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A training algorithm is introduced that takes into account a priori known errors on both inputs and outputs in an MLP network. The new cost function introduced for this case is based on a linear approximation of the network function over the input distribution for a given input pattern. Update formulas, in the form of the gradient of the new cost function, is given for a MLP network, together with expressions for the Hessian matrix. This is later used to calculate error bars in a Bayesian framework. The error bars thus derived are discussed in relation to the more commonly used width of the target posterior predictive distribution. It will also be shown that the taking into account of known input uncertainties in the way suggested in this article will have a strong regularizing effect on the solution.

Modifications in the integration of the source terms in hyperbolic conservation laws such as those governing combustion, detonation and radiative transport, with a first order upwind differencing technique are proposed and analysed. The von Neuman stability and phase error analysis for a linear scalar equation, together with a few test problems is presented in order to compare the performance of the resulting variants of the donor cell scheme. It is established that when the source term is integrated using higher order formulae, the resulting scheme gives better resolution and has better stability limit and phase accuracy, compared to the standard single nodal value replacement. It is shown that integration by the trapezoidal rule gives sufficient accuracy and further improvement may not necessarily be achieved using better methods, such as the Simpson’s rule.

We introduce an information theoretic framework for a quantitative measure of originality to model the impact of various classes of biases, errors and error corrections on scientific research. Some of the open problems are also outlined.

The errors caused by the transitions with large frequency offsets (nonresonant transitions) are calculated analytically for a scalable solid-state quantum computer based on a one-dimensional spin chain with Ising interactions between neighboring spins. Selective excitations of the spins are enabled by a uniform gradient of the external magnetic field. We calculate the probabilities of all unwanted nonresonant transitions associated with the flip of each spin with nonresonant frequency and with flips of two spins: one with resonant and one with nonresonant frequencies. It is shown that these errors oscillate with changing gradient of the external magnetic field. Choosing the optimal values of this gradient allows us to decrease these errors by 50%.

An implicit compact scheme is proposed to approximate the solution of parabolic partial differential equations (PDEs) of Burgers’ type in two dimensions. These nonlinear PDEs are essential because they describe various mechanisms in engineering and physics. The nonlinear convective and advective processes are discretized with high-order accuracy on an arbitrary grid, which results in a family of high-resolution discrete replacements of given PDEs. The essence of the new scheme lies in its compact character and two-level single-cell discretization, so that one discrete equation leads to the accuracy of orders three or four, depending upon the choice of the grid network. The scheme is used for solving celebrated nonlinear PDEs, such as the nondegenerate convection–diffusion equation, the generalized Burgers–Huxley equation, the Buckley–Leverett equation, and the Burgers–Fisher equation. Many computational results are presented to demonstrate the high-resolution character of the newly proposed scheme.

Lattice QCD results can be extrapolated to physical quark masses using Chiral Perturbation Theory. Here, treatment of statistical and systematic errors is discussed. One way of estimating the theoretical uncertainty is to perform a matching of the theory to a framework with an additional degree of freedom. This is illustrated for the nucleon axial vector coupling constant g_A by effectively integrating out the leading Δ(1232) contribution.

Much experimental effort has been expended in attempts to establish the relative superiority of Expected Utility theory and the many recently-developed alternatives as descriptions of the behaviour of subjects in risky choice decision problems. The cumulative evidence shows clearly that there is a great deal of noise in the experimental data, which makes it difficult to identify the ‘best’ description of such behaviour. This paper reports on an experiment which seeks to determine whether such noise is relatively transitory and decays with experience and repetition, and thus whether a clearly ‘best’ theory emerges as a result of such repetition. We find that for some subjects this does indeed appear to be the case, while for other subjects the noise remains high and the identification of the underlying preference function remains difficult.

This paper investigates whether some part of the preference reversal phenomenon can be attributed to errors in the responses of subjects in experiments. Such errors have been well documented in other investigations of behaviour in risky decision problems, but their relevance to the preference reversal phenomenon has not been explored. Building on earlier work, we develop an extended error model and apply it to the results of an experiment in which subjects tackle risky choice problems on five separate occasions. In this experiment subjects had to answer choice questions in three occasions and to state selling and buying prices in the remaining two occasions. Our results indicate that scale compatibility can be ruled out as a significant sole explanation of the preference reversal phenomenon. Moreover, we can show that a considerable fraction of observed preference reversals can be classified as pricing errors, whereas choice errors turn out to play a minor role.

Two recent papers, Harless and Camerer(1994) and Hey and Orme(1994) are both addressed to the same question: which is the ‘best’ theory of decision making under risk? As an essential part of their separate approaches to an answer to this question, both sets of authors had to make an assumption about the underlying stochastic nature of their data. In this context this implied an assumption about the ‘errors’ made by the subjects in the experiments generating the data under analysis. The two different sets of authors adopted different assumptions: the purpose of this current paper is to compare and contrast these two different error stories — in an attempt to discover which of the two is ‘best’.

Many, if not all, of the recent theories of decision making under risk, that have been developed in the light of experimentally observed violations of Expected Utility theory, are essentially deterministic in nature, yet it is clear that actual decision making contains a random or error component. This paper surveys the assumptions that have been employed in previous analyses of such experimental data, and tries to find better explanations (both from an economic and an econometrics point of view), of such errors. Hopefully, such work will lead to a unified theory, in which the stochastic component is an integral part.

This paper describes a convolutional encoder for generating tree codes whose distinct codewords are orthogonal over the constraint length of the code. The performance of this class of codes is analyzed and the error probability is shown to decrease exponentially with the energy-to-noise ratio over the constraint length period of the code. The performance is compared with well-known results for orthogonal block codes and shown to be considerably superior to the latter. Asymptotic results are also obtained which coincide with results for the class of very noisy memoryless channels.