A Small-Gain Theorem with Applications to Input/Output Systems, Incremental Stability, Detectability, and Interconnections

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.Comment: 16 pages, no figure

Stanford telemetry monitoring experiment on Lunar Explorer 35 Final report

Explorer 35 data analysis including occultation study and antenna pattern interpretation along with electromagnetic property experiment

Remarks on computing the Grothendieck rings of C*-algebras

In this paper, we present a captivating construction by Grothendieck, originally formulated for algebraic varieties, and adapt it to the realm of C*-algebras. Our main objective is to investigate the conditions under which this particular class of C*-algebras possesses a nontrivial Grothendieck ring. To achieve this, we explore the existence of nontrivial characters, which significantly enriches our understanding of these algebras. In particular, we conduct a detailed study of rings of C*-algebras over $\mathbb{C}$, $\mathbb{R}$, and $\mathbb{H}$

A quantitative model of the initiation of DNA replication in Saccharomyces cerevisiae predicts the effects of system perturbations.

BackgroundEukaryotic cell proliferation involves DNA replication, a tightly regulated process mediated by a multitude of protein factors. In budding yeast, the initiation of replication is facilitated by the heterohexameric origin recognition complex (ORC). ORC binds to specific origins of replication and then serves as a scaffold for the recruitment of other factors such as Cdt1, Cdc6, the Mcm2-7 complex, Cdc45 and the Dbf4-Cdc7 kinase complex. While many of the mechanisms controlling these associations are well documented, mathematical models are needed to explore the network's dynamic behaviour. We have developed an ordinary differential equation-based model of the protein-protein interaction network describing replication initiation.ResultsThe model was validated against quantified levels of protein factors over a range of cell cycle timepoints. Using chromatin extracts from synchronized Saccharomyces cerevisiae cell cultures, we were able to monitor the in vivo fluctuations of several of the aforementioned proteins, with additional data obtained from the literature. The model behaviour conforms to perturbation trials previously reported in the literature, and accurately predicts the results of our own knockdown experiments. Furthermore, we successfully incorporated our replication initiation model into an established model of the entire yeast cell cycle, thus providing a comprehensive description of these processes.ConclusionsThis study establishes a robust model of the processes driving DNA replication initiation. The model was validated against observed cell concentrations of the driving factors, and characterizes the interactions between factors implicated in eukaryotic DNA replication. Finally, this model can serve as a guide in efforts to generate a comprehensive model of the mammalian cell cycle in order to explore cancer-related phenotypes

Commercial-off-the-shelf simulation package interoperability: Issues and futures

Commercial-Off-The-Shelf Simulation Packages (CSPs) are widely used in industry to simulate discrete-event models. Interoperability of CSPs requires the use of distributed simulation techniques. Literature presents us with many examples of achieving CSP interoperability using bespoke solutions. However, for the wider adoption of CSP-based distributed simulation it is essential that, first and foremost, a standard for CSP interoperability be created, and secondly, these standards are adhered to by the CSP vendors. This advanced tutorial is on an emerging standard relating to CSP interoperability. It gives an overview of this standard and presents case studies that implement some of the proposed standards. Furthermore, interoperability is discussed in relation to large and complex models developed using CSPs that require large amount of computing resources. It is hoped that this tutorial will inform the simulation community of the issues associated with CSP interoperability, the importance of these standards and its future