A simplified model of the Martian atmosphere - Part 1: a diagnostic analysis

In this paper we derive a reduced-order approximation to the vertical and horizontal structure of a simplified model of the baroclinically unstable Martian atmosphere. The original model uses the full hydrostatic primitive equations on a sphere, but has only highly simplified schemes to represent the detailed physics of the Martian atmosphere, e.g. forcing towards a plausible zonal mean temperature state using Newtonian cooling. Three different norms are used to monitor energy conversion processes in the model and are then compared. When four vertical modes (the barotropic and first three baroclinic modes) are retained in the reduced-order approximation, the correlation norm captures approximately 90% of the variance, while the kinetic energy and total energy norms capture approximately 83% and 78% of the kinetic and total energy respectively. We show that the leading order Proper Orthogonal Decomposition (POD) modes represent the dominant travelling waves in the baroclinically-unstable, winter hemisphere. In part 2 of our study we will develop a hierarchy of truncated POD-Galerkin expansions of the model equations using up to four vertical modes

A simplified model of the Martian atmosphere - Part 2: a POD-Galerkin analysis

In Part I of this study Whitehouse et al. (2005) performed a diagnostic analysis of a simplied model of the Martian atmosphere, in which topography was absent and in which heating was modelled as Newtonian relaxation towards a zonally symmetric equilibrium temperature field. There we derived a reduced-order approximation to the vertical and the horizonal structure of the baroclinically unstable Martian atmosphere, retaining only the barotropic mode and the leading order baroclinic modes. Our objectives in Part II of the study are to incorporate these approximations into a Proper Orthogonal Decomposition-Galerkin expansion of the spherical quasi-geostrophic model in order to derive hierarchies of nonlinear ordinary differential equations for the time-varying coefficients of the spatial structures. Two different vertical truncations are considered, as well as three different norms and 3 different Galerkin truncations. We investigate each in turn, using tools from bifurcation theory, to determine which of the systems most closely resembles the data for which the original diagnostics were performed

American skullcap (Scutellaria lateriflora): an ancient remedy for today’s anxiety?

Anxiety is a common but potentially serious disorder as it can lead to somatic and social dysfunction. Orthodox anxiolytics are associated with unpleasant side-effects and dependency. American skullcap (Scutellaria lateriflora) is a popular herb in traditional medicine systems and the western materia medica for anxiety and related disorders. Preliminary clinical and in vitro research provides encouraging support for its potential as a safe, well-tolerated and effective alternative

Exact averages of central values of triple product L-functions

We obtain exact formulas for central values of triple product L-functions averaged over newforms of weight 2 and prime level. We apply these formulas to non-vanishing problems. This paper uses a period formula for the triple product L-function proved by Gross and Kudla

Testing for a unit root against ESTAR stationarity

In this paper we examine the local power of unit root tests against globally stationary exponential smooth transition autoregressive [ESTAR] alternatives under two sources of uncertainty: the degree of nonlinearity in the ESTAR model, and the presence of a linear deterministic trend. First, we show that the Kapetanios, Shin and Snell (2003, Journal of Econometrics 112, 359.379) [KSS] test for nonlinear stationarity has local asymptotic power gains over standard Dickey-Fuller [DF] tests for certain degrees of nonlinearity in the ESTAR model, but that for other degrees of nonlinearity, the linear DF test has superior power. Second, we derive limiting distributions of demeaned, and demeaned and detrended KSS and DF tests under a local ESTAR alternative when a local trend is present in the DGP. We show that the power of the demeaned tests outperforms that of the detrended tests when no trend is present in the DGP, but deteriorates as the magnitude of the trend increases. We propose a union of rejections testing procedure that combines all four individual tests and show that this captures most of the power available from the individual tests across different degrees of nonlinearity and trend magnitudes. We also show that incorporating a trend detection procedure into this union testing strategy can result in higher power when a large trend is present in the DGP

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

The first legal mortgagor: a consumer without adequate protection?

This article contends that the UK government’s attempt to create a well-functioning consumer credit market will be undermined if it fails to reform the private law framework relating to the first legal mortgage. Such agreements are governed by two distinct regulatory regimes that are founded upon very different conceptions of the mortgagor. The first, the regulation of financial services overseen by the Financial Conduct Authority, derives from public law and is founded upon a conception of the mortgagor as “consumer”. The other is land law, private law regulation implemented by the judiciary and underpinned by a conception of the mortgagor as “landowner”. Evidence suggests that the operation of these two regimes prevents mortgagors from receiving fair and consistent treatment. The current reform of financial services regulation therefore will change only one part of this governance regime and will leave mortgagors heavily reliant upon a regulator that still has to prove itself. What this article argues is that reform of the rules of private law must also be undertaken with the aim of initiating a paradigm shift in the conception of the mortgagor from “landowner” to “consumer”. Cultural shifts of this kind take time but the hope is that this conceptual transformation will occur in time to deter the predicted rise in mortgage possessions

The 2013 Multi-objective Physical Travelling Salesman Problem Competition

This paper presents the game, framework, rules and results of the Multi-objective Physical Travelling Salesman Problem (MO-PTSP) Competition, that was held at the 2013 IEEE Conference on Computational Intelligence in Games (CIG). The MO-PTSP is a real-time game that can be seen as a modification of the Travelling Salesman Problem, where the player controls a ship that must visit a series of waypoints in a maze while minimizing three opposing goals: Time spent, fuel consumed and damage taken. The rankings of the competition are computed using multi-objective concepts, a novel approach in the field of game artificial intelligence competitions. The winning entry of the contest is also explained in detail. This controller is based on the Monte Carlo Tree Search algorithm, and employed Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for parameter tuning