Computation with infinite neural networks

For neural networks with a wide class of weight priors, it can be shown that in the limit of an infinite number of hidden units, the prior over functions tends to a gaussian process. In this article, analytic forms are derived for the covariance function of the gaussian processes corresponding to networks with sigmoidal and gaussian hidden units. This allows predictions to be made efficiently using networks with an infinite number of hidden units and shows, somewhat paradoxically, that it may be easier to carry out Bayesian prediction with infinite networks rather than finite ones.

Mixture density network training by computation in parameter space

Training Mixture Density Network (MDN) configurations within the NETLAB framework takes time due to the nature of the computation of the error function and the gradient of the error function. By optimising the computation of these functions, so that gradient information is computed in parameter space, training time is decreased by at least a factor of sixty for the example given. Decreased training time increases the spectrum of problems to which MDNs can be practically applied making the MDN framework an attractive method to the applied problem solver.

Development of a quality control material for the measurement of 8-oxo-7,8-dihydro-2'-deoxyguanosine, an in vivo marker of oxidative stress, and comparison of results from different laboratories

The measurement of 8-oxo-7,8-dihydro-2'-deoxyguanosine is an increasingly popular marker of in vivo oxidative damage to DNA. A random-sequence 21-mer oligonucleotide 5'-TCA GXC GTA CGT GAT CTC AGT-3' in which X was 8-oxo-guanine (8-oxo-G) was purified and accurate determination of the oxidised base was confirmed by a 32P-end labelling strategy. The lyophilised material was analysed for its absolute content of 8-oxo-dG by several major laboratories in Europe and one in Japan. Most laboratories using HPLC-ECD underestimated, while GC-MS-SIM overestimated the level of the lesion. HPLC-ECD measured the target value with greatest accuracy. The results also suggest that none of the procedures can accurately quantitate levels of 1 in 10(6) 8-oxo-(d)G in DNA.

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.

Analogue computation of the impedence of a powered flying control system

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A data structure for improved gp analysis via efficient computation and visualisation of population measures

Population measures for genetic programs are defined and analysed in an attempt to better understand the behaviour of genetic programming. Some measures are simple, but do not provide sufficient insight. The more meaningful ones are complex and take extra computation time. Here we present a unified view on the computation of population measures through an information hypertree (iTree). The iTree allows for a unified and efficient calculation of population measures via a basic tree traversal. © Springer-Verlag 2004.

On reliable computation by noisy random Boolean formulas

We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from a single majority-like gate. We show that these gates can be used to compute any Boolean function reliably below the noise bound.

Efficient computation of decoherent quantum walks through eigenvalue perturbation

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly,it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving state vector whose sizes quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report,we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n2×n2 Lindblad super-operator from the eigendecomposition of the n×n graph Hamiltonian.

Computation of rare transitions in the barotropic quasi-geostrophic equations

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherWe adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.