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...
Parameter estimation for Boolean models of biological networks (2009)
Dimitrova, Elena, Garcia-Puente, Luis David, Hinkelmann, Franziska, Jarrah, Abdul S., Laubenbacher, Reinhard, Stigler, Brandilyn, ...
Boolean networks have long been used as models of molecular networks and play an increasingly important role in systems biology. This paper describes a software package, Polynome, offered as a web...
Elena Dimitrova, John Mcgee, Reinhard Laubenbacher
Applications requiring discrete data: • reverse engineering of gene regulatory networks, • machine learning algorithms,
Reverse Engineering Gene Regulatory Networks (2008)
Ilyn Stigler, Reinhard Laubenbacher
Systems biology aims to integrate biological data to understand biological systems. Mathematical methods are needed to build models of these systems.
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...
Karen Duca, Abdul Jarrah, Reinhard Laubenbacher, Donna Hochberg, David Thorley-lawson
Motivation: Epstein-Barr virus (EBV) infects greater than 90 % of humans benignly for life but can be associated with tumors. It is a uniquely human pathogen that is amenable to quantitative...
1 UPDATE SCHEDULES OF SEQUENTIAL DYNAMICAL SYSTEMS (2008)
Reinhard Laubenbacher, Bodo Pareigis
Abstract. Sequential dynamical systems have the property, that the updates of states of individual cells occur sequentially, so that the global update of the system depends on the order of the...
Computer algebra in systems biology (2007)
Laubenbacher, Reinhard, Sturmfels, Bernd
Systems biology focuses on the study of entire biological systems rather than on their individual components. With the emergence of high-throughput data generation technologies for molecular biology...
Lagrange and the Solution of Numerical Equations (2007)
Reinhard Laubenbacher, Gary Mcgrath, David Pengelley
In 1798 J.-L. Lagrange published an extensive book on the solution of numerical equations. Lagrange had developed a general systematic algorithm for detecting, isolating, and approximating all real...
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...
A Virtual Look at Epstein–Barr Virus Infection: Biological Interpretations (2007)
Karen A. Duca, Michael Shapiro, Edgar Delgado-Eckert, Vey Hadinoto, Abdul S. Jarrah, Reinhard Laubenbacher, ...
The possibility of using computer simulation and mathematical modeling to gain insight into biological and other complex systems is receiving increased attention. However, it is as yet unclear to...
Simulating Epstein-Barr virus infection with C-ImmSim (2007)
Castiglione, Filippo, Duca, Karen, Jarrah, Abdul, Laubenbacher, Reinhard, Hochberg, Donna, Thorley-Lawson, David
Motivation: Epstein-Barr virus (EBV) infects greater than 90% of humans benignly for life but can be associated with tumors. It is a uniquely human pathogen that is amenable to quantitative analysis;...
Farid Merchant, Henning S. Mortveit, Chris L. Barrett, Reinhard Laubenbacher, Farid Merchant
Every year three million deaths are attributed to malaria, of which one-third are of children. Malaria is a vector-borne disease, where a mosquito acts as the vector that transmits the disease. In...
“Voici ce que j’ai trouvé: ” Sophie Germain’s grand plan to prove Fermat’s Last Theorem y (2007)
Reinhard Laubenbacher, David Pengelley Z
A study of Sophie Germain’s extensive manuscripts on Fermat’s Last Theorem calls for a reassessment of her work in number theory. There is much in these manuscripts beyond the single theorem for...
Olgamary Rivera-marrero, Penny Burge, Carlos Evia, Reinhard Laubenbacher, Olgamary Rivera-marrero
The integration of discrete mathematics into the secondary school curriculum (grades 7-12) is an important consideration because the mathematical area is dynamic and interesting, providing students...
An algorithm for the Quillen-Suslin theorem for monoid rings (1997)
Reinhard Laubenbacher, Karen Schlauch
Abstract. This paper presents an algorithm for the Quillen-Suslin Theorem for quotients of polynomial rings by monomial ideals, that is, quotients of the form A = k[x0;:::; xn]=I, with I a monomial...
Mathematical masterpieces: teaching with original sources (1996)
Reinhard Laubenbacher, David Pengelley
masterpieces from antiquity to the present. Following a common practice in the humanities, for example in Chicago's Great Books program and St. John's College curriculum, we have students...
Mathematical masterpieces: teaching with original sources (1996)
Reinhard Laubenbacher, David Pengelley
masterpieces from antiquity to the present. Following a common practice in the humanities, for example in Chicago’s Great Books program and St. John’s College curriculum, we have students read...
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...