S. Janson [Poset limits and exchangeable random posets, Combinatorica 31 (2011), 529–563] defined limits of finite posets in parallel to the emerging theory of limits of dense graphs. We prove that each poset limit can be represented as a kernel on the unit interval with the standard order, thus answering an open question of Janson. We provide two proofs: real-analytic and combinatorial. The co...

We study infinite limits of graphs generated by the duplication model for biological networks. We prove that with probability 1, the sole nontrivial connected component of the limits is unique up to isomorphism. We describe certain infinite deterministic graphs which arise naturally from the model. We characterize the isomorphism type and induced subgraph structure of these infinite graphs usin...

Many real-life networks can be modelled by stochastic processes with a spatial embedding. In such processes, the link probability decreases with distance. Using the theory of graph limits, we show how to recognize graph sequences produced by random graph processes with a linear embedding (a natural embedding into R). We define an operator Γ which applies to graph limits, which assumes the value...

A probability-based robust control design methodology is presented that is applied to the \benchmark system," which is a highdelity model of an active-mass-driver laboratory structure. For the controller design, the objective is to maximize the probability that the uncertain structure/controller system achieves satisfactory performance when subject to uncertain excitation. The controller's robu...

control chart is the most well-known chart to monitor the number of nonconformities per inspection unit where each sample consists of constant size. generally, the design of a control chart requires determination of sample size, sampling interval, and control limits width. optimally selecting these parameters depends on several process parameters, which have been considered from statistical and...