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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
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 …
Identification Of Control Targets In Boolean Molecular Network Models Via Computational Algebra, David Murrugarra, Alan Veliz-Cuba, Boris Aguilar, Reinhard Laubenbacher
Identification Of Control Targets In Boolean Molecular Network Models Via Computational Algebra, David Murrugarra, Alan Veliz-Cuba, Boris Aguilar, Reinhard Laubenbacher
Mathematics Faculty Publications
Background: Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type …
A Note On The Γ-Coefficients Of The Tree Eulerian Polynomial, Rafael S. González D'León
A Note On The Γ-Coefficients Of The Tree Eulerian Polynomial, Rafael S. González D'León
Mathematics Faculty Publications
We consider the generating polynomial of the number of rooted trees on the set {1,2,...,n} counted by the number of descending edges (a parent with a greater label than a child). This polynomial is an extension of the descent generating polynomial of the set of permutations of a totally ordered n-set, known as the Eulerian polynomial. We show how this extension shares some of the properties of the classical one. A classical product formula shows that this polynomial factors completely over the integers. From this product formula it can be concluded that this polynomial has positive coefficients …
A Model For Spheroid Versus Monolayer Response Of Sk-N-Sh Neuroblastoma Cells To Treatment With 15-Deoxy-Pgj2, Dorothy I. Wallace, Ann Dunham, Paula X. Chen, Michelle Chen, Milan Huynh, Evan Rheingold, Olivia F. Prosper
A Model For Spheroid Versus Monolayer Response Of Sk-N-Sh Neuroblastoma Cells To Treatment With 15-Deoxy-Pgj2, Dorothy I. Wallace, Ann Dunham, Paula X. Chen, Michelle Chen, Milan Huynh, Evan Rheingold, Olivia F. Prosper
Mathematics Faculty Publications
Researchers have observed that response of tumor cells to treatment varies depending on whether the cells are grown in monolayer, as in vitro spheroids or in vivo. This study uses data from the literature on monolayer treatment of SK-N-SH neuroblastoma cells with 15-deoxy-PGJ2 and couples it with data on growth rates for untreated SK-N-SH neuroblastoma cells grown as multicellular spheroids. A linear model is constructed for untreated and treated monolayer data sets, which is tuned to growth, death, and cell cycle data for the monolayer case for both control and treatment with 15-deoxy-PGJ2. The monolayer …
The Spruce Budworm And Forest: A Qualitative Comparison Of Ode And Boolean Models, Raina Robeva, David Murrugarra
The Spruce Budworm And Forest: A Qualitative Comparison Of Ode And Boolean Models, Raina Robeva, David Murrugarra
Mathematics Faculty Publications
Boolean and polynomial models of biological systems have emerged recently as viable companions to differential equations models. It is not immediately clear however whether such models are capable of capturing the multi-stable behaviour of certain biological systems: this behaviour is often sensitive to changes in the values of the model parameters, while Boolean and polynomial models are qualitative in nature. In the past few years, Boolean models of gene regulatory systems have been shown to capture multi-stability at the molecular level, confirming that such models can be used to obtain information about the system’s qualitative dynamics when precise information regarding …