Tracking quintessence and k-essence in a general cosmological background

We derive conditions for stable tracker solutions for both quintessence and k-essence in a general cosmological background, H^2 \propto f(\rho). We find that tracker solutions are possible only when \eta = d ln f /d ln \rho is constant, aside from a few special cases, which are enumerated. Expressions for the quintessence or k-essence equation of state are derived as a function of \eta and the equation of state of the dominant background component.Comment: 6 pages, no figure

Radiation can never again dominate Matter in a Vacuum Dominated Universe

We demonstrate that in a vacuum-energy-dominated expansion phase, surprisingly neither the decay of matter nor matter-antimatter annihilation into relativistic particles can ever cause radiation to once again dominate over matter in the future history of the universe.Comment: updated version, as it will appear in Phys. Rev D. Title change, and some other minor alteration

Consistency of System Identification by Global Total Least Squares

Global total least squares (GTLS) is a method for the identification of linear systems where no distinction between input and output variables is required. This method has been developed within the deterministic behavioural approach to systems. In this paper we analyse statistical properties of this method when the observations are generated by a multivariable stationary stochastic process. In particular, sufficient conditions for the consistency of GTLS are derived. This means that, when the number of observations tends to infinity, the identified deterministic system converges to the system that provides an optimal appoximation of the data generating process. The two main results are the following. GTLS is consistent if a guaranteed stability bound can be given a priori. If this information is not available, then consistency is obtained (at some loss of finite sample efficiency) if GTLS is applied to the observed data extended with zero values in past and future

Behavioural Approximation of Stochastic Processes by Rank Reduced Spectra

Behaviours provide an elegant, parameter free characterization of deterministic systems. We discuss a possible application of behaviours in the approximation of stochastic systems. This can be seen as an extension to the dynamic case of the well-known static factor analysis model. An essential difference is that we see modelling primarily as a matter of process approximation, not as a method to recover the true data generating process. In particular we see "noise properties" as a kind of prior model assumption that can be compared with the resulting quality of the process approximation

Identification of System Behaviours by Approximation of Time Series Data

The behavioural framework has several attractions to offer for the identification of multivariable systems. Some of the variables may be left unexplained without the need for a distinction between inputs and outputs; criteria for model quality are independent of the chosen parametrization; and behaviours allow for a global (i.e., non-local) approximation of the system dynamics. This is illustrated with a behavioural least squares method with an application in dynamic factor analysis

Consistency of global total least squares in stochastic system identification

Global total least squares has been introduced as a method for the identification of deterministic system behaviours. We analyse this method within a stochastic framework, where the observed data are generated by a stationary stochastic process. Conditions are formulated so that the method is consistent in the sense that, when the number of observations tends to infinity, the identified deterministic behaviour converges to the behaviour that provides an optimal appoximation of the data generating process

Behavioural Approximation of Stochastic Processes by Rank Reduced Spectra

Behaviours provide an elegant, parameter free characterization of deterministic systems. We discuss a possible application of behaviours in the approximation of stochastic systems. This can be seen as an extension to the dynamic case of the well-known static factor analysis model. An essential difference is that we see modelling primarily as a matter of process approximation, not as a method to recover the true data generating process. In particular we see "noise properties" as a kind of prior model assumption that can be compared with the resulting quality of the process approximation.factor analysis;behaviours;least squares;lineair systems;stationary processes

Public Private Partnership in the European Union: Experiences in the UK, Germany and Austria

The political context of governments differs between the UK, Germany and Austria, but each government currently has a positive view of Public private Partnership (PPP). There are many similarities to the drivers for PPPs in Austria, Germany and the UK. The UK has had more experience, and the conservative-led government in Austria has been moving towards greater use of PPPs of the “privatisation”-type, but only very cautiously towards PPPs of the “PFI-type”. The major motives for moving towards PPPs are macroeconomic or budgetary, especially in Germany and Austria, but also microeconomic or improving the efficiency of public service delivery, especially in the UK. In all three countries PPPs appear to be a systematic middle response to the alternatives of privatisation or public service provision of infrastructure and operational support. There are more significant multi-tiered levels of government in the Federal systems of Germany and Austria, with many autonomous players including federal government, states and municipalities. Investment by the latter two exceeds investment expenditure of the federal government. In the more centralised UK system policies towards PPPs have been relatively rapid and similar, although not identical, across the UK. In Germany the search for a comprehensive approach (Gesamtkonzept) has slowed the dissemination of PPP; Austria seems to handle the issue more pragmatically. One issue that remains crucial to the future impacts of PPPs is whether they offer genuine and sustainable increases in efficiency and effectiveness compared to the alternatives. If they do then they should have a positive impact on future public resource availability, but if they do not then they may provide short-term financial and political benefits, but at the cost of constraining future decision makers and placing greater pressures on public finances in the longer-term