Components of learning and assessment in linear algebra

Linear algebra provides theory and technology that are the cornerstones of a range of cutting edge mathematical applications, from designing computer games to complex industrial problems, as well as more traditional applications in statistics and mathematical modelling. Once past introductions to matrices and vectors, the challenges of balancing theory, applications and computational work across mathematical and statistical topics and problems are considerable, particularly given the diversity of abilities and interests in typical cohorts. This paper considers two such cohorts in a second level linear algebra course in different years. The course objectives and materials were almost the same, but some changes were made in the assessment package. In addition to considering effects of these changes, the links with achievement in first year courses are analysed, together with achievement in a following computational mathematics course. Some results that may initially appear surprising provide insight into the components of student learning in linear algebra.

An Investigation of Cognitive, Emotional and Negative Behavioural Responses to Service Recovery Strategies

Despite the best intentions of service providers and organisations, service delivery is rarely error-free. While numerous studies have investigated specific cognitive, emotional or behavioural responses to service failure and recovery, these studies do not fully capture the complexity of the services encounter. Consequently, this research develops a more holistic understanding of how specific service recovery strategies affect the responses of customers by combining two existing models—Smith & Bolton’s (2002) model of emotional responses to service performance and Fullerton and Punj’s (1993) structural model of aberrant consumer behaviour—into a conceptual framework. Specific service recovery strategies are proposed to influence consumer cognition, emotion and behaviour. This research was conducted using a 2x2 between-subjects quasi-experimental design that was administered via written survey. The experimental design manipulated two levels of two specific service recovery strategies: compensation and apology. The effect of the four recovery strategies were investigated by collecting data from 18-25 year olds and were analysed using multivariate analysis of covariance and multiple regression analysis. The results suggest that different service recovery strategies are associated with varying scores of satisfaction, perceived distributive justice, positive emotions, negative emotions and negative functional behaviour, but not dysfunctional behaviour. These finding have significant implications for the theory and practice of managing service recovery.

They also serve who only stand and wait

Purpose Waiting for service by customers is an important problem for many financial service marketers. Two new approaches are proposed. First, customer evaluation of the service is increased with an ambient scent. Second a cognitive variable is identified which different iates customers by the way they value time so that they can be segmented. Methodology Pretests included focus groups which highlighted financial services and a pilot test were foll owed by a main sample of 607 subjects. Structural equation modelling and multivariate analysis of covariance were used for analysis. Findings A cognitive variable, the need for time management can be used, together with demographic and customer net worth data, to segment a customer base. Two environmental interventions, music and scent, can increase customer satisfaction among customers kept waiting in a line. Research implications Two original approaches to a rapidly growing service marketing problem are identified. Practical implications Service contact points can reduce incidence of "queue rage" and enhance customer satisfaction by either or both of two simple modifications to the service environment or a preventive strategy of offering targeted customers an alternative. Originality A new method of segmentation and a new environmental intervention are proposed .

Delay-dependent robust H-infinity control for uncertain systems with time-varying delay

This paper proposes a new approach for delay-dependent robust H-infinity stability analysis and control synthesis of uncertain systems with time-varying delay. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional, the construction of an augmented matrix with uncorrelated terms, and the employment of a tighter bounding technique. As a result, significant performance improvement is achieved in system analysis and synthesis without using either free weighting matrices or model transformation. Examples are given to demonstrate the effectiveness of the proposed approach.

Fingerprinting of complex mixtures with the use of high performance liquid chromatography, inductively coupled plasma atomic emission spectroscopy and chemometrics

The molecular and metal profile fingerprints were obtained from a complex substance, Atractylis chinensis DC—a traditional Chinese medicine (TCM), with the use of the high performance liquid chromatography (HPLC) and inductively coupled plasma atomic emission spectroscopy (ICP-AES) techniques. This substance was used in this work as an example of a complex biological material, which has found application as a TCM. Such TCM samples are traditionally processed by the Bran, Cut, Fried and Swill methods, and were collected from five provinces in China. The data matrices obtained from the two types of analysis produced two principal component biplots, which showed that the HPLC fingerprint data were discriminated on the basis of the methods for processing the raw TCM, while the metal analysis grouped according to the geographical origin. When the two data matrices were combined into a one two-way matrix, the resulting biplot showed a clear separation on the basis of the HPLC fingerprints. Importantly, within each different grouping the objects separated according to their geographical origin, and they ranked approximately in the same order in each group. This result suggested that by using such an approach, it is possible to derive improved characterisation of the complex TCM materials on the basis of the two kinds of analytical data. In addition, two supervised pattern recognition methods, K-nearest neighbors (KNNs) method, and linear discriminant analysis (LDA), were successfully applied to the individual data matrices—thus, supporting the PCA approach.

Small molecule–biopolymer interactions : Ultraviolet–visible and fluorescence spectroscopy and chemometrics

Interactions between small molecules with biopolymers e.g. the bovine serum albumin (BSA protein), are important, and significant information is recorded in the UV–vis and fluorescence spectra of their reaction mixtures. The extraction of this information is difficult conventionally and principally because there is significant overlapping of the spectra of the three analytes in the mixture. The interaction of berberine chloride (BC) and the BSA protein provides an interesting example of such complex systems. UV–vis and fluorescence spectra of BC and BSA mixtures were investigated in pH 7.4 Tris–HCl buffer at 37 °C. Two sample series were measured by each technique: (1) [BSA] was kept constant and the [BC] was varied and (2) [BC] was kept constant and the [BSA] was varied. This produced four spectral data matrices, which were combined into one expanded spectral matrix. This was processed by the multivariate curve resolution–alternating least squares method (MCR–ALS). The results produced: (1) the extracted pure BC, BSA and the BC–BSA complex spectra from the measured heavily overlapping composite responses, (2) the concentration profiles of BC, BSA and the BC–BSA complex, which are difficult to obtain by conventional means, and (3) estimates of the number of binding sites of BC.

Comparison of molecular markers to detect fresh sewage in environmental waters

Human-specific Bacteroides HF183 (HS-HF183), human-specific Enterococci faecium esp (HS-esp), human-specific adenoviruses (HS-AVs) and human-specific polyomaviruses (HS-PVs) assays were evaluated in freshwater, seawater and distilled water to detect fresh sewage. The sewage spiked water samples were also tested for the concentrations of traditional fecal indicators (i.e., Escherichia coli, enterococci and Clostridium perfringens) and enteric viruses such as enteroviruses (EVs), sapoviruses (SVs), and torquetenoviruses (TVs). The overall host-specificity of the HS-HF183 marker to differentiate between humans and other animals was 98%. However, the HS-esp, HS-AVs and HS-PVs showed 100% hostspecificity. All the human-specific markers showed >97% sensitivity to detect human fecal pollution. E. coli, enterococci and, C. perfringens were detected up to dilutions of sewage 10_5, 10_4 and 10_3 respectively.HS-esp, HS-AVs, HS-PVs, SVs and TVs were detected up to dilution of sewage 10_4 whilst EVs were detected up to dilution 10_5. The ability of the HS-HF183 marker to detect freshsewagewas3–4 orders ofmagnitude higher than that of the HS-esp and viral markers. The ability to detect fresh sewage in freshwater, seawater and distilled water matrices was similar for human-specific bacterial and viral marker. Based on our data, it appears that human-specific molecular markers are sensitive measures of fresh sewage pollution, and the HS-HF183 marker appears to be the most sensitive among these markers in terms of detecting fresh sewage. However, the presence of the HS-HF183 marker in environmental waters may not necessarily indicate the presence of enteric viruses due to their high abundance in sewage compared to enteric viruses. More research is required on the persistency of these markers in environmental water samples in relation to traditional fecal indicators and enteric pathogens.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

Using information criteria to select the correct variance–covariance structure for longitudinal data in ecology

1. Ecological data sets often use clustered measurements or use repeated sampling in a longitudinal design. Choosing the correct covariance structure is an important step in the analysis of such data, as the covariance describes the degree of similarity among the repeated observations. 2. Three methods for choosing the covariance are: the Akaike information criterion (AIC), the quasi-information criterion (QIC), and the deviance information criterion (DIC). We compared the methods using a simulation study and using a data set that explored effects of forest fragmentation on avian species richness over 15 years. 3. The overall success was 80.6% for the AIC, 29.4% for the QIC and 81.6% for the DIC. For the forest fragmentation study the AIC and DIC selected the unstructured covariance, whereas the QIC selected the simpler autoregressive covariance. Graphical diagnostics suggested that the unstructured covariance was probably correct. 4. We recommend using DIC for selecting the correct covariance structure.

Synthesis and characterization of sodalite–polyimide nanocomposite membranes

Nanocomposite membranes are fabricated from sodalite nanocrystals (Sod-N) dispersed in BTDA-MDA polyimide matrices and then characterized structurally and for gas separation. No voids are found upon investigation of the interfacial contact between the inorganic and organic phases, even at a Sod-N loading of up to 35 wt.%. This is due to the functionalization of the zeolite nanocrystals with amino groups (==Si_(CH3)(CH2)3NH2), which covalently link the particles to the polyimide chains in the matrices. The addition of Sod-N increases the hydrogen-gas permeability of the membranes, while nitrogen permeability decreases. Overall, these nanocomposite membranes display substantial selectivity improvements. The sodalite–polyimide membrane containing 35 wt.% Sod-N has a hydrogen permeability of 8.0 Barrers and a H2/N2 ideal selectivity of 281 at 25 C whereas the plain polyimide membrane exhibits a hydrogen permeability of 7.0 Barrers and a H2/N2 ideal selectivity of 198 at the same testing temperature.

The role of fluid and emotional intelligence in malingering

The purpose of the present study was to examine the role of fluid (gf), social (SI) and emotional intelligence (EI) in faking the Beck Depression Inventory (2nd ed., BDI-II). Twenty-two students and 26 non-students completed Raven’s Advanced Progressive Matrices (APM), a social insight test, the Schutte et al. self-report EI scale, and the BDI-II under honest and faking instructions. Results were consistent with a new model of successful faking, in which a participant’s original response must be manipulated into a strategic response, which must match diagnostic criteria. As hypothesised, the BDI-II could be faked, and gf was not related to faking ability. Counter to expectations, however, SI and EI were not related to faking ability. A second study explored why EI failed to facilitate faking. Forty-nine students and 50 non-students completed the EI measure, the Marlowe-Crown Scale and the Levenson et al. Psychopathy Scale. As hypothesised, EI was negatively correlated with psychopathy, but EI showed no relationship with socially desirable responding. It was concluded that in the first experiment, high-EI people did fake effectively, but high-psychopathy people (who had low EI) were also faking effectively, resulting in a distribution that showed no advantage to high EI individuals.

New Approach on Robust Delay-Dependent H∞ Control for Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust H∞ control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

Population Monte Carlo Algorithm in High Dimensions

The population Monte Carlo algorithm is an iterative importance sampling scheme for solving static problems. We examine the population Monte Carlo algorithm in a simplified setting, a single step of the general algorithm, and study a fundamental problem that occurs in applying importance sampling to high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of estimate under conditions on the importance function. We demonstrate the exponential growth of the asymptotic variance with the dimension and show that the optimal covariance matrix for the importance function can be estimated in special cases.

Diurnal variation of corneal shape and thickness

Purpose: To investigate associations between the diurnal variation in a range of corneal parameters, including anterior and posterior corneal topography, and regional corneal thickness. ----- Methods: Fifteen subjects had their corneas measured using a rotating Scheimpflug camera (Pentacam) every 3-7 hours over a 24-hour period. Anterior and posterior corneal axial curvature, pachymetry and anterior chamber depth were analysed. The best fitting corneal sphero-cylinder from the axial curvature, and the average corneal thickness for a series of different corneal regions were calculated. Intraocular pressure and axial length were also measured at each measurement session. Repeated measures ANOVA were used to investigate diurnal change in these parameters. Analysis of covariance was used to examine associations between the measured ocular parameters. ----- Results: Significant diurnal variation was found to occur in both the anterior and posterior corneal curvature and in the regional corneal thickness. Flattening of the anterior corneal best sphere was observed at the early morning measurement (p < 0.0001). The posterior cornea also underwent a significant steepening (p < 0.0001) and change in astigmatism 90/180° at this time. A significant swelling of the cornea (p < 0.0001) was also found to occur immediately after waking. Highly significant associations were found between the diurnal variation in corneal thickness and the changes in corneal curvature. ----- Conclusions: Significant diurnal variation occurs in the regional thickness and the shape of the anterior and posterior cornea. The largest changes in the cornea were typically evident upon waking. The observed non-uniform regional corneal thickness changes resulted in a steepening of the posterior cornea, and a flattening of the anterior cornea to occur at this time.

Concentrations of polybrominated diphenyl ethers (PBDEs) in matched samples of human milk, dust and indoor air

Polybrominated diphenyl ethers (PBDEs) are lipophilic, persistent pollutants found worldwide in environmental and human samples. Exposure pathways for PBDEs remain unclear but may include food, air and dust. The aim of this study was to conduct an integrated assessment of PBDE exposure and human body burden using 10 matched samples of human milk, indoor air and dust collected in 2007–2008 in Brisbane, Australia. In addition, temporal analysis was investigated comparing the results of the current study with PBDE concentrations in human milk collected in 2002–2003 from the same region. PBDEs were detected in all matrices and the median concentrations of BDEs -47 and -209 in human milk, air and dust were: 4.2 and 0.3 ng/g lipid; 25 and 7.8 pg/m3; and 56 and 291 ng/g dust, respectively. Significant correlations were observed between the concentrations of BDE-99 in air and human milk (r = 0.661, p = 0.038) and BDE-153 in dust and BDE-183 in human milk (r = 0.697, p = 0.025). These correlations do not suggest causal relationships — there is no hypothesis that can be offered to explain why BDE-153 in dust and BDE-183 in milk are correlated. The fact that so few correlations were found in the data could be a function of the small sample size, or because additional factors, such as sources of exposure not considered or measured in the study, might be important in explaining exposure to PBDEs. There was a slight decrease in PBDE concentrations from 2002–2003 to 2007–2008 but this may be due to sampling and analytical differences. Overall, average PBDE concentrations from these individual samples were similar to results from pooled human milk collected in Brisbane in 2002–2003 indicating that pooling may be an efficient, cost-effective strategy of assessing PBDE concentrations on a population basis. The results of this study were used to estimate an infant's daily PBDE intake via inhalation, dust ingestion and human milk consumption. Differences in PBDE intake of individual congeners from the different matrices were observed. Specifically, as the level of bromination increased, the contribution of PBDE intake decreased via human milk and increased via dust. As the impacts of the ban of the lower brominated (penta- and octa-BDE) products become evident, an increased use of the higher brominated deca-BDE product may result in dust making a greater contribution to infant exposure than it does currently. To better understand human body burden, further research is required into the sources and exposure pathways of PBDEs and metabolic differences influencing an individual's response to exposure. In addition, temporal trend analysis is necessary with continued monitoring of PBDEs in the human population as well as in the suggested exposure matrices of food, dust and air.