A finite memory is introduced in the score dynamics of Minority Games. As expected, this removes the dependence of the stationary state on the initial conditions. However, it also causes an unexpected increase of fluctuations in grand-canonical models for very large times. Current analytical methods are inadequate to solve this simple and natural extension.

This paper considers a Ramsey model of linear capital and labor income taxation in which the government cannot commit ex-ante to a sequence of policies for the future. In this setup, if the government is more impatient than the government, the capital income tax will always be positive in steady state. Thus, impatience and lack of commitment are able to generate positive capital taxes in the lo...

Analytic results are presented for preheating in both flat and open models of chaotic inflation, for the case of massless inflaton decay into further inflaton quanta. It is demonstrated that preheating in both these cases closely resembles that in Minkowski spacetime. Furthermore, quantitative differences between preheating in spatially flat and open models of inflation remain of order 10 for t...

The paper deals with a selection of the initial state for Kalman filtering. The prior knowledge about it can be highly uncertain. In practice the initial state mean and covariance are often chosen arbitrarily. The present paper considers the problem from the position of knowledge elicitation and proposes a methodology to extract the prior knowledge from available information by the respective p...

If it is assumed that the Universe did not start in a singularity and that the laws of physics apply equally to the time 13.75 billion years ago then the Universe at that time should correspond to a wavefunction or state vector. We shall find that this state vector should be very special and highly symmetrical. By making some reasonable assumptions about the initial conditions of the Universe w...

A new method to deal with reduced dynamics of open systems by means of the Schrödinger equation is presented. It allows one to consider the reduced time evolution for correlated and uncorrelated initial conditions.

This paper explores the effect of initial conditions on the behavior of coupled frictional elastic systems subject to periodic loading. Previously, it has been conjectured that the long term response will be independent of initial conditions if all nodes slip at least once during each loading cycle. Here, this conjecture is disproved in the context of a simple two-node system. Counter examples ...

This paper develops new results on the stability and control of a class of linear repetitive processes described by a second-order matrix discrete or differential equation. These are developed by transformation of the secondorder dynamics to those of an equivalent first-order descriptor state-space model, thus avoiding the need to invert a possibly ill-conditioned leading coefficient matrix in ...

We prove the existence of a time evolution for infinite anharmonic crystals for a large class of initial configurations. When there are strong forces tying particles to their equilibrium positions then the class of permissible initial conditions can be specified explicitly; otherwise it can only be shown to have full measure with respect to the appropriate Gibbs state. Uniqueness of the time ev...

We prove the existence of a time evolution for infinite anharmonic crystals for a large class of initial configurations. When there are strong forces tying particles to their equilibrium positions then the class of permissible initial conditions can be specified explicitly; otherwise it can only be shown to have full measure with respect to the appropriate Gibbs state. Uniqueness of the time ev...