The dynamics of matrix momentum

We analyse the matrix momentum algorithm, which provides an efficient approximation to on-line Newton's method, by extending a recent statistical mechanics framework to include second order algorithms. We study the efficacy of this method when the Hessian is available and also consider a practical implementation which uses a single example estimate of the Hessian. The method is shown to provide excellent asymptotic performance, although the single example implementation is sensitive to the choice of training parameters. We conjecture that matrix momentum could provide efficient matrix inversion for other second order algorithms.

Natural gradient matrix momentum

Natural gradient learning is an efficient and principled method for improving on-line learning. In practical applications there will be an increased cost required in estimating and inverting the Fisher information matrix. We propose to use the matrix momentum algorithm in order to carry out efficient inversion and study the efficacy of a single step estimation of the Fisher information matrix. We analyse the proposed algorithm in a two-layer network, using a statistical mechanics framework which allows us to describe analytically the learning dynamics, and compare performance with true natural gradient learning and standard gradient descent.

Momentum profits in alternative stock market structures

The aim of this study is to examine the relationship between momentum profitability and the stock market trading mechanism and is motivated by recent changes to the trading systems that have taken place on the London Stock Exchange. Since 1975 the London stock market has employed three different trading systems: a floor based system, a computerized dealer system called SEAQ and the automated auction system SETS. Since each new trading system has reduced the level of execution costs, one might expect, a priori, the magnitude of momentum profits to decline with each amendment to the trading system. However, the opposite empirical result is found showing that shares trading on the automated system generate higher momentum profits than those trading on the floor system and companies trading on the SETS system display greater momentum profitability than those trading on SEAQ. Our empirical results concur with the theoretical findings of the trader’s hesitation model of Du [Du, J., 2002. Heterogeneity in investor confidence and asset market under- and overreaction. Working paper] and the empirical findings of Arena et al. [Arena, M., Haggard, S., Yan, X., Price momentum and idiosyncratic volatility. Financial Review, in press].

Momentum profits following bull and bear markets

This paper examines the profitability that the widely published momentum strategy achieves following bull and bear markets. Investors can gain stronger momentum profits by adopting the continuation strategy after poor lagged market returns. The longer the duration used to describe the bear state, the stronger the momentum returns that are realised. The results contradict the theoretical findings of the investors' overconfidence model of Daniel et al. (`Investor Psychology and Security Market Under- and Over-Reactions', Journal of Finance, 53, 1839-85, 1998) and the follow-the-trend model of Kim (`Long-term Momentum Hypothesis: Contrarian and Momentum Strategies', Working Paper, 2002), but concur with the theoretical results of the traders' hesitation model of Du (`Heterogeneity in Investor Confidence and Asset Market Under- and Overreaction', Working Paper, 2002).

Momentum profits and macroeconomic factors

This article tests whether macroeconomic variables and market sentiment influence the size of momentum profits. It finds that although returns to the winner and loser portfolios are influenced by a range of macroeconomic and market wide variables; momentum profits are influenced only by the scale of portfolio outflows. Thus, when investors are sending their capital elsewhere, reduced funds at home, dampen the profitability of the momentum trading strategy. It also finds that when the market closes, below its opening level in the previous six months, momentum profits are higher, which might be a reflection of mean reversion in the market. © 2004 Taylor and Francis Ltd.

CFD modelling of the fast pyrolysis of biomass in fluidised bed reactors. Part B: Heat, momentum and mass transport in bubbling fluidised beds

The fluid–particle interaction inside a 150 g/h fluidised bed reactor is modelled. The biomass particle is injected into the fluidised bed and the heat, momentum and mass transport from the fluidising gas and fluidised sand is modelled. The Eulerian approach is used to model the bubbling behaviour of the sand, which is treated as a continuum. Heat transfer from the bubbling bed to the discrete biomass particle, as well as biomass reaction kinetics are modelled according to the literature. The particle motion inside the reactor is computed using drag laws, dependent on the local volume fraction of each phase. FLUENT 6.2 has been used as the modelling framework of the simulations with the whole pyrolysis model incorporated in the form of user-defined function (UDF). The study completes the fast pyrolysis modelling in bubbling fluidised bed reactors.

CFD modelling of the fast pyrolysis of biomass in fluidised bed reactors, Part A: Eulerian computation of momentum transport in bubbling fluidised beds

The fluid–particle interaction inside a 150 g/h fluidised bed reactor is modelled. The biomass particle is injected into the fluidised bed and the momentum transport from the fluidising gas and fluidised sand is modelled. The Eulerian approach is used to model the bubbling behaviour of the sand, which is treated as a continuum. The particle motion inside the reactor is computed using drag laws, dependent on the local volume fraction of each phase, according to the literature. FLUENT 6.2 has been used as the modelling framework of the simulations with a completely revised drag model, in the form of user defined function (UDF), to calculate the forces exerted on the particle as well as its velocity components. 2-D and 3-D simulations are tested and compared. The study is the first part of a complete pyrolysis model in fluidised bed reactors.