Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Effect of amblyopia on the developmental eye movement test in children

Purpose. To investigate the functional impact of amblyopia in children, the performance of amblyopic and age-matched control children on a clinical test of eye movements was compared. The influence of visual factors on test outcome measures was explored. Methods. Eye movements were assessed with the Developmental Eye Movement (DEM) test, in a group of children with amblyopia (n = 39; age, 9.1 ± 0.9 years) of different causes (infantile esotropia, n = 7; acquired strabismus, n = 10; anisometropia, n = 8; mixed, n = 8; deprivation, n = 6) and in an age-matched control group (n = 42; age, 9.3 ± 0.4 years). LogMAR visual acuity (VA), stereoacuity, and refractive error were also recorded in both groups. Results. No significant difference was found between the amblyopic and age-matched control group for any of the outcome measures of the DEM (vertical time, horizontal time, number of errors and ratio(horizontal time/vertical time)). The DEM measures were not significantly related to VA in either eye, level of binocular function (stereoacuity), history of strabismus, or refractive error. Conclusions. The performance of amblyopic children on the DEM, a commonly used clinical measure of eye movements, has not previously been reported. Under habitual binocular viewing conditions, amblyopia has no effect on DEM outcome scores despite significant impairment of binocular vision and decreased VA in both the better and worse eye.

The effect of Amblyopia on motor and psychosocial skills in children

Background/Aims: In an investigation of the functional impact of amblyopia on children, the fine motor skills, perceived self-esteem and eye movements of amblyopic children were compared with that of age-matched controls. The influence of amblyogenic condition or treatment factors that might predict any decrement in outcome measures was investigated. The relationship between indirect measures of eye movements that are used clinically and eye movement characteristics recorded during reading was examined and the relevance of proficiency in fine motor skills to performance on standardised educational tests was explored in a sub-group of the control children. Methods: Children with amblyopia (n=82; age 8.2 ± 1.3 years) from differing causes (infantile esotropia n=17, acquired strabismus n=28, anisometropia n=15, mixed n=13 and deprivation n=9), and a control group of children (n=106; age 9.5 ± 1.2 years) participated in this study. Measures of visual function included monocular logMAR visual acuity (VA) and stereopsis assessed with the Randot Preschool Stereoacuity test, while fine motor skills were measured using the Visual-Motor Control (VMC) and Upper Limb Speed and Dexterity (ULSD) subtests of the Brunicks-Oseretsky Test of Motor Proficiency. Perceived self esteem was assessed for those children from grade 3 school level with the Harter Self Perception Profile for Children and for those in younger grades (preschool to grade 2) with the Pictorial Scale of Perceived Competence and Acceptance for Young Children. A clinical measure of eye movements was made with the Developmental Eye Movement (DEM) test for those children aged eight years and above. For appropriate case-control comparison of data, the results from amblyopic children were compared with age-matched sub-samples drawn from the group of children with normal vision who completed the tests. Eye movements during reading for comprehension were recorded by the Visagraph infra-red recording system and results of standardised tests of educational performance were also obtained for a sub-set of the control group. Results Amblyopic children (n=82; age 8.2 ± 1.7 years) performed significantly poorer than age-matched control children (n=37; age 8.3 ± 1.3 years) on 9 of 16 fine motor skills sub-items and for the overall age-standardised scores for both VMC and ULSD items (p<0.05); differences were most evident on timed manual dexterity tasks. The underlying aetiology of amblyopia and level of stereoacuity significantly affected fine motor skill performance on both items. However, when examined in a multiple regression model that took into account the inter-correlation between visual characteristics, poorer fine motor skills performance was only associated with strabismus (F1,75 = 5.428; p =0. 022), and not with the level of stereoacuity, refractive error or visual acuity in either eye. Amblyopic children from grade 3 school level and above (n=47; age 9.2 ± 1.3 years), particularly those with acquired strabismus, had significantly lower social acceptance scores than age-matched control children (n=52; age 9.4 ± 0.5 years) (F(5,93) = 3.14; p = 0.012). However, the scores of the amblyopic children were not significantly different to controls for other areas related to self-esteem, including scholastic competence, physical appearance, athletic competence, behavioural conduct and global self worth. A lower social acceptance score was independently associated with a history of treatment with patching but not with a history of strabismus or wearing glasses. Amblyopic children from pre-school to grade 2 school level (n=29; age = 6.6 ± 0.6 years) had similar self-perception scores to their age-matched peers (n=20; age = 6.4 ± 0.5 years). There were no significant differences between the amblyopic (n=39; age 9.1 ± 0.9 years) and age-matched control (n = 42; age = 9.3 ± 0.38 years) groups for any of the DEM outcome measures (Vertical Time, Horizontal Time, Number of Errors and Ratio (Horizontal time/Vertical time)). Performance on the DEM did not significantly relate to measures of VA in either eye, level of binocular function, history of strabismus or refractive error. Developmental Eye Movement test outcome measures Horizontal Time and Vertical Time were significantly correlated with reading rates measured by the Visagraph for both reading for comprehension and naming numbers (r>0.5). Some moderate correlations were also seen between the DEM Ratio and word reading rates as recorded by Visagraph (r=0.37). In children with normal vision, academic scores in mathematics, spelling and reading were associated with measures of fine motor skills. Strongest effect sizes were seen with the timed manual dexterity domain, Upper Limb Speed and Dexterity. Conclusions Amblyopia may have a negative impact on a child’s fine motor skills and an older child’s sense of acceptance by their peers may be influenced by treatment that includes eye patching. Clinical measures of eye movements were not affected in amblyopic children. A number of the outcome measures of the DEM are associated with objective recordings of reading rates, supporting its clinical use for identification of children with slower reading rates. In children with normal vision, proficiency on clinical measures of fine motor skill are associated with outcomes on standardised measures of educational performance. Scores on timed manual dexterity tasks had the strongest association with educational performance. Collectively, the results of this study indicate that, in addition to the reduction in visual acuity and binocular function that define the condition, amblyopes have functional impairment in childhood development skills that underlie proficiency in everyday activities. The study provides support for strategies aimed at early identification and remediation of amblyopia and the co-morbidities that arise from abnormal visual neurodevelopment.

Mixing colours : an ICT tool based on a semiotic framework for mathematical meaning-making about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

The efficacy of the Sortino ratio and other benchmarked performance measures under skewed return distributions

This paper will investigate the suitability of existing performance measures under the assumption of a clearly defined benchmark. A range of measures are examined including the Sortino Ratio, the Sharpe Selection ratio (SSR), the Student’s t-test and a decay rate measure. A simulation study is used to assess the power and bias of these measures based on variations in sample size and mean performance of two simulated funds. The Sortino Ratio is found to be the superior performance measure exhibiting more power and less bias than the SSR when the distribution of excess returns are skewed.

The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

A preliminary investigation of the role of the Phenylalynine: Tyrosine Ratio in children with early and continuously treated phenylketonuria : toward identification of “safe” levels

Children with early and continuously treated phenylketonuria (ECT-PKU) remain at risk of developing executive function (EF) deficits. There is some evidence that a high phenylalanine to tyrosine ratio (phe:tyr) is more strongly associated with impaired EF development than high phenylalanine alone. This study examined EF in a sample of 11 adolescents against concurrent and historical levels of phenylalanine, phe:tyr, and tyrosine. Lifetime measures of phe:tyr were more strongly associated with EF than phenylalanine-only measures. Children with a lifetime phe:tyr less than 6 demonstrated normal EF, whereas children who had a lifetime phe:tyr above 6, on average, demonstrated clinically impaired EF.

Are SC-FDE systems robust to CFO?

This paper investigates the impact of carrier frequency offset (CFO) on Single Carrier wireless communication systems with Frequency Domain Equalization (SC-FDE). We show that CFO in SC-FDE systems causes irrecoverable channel estimation error, which leads to inter-symbol-interference (ISI). The impact of CFO on SC-FDE and OFDM is compared in the presence of CFO and channel estimation errors. Closed form expressions of signal to interference and noise ratio (SINR) are derived for both systems, and verified by simulation results. We find that when channel estimation errors are considered, SC-FDE is similarly or even more sensitive to CFO, compared to OFDM. In particular, in SC-FDE systems, CFO mainly deteriorates the system performance via degrading the channel estimation. Both analytical and simulation results highlight the importance of accurate CFO estimation in SC-FDE systems.

Peak-to-average power ratio of IEEE 802.11a PHY layer signals

In this chapter we propose clipping with amplitude and phase corrections to reduce the peak-to-average power ratio (PAR) of orthogonal frequency division multiplexed (OFDM) signals in high-speed wireless local area networks defined in IEEE 802.11a physical layer. The proposed techniques can be implemented with a small modification at the transmitter and the receiver remains standard compliant. PAR reduction as much as 4dB can be achieved by selecting a suitable clipping ratio and a correction factor depending on the constellation used. Out of band noise (OBN) is also reduced.

Coding speech signals at very low rates (below 1 kb/s) with high intelligibility

This thesis presents an original approach to parametric speech coding at rates below 1 kbitsjsec, primarily for speech storage applications. Essential processes considered in this research encompass efficient characterization of evolutionary configuration of vocal tract to follow phonemic features with high fidelity, representation of speech excitation using minimal parameters with minor degradation in naturalness of synthesized speech, and finally, quantization of resulting parameters at the nominated rates. For encoding speech spectral features, a new method relying on Temporal Decomposition (TD) is developed which efficiently compresses spectral information through interpolation between most steady points over time trajectories of spectral parameters using a new basis function. The compression ratio provided by the method is independent of the updating rate of the feature vectors, hence allows high resolution in tracking significant temporal variations of speech formants with no effect on the spectral data rate. Accordingly, regardless of the quantization technique employed, the method yields a high compression ratio without sacrificing speech intelligibility. Several new techniques for improving performance of the interpolation of spectral parameters through phonetically-based analysis are proposed and implemented in this research, comprising event approximated TD, near-optimal shaping event approximating functions, efficient speech parametrization for TD on the basis of an extensive investigation originally reported in this thesis, and a hierarchical error minimization algorithm for decomposition of feature parameters which significantly reduces the complexity of the interpolation process. Speech excitation in this work is characterized based on a novel Multi-Band Excitation paradigm which accurately determines the harmonic structure in the LPC (linear predictive coding) residual spectra, within individual bands, using the concept 11 of Instantaneous Frequency (IF) estimation in frequency domain. The model yields aneffective two-band approximation to excitation and computes pitch and voicing with high accuracy as well. New methods for interpolative coding of pitch and gain contours are also developed in this thesis. For pitch, relying on the correlation between phonetic evolution and pitch variations during voiced speech segments, TD is employed to interpolate the pitch contour between critical points introduced by event centroids. This compresses pitch contour in the ratio of about 1/10 with negligible error. To approximate gain contour, a set of uniformly-distributed Gaussian event-like functions is used which reduces the amount of gain information to about 1/6 with acceptable accuracy. The thesis also addresses a new quantization method applied to spectral features on the basis of statistical properties and spectral sensitivity of spectral parameters extracted from TD-based analysis. The experimental results show that good quality speech, comparable to that of conventional coders at rates over 2 kbits/sec, can be achieved at rates 650-990 bits/sec.

Adaptive instantaneous frequency estimation: Techniques and algorithms

This thesis deals with the problem of the instantaneous frequency (IF) estimation of sinusoidal signals. This topic plays significant role in signal processing and communications. Depending on the type of the signal, two major approaches are considered. For IF estimation of single-tone or digitally-modulated sinusoidal signals (like frequency shift keying signals) the approach of digital phase-locked loops (DPLLs) is considered, and this is Part-I of this thesis. For FM signals the approach of time-frequency analysis is considered, and this is Part-II of the thesis. In part-I we have utilized sinusoidal DPLLs with non-uniform sampling scheme as this type is widely used in communication systems. The digital tanlock loop (DTL) has introduced significant advantages over other existing DPLLs. In the last 10 years many efforts have been made to improve DTL performance. However, this loop and all of its modifications utilizes Hilbert transformer (HT) to produce a signal-independent 90-degree phase-shifted version of the input signal. Hilbert transformer can be realized approximately using a finite impulse response (FIR) digital filter. This realization introduces further complexity in the loop in addition to approximations and frequency limitations on the input signal. We have tried to avoid practical difficulties associated with the conventional tanlock scheme while keeping its advantages. A time-delay is utilized in the tanlock scheme of DTL to produce a signal-dependent phase shift. This gave rise to the time-delay digital tanlock loop (TDTL). Fixed point theorems are used to analyze the behavior of the new loop. As such TDTL combines the two major approaches in DPLLs: the non-linear approach of sinusoidal DPLL based on fixed point analysis, and the linear tanlock approach based on the arctan phase detection. TDTL preserves the main advantages of the DTL despite its reduced structure. An application of TDTL in FSK demodulation is also considered. This idea of replacing HT by a time-delay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the time-delay in the presence of additive Gaussian noise. Based on the above analysis, the behavior of the first and second-order TDTLs has been analyzed in additive Gaussian noise. Since DPLLs need time for locking, they are normally not efficient in tracking the continuously changing frequencies of non-stationary signals, i.e. signals with time-varying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequency-modulated (FM) signals widely used in communication systems. Part-II of this thesis is dedicated for the IF estimation of non-stationary signals. For such signals the classical spectral techniques break down, due to the time-varying nature of their spectra, and more advanced techniques should be utilized. For the purpose of instantaneous frequency estimation of non-stationary signals there are two major approaches: parametric and non-parametric. We chose the non-parametric approach which is based on time-frequency analysis. This approach is computationally less expensive and more effective in dealing with multicomponent signals, which are the main aim of this part of the thesis. A time-frequency distribution (TFD) of a signal is a two-dimensional transformation of the signal to the time-frequency domain. Multicomponent signals can be identified by multiple energy peaks in the time-frequency domain. Many real life and synthetic signals are of multicomponent nature and there is little in the literature concerning IF estimation of such signals. This is why we have concentrated on multicomponent signals in Part-H. An adaptive algorithm for IF estimation using the quadratic time-frequency distributions has been analyzed. A class of time-frequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are time-only or one-dimensional, rather than the time-lag (two-dimensional) kernels. Hence this class has been named as the T -class. If the parameters of these TFDs are properly chosen, they are more efficient than the existing fixed-kernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The T-distributions has been used in the IF adaptive algorithm and proved to be efficient in tracking rapidly changing frequencies. They also enables direct amplitude estimation for the components of a multicomponent

Modelling photochemical production of fine particulates in a toluene/NOx/water vapour system

This work investigates the computer modelling of the photochemical formation of smog products such as ozone and aerosol, in a system containing toluene, NOx and water vapour. In particular, the problem of modelling this process in the Commonwealth Scientific and Industrial Research Organization (CSIRO) smog chambers, which utilize outdoor exposure, is addressed. The primary requirement for such modelling is a knowledge of the photolytic rate coefficients. Photolytic rate coefficients of species other than N02 are often related to JNo2 (rate coefficient for the photolysis ofN02) by a simple factor, but for outdoor chambers, this method is prone to error as the diurnal profiles may not be similar in shape. Three methods for the calculation of diurnal JNo2 are investigated. The most suitable method for incorporation into a general model, is found to be one which determines the photolytic rate coefficients for N02, as well as several other species, from actinic flux, absorption cross section and quantum yields. A computer model was developed, based on this method, to calculate in-chamber photolysis rate coefficients for the CSIRO smog chambers, in which ex-chamber rate coefficients are adjusted by accounting for variation in light intensity by transmittance through the Teflon walls, albedo from the chamber floor and radiation attenuation due to clouds. The photochemical formation of secondary aerosol is investigated in a series of toluene-NOx experiments, which were performed in the CSIRO smog chambers. Three stages of aerosol formation, in plots of total particulate volume versus time, are identified: a delay period in which no significant mass of aerosol is formed, a regime of rapid aerosol formation (regime 1) and a second regime of slowed aerosol formation (regime 2). Two models are presented which were developed from the experimental data. One model is empirically based on observations of discrete stages of aerosol formation and readily allows aerosol growth profiles to be calculated. The second model is based on an adaptation of published toluene photooxidation mechanisms and provides some chemical information about the oxidation products. Both models compare favorably against the experimental data. The gross effects of precursor concentrations (toluene, NOx and H20) and ambient conditions (temperature, photolysis rate) on the formation of secondary aerosol are also investigated, primarily using the mechanism model. An increase in [NOx]o results in increased delay time, rate of aerosol formation in regime 1 and volume of aerosol formed in regime 1. This is due to increased formation of dinitrocresol and furanone products. An increase in toluene results in a decrease in the delay time and an increase in the rate of aerosol formation in regime 1, due to enhanced reactivity from the toluene products, such as the radicals from the photolysis of benzaldehyde. Water vapor has very little effect on the formation of aerosol volume, except that rates are slightly increased due to more OH radicals from reaction with 0(1D) from ozone photolysis. Increased temperature results in increased volume of aerosol formed in regime 1 (increased dinitrocresol formation), while increased photolysis rate results in increased rate of aerosol formation in regime 1. Both the rate and volume of aerosol formed in regime 2 are increased by increased temperature or photolysis rate. Both models indicate that the yield of secondary particulates from hydrocarbons (mass concentration aerosol formed/mass concentration hydrocarbon precursor) is proportional to the ratio [NOx]0/[hydrocarbon]0