Second Order Perturbations During Inflation Beyond Slow-roll

We numerically calculate the evolution of second order cosmological perturbations for an inflationary scalar field without resorting to the slow-roll approximation or assuming large scales. In contrast to previous approaches we therefore use the full non-slow-roll source term for the second order Klein-Gordon equation which is valid on all scales. The numerical results are consistent with the ones obtained previously where slow-roll is a good approximation. We investigate the effect of localised features in the scalar field potential which break slow-roll for some portion of the evolution. The numerical package solving the second order Klein-Gordon equation has been released under an open source license and is available for download.Comment: v2: version published in JCAP, references added; v1: 21 pages, 11 figures, numerical package available at http://pyflation.ianhuston.ne

Financial liberalization and capital adequacy in models of financial crises

We characterize the effects of financial liberalization indices on OECD banking crises, controlling for the standard macro prudential variables that prevail in the current literature. We use the Fraser Institute’s Economic Freedom of the World database. This yields a variable that captures credit market regulations which broadly measures the restrictions under which banks operate. We then test for the direct impacts of some of its components, deposit interest rate regulations and private sector credit controls, on crisis probabilities and their indirect effects via capital adequacy. Over the period 1980 – 2012, we find that less regulated markets are associated with a lower crisis frequency, and it appears that the channel comes through strengthening the defence that capital provides. Deposit interest rate liberalisation adds to the strength of capital in protecting against crises. However, private sector credit liberalisation, appears to increase the probability of having a crisis, albeit not significantly. If policy makers are concerned about the costs of low risk events, they may wish to control private sector credit even if it has a probability of affecting significantly crises of between 10 and 20 per cent

Double power series method for approximating cosmological perturbations

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a non-cosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on sub-horizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well known growing and decaying M\'esz\'aros solutions, these oscillating modes provide a complete set of sub-horizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.Comment: 22 pages, 10 figures, 2 tables. Mathematica notebook available from Github at https://github.com/AndrewWren/Double-power-series.gi

OSCAR: A Collaborative Bandwidth Aggregation System

The exponential increase in mobile data demand, coupled with growing user expectation to be connected in all places at all times, have introduced novel challenges for researchers to address. Fortunately, the wide spread deployment of various network technologies and the increased adoption of multi-interface enabled devices have enabled researchers to develop solutions for those challenges. Such solutions aim to exploit available interfaces on such devices in both solitary and collaborative forms. These solutions, however, have faced a steep deployment barrier. In this paper, we present OSCAR, a multi-objective, incentive-based, collaborative, and deployable bandwidth aggregation system. We present the OSCAR architecture that does not introduce any intermediate hardware nor require changes to current applications or legacy servers. The OSCAR architecture is designed to automatically estimate the system's context, dynamically schedule various connections and/or packets to different interfaces, be backwards compatible with the current Internet architecture, and provide the user with incentives for collaboration. We also formulate the OSCAR scheduler as a multi-objective, multi-modal scheduler that maximizes system throughput while minimizing energy consumption or financial cost. We evaluate OSCAR via implementation on Linux, as well as via simulation, and compare our results to the current optimal achievable throughput, cost, and energy consumption. Our evaluation shows that, in the throughput maximization mode, we provide up to 150% enhancement in throughput compared to current operating systems, without any changes to legacy servers. Moreover, this performance gain further increases with the availability of connection resume-supporting, or OSCAR-enabled servers, reaching the maximum achievable upper-bound throughput