Electronic mail address: (2009)
Matthew Scott, Brian P. Ingalls, Matthew Scott, Brian Ingalls
reaction networks
Small-gain statements play a key role in system analysis. These results state that the interconnection of two stable systems is stable provided that the closed loop gain is less than unity. This...
Sensitivity Analysis: from model parameters to system behaviour (2008)
parameter perturbation, model parametrization Abstract Sensitivity analysis addresses the manner in which model behaviour depends on model parametrization. Global sensitivity analysis makes use of...
The Linear Noise Approximation offers an elegant analytic method to probe the effects of molecular noise on small-scale chemical reaction pathways by expanding the full chemical Master equation in...
Optimal metabolic pathway activation (2008)
Oyarzún, Diego, Ingalls, Brian, Middleton, Richard, Kalamatianos, Dimitrios
This paper deals with temporal enzyme distribution in the activation of biochemical pathways. Pathway activation arises when production of a certain biomolecule is required due to changing...
MAPK Cascades as Feedback Amplifiers (2007)
Sauro, Herbert M, Ingalls, Brian
Interconvertible enzyme cascades, exemplified by the mitogen activated protein kinase (MAPK) cascade, are a frequent mechanism in signal transduction pathways. There has been much speculation as to...
Deterministic characterization of stochastic genetic circuits (2007)
Scott, Matthew, Hwa, Terence, Ingalls, Brian
For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that...
Conservation analysis in biochemical networks: computational issues for software writers (2004)
Herbert M. Sauro, Brian Ingalls
Large scale genomic studies are generating significant amounts of data on the structure of cellular networks. This is in contrast to kinetic data which is frequently absent, unreliable or...
An infinite-time relaxation theorem for differential inclusions (2003)
Abstract The fundamental relaxation result for Lipschitz differential inclusions is the FilippovWa^zewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on...
Control theory in biology: From mca to chemotaxis (2003)
Tau-mu Yi, Pablo Iglesias, Brian Ingalls
The goal of the tutorial is to introduce Systems Biologists to the application of control theory to biology. The tools of systems and control theory have been instrumental in the successful design of...
An infinite-time relaxation theorem for differential inclusions (2003)
Brian Ingalls, Eduardo D. Sontag, Yuan Wang
Abstract. The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Waˇzewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion...
Brian Ingalls, Eduardo D. Sontag
Abstract A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form....
Eduardo D. Sontag, Brian Ingalls
A general input-to-state stability (ISS)-type small-gain result is presented. It specializes to a small-gainthallfor ISS operators, and it also recoversth classical statement for ISS systems in...
Ingalls, Brian, Sontag, Eduardo D.
A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form. In...
Integral-Input-Output to State Stability (2001)
A notion of detectability for nonlinear systems is discussed. Within the framework of ``input to state stability'' (ISS), a dual notion of ``output to state stability'' (OSS), and a more complete...
An Infinite-Time Relaxation Theorem for Differential Inclusions (2001)
Ingalls, Brian, Sontag, Eduardo D., Wang, Yuan
The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wazewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite...
The Bivariate Contouring Problem (2000)
Thomas Grandine, Bogdan Craciun, Noel Heitmann, Brian Ingalls, Richard Tsai, ...
An algorithm is presented for determining a connected component of the zero level set of a function f :# # R n-2 , where# is a bounded subset of R n . Two di#erent numerical methods are employed and...
Thomas Grandine ¡ The Bivariate Contouring Problem (2000)
Quoc Thong, Le Gia, Bogdan Craciun, Noel Heitmann, Brian Ingalls, Miao-jung Ou, ...
An algorithm is presented for determining a connected component of the zero level set of a function ©������������� � , where � is a bounded subset of �� �. Two...
Resonant Tidal Disruption in Galactic Nuclei (1997)
Rauch, Kevin P., Ingalls, Brian
It has recently been shown that the rate of angular momentum relaxation in nearly-Keplerian star clusters is greatly increased by a process termed resonant relaxation (Rauch & Tremaine 1996), who...
Deterministic characterization of stochastic genetic circuits
Scott, Matthew, Hwa, Terence, Ingalls, Brian
For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that...