The effect of negative feedback loops on the dynamics of Boolean networks 1 (2009)
Eduardo Sontag, Alan Veliz-cuba, Reinhard Laubenbacher, Abdul Salam Jarrah
Feedback loops play an important role in determining the dynamics of biological networks. In order to study the role of negative feedback loops, this paper introduces the notion of “distance to...
The Dynamics of Conjunctive and Disjunctive Boolean Networks (2008)
Jarrah, Abdul Salam, Laubenbacher, Reinhard, Veliz-Cuba, Alan
The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of...
GENERIC IDEALS AND MORENO-SOC IAS CONJECTURE (2007)
Edith Aguirre, Abdul Salam Jarrah, Reinhard Laubenbacher, Ariel Ortiz-navarro, Rogelio Torrez
Abstract. Let f1; : : : ; fn be homogeneous polynomials generating a generic ideal I in the ring of polynomials in n variables over an infinite field. MorenoSoc ' ias conjectured that for the...
The effect of negative feedback loops on the dynamics of Boolean networks (2007)
Sontag, Eduardo, Veliz-Cuba, Alan, Laubenbacher, Reinhard, Jarrah, Abdul Salam
Feedback loops in a dynamic network play an important role in determining the dynamics of that network. Through a computational study, in this paper we show that networks with fewer independent...
Nested Canalyzing, unate cascade, and polynomial functions (2006)
Jarrah, Abdul Salam, Raposa, Blessilda, Laubenbacher, Reinhard
This paper focuses on the study of certain classes of Boolean functions that have appeared in several different contexts. Nested canalyzing functions have been studied recently in the context of...
Reverse-engineering of polynomial dynamical systems (2006)
Jarrah, Abdul Salam, Laubenbacher, Reinhard, Stigler, Brandilyn, Stillman, Michael
Multivariate polynomial dynamical systems over finite fields have been studied in several contexts, including engineering and mathematical biology. An important problem is to construct models of such...
Generic Cohen-Macaulay monomial ideals (2003)
Jarrah, Abdul Salam, Laubenbacher, Reinhard
Given a simplicial complex, it is easy to construct a generic deformation of its Stanley-Reisner ideal. The main question under investigation in this paper is how to characterize the simplicial...
Classification of Finite Dynamical Systems (2001)
Garcia, Luis, Jarrah, Abdul Salam, Laubenbacher, Reinhard
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems...
Integral Closures of Cohen-Macaulay monomial ideals (2001)
The purpose of this paper is to present a family of Cohen-Macaulay monomial ideals such that their integral closures have embedded components and hence are not Cohen-Macaulay.
Generic ideals and Moreno-Soc{\'\i}as conjecture (2001)
Aguirre, Edith, Jarrah, Abdul Salam, Laubenbacher, Reinhard, Ortiz-Navarro, Juan Ariel, Torrez, Rogelio
Let $f_1, ..., f_n$ be homogeneous polynomials generating a generic ideal $I$ in the ring of polynomials in $n$ variables over an infinite field. Moreno-Soc\'ias conjectured that for the graded...
The Center Variety of Polynomial Differential Systems (2000)
Jarrah, Abdul Salam, Laubenbacher, Reinhard, Romanovski, Valery
We investigate the symmetry component of the center variety of polynomial differential systems, corresponding to systems with an axis of symmetry in the real plane. We give a general algorithm to...
The Effect of Negative Feedback Loops on the Dynamics of Boolean Networks
Sontag, Eduardo, Veliz-Cuba, Alan, Laubenbacher, Reinhard, Jarrah, Abdul Salam
Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of...