– The deÞning characteristic of a networked control system (NCS) is having a feedback loop that passes through a local area computer network. Our two-step design approach includes using standard control methodologies and choosing the network protocol and bandwidth in order to ensure important closed-loop properties are preserved when a computer network is inserted into the feedback loop. For su...

Aldous (2007) defined a gossip process in which space is a discrete N ×N torus, and the state of the process at time t is the set of individuals who know the information. Information spreads from a site to its nearest neighbors at rate 1/4 each and at rate N−α to a site chosen at random from the torus. We will be interested in the case in which α < 3, where the long range transmission significa...

We study the asymptotic behavior of stream cipher security measures associated with classes of sequence generators such as linear feedback shift registers and feedback with carry shift registers. For nonperiodic sequences we consider normalized measures and study the set of accumulation points for a fixed sequence. We see that the the set of accumulation points is always a closed subinterval of...

Mortgage prepayments play a crucial role in the pricing and hedging of mortgage backed securities. An important feature of mortgage prepayment modeling is burnout; as time goes on those borrowers who have the greatest tendency to refinance are removed from the pool leaving only those that are less likely to refinance. In this paper we examine the implications of burnout on the late time prepaym...

In this paper, we consider the asymptotic behavior of two Teichmüller geodesic rays determined by Jenkins-Strebel differentials, and we obtain a generalization of a theorem by the author in On behavior of pairs of Teichmüller geodesic rays, 2014 . We also consider the infimum of the asymptotic distance up to choice of base points of the rays along the geodesics. We show that the infimum is repr...

We study the inflated phase of two dimensional lattice polygons with fixed perimeter N and variable area, associating a weight exp[pA− Jb] to a polygon with area A and b bends. For convex and column-convex polygons, we show that 〈A〉/Amax = 1−K(J)/p̃ 2 + O(ρ), where p̃ = pN ≫ 1, and ρ < 1. The constant K(J) is found to be the same for both types of polygons. We argue that self-avoiding polygons sh...

This research was partially supported by research grants to each of the authors from the National Science Foundation We study two families of excitable cellular automata known as the Greenberg–Hastings model and the cyclic cellular automaton. Each family consists of local deterministic oscillating lattice dynamics, with parallel discrete-time updating, parametrized by the range of interaction, ...

We study Eigen's quasispecies model in the asymptotic regime where the length of the genotypes goes to [Formula: see text] and the mutation probability goes to 0. A limiting infinite system of differential equations is obtained. We prove convergence of trajectories, as well as convergence of the equilibrium solutions. We give analogous results for a discrete-time version of Eigen's model, which...

The mean discount rate for a simple stochastic model behaves asymptotically roughly like 1/ √ n in contrast to the usual geometric discounting in a deterministic model. AMS (2000) subject classifications. 60F99, 60J05, 60G42.

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unst...