The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wažewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite intervals. A complementary result is presented, which provides approximations on infinite intervals, but does not guarantee that the approximation and the… (More)
In previous work the notion of input to state stability (ISS) has been generalized to systems with outputs, yielding a number of useful concepts. When considering a system whose output is to be kept small (i.e. an error output), the notion of input to output stability (IOS) arises. Alternatively , when considering a system whose output is meant to provide… (More)
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 addition, we highlight applications to incrementally stable systems, detectable systems, and to interconnections of stable systems.
The fundamental Filippov–Wažwski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz inclusion is dense in the solution set of the same initial value problem for the corresponding relaxation inclusion on compact intervals. In our recent work, a complementary result was provided for inclusions with finite… (More)
The chemotaxis pathway of the bacterium Rhodobacter sphaeroides shares many similarities with that of Escherichia coli. It exhibits robust adaptation and has several homologues of the latter's chemotaxis proteins. Recent theoretical results have correctly predicted that the E. coli output behaviour is unchanged under scaling of its ligand input signal; this… (More)
The chemotaxis pathway of the bacterium Rhodobacter sphaeroides has many similarities to the well-studied pathway in Escherichia coli. It exhibits robust adaptation and has several homologues of the latter's chemotaxis proteins. Recent theoretical results have been able to correctly predict that the chemotactic response of Escherichia coli exhibits the same… (More)
We explore whether the process of multimerization can be used as a means to regulate noise in the abundance of functional protein complexes. Additionally, we analyze how this process affects the mean level of these functional units, response time of a gene, and temporal correlation between the numbers of expressed proteins and of the functional multimers.… (More)
chemotaxis sphaeroides Rhodobacter discrimination: fold-change detection in Transient dynamic phenotypes as criteria for model Supplementary data l (103 articles) systems biology (198 articles) biomathematics Articles on similar topics can be found in the following collections Email alerting service here right-hand corner of the article or click Receive… (More)