Statnote 15: the non-parametric correlation coefficients

If in a correlation test, one or both variables are small whole numbers, scores based on a limited scale, or percentages, a non-parametric correlation coefficient should be considered as an alternative to Pearson’s ‘r’. Kendall’s t and Spearman’s rs are similar tests but the former should be considered if the analysis is to be extended to include partial correlations. If the data contain many tied values, then gamma should be considered as a suitable test.

Comparison of near visual acuity and reading metrics in presbyopia correction

PURPOSE: To provide a consistent standard for the evaluation of different types of presbyopic correction. SETTING: Eye Clinic, School of Life and Health Sciences, Aston University, Birmingham, United Kingdom. METHODS: Presbyopic corrections examined were accommodating intraocular lenses (IOLs), simultaneous multifocal and monovision contact lenses, and varifocal spectacles. Binocular near visual acuity measured with different optotypes (uppercase letters, lowercase letters, and words) and reading metrics assessed with the Minnesota Near Reading chart (reading acuity, critical print size [CPS], CPS reading speed) were intercorrelated (Pearson product moment correlations) and assessed for concordance (intraclass correlation coefficients [ICC]) and agreement (Bland-Altman analysis) for indication of clinical usefulness. RESULTS: Nineteen accommodating IOL cases, 40 simultaneous contact lens cases, and 38 varifocal spectacle cases were evaluated. Other than CPS reading speed, all near visual acuity and reading metrics correlated well with each other (r>0.70, P<.001). Near visual acuity measured with uppercase letters was highly concordant (ICC, 0.78) and in close agreement with lowercase letters (+/- 0.17 logMAR). Near word acuity agreed well with reading acuity (+/- 0.16 logMAR), which in turn agreed well with near visual acuity measured with uppercase letters 0.16 logMAR). Concordance (ICC, 0.18 to 0.46) and agreement (+/- 0.24 to 0.30 logMAR) of CPS with the other near metrics was moderate. CONCLUSION: Measurement of near visual ability in presbyopia should be standardized to include assessment of near visual acuity with logMAR uppercase-letter optotypes, smallest logMAR print size that maintains maximum reading speed (CPS), and reading speed. J Cataract Refract Surg 2009; 35:1401-1409 (C) 2009 ASCRS and ESCRS

Composite materials impact damage detection using neural networks

This thesis considers two basic aspects of impact damage in composite materials, namely damage severity discrimination and impact damage location by using Acoustic Emissions (AE) and Artificial Neural Networks (ANNs). The experimental work embodies a study of such factors as the application of AE as Non-destructive Damage Testing (NDT), and the evaluation of ANNs modelling. ANNs, however, played an important role in modelling implementation. In the first aspect of the study, different impact energies were used to produce different level of damage in two composite materials (T300/914 and T800/5245). The impacts were detected by their acoustic emissions (AE). The AE waveform signals were analysed and modelled using a Back Propagation (BP) neural network model. The Mean Square Error (MSE) from the output was then used as a damage indicator in the damage severity discrimination study. To evaluate the ANN model, a comparison was made of the correlation coefficients of different parameters, such as MSE, AE energy, AE counts, etc. MSE produced an outstanding result based on the best performance of correlation. In the second aspect, a new artificial neural network model was developed to provide impact damage location on a quasi-isotropic composite panel. It was successfully trained to locate impact sites by correlating the relationship between arriving time differences of AE signals at transducers located on the panel and the impact site coordinates. The performance of the ANN model, which was evaluated by calculating the distance deviation between model output and real location coordinates, supports the application of ANN as an impact damage location identifier. In the study, the accuracy of location prediction decreased when approaching the central area of the panel. Further investigation indicated that this is due to the small arrival time differences, which defect the performance of ANN prediction. This research suggested increasing the number of processing neurons in the ANNs as a practical solution.

The appraisal and management of multi-storey dwelling blocks using large concrete panel systems

This exploratory study is concerned with the integrated appraisal of multi-storey dwelling blocks which incorporate large concrete panel systems (LPS). The first step was to look at U.K. multi-storey dwelling stock in general, and under the management of Birmingham City Council in particular. The information has been taken from the databases of three departments in the City of Birmingham, and rearranged in a new database using a suite of PC software called `PROXIMA' for clarity and analysis. One hundred of their stock were built large concrete panel system. Thirteen LPS blocks were chosen for the purpose of this study as case-studies depending mainly on the height and age factors of the block. A new integrated appraisal technique has been created for the LPS dwelling blocks, which takes into account the most physical and social factors affecting the condition and acceptability of these blocks. This appraisal technique is built up in a hierarchical form moving from the general approach to particular elements (a tree model). It comprises two main approaches; physical and social. In the physical approach, the building is viewed as a series of manageable elements and sub-elements to cover every single physical or environmental factor of the block, in which the condition of the block is analysed. A quality score system has been developed which depends mainly on the qualitative and quantitative conditions of each category in the appraisal tree model, and leads to physical ranking order of the study blocks. In the social appraisal approach, the residents' satisfaction and attitude toward their multi-storey dwelling block was analysed in relation to: a. biographical and housing related characteristics; and b. social, physical and environmental factors associated with this sort of dwelling, block and estate in general.The random sample consisted of 268 residents living in the 13 case study blocks. Data collected was analysed using frequency counts, percentages, means, standard deviations, Kendall's tue, r-correlation coefficients, t-test, analysis of variance (ANOVA) and multiple regression analysis. The analysis showed a marginally positive satisfaction and attitude towards living in the block. The five most significant factors associated with the residents' satisfaction and attitude in descending order were: the estate, in general; the service categories in the block, including heating system and lift services; vandalism; the neighbours; and the security system of the block. An important attribute of this method, is that it is relatively inexpensive to implement, especially when compared to alternatives adopted by some local authorities and the BRE. It is designed to save time, money and effort, to aid decision making, and to provide ranked priority to the multi-storey dwelling stock, in addition to many other advantages. A series of solution options to the problems of the block was sought for selection and testing before implementation. The traditional solutions have usually resulted in either demolition or costly physical maintenance and social improvement of the blocks. However, a new solution has now emerged, which is particularly suited to structurally sound units. The solution of `re-cycling' might incorporate the reuse of an entire block or part of it, by removing panels, slabs and so forth from the upper floors in order to reconstruct them as low-rise accommodations.

Structural funds and the knowledge-based economy:a regional case-study (1999-2009)

The research presented in this thesis investigates the nature of the relationship between the development of the Knowledge-Based Economy (KBE) and Structural Funds (SF) in European regions. A particular focus is placed on the West Midlands (UK) and Silesia (Poland). The time-frame taken into account in this research is the years 1999 to 2009. This is methodologically addressed by firstly establishing a new way of calculating the General Index of the KBE for all of the EU regions; secondly, applying a number of statistical methods to measure the influence of the Funds on the changes in the regional KBE over time; and finally, by conducting a series of semi-structured stakeholder interviews in the two key case study regions: the West Midlands and Silesia. The three main findings of the thesis are: first, over the examined time-frame, the values of the KBE General Index increased in over 66% of the EU regions; furthermore, the number of the “new” EU regions in which the KBE increased over time is far higher than in the “old” EU. Second, any impact of Structural Funds on the regional KBE occurs only in the minority of the European regions and any form of functional dependency between the two can be observed only in 30% of the regions. Third, although the pattern of development of the regional KBE and the correlation coefficients differ in the cases of Silesia and the West Midlands, the analysis of variance carried out yields identical results for both regions. Furthermore, the qualitative analysis’ results show similarities in the approach towards the Structural Funds in the two key case-study regions.

Body iron is associated with cognitive executive planning function in college women

Evidence of the relationship between altered cognitive function and depleted Fe status is accumulating in women of reproductive age but the degree of Fe deficiency associated with negative neuropsychological outcomes needs to be delineated. Data are limited regarding this relationship in university women in whom optimal cognitive function is critical to academic success. The aim of the present study was to examine the relationship between body Fe, in the absence of Fe-deficiency anaemia, and neuropsychological function in young college women. Healthy, non-Anaemic undergraduate women (n 42) provided a blood sample and completed a standardised cognitive test battery consisting of one manual (Tower of London (TOL), a measure of central executive function) and five computerised (Bakan vigilance task, mental rotation, simple reaction time, immediate word recall and two-finger tapping) tasks. Women's body Fe ranged from - 4·2 to 8·1 mg/kg. General linear model ANOVA revealed a significant effect of body Fe on TOL planning time (P= 0.002). Spearman's correlation coefficients showed a significant inverse relationship between body Fe and TOL planning time for move categories 4 (r - 0.39, P= 0.01) and 5 (r - 0.47, P= 0.002). Performance on the computerised cognitive tasks was not affected by body Fe level. These findings suggest that Fe status in the absence of anaemia is positively associated with central executive function in otherwise healthy college women. Copyright © The Authors 2012.

Thermalized polarization dynamics of a discrete optical-waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line T=∞ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained, which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.

Identification of nonlinear systems by correlation using pseudorandom signals

This thesis is concerned with the measurement of the characteristics of nonlinear systems by crosscorrelation, using pseudorandom input signals based on m sequences. The systems are characterised by Volterra series, and analytical expressions relating the rth order Volterra kernel to r-dimensional crosscorrelation measurements are derived. It is shown that the two-dimensional crosscorrelation measurements are related to the corresponding second order kernel values by a set of equations which may be structured into a number of independent subsets. The m sequence properties determine how the maximum order of the subsets for off-diagonal values is related to the upper bound of the arguments for nonzero kernel values. The upper bound of the arguments is used as a performance index, and the performance of antisymmetric pseudorandom binary, ternary and quinary signals is investigated. The performance indices obtained above are small in relation to the periods of the corresponding signals. To achieve higher performance with ternary signals, a method is proposed for combining the estimates of the second order kernel values so that the effects of some of the undesirable nonzero values in the fourth order autocorrelation function of the input signal are removed. The identification of the dynamics of two-input, single-output systems with multiplicative nonlinearity is investigated. It is shown that the characteristics of such a system may be determined by crosscorrelation experiments using phase-shifted versions of a common signal as inputs. The effects of nonlinearities on the estimates of system weighting functions obtained by crosscorrelation are also investigated. Results obtained by correlation testing of an industrial process are presented, and the differences between theoretical and experimental results discussed for this case;

Assessing interactions of linear and nonlinear neuronal sources using MEG beamformers:a proof of concept

Objective: This study aimed to explore methods of assessing interactions between neuronal sources using MEG beamformers. However, beamformer methodology is based on the assumption of no linear long-term source interdependencies [VanVeen BD, vanDrongelen W, Yuchtman M, Suzuki A. Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans Biomed Eng 1997;44:867-80; Robinson SE, Vrba J. Functional neuroimaging by synthetic aperture magnetometry (SAM). In: Recent advances in Biomagnetism. Sendai: Tohoku University Press; 1999. p. 302-5]. Although such long-term correlations are not efficient and should not be anticipated in a healthy brain [Friston KJ. The labile brain. I. Neuronal transients and nonlinear coupling. Philos Trans R Soc Lond B Biol Sci 2000;355:215-36], transient correlations seem to underlie functional cortical coordination [Singer W. Neuronal synchrony: a versatile code for the definition of relations? Neuron 1999;49-65; Rodriguez E, George N, Lachaux J, Martinerie J, Renault B, Varela F. Perception's shadow: long-distance synchronization of human brain activity. Nature 1999;397:430-3; Bressler SL, Kelso J. Cortical coordination dynamics and cognition. Trends Cogn Sci 2001;5:26-36]. Methods: Two periodic sources were simulated and the effects of transient source correlation on the spatial and temporal performance of the MEG beamformer were examined. Subsequently, the interdependencies of the reconstructed sources were investigated using coherence and phase synchronization analysis based on Mutual Information. Finally, two interacting nonlinear systems served as neuronal sources and their phase interdependencies were studied under realistic measurement conditions. Results: Both the spatial and the temporal beamformer source reconstructions were accurate as long as the transient source correlation did not exceed 30-40 percent of the duration of beamformer analysis. In addition, the interdependencies of periodic sources were preserved by the beamformer and phase synchronization of interacting nonlinear sources could be detected. Conclusions: MEG beamformer methods in conjunction with analysis of source interdependencies could provide accurate spatial and temporal descriptions of interactions between linear and nonlinear neuronal sources. Significance: The proposed methods can be used for the study of interactions between neuronal sources. © 2005 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Transfer coefficients over inclined tube banks

The thesis presents experimental results for shell-side transfer coefficients and pressure drops across four different tube banks, using small-scale models, with yawed tubes, as found in many types of heat exchangers, boilers and nuclear reactors. The tube banks investigated have a staggered tube layout on a rotated square pitch, with a 1.25 pitch-to-diameter ratio. The angle of attack was varied between 45o and 90o. An extensive range of Reynolds number, i.e. 0.5. to 12,600, covering so-called laminar, transition and turbulent flows, was investigated. A diffusion-controlled electrochemical mass transfer technique has been employed to measure mass transfer coefficients. The heat transfer coefficients may be then readily obtained from the mass transfer values by applying the well-established Chilton-Colburn analogy. The results for the normal tube bank, which forms the base case for the study on inclined tube banks, show close agreement with previous work. The transfer coefficients and pressure drops of the inclined tube banks are compared with results from the ideal normal tube bank to examine the effect of inclination angle on heat transfer and pressure drop variations. The variation of the transfer coefficients row-by-row and the entrance and exit effects have also been investigated. An auxilary investigation has been carried out on the role of natural convection. A preliminary correlation of transfer coefficients and pressure drops against the variation in the yaw angle has been attempted. The results are discussed in the light of the few existing theoretical treatments and experimental data for these situations, and recommendations made for future work.

Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm

We investigate a digital back-propagation simplification method to enable computationally-efficient digital nonlinearity compensation for a coherently-detected 112 Gb/s polarization multiplexed quadrature phase shifted keying transmission over a 1,600 km link (20x80km) with no inline compensation. Through numerical simulation, we report up to 80% reduction in required back-propagation steps to perform nonlinear compensation, in comparison to the standard back-propagation algorithm. This method takes into account the correlation between adjacent symbols at a given instant using a weighted-average approach, and optimization of the position of nonlinear compensator stage to enable practical digital back-propagation.

Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers [Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013)1751-811310.1088/1751-8113/46/3/035501; Nath, Phys. Rev. E 88, 013010 (2013)PLEEE81539-375510.1103/PhysRevE.88.013010] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a "cold" accretion flow at 3000 K is too "hot" in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Quadratic behavior of fiber Bragg grating temperature coefficients

We describe the characterization of the temperature and strain responses of fiber Bragg grating sensors by use of an interferometric interrogation technique to provide an absolute measurement of the grating wavelength. The fiber Bragg grating temperature response was found to be nonlinear over the temperature range -70°C to 80°C. The nonlinearity was observed to be a quadratic function of temperature, arising from the linear dependence on temperature of the thermo-optic coefficient of silica glass over this range, and is in good agreement with a theoretical model.

Reduction of nonlinear intrachannel effects by channel asymmetry in transmission lines with strong bit overlapping

We have examined the statistics of simulated bit-error rates in optical transmission systems with strong patterning effects and have found strong correlation between the probability of marks in a pseudorandom pattern and the error-free transmission distance. We discuss how a reduced density of marks can be achieved by preencoding optical data.

Quadratic behaviour of fibre Bragg grating temperature coefficients

We describe the characterization of the temperature and strain responses of fiber Bragg grating sensors by use of an interferometric interrogation technique to provide an absolute measurement of the grating wavelength. The fiber Bragg grating temperature response was found to be nonlinear over the temperature range -70 °C to 80 °C. The nonlinearity was observed to be a quadratic function of temperature, arising from the linear dependence on temperature of the thermo-optic coefficient of silica glass over this range, and is in good agreement with a theoretical model.