Bramwell–Holdsworth–Pinton Research Articles

Phase II monitoring of linear profiles with random explanatory variable under Bayesian framework

Linear profiles monitoring have been successfully implemented in many industrial applications. The design structures of control charts for profiles monitoring are mostly based on two major classifications namely Classical and Bayesian. This study investigates the novel Bayesian exponentially weighted moving average and multivariate exponentially weighted moving average control charts for the monitoring of linear profiles, when explanatory variable(s) are random. The informative priors of normal and inverse gamma; and Bramwell, Holdsworth, Pinton (BHP) and Levy distributions are considered as conjugate and non-conjugate priors respectively. The proposed Bayesian schemes are evaluated using different run length characteristics. The schemes are also validated with simulation study and real-world data sets. The outcomes demonstrate that the Bayesian methods perform effectively better than the competing methods. The specified values of hyper-parameters are selected carefully after elicitation and sensitivity analysis of hyper-parameters. It has been observed that careful consideration is required while selecting the priors and possible values of hyper-parameters. The selection of appropriate priors and corresponding hyper-parameters comes up with efficient control structures which provide tangible benefits.

Modelling and detection of failure in medical electrodes

In this paper we have studied the failures in medical electrodes such as electroencephalogram electrodes (EEG) being used for collecting brain signals. As those electrodes have to guarantee high level of reliability it is important to explore and predict the possible occurrence of failures in there structure. The electrode tip (needle) made of stainless steel is covered with thin oxide film acting as a dielectric and determing the total electrode resistance. In fact, studying the fluctuations of that resistance gives the insight into defects of the whole structure. The electrical properties of the oxide layer are characterized by charge hopping mechanism and the total resistance could be modeled by implementing random resistance network (RRN) methodology.The applied computational algorithm is based on Monte Carlo simulation procedure with direct and iteration methods. The obtained simulation results show non-gaussian Bramwell-Holdsworth-Pinton (BHP) distribution of the total resistance fluctuations, and they verified by the experiments.

Universality in the stock exchange market

We consider the α re-scaled Standard & Poor's 100 (SP100) daily index positive returns and negative returns ( that we call, after normalization, the α positive fluctuations and α negative fluctuations, respectively. We use the Kolmogorov–Smirnov statistical test as a method to find the values of α that optimize the data collapse of the histogram of the α fluctuations with the truncated Bramwell–Holdsworth–Pinton (BHP) probability density function (pdf) and the truncated generalized log-normal pdf f LN that best approximates the truncated BHP pdf. The optimal parameters we found are , , and . Using the optimal α′s, we compute analytical approximations of the probability distributions of the normalized positive and negative SP100 index daily returns r(t). Since the BHP pdf appears in several other dissimilar phenomena, our result reveals a universal feature of the stock exchange markets.

Universal fluctuations of the AEX index

We compute the analytic expression of the probability distributions F A E X , + and F A E X , − of the normalized positive and negative AEX (Netherlands) index daily returns r ( t ) . Furthermore, we define the α re-scaled AEX daily index positive returns r ( t ) α and negative returns ( − r ( t ) ) α , which we call, after normalization, the α positive fluctuations and α negative fluctuations. We use the Kolmogorov–Smirnov statistical test as a method to find the values of α that optimize the data collapse of the histogram of the α fluctuations with the Bramwell–Holdsworth–Pinton (BHP) probability density function. The optimal parameters that we found are α + = 0.46 and α − = 0.43 . Since the BHP probability density function appears in several other dissimilar phenomena, our result reveals a universal feature of stock exchange markets.

CYCLES AND UNIVERSALITY IN SUNSPOT NUMBER FLUCTUATIONS

We analyze the famous Wolf's sunspot numbers. Surprisingly, we discovered that the distribution of the sunspot number fluctuations for both the ascending and descending phases is close to the universal nonparametric Bramwell-Holdsworth-Pinton (BHP) distribution. Since the BHP probability density function appears in several other physical phenomena, our result reveals a universal feature of the Wolf's sunspot numbers.

Fluctuation spectrum and size scaling of river flow and level

We describe the statistical properties of two large river systems: the Danube and the Mississippi. The properties of the two rivers are compared qualitatively to the general properties of a critical steady-state system. Specifically, we test the recent suggestion by Bramwell et al. (Europhys. Lett. 57 (2002) 310) that a universal probability density function (PDF) exists for the fluctuations in river level, namely the Bramwell–Holdsworth–Pinton (BHP) PDF. The statistical properties investigated in this paper are: the PDF of the river flow and river level; moment scaling with basin area; moment to moment scaling or relative scaling; and power spectral properties of the data. We find that the moments of the flow scale approximately with basin area and that the seasonally adjusted flows exhibit relative moment scaling. Compared to the Mississippi, the Danube shows large deviations from spatial scaling and the power spectra show considerable dependence on system size. This might be due to water use and regulations as well as inhomogeneities in the basin area. We also find that the PDF of level data in some, but not all, cases can be qualitatively approximated by the BHP PDF.

Non-Gaussian resistance noise near electrical breakdown in granular materials

The distribution of resistance fluctuations of conducting thin films with granular structure near electrical breakdown is studied by numerical simulations. The film is modeled as a resistor network in a steady state determined by the competition between two biased processes, breaking and recovery. Systems of different sizes and with different levels of internal disorder are considered. Sharp deviations from a Gaussian distribution are found near breakdown and the effect increases with the degree of internal disorder. We show that in general this non-Gaussianity is related to the finite size of the system and vanishes in the large size limit. Nevertheless, near the critical point of the conductor–insulator transition, deviations from Gaussianity persist when the size is increased and the distribution of resistance fluctuations is well fitted by the universal Bramwell–Holdsworth–Pinton distribution.

Non-Gaussianity of resistance fluctuations near electrical breakdown

We study the resistance fluctuation distribution of a thin film near electrical breakdown. The film is modelled as a stationary resistor network under biased percolation. Depending on the value of the external current, on the system sizes and on the level of internal disorder, the fluctuation distribution can exhibit a non-Gaussian behaviour. We analyse this non-Gaussianity in terms of the generalized Gumbel distribution recently introduced in the context of highly correlated systems near criticality. We find that when the average fraction of defects approaches the random percolation threshold, the resistance fluctuation distribution is well described by the universal behaviour of the Bramwell–Holdsworth–Pinton distribution.