162,596 research outputs found
An alternative method to the scrambled Halton sequence for removing correlation between standard Halton sequences in high dimensions
No full textHalton sequences were first introduced in the 1960s as an alternative to pseudo-random number sequences, with the aim of providing better coverage of the area of integration and negative correlation in the simulated probabilities between observations. This is needed in order to achieve variance reduction when using simulation to approximate an integral that does not have a closed-form expression. Such integrals arise in many areas of regional science, for example in the evaluation and estimation of certain types of discrete choice models. While the performance of standard Halton sequences is very good in low dimensions, problems with correlation have been observed between sequences generated from higher primes. This can cause serious problems in the estimation of models with high-dimensional integrals (e.g., models of aspects of spatial choice, such as route or location). Various methods have been proposed to deal with this; one of the most prominent solutions is the scrambled Halton sequence, which uses special predetermined permutations of the coefficients used in the construction of the standard sequence. In this paper, we conduct a detailed analysis of the ability of scrambled Halton sequences to remove the problematic correlation that exists between standard Halton sequences for high primes in the two-dimensional space. The analysis shows that although the scrambled sequences exhibit a lower degree of overall correlation than the standard sequences, for some choices of primes, correlation remains at an unacceptably high level. This paper then proposes an alternative method, based on the idea of using randomly shuffled versions of the one-dimensional standard Halton sequences in the construction of multi-dimensional sequences. We show that the new shuffled sequences produce a significantly higher reduction in correlation than the scrambled sequences, without loss of quality of coverage. Another substantial advantage of this new method is that it can, without any modifications, be used for any number of dimensions, while the use of the scrambled sequences requires the a-priori computation of a matrix of permutations, which for high dimensional problems could lead to significant runtime disadvantages. Repeated runs of the shuffling algorithm will also produce different sequences in different runs, which nevertheless maintain the same quality of one-dimensional coverage. This is not at all the case for the scrambled sequences. In view of the clear advantages in its ability to remove correlation, combined with its runtime and generalization advantages, this paper recommends that this new algorithm should be preferred to the scrambled Halton sequences when dealing with high correlation between standard Halton sequences.
Calculation of Multivariate Normal Probabilities by Simulation, with Applications to Maximum Simulated Likelihood Estimation
No full textWe discuss methods for calculating multivariate normal probabilities by simulation and two new Stata programs for this purpose: mvdraws for deriving draws from the standard uniform density using either Halton or pseudo-random sequences, and an egen function mvnp() for calculating the probabilities themselves. Several illustrations show how the programs may be used for maximum simulated likelihood estimation.Simulation estimation, maximum simulated likelihood, multivariate probit, Halton sequences, pseudo-random sequences, multivariate normal, GHK simulator
Business Papers (MS 80-0003)
No full textWarranty deed from B. F. Halton to J. J. Smith conveying land part of the H. Hendricks survey
On variants of the Halton sequence
No full textA generalisation of the classical Halton sequence (ϕβ(n))n∈N has emerged in recent years based on β-adic expansions of elements of [0, 1). In the case where β is a natural number greater than 1, this reduces to the classical Halton sequence. In this paper, we use ergodic and analytic methods to prove the uniform distribution of a sequence (ϕβ(kj))j∈N for the sequence of integers (kj)j≥0, which is both Hartman uniformly distributed and good universal. This builds on earlier work of M. Hofer, M. R. Iaco and R. Tichy in the special case kj=j(j=0,1,…). Variants of this phenomenon are also studied
Engaging parents and carers with Sure Start New Steps
No full textThis project report discusses the extent to which families in Halton are aware of the Sure Start New Steps programme. Concerns had been raised about the strategies used to inform parents and carers about Sure Start New Steps and how systematically and effectively its activities were introduced and promoted by health professionals and others working with the eligible population.Sure Start New Steps
Radical additions to some strained organic molecules
No full textThe existence of a cyclopropabenzyl radical has not been established. Reactions between cyclopropabenzene Breslow, R., Groves, J.T., and Ryan, G., J. Am. Chem. Soc., 1967, 89, 5048; Breslow, R., and Groves, J.T., J. Am. Chem. Soc., 1970, 92, 984. and radical species result in opening of the three-membered ring. The present study employed 1H-cyclopropa[b]naphthalene Banwell, M.G., Battner, R., Browne, A.R., Craig, J.T., and Halton, B., J. Chem. Soc., Perkin Trans.1, 1977, 1, 2165. and its 1 -phenylmethylene- and 1 -diphenylmethylene derivatives (70a) and (70b), respectively, as substrates for reactions with a variety of radicals with a view to gaining evidence for the existence of the C1 cycloproparenyl radical.
This study has provided no evidence to support the existence of a cycloproparenyl radical. 1H-Cyclopropa[b]naphthalene Banwell, M.G., Battner, R., Browne, A.R., Craig, J.T., reacts with N-bromo-succinimide, sulfuryl chloride, and iodine to give the 2-substituted 3-(substituted-methyl)naphthalenes Gover, and Willard, J. Am. Chem. Soc., 1960, 82, 3816., March, J., Advanced Organic Chemistry - Reaction, Mechanisms, and Structure, 4th Ed., John Wiley and Sons, New York, 1992, 691. Cook, E.S., and Hill, A.J., J. Am. Chem. Soc., 1940, 62, 1995., At this point in the reaction, mixture was found to react very vigorously and escape the containing vessel. Extreme caution should be taken here. ,(137). Arylthiols produce compounds March, J., Advanced Organic Chemistry - Reaction, Mechanisms and Structure, 4th Ed., John Wiley and Sons, New York, 1992, 691.- Krafft, F., and Vorster, W. Ber., 1893, 26, 2831., and tributyltin hydride gives (131) from highly regioselective opening of the three membered ring of Banwell, M.G., Battner, R., Browne, A.R.,Craig, J.T., and Halton, B., J. Chem. Soc., Perkin Trans. 1, 1977, 1, 2165. Similar radical reactions with 1 -phenylmethylene-and 1-diphenylmethylene-1H-cyclopropa[b]naphthalene, (70a) and (70b), failed to provide characterisable products
Business Papers (MS 80-0003)
No full textRelease from B. F. Halton to J. J. Smith releasing his claim to land he sold Smith upon receipt of his notes for land in Limestone County
Halton, H. J. (2 boys)
No full textPhotograph from the C.R. Savage Portrait Studio. Name associated with the photograph: H. J. Halto
Challenges and Opportunities in Developing Sustainable Communities in the North West of England
No full textOrigins of sustainable communities lie in agendas set in a motion passed by the United Nations nearly forty years ago. As part of a sustainable development strategy and to tackle negative aspects of post industrial cities, in 2003, the UK government launched a Sustainable Communities Plan, accompanied by regional action plans, of which a major objective has been to implement regeneration projects aiming to improve quality of life in several areas of England, including the North West. This paper aims to review sustainable development agendas and to establish what needs to be done to improve quality of life indicators for communities of Stockbridge Village (SV), Murdishaw (M) and Halton Brook (HB) in Knowsley Metropolitan Borough (MBC) and Halton Borough Councils (BC), which have been identified as the most deprived post industrial areas in the North West of England. An investigation has been carried out by comparing the economic, social, physical and environmental indicators. Study findings reveal existing challenges and highlight problems that need to be addressed when implementing sustainable development strategy
[Report to Chief J. E. Curry, by an unknown author #1]
No full textReport to Chief J. E. Curry, by an unknown author. The report contains a list of officers who gave depositions to the United States Attorney
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