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...
Analysis Transcriptional control of human p53-regulated genes (2009)
Todd Riley, Eduardo Sontag, Patricia Chen, Arnold Levine
Abstract | The p53 protein regulates the transcription of many different genes in response to a wide variety of stress signals. Following DNA damage, p53 regulates key processes, including DNA...
Michael J. Donahue, Leonid Gurvits, Christian Darken, Eduardo Sontag
This paper deals with sparse approximations by means of convex combinations of elements from a predetermined “basis ” subset S of a function space. Specifically, the focus is on the rate at which...
The Effect of Negative Feedback Loops on the Dynamics of Boolean Networks (2009)
Eduardo Sontag, Alan Veliz-cuba, Y Reinhard Laubenbacher
ABSTRACT 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...
A Symbolic Computational Approach to a Problem Involving Multivariate Poisson Distributions (2009)
Sontag, Eduardo, Zeilberger, Doron
Multivariate Poisson random variables subject to linear integer constraints arise in several application areas, such as queuing and biomolecular networks. This note shows how to compute conditional...
On persistence and cascade decompositions of chemical reaction networks (2009)
Angeli, David, De Leenheer, Patrick, Sontag, Eduardo
New checkable criteria for persistence of chemical reaction networks are proposed, which extend and complement those obtained by the authors in previous work. The new results allow the consideration...
Abstract — We consider the problem of characterizing possible supply functions for a given dissipative nonlinear system, and provide a result that allows some freedom in the modification of such...
The p53HMM algorithm: using profile hidden markov models to detect p53-responsive genes (2009)
Riley, Todd, Yu, Xin, Sontag, Eduardo, Levine, Arnold
Abstract Background A computational method (called p53HMM) is presented that utilizes Profile Hidden Markov Models (PHMMs) to estimate the relative binding affinities of putative p53 response...
A Learning Result for Recurrent Neural Networks ∗ (2008)
The following learning problem is considered, for continuous-time recurrent neural networks having sigmoidal activation functions. Given a “black box ” representing an unknown system,...
Abstract. This paper deals with a notion of “input to output stability ” (ios), which formalizes the idea that outputs depend in an “aymptotically stable ” manner on inputs, while internal...
Michael J. Donahue, Leonid Gurvits, Christian Darken, Eduardo Sontag
This paper deals with sparse approximations by means of convex combinations of elements from a predetermined “basis ” subset S of a function space. Specifically, the focus is on the rate at which...
Asymptotic controllability implies input to state stabilization (2008)
Michael Malisoff, Ludovic Rifford, Eduardo Sontag
Abstract. The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed-loop systems inputto-state...
Sema Kachalo, Ranran Zhang, Eduardo Sontag, Réka Albert, Bhaskar Dasgupta
Summary: We present a software for combined synthesis, inference and simplification of signal transduction networks. The main idea of our method lies in representing observed indirect causal...
Bhaskar Dasgupta Y, Hava T. Siegelmann, Eduardo Sontag
This paper deals with learnability of concept classes de ned by neural networks, showing the hardness of PAC-learning (in the complexity, not merely information-theoretic sense) for networks with a...
This paper presents necessary and sufficient characterizations of several notions of input to output stability. Similar Lyapunov characterizations have been found to play a key role in the analysis...
Asymptotic controllability implies input to state stabilization (2008)
Michael Malisoff, Ludovic Rifford, Eduardo Sontag
Abstract. The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed loop systems input to state...
Eduardo Sontag, Anatoly Kiyatkin, Boris N. Kholodenko
Inferring dynamic architecture of cellular
Asymptotic controllability implies input to state stabilization (2008)
Michael Malisoff, Ludovic Rifford, Eduardo Sontag
Abstract. The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed loop systems input to state...
Kachalo, Sema, Zhang, Ranran, Sontag, Eduardo, Albert, Réka, DasGupta, Bhaskar
Summary: We present a software for combined synthesis, inference and simplification of signal transduction networks. The main idea of our method lies in representing observed indirect causal...
Global Asymptotic Controllability Implies Input to State Stabilization # (2007)
Michael Maliso, Eduardo Sontag
We study nonlinear systems with observation errors. The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control a#ne systems that render...
Global Asymptotic Controllability Implies Input to State Stabilization (2007)
Michael Malisoff, Ludovic Rifford, Eduardo Sontag
The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control a#ne systems that render the closed loop systems input to state stable with...
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...
Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles (2007)
The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the...
Réka Albert, Riccardo Dondi, Eduardo Sontag, Kelly Westbrooks, Bhaskar Dasgupta, Sema Kachalo, ...
In this paper we introduce a new method of combined synthesis and inference of biological signal transduction networks. A main idea of our method lies in representing observed causal relationships as...
A Novel Method for Signal Transduction Network Inference from Indirect Experimental Evidence (2007)
Réka Albert, Bhaskar Dasgupta, Riccardo Dondi, Eduardo Sontag, Er Zelikovsky, Kelly Westbrooks
Abstract. In this paper we introduce a new method of combined synthesis and inference of biological signal transduction networks. A main idea of our method lies in representing observed causal...
The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the...
Piotr Berman, Bhaskar Dasgupta, Eduardo Sontag
This paper studies a computational problem motivated by the modular response analysis method for reverse engineering of protein and gene networks. This set-cover problem is hard to solve exactly for...
Réka Albert, Riccardo Dondi, Eduardo Sontag, Kelly Westbrooks, Bhaskar Dasgupta, Sema Kachalo, ...
In this paper we introduce a new method of combined synthesis and inference of biological signal transduction networks. A main idea of our method lies in representing observed causal relationships as...
A Novel Method for Signal Transduction Network Inference from Indirect Experimental Evidence (2007)
Réka Albert, Bhaskar Dasgupta, Riccardo Dondi, Sema Kachalo, Eduardo Sontag, Er Zelikovsky, ...
Abstract. In this paper we introduce a new method of combined synthesis and inference of biological signal transduction networks. A main idea of our method lies in representing observed causal...
A Novel Method for Signal Transduction Network Inference from Indirect Experimental Evidence (2007)
Réka Albert, Bhaskar Dasgupta, Riccardo Dondi, Sema Kachalo, Eduardo Sontag, Alexander Zelikovsky, ...
In this paper, we introduce a new method of combined synthesis and inference of biological signal transduction networks. A main idea of our method lies in representing observed causal relationships...
Computational aspects of feedback in neural circuits (2006)
Wolfgang Maass, Prashant Joshi, Eduardo Sontag
It had previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with...
A Petri Net approach to the study of persistence in chemical reaction networks (2006)
Angeli, David, De Leenheer, Patrick, Sontag, Eduardo
Persistency is the property, for differential equations in $\R^n$, that solutions starting in the positive orthant do not approach the boundary. For chemical reactions and population models, this...
Bhaskar Dasgupta, Germana. Enciso, Eduardo Sontag, Yi Zhang
Abstract. A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational...
Réka Albert, Riccardo Dondi, Bhaskar Dasgupta, Eduardo Sontag
In this paper we consider the p-ary transitive reduction (TRp) problem where p> 0 is an integer; for p = 2 this problem arises in inferring a sparsest possible (biological) signal transduction...
Bhaskar Dasgupta, João P. Hespanha, James Riehl, Eduardo Sontag
In this paper we investigate the problem of searching for a hidden target in a bounded region of the plane by an autonomous robot which is only able to use local sensory information. The problem is...
Uniqueness of steady states for a certain chemical reaction (2005)
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...
DasGupta, Bhaskar, Enciso, German Andres, Sontag, Eduardo, Zhang, Yi
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems...
E. Sontag’s research was partly supported by NSF grants EIA 0205116 and DMS-0504557. (2005)
Réka Albert, Bhaskar Dasgupta, Riccardo Dondi, Eduardo Sontag, R. Albert, B. Dasgupta, ...
Abstract In this paper we consider the p-ary transitive reduction (TRp) problem where p>0 is an integer; for p = 2 this problem arises in inferring a sparsest possible (biological) signal...
A. Enciso, Eduardo Sontag, German A. Enciso, German A. Enciso, Dissertation Director, Eduardo Sontag
Monotone systems in abstract Banach spaces have strong stability and convergence properties and have been studied in various contexts, especially since the work of Hirsch in the 1980’s [48, 49]. In...
Global Stabilization for Systems Evolving on Manifolds (2004)
Malisoff, Michael, Krichman, Mikhail, Sontag, Eduardo
We show that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since we allow discontinuous feedbacks, we interpret the solutions...
Aggregation-based approaches to honey-pot searching with local sensory information (2004)
Bhaskar Dasgupta, João P. Hespanha, Eduardo Sontag
Abstract — We investigate the problem of searching for a hidden target in a bounded region by an autonomous agent that is only able to use limited local sensory information. We propose an...
Interconnections of Monotone Systems with Steady-State Characteristics (2004)
This paper presents a brief exposition of recent results, with an emphasis on small gain theorems for negative feedback, and the emergence of multi-stability and associated hysteresis e#ects under...
Asymptotic controllability and input-to-state stabilization: The effect of actuator errors (2004)
Michael Malisoff, Eduardo Sontag
We discuss several issues related to the stabilizability of nonlinear systems. For a given continuously stabilizable system, we review some constructions of feedbacks that render the system...
Piotr Berman, Bhaskar Dasgupta, Eduardo Sontag
In this paper we investigate the computational complexities of a combinatorial problem that arises in the reverse engineering of protein and gene networks. Our contributions are as follows: . We...
Piotr Berman, Bhaskar Dasgupta, Eduardo Sontag
Abstract. In this paper we investigate the computational complexities of a combinatorial problem that arises in the reverse engineering of protein and gene networks. Our contributions are as follows:...
Piotr Berman, Bhaskar Dasgupta, Eduardo Sontag
In this paper we investigate the computational complexity of a combinatorial problem that arises in the reverse engineering of protein and gene networks. Our contributions are as follows: • We...
Asymptotic controllability and inputto-state stabilization: The effect of actuator errors (2004)
Michael Malisoff, Eduardo Sontag
Summary. We discuss several issues related to the stabilizability of nonlinear systems. For a given continuously stabilizable system, we review some constructions of feedbacks that render the system...
Aggregation-based approaches to honey-pot searching with local sensory information (2004)
Bhaskar Dasgupta, João P. Hespanha, Eduardo Sontag
We investigate the problem of searching for a hidden target in a bounded region of the plane, by an autonomous robot which is only able to use limited local sensory information. We propose an...
Piotr Berman, Bhaskar Dasgupta, Eduardo Sontag
In this paper we investigate the computational complexity of a combinatorial problem that arises in the reverse engineering of protein and gene networks. Our contributions are as follows: • We...
Sontag, Eduardo, Kiyatkin, Anatoly, Kholodenko, Boris N.
Motivation: High-throughput technologies have facilitated the acquisition of large genomics and proteomics data sets. However, these data provide snapshots of cellular behavior, rather than help us...
Sontag, Eduardo, Kiyatkin, Anatoly, Kholodenko, Boris N.
Motivation: High-throughput technologies have facilitated the acquisition of large genomics and proteomics datasets. However, these data provide snapshots of cellular behavior, rather than help us...
Sontag, Eduardo, Kiyatkin, Anatoly, Kholodenko, Boris N.
Motivation: High-throughput technologies have facilitated the acquisition of large genomics and proteomics data sets. However, these data provide snapshots of cellular behavior, rather than help us...
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...
Global Asymptotic Controllability Implies Input to State Stabilization (2003)
Malisoff, Michael, Rifford, Ludovic, Sontag, Eduardo
We study nonlinear systems with observation errors. The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that...
Computational Complexities of Honey-pot Searching with Local Sensory Information (2003)
Bhaskar Dasgupta, Joao P. Hespanha, Eduardo Sontag
In this paper we investigate the problem of searching for a hidden target in a bounded region of the plane, by an autonomous robot which is only able to use limited local sensory information. We...
Automated tuning of bifurcations via feedback (2002)
Moreau, Luc, Sontag, Eduardo, Arcak, Murat
The present paper studies a feedback regulation problem, which may be interpreted as an adaptive control problem, but has not yet been studied in the control literature. The problem, which arises in...
A Unifying Integral Iss Framework For Stability Of Nonlinear Cascades (2002)
Murat Arcak, David Angeli, Eduardo Sontag
We analyze nonlinear cascades in which the driven subsystem is integral input-tostate stable (ISS), and we characterize the admissible integral ISS gains for stability. This characterization makes...
A unifying integral ISS framework for stability of nonlinear cascades (2002)
Murat Arcak, David Angeli, Eduardo Sontag
Abstract. We analyze nonlinear cascades in which the driven subsystem is integral input-tostate stable (ISS), and we characterize the admissible integral ISS gains for stability. This...
Input-to-state stability for discrete-time nonlinear systems (2001)
Zhong-ping Jiang, Eduardo Sontag, Yuan Wang
Abstract: In this paper the input-to-state stability (iss) property is studied for discrete-time nonlinear systems. We show that many iss results for continuoustime nonlinear systems in earlier...
Further equivalences and semiglobal versions of integral input to state stability, Dynam (2000)
David Angeli, Eduardo Sontag, Yuan Wang
This paper continues the study of the integral input-to-state stability (iiss) property. It is shown that the iiss property is equivalent to one which arises from the consideration of mixed norms on...
Further equivalences and semiglobal versions of integral input to state stability (1999)
Angeli, David, Sontag, Eduardo, Wang, Yuan
This paper continues the study of the integral input-to-state stability (IISS) property. It is shown that the IISS property is equivalent to one which arises from the consideration of mixed norms on...
Input-To-State Stability For Discrete-Time Nonlinear Systems (1999)
Zhong-ping Jiang, Eduardo Sontag, Yuan Wang
: In this paper the input-to-state stability (iss) property is studied for discrete-time nonlinear systems. We show that many iss results for continuoustime nonlinear systems in earlier papers...
Changing Supply Functions in Input/State Stable Systems (1999)
We consider the problem of characterizing possible supply functions for a given dissipative nonlinear system, and provide a result that allows some freedom in the modification of such functions....
Mathematical Theory of Neural Networks (1998)
Sontag, Eduardo, Sussmann, Hector
This report focuses on fundamental theoretical issues relevant to the capabilities, performance, and limitations of artificial neural networks. For static (feedforward) networks, subjects of...
Global Asymptotic Controllability Implies Input to State Stabilization (1998)
Malisoff, Michael, Rifford, Ludovic, Sontag, Eduardo
The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed loop systems input to state stable...
Asymptotic Controllability and Input-to-State Stabilization: The Effect of Actuator Errors (1998)
Malisoff, Michael, Sontag, Eduardo
We discuss several issues related to the stabilization of nonlinear systems. For a given continuously stabilizable system, we review some constructions of feedbacks that render the system...
A Learning Result for Continuous-Time Recurrent Neural Networks (1998)
The following learning problem is considered, for continuous-time recurrent neural networks having sigmoidal activation functions. Given a "black box" representing an unknown system,...
Complete Controllability of Continuous-Time Recurrent Neural Networks (1997)
This paper presents a characterization of controllability for the class of control systems commonly called (continuous-time) recurrent neural networks. The characterization involves a simple...
Notions of Input to Output Stability (1997)
This paper deals with several related notions of output stability with respect to inputs (which may be thought of as disturbances). The main such notion is called input to output stability (ios), and...
Complete Controllability of Continuous-Time Recurrent Neural Networks (1997)
Eduardo Sontag, Héctor Sussmann
This paper presents a characterization of controllability for the class of control systems commonly called (continuous-time) recurrent neural networks. The characterization involves a simple...
Recurrent Neural Networks: Some Systems-Theoretic Aspects (1997)
This paper provides an exposition of some recent research regarding system-theoretic aspects of continuous-time recurrent (dynamic) neural networks with sigmoidal activation functions. The class of...
Recurrent neural networks: Some systems-theoretic aspects (1997)
This paper provides an exposition of some recent research regarding system-theoretic aspects of continuous-time recurrent (dynamic) neural networks with sigmoidal activation functions. The class of...
Complete controllability of continuous-time recurrent neural networks (1997)
Eduardo Sontag, Héctor Sussmann
This paper studies controllability for the class of control systems commonly called (continuous-time) recurrent neural networks. It is shown that, under a generic condition on the input matrix, the...
Constructive Approximation (1997)
Springer-Verlag Newyork, Michael J. Donahue, Leonid Gurvits, Christian Darken, Eduardo Sontag
. This paper deals with sparse approximations by means of convex combinations of elements from a predetermined "basis" subset S of a function space. Specifically, the focus is on the rate...
Asymptotic Controllability And Feedback Stabilization (1996)
F.H. Clarke, Yu.S. Ledyaev, Eduardo Sontag, A. I. Subbotin
It is shown that every asymptotically controllable system can be stabilized by means of some (discontinuous) feedback law. One of the contributions of the paper is in defining precisely the meaning...
Detectability of nonlinear systems (1996)
We propose a definition of detectability for nonlinear systems. This definition generalizes naturally the standard property in the linear case, and is consistent with the “input to state stability...
On finite gain stabilizability of linear systems subject to input saturation (1996)
Wensheng Liu, Yacine Chitour, Eduardo Sontag
Abstract. This paper deals with (global) finite-gain input/output stabilization of linear systems with saturated controls. For neutrally stable systems, it is shown that the linear feedback law...
On the Complexity of Training Neural Networks with Continuous Activation Functions (1995)
Bhaskar Dasgupta, Hava T. Siegelmann, Eduardo Sontag
We deal with computational issues of loading a fixed-architecture neural network with a set of positive and negative examples. This is the first result on the hardness of loading a simple 3-node...
Nonsmooth Control-Lyapunov Functions (1995)
Eduardo Sontag, Héctor J. Sussmann
It is shown that the existence of a continuous controlLyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finitedimensional control systems. The CLF...
From Linear to Nonlinear: Some Complexity Comparisons (1995)
95 CDC- Keywords: complexity, controllability, nonlinear Extended Summary for Invited Session entitled Computational Complexity Issues in Control 1. Introduction It is obvious that many control...
On the continuity and incremental-gain properties of certain saturated linear feedback loops (1995)
Yacine Chitour, Wensheng Liu, Eduardo Sontag
summary This paper discusses various continuity and incremental-gain properties for neutrally stable linear systems under linear feedback subject to actuator saturation. The results complement our...
Nonsmooth controllyapunov functions (1995)
It is shown that the existence of a continuous control-Lyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finitedimensional control systems. The CLF...
On the complexity of training neural networks with continuous activation functions (1995)
Bhaskar Dasgupta, Eduardo Sontag, Hava T. Siegelmann
We deal with computational issues of loading a fixed-architecture neural network with a set of positive and negative examples. This is the first result on the hardness of loading a simple 3-node...
Spaces of observables in nonlinear control (1995)
Engineering design and optimization techniques for control typically rely upon the theory of irreducible finite-dimensional representations of linear shift-invariant integral operators. A...
Rates of Convex Approximation in Non-Hilbert Spaces (1994)
Michael J. Donahue, Leonid Gurvits, Christian Darken, Eduardo Sontag
. This paper deals with sparse approximations by means of convex combinations of elements from a predetermined "basis" subset S of a function space. Specifically, the focus is on the rate...
Spaces of Observables in Nonlinear Control (1994)
1.6> ct : rationality of the Laplace transform matrix K(s)= R 1 0 K(t)e \Gammast dt; existence of some nontrivial algebraic-differential equation E(!(t); ! 0 (t); : : : ! (s) (t); j(t); j 0 (t); :...
A General Result on the Stabilization of Linear Systems Using Bounded Controls (1994)
Héctor Sussmann, Eduardo Sontag, Yudi Yang
We present two constructions of controllers that globally stabilize linear systems subject to control saturation. The only conditions imposed are the obvious necessary ones, namely that no...
On the Continuity and Incremental-Gain Properties of Certain Saturated Linear Feedback Loops (1994)
Yacine Chitour, Wensheng Liu, Eduardo Sontag
This paper discusses various continuity and incremental-gain properties for neutrally stable linear systems under linear feedback subject to actuator saturation. The results complement our previous...
Separating Bi-Chromatic Points by Parallel Lines (1994)
Tetsuo Asano, John Hershberger, János Pach, Eduardo Sontag, Diane Souvaine, Subhash Suri
Given a 2-coloring of the vertices of a regular n-gon P , how many parallel lines are needed to separate the vertices into monochromatic subsets? We prove that bn=2c is a tight upper bound, and also...
On a Learnability Question Associated to Neural Networks with Continuous Activations (1994)
Bhaskar Dasgupta, Hava T. Siegelmann, Eduardo Sontag
) z Bhaskar DasGupta y Department of Computer Science University of Minnesota Minneapolis, MN 55455-0159 dasgupta@cs.umn.edu Hava T. Siegelmann Department of Computer Science Bar-Ilan University...
On Finite Gain Stabilizability of Linear Systems Subject to Input Saturation (1993)
Wensheng Liu, Yacine Chitour, Eduardo Sontag
This paper deals with (global) finite-gain input/output stabilization of linear systems with saturated controls. For neutrally stable systems, it is shown that the linear feedback law suggested by...
Nonlinear Output Feedback Design for Linear Systems With Saturating Controls (1990)
Eduardo Sontag, Hector J. Sussmann
This paper shows the existence of (nonlinear) smooth dynamic feedback stabilizers for linear time invariant systems under input constraints, assuming only that open-loop asymptotic controllability...
Separating Bi-Chromatic Points by Parallel Lines (1990)
Tetsuo Asano, John Hershberger, János Pach, Eduardo Sontag, Diane Souvaine, Subhash Suri
Given a 2-coloring of the vertices of a regular n-gon P, how many parallel lines are needed to separate the vertices into monochromatic subsets? We prove that ⌊n/2 ⌋ is a tight upper bound, and...
A Chow Property For Sampled Bilinear Systems (1987)
this paper is as follows. We first give definitions and state the main results. After that we shall recall details of the linear case, giving an abstract proof of the classical result, and finally we...
Untangling the wires: A strategy to trace functional interactions in signaling and gene networks
Kholodenko, Boris N., Kiyatkin, Anatoly, Bruggeman, Frank J., Sontag, Eduardo, Westerhoff, Hans V., Hoek, Jan B.
Emerging technologies have enabled the acquisition of large genomics and proteomics data sets. However, current methodologies for analysis do not permit interpretation of the data in ways that...
Untangling the wires: A strategy to trace functional interactions in signaling and gene networks
Kholodenko, Boris N., Kiyatkin, Anatoly, Bruggeman, Frank J., Sontag, Eduardo, Westerhoff, Hans V., Hoek, Jan B.
Emerging technologies have enabled the acquisition of large genomics and proteomics data sets. However, current methodologies for analysis do not permit interpretation of the data in ways that...
Lyapunov Characterizations of Input to Output Stability
Eduardo Sontag Dept, Eduardo Sontag, Yuan Wang
This paper presents necessary and sufficient characterizations of several notions of input to output stability. Similar Lyapunov characterizations have been found to play a key role in the analysis...
A Remark On Robust Stabilization Of General Asymptotically Controllable Systems
Yu. S. Ledyaev, Eduardo Sontag
It was shown recently by Clarke, Ledyaev, Sontag and Subbotin that any asymptotically controllable system can be stabilized by means of a certain type of discontinuous feedback. The feedback laws...
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...