Time complexity and convergence analysis of domain theoretic Picard method

We present an implementation of the domain-theoretic Picard method for solving initial value problems (IVPs) introduced by Edalat and Pattinson [1]. Compared to Edalat and Pattinson's implementation, our algorithm uses a more efficient arithmetic based on an arbitrary precision floating-point library. Despite the additional overestimations due to floating-point rounding, we obtain a similar bound on the convergence rate of the produced approximations. Moreover, our convergence analysis is detailed enough to allow a static optimisation in the growth of the precision used in successive Picard iterations. Such optimisation greatly improves the efficiency of the solving process. Although a similar optimisation could be performed dynamically without our analysis, a static one gives us a significant advantage: we are able to predict the time it will take the solver to obtain an approximation of a certain (arbitrarily high) quality.

Appearance of bound states in random potentials with applications to soliton theory

We analyze the stochastic creation of a single bound state (BS) in a random potential with a compact support. We study both the Hermitian Schrödinger equation and non-Hermitian Zakharov-Shabat systems. These problems are of special interest in the inverse scattering method for Korteveg–de-Vries and the nonlinear Schrödinger equations since soliton solutions of these two equations correspond to the BSs of the two aforementioned linear eigenvalue problems. Analytical expressions for the average width of the potential required for the creation of the first BS are given in the approximation of delta-correlated Gaussian potential and additionally different scenarios of eigenvalue creation are discussed for the non-Hermitian case.

A smart sensing platform for the discrimination of human movement

This thesis documents the design, implementation and testing of a smart sensing platform that is able to discriminate between differences or small changes in a persons walking. The distributive tactile sensing method is used to monitor the deflection of the platform surface using just a small number of sensors and, through the use of neural networks, infer the characteristics of the object in contact with the surface. The thesis first describes the development of a mathematical model which uses a novel method to track the position of a moving load as it passes over the smart sensing surface. Experimental methods are then described for using the platform to track the position of swinging pendulum in three dimensions. It is demonstrated that the method can be extended to that of real-time measurement of balance and sway of a person during quiet standing. Current classification methods are then investigated for use in the classification of different gait patterns, in particular to identify individuals by their unique gait pattern. Based on these observations, a novel algorithm is developed that is able to discriminate between abnormal and affected gait. This algorithm, using the distributive tactile sensing method, was found to have greater accuracy than other methods investigated and was designed to be able to cope with any type of gait variation. The system developed in this thesis has applications in the area of medical diagnostics, either as an initial screening tool for detecting walking disorders or to be able to automatically detect changes in gait over time. The system could also be used as a discrete biometric identification method, for example identifying office workers as they pass over the surface.

Developing solid particulate vaccine adjuvants - surface bound antigen favouring a humoural response, whereas entrapped antigen shows a tendency for cell mediated immunity

This present study compares the efficacy of microsphere formulations, and their method of antigen presentation, for the delivery of the TB sub-unit vaccine antigen, Ag85B-ESAT-6. Microspheres based on poly(lactide-co-glycolide) (PLGA) and chitosan incorporating dimethyldioctadecylammonium bromide (DDA) were prepared by either the w/o/w double emulsion method (entrapped antigen) or the o/w single emulsion method (surface bound antigen), and characterised for their physico-chemical properties and their ability to promote an immune response to Ag85B-ESAT-6. The method of preparation, and hence method of antigen association, had a pronounced effect on the type of immune response achieved from the microsphere formulations, with surface bound antigen favouring a humoural response, whereas entrapped antigen favoured a cellular response.

A method of fundamental solutions for two-dimensional heat conduction

We investigate an application of the method of fundamental solutions (MFS) to heat conduction in two-dimensional bodies, where the thermal diffusivity is piecewise constant. We extend the MFS proposed in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction, Eng. Anal. Bound. Elem. 32 (2008), pp. 697–703] for one-dimensional heat conduction with the sources placed outside the space domain of interest, to the two-dimensional setting. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be obtained efficiently with small computational cost.

Developing solid particulate vaccine adjuvants:surface bound antigen favouring a humoural response, whereas entrapped antigen shows a tendency for cell mediated immunity

This present study compares the efficacy of microsphere formulations, and their method of antigen presentation, for the delivery of the TB sub-unit vaccine antigen, Ag85B-ESAT-6. Microspheres based on poly(lactide-co-glycolide) (PLGA) and chitosan incorporating dimethyldioctadecylammonium bromide (DDA) were prepared by either the w/o/w double emulsion method (entrapped antigen) or the o/w single emulsion method (surface bound antigen), and characterised for their physico-chemical properties and their ability to promote an immune response to Ag85B-ESAT-6. The method of preparation, and hence method of antigen association, had a pronounced effect on the type of immune response achieved from the microsphere formulations, with surface bound antigen favouring a humoural response, whereas entrapped antigen favoured a cellular response.

FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials

In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results indicate that whereas F LQ runs on average faster (or quite faster) than LM Q, nonetheless the quality of the bounds computed by both is about the same; moreover, it was revealed that when VAS-CF is run on our benchmark polynomials using F LQ, LM Q and min(F LQ, LM Q) all three versions run equally well and, hence, it is inconclusive which one should be used in the VAS-CF method.

Discrimination of healthy and cancer cells of the bladder by metabolic state, based on autofluorescence

Bladder cancer is among the most common cancers worldwide (4th in men). It is responsible for high patient morbidity and displays rapid recurrence and progression. Lack of sensitivity of gold standard techniques (white light cystoscopy, voided urine cytology) means many early treatable cases are missed. The result is a large number of advanced cases of bladder cancer which require extensive treatment and monitoring. For this reason, bladder cancer is the single most expensive cancer to treat on a per patient basis. In recent years, autofluorescence spectroscopy has begun to shed light into disease research. Of particular interest in cancer research are the fluorescent metabolic cofactors NADH and FAD. Early in tumour development, cancer cells often undergo a metabolic shift (the Warburg effect) resulting in increased NADH. The ratio of NADH to FAD ("redox ratio") can therefore be used as an indicator of the metabolic status of cells. Redox ratio measurements have been used to differentiate between healthy and cancer breast cells and to monitor cellular responses to therapies. Here, we have demonstrated, using healthy and bladder cancer cell lines, a statistically significant difference in the redox ratio of bladder cancer cells, indicative of a metabolic shift. To do this we customised a standard flow cytometer to excite and record fluorescence specifically from NADH and FAD, along with a method for automatically calculating the redox ratio of individual cells within large populations. These results could inform the design of novel probes and screening systems for the early detection of bladder cancer.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

The discrimination and association of float glass and the quantitative analysis of liquids from aerosols and microdrops using laser induced breakdown spectroscopy

Glass is a common form of trace evidence found at many scenes of crimes in the form of small fragments. These glass fragments can transfer to surrounding objects and/or persons and may provide forensic investigators valuable information to link a suspect to the scene of a crime. Since the elemental composition of different glass sources can be very similar, a highly discriminating technique is required to distinguish between fragments that have originated from different sources. ^ The research presented here demonstrates that Laser Induced Breakdown Spectroscopy (LIBS) is a viable analytical technique for the association and discrimination of glass fragments. The first part of this research describes the optimization of the LIBS experiments including the use of different laser wavelengths to investigate laser-material interaction. The use of a 266 nm excitation laser provided the best analytical figures of merit with minimal damage to the sample. The resulting analytical figures of merit are presented. The second part of this research evaluated the sensitivity of LIBS to associate or discriminate float glass samples originating from the same manufacturing plants and produced at approximately the same time period. Two different sample sets were analyzed ranging in manufacturing dates from days to years apart. Eighteen (18) atomic emission lines corresponding to the elements Sr, K, Fe, Ca, Al, Ba, Na, Mg and Ti, were chosen because of their detection above the method detection limits and for presenting differences between the samples. Ten elemental ratios producing the most discrimination were selected for each set. When all the ratios are combined in a comparison, 99% of the possible pairs were discriminated using the optimized LIBS method generating typical analytical precisions of ∼5% RSD. ^ The final study consisted of the development of a new approach for the use of LIBS as a quantitative analysis of ultra-low volume solution analysis using aerosols and microdrops. Laser induced breakdown spectroscopy demonstrated to be an effective technique for the analysis of as low as 90 pL for microdrop LIBS with 1 pg absolute LOD and 20 µL for aerosol LIBS with an absolute LOD of ∼100 fg.^

A comparison of the Kodaly method and the traditional method to determine pitch accuracy in grade 6 choral sight-singing

The purpose of this study was to determine which of the two methods is more appropriate to teach pitch discrimination to Grade 6 choral students to improve sight-singing note accuracy. This study consisted of three phases: pre-testing, instruction and post-testing. During the four week study, the experimental group received training using the Kodaly method while the control group received training using the traditional method. The pre and post tests were evaluated by three trained musicians. The analysis of the data utilized an independent t-test and a paired t-test with the methods of teaching (experimental and control) as a factor. Quantitative results suggest that the experimental subjects, those receiving Kodaly instruction at post-treatment showed a significant improvement in the pitch accuracy than the control group. The specific change resulted in the Kodaly method to be more effective in producing accurate pitch in sight-singing.

Absolute abundances of dinoflagellate cysts in surface sediment samples from four sites: Lycopodium marker-grain method

Absolute abundances (concentrations) of dinoflagellate cysts are often determined through the addition of Lycopodium clavatum marker-grains as a spike to a sample before palynological processing. An inter-laboratory calibration exercise was set up in order to test the comparability of results obtained in different laboratories, each using its own preparation method. Each of the 23 laboratories received the same amount of homogenized splits of four Quaternary sediment samples. The samples originate from different localities and consisted of a variety of lithologies. Dinoflagellate cysts were extracted and counted, and relative and absolute abundances were calculated. The relative abundances proved to be fairly reproducible, notwithstanding a need for taxonomic calibration. By contrast, excessive loss of Lycopodium spores during sample preparation resulted in non-reproducibility of absolute abundances. Use of oxidation, KOH, warm acids, acetolysis, mesh sizes larger than 15 µm and long ultrasonication (> 1 min) must be avoided to determine reproducible absolute abundances. The results of this work therefore indicate that the dinoflagellate cyst worker should make a choice between using the proposed standard method which circumvents critical steps, adding Lycopodium tablets at the end of the preparation and using an alternative method.

Improving the estimation of psychometric functions in 2AFC discrimination tasks.

Ulrich and Vorberg (2009) presented a method that fits distinct functions for each order of presentation of standard and test stimuli in a two-alternative forced-choice (2AFC) discrimination task, which removes the contaminating influence of order effects from estimates of the difference limen. The two functions are fitted simultaneously under the constraint that their average evaluates to 0.5 when test and standard have the same magnitude, which was regarded as a general property of 2AFC tasks. This constraint implies that physical identity produces indistinguishability, which is valid when test and standard are identical except for magnitude along the dimension of comparison. However, indistinguishability does not occur at physical identity when test and standard differ on dimensions other than that along which they are compared (e.g., vertical and horizontal lines of the same length are not perceived to have the same length). In these cases, the method of Ulrich and Vorberg cannot be used. We propose a generalization of their method for use in such cases and illustrate it with data from a 2AFC experiment involving length discrimination of horizontal and vertical lines. The resultant data could be fitted with our generalization but not with the method of Ulrich and Vorberg. Further extensions of this method are discussed.

Visual Discrimination Increase by Yellow Filters in Retinitis Pigmentosa

PURPOSE: The objective of this study was to evaluate, by halometry and under low illumination conditions, the effects of short-wavelength light absorbance filters on visual discrimination capacity in retinitis pigmentosa patients. METHODS: This was an observational, prospective, analytic, and transversal study on 109 eyes of 57 retinitis pigmentosa patients with visual acuity better than 1.25 logMAR. Visual disturbance index (VDI) was determined using the software Halo 1.0, with and without the interposition of filters which absorb (totally or partially) short-wavelength light between 380 and 500 nm. RESULTS: A statistically significant reduction in the VDI values determined using filters which absorb short-wavelength light was observed (p < 0.0001). The established VDIs in patients with VA logMAR <0.4 were 0.30 ± 0.05 (95% CI, 0.26–0.36) for the lens alone, 0.20 ± 0.04 (95% CI, 0.16–0.24) with the filter that completely absorbs wavelengths shorter than 450 nm, and 0.24 ± 0.04 (95% CI, 0.20–0.28) with the filter that partially absorbs wavelengths shorter than 450 nm, which implies a 20 to 33% visual discrimination capacity increase. In addition, a decrease of VDI in at least one eye was observed in more than 90% of patients when using a filter. CONCLUSIONS: Short-wavelength light absorbance filters increase visual discrimination capacity under low illumination conditions in retinitis pigmentosa patients. Use of such filters constitutes a suitable method to improve visual quality related to intraocular light visual disturbances under low illumination conditions in this group of patients. © 2016 American Academy of Optometry

Origin discrimination and quality evaluation of Gastrodiae rhizoma (Orchidaceae) by high-performance liquid chromatographic fingerprint

Purpose: To develop a high-performance liquid chromatography (HPLC) fingerprint method for the quality control and origin discrimination of Gastrodiae rhizoma . Methods: Twelve batches of G. rhizoma collected from Sichuan, Guizhou and Shanxi provinces in china were used to establish the fingerprint. The chromatographic peak (gastrodin) was taken as the reference peak, and all sample separation was performed on a Agilent C18 (250 mm×4.6 mmx5 μm) column with a column temperature of 25 °C. The mobile phase was acetonitrile/0.8 % phosphate water solution (in a gradient elution mode) and the flow rate of 1 mL/min. The detection wavelength was 270 nm. The method was validated as per the guidelines of Chinese Pharmacopoeia. Results: The chromatograms of the samples showed 11 common peaks, of which no. 4 was identified as that of Gastrodin. Data for the samples were analyzed statistically using similarity analysis and hierarchical cluster analysis (HCA). The similarity index between reference chromatogram and samples’ chromatograms were all > 0.80. The similarity index of G. rhizoma from Guizhou, Shanxi and Sichuan is evident as follows: 0.854 - 0.885, 0.915 - 0.930 and 0.820 - 0.848, respectively. The samples could be divided into three clusters at a rescaled distance of 7.5: S1 - S4 as cluster 1; S5 - S8 cluster 2, and others grouped into cluster 3. Conclusion: The findings indicate that HPLC fingerprinting technology is appropriate for quality control and origin discrimination of G. rhizoma.