A comparisation of methods for the optimisation of a non-linear function subject to non-linear constraints

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The electron optical limits of performance of single-polepiece magnetic electron lenses

The thesis is concerned with the electron properties of single-polepiece magnetic electron lenses especially under conditions of extreme polepiece saturation. The electron optical properties are first analysed under conditions of high polepiece permeability. From this analysis, a general idea can be obtained of the important parameters that affect ultimate lens performance. In addition, useful information is obtained concerning the design of improved lenses operating under conditions of extreme polepiece saturation, for example at flux densities of the order of 10 Tesla. It is shown that in a single-polepiece lens , the position and shape of the lens exciting coil plays an important role. In particular, the maximum permissible current density in the windings,rather than the properties of the iron, can set a limit to lens performance. This factor was therefore investigated in some detail. The axial field distribution of a single-polepiece lens, unlike that of a conventional lens, is highly asymmetrical. There are therefore two possible physical arrangements of the lens with respect to the incoming electron beam. In general these two orientations will result in different aberration coefficients. This feature has also been investigated in some detail. Single-pole piece lenses are thus considerably more complicated electron- optically than conventional double polepiece lenses. In particular, the absence of the usual second polepiece causes most of the axial magnetic flux density distribution to lie outside the body of the lens. This can have many advantages in electron microscopy but it creates problems in calculating the magnetic field distribution. In particular, presently available computer programs are liable to be considerably in error when applied to such structures. It was therefore necessary to find independent ways of checking the field calculations. Furthermore, if the polepiece is allowed to saturate, much more calculation is involved since the field distribution becomes a non-linear function of the lens excitation. In searching for optimum lens designs, care was therefore taken to ensure that the coil was placed in the optimum position. If this condition is satisfied there seems to be no theoretical limit to the maximum flux density that can be attained at the polepiece tip. However , under iron saturation condition, some broadening of the axial field distribution will take place, thereby changing the lens aberrations . Extensive calculations were therefore made to find the minimum spherical and chromatic aberration coefficients . The focal properties of such lens designs are presented and compared with the best conventional double-polepiece lenses presently available.

Incremental nature of anterior eye grading scales determined by objective image analysis

Aim: To use previously validated image analysis techniques to determine the incremental nature of printed subjective anterior eye grading scales. Methods: A purpose designed computer program was written to detect edges using a 3 × 3 kernal and to extract colour planes in the selected area of an image. Annunziato and Efron pictorial, and CCLRU and Vistakon-Synoptik photographic grades of bulbar hyperaemia, palpebral hyperaemia roughness, and corneal staining were analysed. Results: The increments of the grading scales were best described by a quadratic rather than a linear function. Edge detection and colour extraction image analysis for bulbar hyperaemia (r2 = 0.35-0.99), palpebral hyperaemia (r2 = 0.71-0.99), palpebral roughness (r2 = 0.30-0.94), and corneal staining (r2 = 0.57-0.99) correlated well with scale grades, although the increments varied in magnitude and direction between different scales. Repeated image analysis measures had a 95% confidence interval of between 0.02 (colour extraction) and 0.10 (edge detection) scale units (on a 0-4 scale). Conclusion: The printed grading scales were more sensitive for grading features of low severity, but grades were not comparable between grading scales. Palpebral hyperaemia and staining grading is complicated by the variable presentations possible. Image analysis techniques are 6-35 times more repeatable than subjective grading, with a sensitivity of 1.2-2.8% of the scale.

Quantification of the relationship between, magnetoencephalographic (MEG) and blood oxygenation dependent (BOLD) images of brain function

Magnetoencephalography (MEG) is the measurement of the magnetic fields generated outside the head by the brain’s electrical activity. The technique offers the promise of high temporal and spatial resolution. There is however an ambiguity in the inversion process of estimating what goes on inside the head from what is measured outside. Other techniques, such as functional Magnetic Resonance Imaging (fMRI) have no such inversion problems yet suffer from poorer temporal resolution. In this study we examined metrics of mutual information and linear correlation between volumetric images from the two modalities. Measures of mutual information reveal a significant, non-linear, relationship between MEG and fMRI datasets across a number of frequency bands.

A randomized controlled trial of the effect of thyroxine replacement on cognitive function in community-living elderly subjects with subclinical hypothyroidism: the Birmingham elderly thyroid study

Context: Subclinical hypothyroidism (SCH) and cognitive dysfunction are both common in the elderly and have been linked. It is important to determine whether T4 replacement therapy in SCH confers cognitive benefit. Objective: Our objective was to determine whether administration of T4 replacement to achieve biochemical euthyroidism in subjects with SCH improves cognitive function. Design and Setting: We conducted a double-blind placebo-controlled randomized controlled trial in the context of United Kingdom primary care. Patients: Ninety-four subjects aged 65 yr and over (57 females, 37 males) with SCH were recruited from a population of 147 identified by screening. Intervention: T4 or placebo was given at an initial dosage of one tablet of either placebo or 25 µg T4 per day for 12 months. Thyroid function tests were performed at 8-weekly intervals with dosage adjusted in one-tablet increments to achieve TSH within the reference range for subjects in treatment arm. Fifty-two subjects received T4 (31 females, 21 males; mean age 73.5 yr, range 65–94 yr); 42 subjects received placebo (26 females, 16 males; mean age 74.2 yr, 66–84 yr). Main Outcome Measures: Mini-Mental State Examination, Middlesex Elderly Assessment of Mental State (covering orientation, learning, memory, numeracy, perception, attention, and language skills), and Trail-Making A and B were administered. Results: Eighty-two percent and 84% in the T4 group achieved euthyroidism at 6- and 12-month intervals, respectively. Cognitive function scores at baseline and 6 and 12 months were as follows: Mini-Mental State Examination T4 group, 28.26, 28.9, and 28.28, and placebo group, 28.17, 27.82, and 28.25 [not significant (NS)]; Middlesex Elderly Assessment of Mental State T4 group, 11.72, 11.67, and 11.78, and placebo group, 11.21, 11.47, and 11.44 (NS); Trail-Making A T4 group, 45.72, 47.65, and 44.52, and placebo group, 50.29, 49.00, and 46.97 (NS); and Trail-Making B T4 group, 110.57, 106.61, and 96.67, and placebo group, 131.46, 119.13, and 108.38 (NS). Linear mixed-model analysis demonstrated no significant changes in any of the measures of cognitive function over time and no between-group difference in cognitive scores at 6 and 12 months. Conclusions: This RCT provides no evidence for treating elderly subjects with SCH with T4 replacement therapy to improve cognitive function.

A stepwise fuzzy linear programming model with possibility and necessity relations

Linear programming (LP) is the most widely used optimization technique for solving real-life problems because of its simplicity and efficiency. Although conventional LP models require precise data, managers and decision makers dealing with real-world optimization problems often do not have access to exact values. Fuzzy sets have been used in the fuzzy LP (FLP) problems to deal with the imprecise data in the decision variables, objective function and/or the constraints. The imprecisions in the FLP problems could be related to (1) the decision variables; (2) the coefficients of the decision variables in the objective function; (3) the coefficients of the decision variables in the constraints; (4) the right-hand-side of the constraints; or (5) all of these parameters. In this paper, we develop a new stepwise FLP model where fuzzy numbers are considered for the coefficients of the decision variables in the objective function, the coefficients of the decision variables in the constraints and the right-hand-side of the constraints. In the first step, we use the possibility and necessity relations for fuzzy constraints without considering the fuzzy objective function. In the subsequent step, we extend our method to the fuzzy objective function. We use two numerical examples from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and the computational efficiency of the procedures and algorithms. © 2013-IOS Press and the authors. All rights reserved.

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs. © 2014 Springer International Publishing Switzerland.

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.

Impact of reduced complexity inverse Volterra series transfer function-based nonlinear equalizer in coherent OFDM systems for next-generation core networks

A modern electronic nonlinearity equalizer (NLE) based on inverse Volterra series transfer function (IVSTF) with reduced complexity is applied on coherent optical orthogonal frequency-division multiplexing (CO-OFDM) signals for next-generation long- and ultra-long-haul applications. The OFDM inter-subcarrier crosstalk effects are explored thoroughly using the IVSTF-NLE and compared with the case of linear equalization (LE) for transmission distances of up to 7000 km. © 2013 IEEE.

Monocyte subset counts associations with left ventricular systolic function post ST elevation myocardial infarction

Background: Monocytes are implicated in the initiation and progression of theatherosclerotic plaque contributing to plaque instability and rupture. Little is knownof the role played by the 3 phenotypically and functionally different monocytesubpopulations in determining ventricular remodeling following ST elevation my-ocardial infarction (STEMI). Mon1 are "classical" inflammatory monocytes, whilstMon3 are considered reparative with fibroblast deposition ability. The function ofthe newly described Mon2 is yet to be elucidated. Method: STEMI patients (n=196, mean age 62±13 years; 72% male) treatedwith percutaneous revascularization were recruited within the first 24 hours. Pe-ripheral blood monocyte subpopulations were enumerated and characterizedusing flow cytometry after staining for CD14, CD16 and CCR2. Phenotypi-cally, monocyte subpopulations are defined as: CD14+CD16-CCR2+ (Mon1),CD14+CD16+CCR+ (Mon2) and CD14lowCD16+CCR2- (Mon3) cells. Transtho-racic 2D echocardiography was performed within 7 days and 6 months post infarctto assess ventricular volumes, mass, systolic, and diastolic functions. Results: Using linear regression analysis higher counts for Mon1, and lowercounts for Mon2 and Mon3 were significantly associated with the baseline leftventricular ejection fraction (LVEF) within seven days post infarction. At 6 monthspost STEMI lower counts of Mon2 remained positively associated with decreasedLVEF (p value= 0.002).Monocyte subsets correlation with LVEFMonocytes mean florescence Baseline left ventricular Left ventricular ejectionintensity (cells/μl) ejection fraction (%) fraction (%) at 6 months post infarctβ-value P-valueβ-value P-valueTotal Mon0.31 P<0.001 0.360.009Mon 10.019 0.020.070.62Mon 2−0.28 0.001 −0.420.002Mon 3−0.27 0.001 −0.180.21 Conclusion: Peripheral monocytes of all three subsets correlate with LVEF af-ter a myocardial infarction. High counts of the inflammatory Mon1 are associatedwith reduction in the baseline LVEF. Post remodelling, the convalescent EF wasindependently predicted by monocyte subpopulation 2. As lower counts depictednegative ventricular remodeling, this suggests a reparative role for the newly de-scribed Mon2, possibly via myofibroblast deposition and angiogenesis, in contrastto an anticipated inflammatory role.

Green's function for paraxial equation

The theory and experimental applications of optical Airy beams are in active development recently. The Airy beams are characterised by very special properties: they are non-diffractive and propagate along parabolic trajectories. Among the striking applications of the optical Airy beams are optical micro-manipulation implemented as the transport of small particles along the parabolic trajectory, Airy-Bessel linear light bullets, electron acceleration by the Airy beams, plasmonic energy routing. The detailed analysis of the mathematical aspects as well as physical interpretation of the electromagnetic Airy beams was done by considering the wave as a function of spatial coordinates only, related by the parabolic dependence between the transverse and the longitudinal coordinates. Their time dependence is assumed to be harmonic. Only a few papers consider a more general temporal dependence where such a relationship exists between the temporal and the spatial variables. This relationship is derived mostly by applying the Fourier transform to the expressions obtained for the harmonic time dependence or by a Fourier synthesis using the specific modulated spectrum near some central frequency. Spatial-temporal Airy pulses in the form of contour integrals is analysed near the caustic and the numerical solution of the nonlinear paraxial equation in time domain shows soliton shedding from the Airy pulse in Kerr medium. In this paper the explicitly time dependent solutions of the electromagnetic problem in the form of time-spatial pulses are derived in paraxial approximation through the Green's function for the paraxial equation. It is shown that a Gaussian and an Airy pulse can be obtained by applying the Green's function to a proper source current. We emphasize that the processes in time domain are directional, which leads to unexpected conclusions especially for the paraxial approximation.

On the group delay statistics of few-mode fibres with intermediate linear mode coupling

We report an investigation on the statistics of group delay for few-mode fibres operating in the weak and strong linear coupling regimes as well as in the intermediate coupling regime. A single expression linking the standard deviation of the group delay spread to the fibre linear mode coupling is validated for any coupling regime, considering up to six linearly polarized guided modes. Furthermore, the study of the probability density function of the group delays allowed deriving and validating an analytical estimation for the maximum group delay spread as a function of linear mode coupling.