The learning-from-experience model of Malmendier and Nagel [(2016) Quarterly Journal of Economics 131, 53–87] successfully reproduces the heterogeneity in inflation expectations across age groups. However, inflation expectations presumably depend on not only age and experience but also inflation regime. Therefore, this paper proposes an extended learning-from-experience model, in which expectation formation depends on inflation regime. Estimating the model with US data, I find that when inflation is higher and more volatile, households place more weight on recent data when making private forecasts. Moreover, in this regime, households rely more heavily on private forecasts than on public information.

Soils usually exhibit state-dependent frictional behaviour that undergoes plastic volumetric deformation. To correctly capture such response under the framework of classical plasticity, a non-associated flow rule using additional plastic potential is inevitably needed. Recently, a novel fractional plasticity (FP) without using plastic potential has been developed, and successfully applied in modelling the state-dependent nonassociated behaviour of soils. However, the energy dissipation characteristics of FP has not been probed in depth. This note examines the plastic dissipation behaviour of FP, when modelling the constitutive behaviour of soils. It is found that the plastic dissipation of FP increases continuously with the shear strain. However, the rate of plastic dissipation depends on the initial material state in relation to the critical state line.

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network.

This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

A number of papers have recently appeared in the literature in which customers, in moving from node to node in the network arrive as either a positive customer or as a batch of negative customers. A positive customer joining its queue increases the number of customers at the queue by 1 and each negative customer decreases the queue length by 1, if possible. It has been shown that the equilibrium distribution for these networks assumes a geometric product form, that certain partial balance equations prevail and that the parameters of the geometric distributions are, as in Jackson networks, the service facility throughputs of customers. In this paper the previous work is generalised by allowing state dependence into both the service and routing intensities and by allowing the possibility, although not the necessity, for negative customers to build up at the nodes.

Some classes of population-size-dependent Galton-Watson processes are considered where extinction occurs with probability 1. Results on the asymptotic behaviour of the probability of survival up to time t, mean population size and conditioned limit distributions are found to hold. They correspond to those obtained in the study of Galton-Watson processes with immigration stopped at 0.

In a class of population-size-dependent Galton-Watson processes where extinction does not occur with probability 1 we describe the rate of decay of qi (the probability that the process starting from i ancestors will become extinct) as the number i of ancestors increases.

The results are related to the asymptotic behavior of the Green's function of the critical Galton-Watson process with immigration.

An analogue of the Kesten–Stigum theorem, and sufficient conditions for the geometric rate of growth in the rth mean and almost surely, are obtained for population-size-dependent branching processes.

The process we consider is a binary splitting, where the probability of division, , depends on the population size, 2i. We show that Zn converges to ∞ almost surely on a set of positive probability. Zn/n converges in distribution to a proper limit, diverges almost surely on converges almost surely on and there are no constants cn such that Zn/cn converges in probability to a non-degenerate limit.