updating each node. Stochastic Discrete Dynamical Systems (SDDS) are a modeling framework that considers two propensity parameters for updating each node …
Logical Reduction Of Biological Networks To Their Most Determinative Components, Mihaela Teodora Matache, Valentin Matache
Logical Reduction Of Biological Networks To Their Most Determinative Components, Mihaela Teodora Matache, Valentin Matache
Mathematics Faculty Publications
Boolean networks have been widely used as models for gene regulatory networks, signal transduction networks, or neural networks, among many others. One of the main difficulties in analyzing the dynamics of a Boolean network and its sensitivity to perturbations or mutations is the fact that it grows exponentially with the number of nodes. Therefore, various approaches for simplifying the computations and reducing the network to a subset of relevant nodes have been proposed in the past few years. We consider a recently introduced method for reducing a Boolean network to its most determinative nodes that yield the highest information gain. …
Boolean Modeling Of Biochemical Networks, Tomáš Helikar, Naomi Kochi, John Konvalina, Jim A. Rogers
Boolean Modeling Of Biochemical Networks, Tomáš Helikar, Naomi Kochi, John Konvalina, Jim A. Rogers
Mathematics Faculty Publications
The use of modeling to observe and analyze the mechanisms of complex biochemical network function is becoming an important methodological tool in the systems biology era. Number of different approaches to model these networks have been utilized-- they range from analysis of static connection graphs to dynamical models based on kinetic interaction data. Dynamical models have a distinct appeal in that they make it possible to observe these networks in action, but they also pose a distinct challenge in that they require detailed information describing how the individual components of these networks interact in living cells. Because this level of …