eduardo sontag | Rutgers, The State University of New Jersey (original) (raw)

Papers by eduardo sontag

Some biological systems operate at the critical point between stability and instability and this ... more Some biological systems operate at the critical point between stability and instability and this requires a fine-tuning of parameters. We bring together two examples from the literature that illustrate this: neural integration in the nervous system and hair cell oscillations in the auditory system. In both examples the question arises as to how the required fine-tuning may be achieved and maintained in a robust and reliable way. We study this question using tools from nonlinear and adaptive control theory. We illustrate our approach on a simple model which captures some of the essential features of neural integration. As a result, we propose a large class of feedback adaptation rules that may be responsible for the experimentally observed robustness of neural integration. We mention extensions of our approach to the case of hair cell oscillations in the ear.

The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A... more The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A useful approach to the study of these complex systems is to view them as decomposed into feedback loops around open loop monotone systems. Key features of the dynamics of the original system are then deduced from the input-output characteristics of the open loop system and the sign of the feedback. This paper extends these results, showing how to use the same framework of input-output systems in order to prove existence of oscillations, if the slowly varying strength of the feedback depends on the state of the system.

1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes, 1976

Samoilov, Plyasunov, and Arkin provide an example of a chemical reaction whose full stochastic (M... more Samoilov, Plyasunov, and Arkin provide an example of a chemical reaction whose full stochastic (Master Equation) model exhibits bistable behavior, but for which the deterministic (mean field) version has a unique steady state at least for special parameter values. In this short note, we provide a proof of uniqueness valid for all possible parameter values.


This paper studies aspects of the dynamics of a conventional mechanism of ligand-receptor interac... more This paper studies aspects of the dynamics of a conventional mechanism of ligand-receptor interactions, with a focus on the stability and location of steady-states. A theoretical framework is developed, which is based upon the rich and deep formalism of irreducible biochemical networks. When represented in this manner, the mass action kinetics of biochemical processes can be clearly seen in terms of their component biochemical interactions, their kinetic rate constants, and the stoichiometry for the system. A minimal parametrization is provided for models for two-or multi-state receptor interaction with ligand, and an ''affinity quotient'' is introduced, which allows an elegant classification of ligands into agonists, neutral agonists, and inverse agonists. r

49Th Ieee Conference on Decision and Control, 2010

ABSTRACT

Systems Control Letters, 1998

This note discusses two integral variants of the input-to-state stability (ISS) property, which r... more This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L2 stability, in much the same way that ISS generalizes L∞ stability. Both variants are equivalent to ISS for linear systems. For general nonlinear systems, it is shown that one of the new properties is strictly weaker than ISS, while the other one is equivalent to it. For bilinear systems, a complete characterization is provided of the weaker property. An interesting fact about functions of type is proved as well.

53Rd Ieee Conference on Decision and Control, Dec 1, 2014

Lecture Notes in Mathematics, 2008

Lecture Notes in Control and Information Sciences, 1984

We continue here our investigation into the preservation of structural properties under the sampl... more We continue here our investigation into the preservation of structural properties under the sampling of nonlinear systems. The main new result is that, under minimal hypothesis, a controllable system always satisfies a strong type of approximate sampled controllability.

Proceedings of 1994 American Control Conference - ACC '94, 1994

This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and... more This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems. In a unied and natural manner, it (1) includes arbitrary bounded disturbances acting on the system, (2) deals with global asymptotic stability, (3) results in smooth (innitely dierentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets.

Proceedings of the sixth annual conference on Computational learning theory - COLT '93, 1993

The set of functions which a single hidden layer neural network can approximate is increasingly w... more The set of functions which a single hidden layer neural network can approximate is increasingly well understood, yet our knowledge of how the approximation error depends upon the num-ber of hidden units, ie the rate of approx-imation, remains relatively primitive. Barron ...

Proceedings of the National Academy of Sciences of the United States of America, Jan 13, 2015

Reverse engineering of biological pathways involves an iterative process between experiments, dat... more Reverse engineering of biological pathways involves an iterative process between experiments, data processing, and theoretical analysis. Despite concurrent advances in quality and quantity of data as well as computing resources and algorithms, difficulties in deciphering direct and indirect network connections are prevalent. Here, we adopt the notions of abstraction, emulation, benchmarking, and validation in the context of discovering features specific to this family of connectivities. After subjecting benchmark synthetic circuits to perturbations, we inferred the network connections using a combination of nonparametric single-cell data resampling and modular response analysis. Intriguingly, we discovered that recovered weights of specific network edges undergo divergent shifts under differential perturbations, and that the particular behavior is markedly different between topologies. Our results point to a conceptual advance for reverse engineering beyond weight inference. Investi...

Proceedings of ICNN'95 - International Conference on Neural Networks, 1995

ABSTRACT

The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A... more The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A useful approach to the study of these complex systems is to view them as decomposed into feedback loops around open loop monotone systems. Key features of the dynamics of the original system are then deduced from the input-output characteristics of the open loop system and the sign of the feedback. This paper extends these results, showing how to use the same framework of input-output systems in order to prove existence of oscillations, if the slowly varying strength of the feedback depends on the state of the system.

53rd IEEE Conference on Decision and Control, 2014

Interfaces, 2000

We study a single species in a chemostat, limited by two nutrients, and separate nutrient uptake ... more We study a single species in a chemostat, limited by two nutrients, and separate nutrient uptake from growth. For a broad class of uptake and growth functions it is proved that a nontrivial equilibrium may exist. Moreover, if it exists it is unique and globally stable, generalizing a result in (15).

Nonlinear Control Systems Design 1992, 1993

ABSTRACT

Some biological systems operate at the critical point between stability and instability and this ... more Some biological systems operate at the critical point between stability and instability and this requires a fine-tuning of parameters. We bring together two examples from the literature that illustrate this: neural integration in the nervous system and hair cell oscillations in the auditory system. In both examples the question arises as to how the required fine-tuning may be achieved and maintained in a robust and reliable way. We study this question using tools from nonlinear and adaptive control theory. We illustrate our approach on a simple model which captures some of the essential features of neural integration. As a result, we propose a large class of feedback adaptation rules that may be responsible for the experimentally observed robustness of neural integration. We mention extensions of our approach to the case of hair cell oscillations in the ear.

The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A... more The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A useful approach to the study of these complex systems is to view them as decomposed into feedback loops around open loop monotone systems. Key features of the dynamics of the original system are then deduced from the input-output characteristics of the open loop system and the sign of the feedback. This paper extends these results, showing how to use the same framework of input-output systems in order to prove existence of oscillations, if the slowly varying strength of the feedback depends on the state of the system.

1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes, 1976

Samoilov, Plyasunov, and Arkin provide an example of a chemical reaction whose full stochastic (M... more Samoilov, Plyasunov, and Arkin provide an example of a chemical reaction whose full stochastic (Master Equation) model exhibits bistable behavior, but for which the deterministic (mean field) version has a unique steady state at least for special parameter values. In this short note, we provide a proof of uniqueness valid for all possible parameter values.


This paper studies aspects of the dynamics of a conventional mechanism of ligand-receptor interac... more This paper studies aspects of the dynamics of a conventional mechanism of ligand-receptor interactions, with a focus on the stability and location of steady-states. A theoretical framework is developed, which is based upon the rich and deep formalism of irreducible biochemical networks. When represented in this manner, the mass action kinetics of biochemical processes can be clearly seen in terms of their component biochemical interactions, their kinetic rate constants, and the stoichiometry for the system. A minimal parametrization is provided for models for two-or multi-state receptor interaction with ligand, and an ''affinity quotient'' is introduced, which allows an elegant classification of ligands into agonists, neutral agonists, and inverse agonists. r

49Th Ieee Conference on Decision and Control, 2010

ABSTRACT

Systems Control Letters, 1998

This note discusses two integral variants of the input-to-state stability (ISS) property, which r... more This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L2 stability, in much the same way that ISS generalizes L∞ stability. Both variants are equivalent to ISS for linear systems. For general nonlinear systems, it is shown that one of the new properties is strictly weaker than ISS, while the other one is equivalent to it. For bilinear systems, a complete characterization is provided of the weaker property. An interesting fact about functions of type is proved as well.

53Rd Ieee Conference on Decision and Control, Dec 1, 2014

Lecture Notes in Mathematics, 2008

Lecture Notes in Control and Information Sciences, 1984

We continue here our investigation into the preservation of structural properties under the sampl... more We continue here our investigation into the preservation of structural properties under the sampling of nonlinear systems. The main new result is that, under minimal hypothesis, a controllable system always satisfies a strong type of approximate sampled controllability.

Proceedings of 1994 American Control Conference - ACC '94, 1994

This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and... more This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems. In a unied and natural manner, it (1) includes arbitrary bounded disturbances acting on the system, (2) deals with global asymptotic stability, (3) results in smooth (innitely dierentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets.

Proceedings of the sixth annual conference on Computational learning theory - COLT '93, 1993

The set of functions which a single hidden layer neural network can approximate is increasingly w... more The set of functions which a single hidden layer neural network can approximate is increasingly well understood, yet our knowledge of how the approximation error depends upon the num-ber of hidden units, ie the rate of approx-imation, remains relatively primitive. Barron ...

Proceedings of the National Academy of Sciences of the United States of America, Jan 13, 2015

Reverse engineering of biological pathways involves an iterative process between experiments, dat... more Reverse engineering of biological pathways involves an iterative process between experiments, data processing, and theoretical analysis. Despite concurrent advances in quality and quantity of data as well as computing resources and algorithms, difficulties in deciphering direct and indirect network connections are prevalent. Here, we adopt the notions of abstraction, emulation, benchmarking, and validation in the context of discovering features specific to this family of connectivities. After subjecting benchmark synthetic circuits to perturbations, we inferred the network connections using a combination of nonparametric single-cell data resampling and modular response analysis. Intriguingly, we discovered that recovered weights of specific network edges undergo divergent shifts under differential perturbations, and that the particular behavior is markedly different between topologies. Our results point to a conceptual advance for reverse engineering beyond weight inference. Investi...

Proceedings of ICNN'95 - International Conference on Neural Networks, 1995

ABSTRACT

The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A... more The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A useful approach to the study of these complex systems is to view them as decomposed into feedback loops around open loop monotone systems. Key features of the dynamics of the original system are then deduced from the input-output characteristics of the open loop system and the sign of the feedback. This paper extends these results, showing how to use the same framework of input-output systems in order to prove existence of oscillations, if the slowly varying strength of the feedback depends on the state of the system.

53rd IEEE Conference on Decision and Control, 2014

Interfaces, 2000

We study a single species in a chemostat, limited by two nutrients, and separate nutrient uptake ... more We study a single species in a chemostat, limited by two nutrients, and separate nutrient uptake from growth. For a broad class of uptake and growth functions it is proved that a nontrivial equilibrium may exist. Moreover, if it exists it is unique and globally stable, generalizing a result in (15).

Nonlinear Control Systems Design 1992, 1993

ABSTRACT