Promoting Statistical Literacy Through Data Modelling in the Early School Years

This chapter addresses data modelling as a means of promoting statistical literacy in the early grades. Consideration is first given to the importance of increasing young children’s exposure to statistical reasoning experiences and how data modelling can be a rich means of doing so. Selected components of data modelling are then reviewed, followed by a report on some findings from the third-year of a three-year longitudinal study across grades one through three.

Does counting still count? Revisiting the security of counting based user authentication protocols against statistical attacks

At NDSS 2012, Yan et al. analyzed the security of several challenge-response type user authentication protocols against passive observers, and proposed a generic counting based statistical attack to recover the secret of some counting based protocols given a number of observed authentication sessions. Roughly speaking, the attack is based on the fact that secret (pass) objects appear in challenges with a different probability from non-secret (decoy) objects when the responses are taken into account. Although they mentioned that a protocol susceptible to this attack should minimize this difference, they did not give details as to how this can be achieved barring a few suggestions. In this paper, we attempt to fill this gap by generalizing the attack with a much more comprehensive theoretical analysis. Our treatment is more quantitative which enables us to describe a method to theoretically estimate a lower bound on the number of sessions a protocol can be safely used against the attack. Our results include 1) two proposed fixes to make counting protocols practically safe against the attack at the cost of usability, 2) the observation that the attack can be used on non-counting based protocols too as long as challenge generation is contrived, 3) and two main design principles for user authentication protocols which can be considered as extensions of the principles from Yan et al. This detailed theoretical treatment can be used as a guideline during the design of counting based protocols to determine their susceptibility to this attack. The Foxtail protocol, one of the protocols analyzed by Yan et al., is used as a representative to illustrate our theoretical and experimental results.

Multiscale coupling and multiphysics approaches in earth sciences : theory

Measuring Earth material behaviour on time scales of millions of years transcends our current capability in the laboratory. We review an alternative path considering multiscale and multiphysics approaches with quantitative structure-property relationships. This approach allows a sound basis to incorporate physical principles such as chemistry, thermodynamics, diffusion and geometry-energy relations into simulations and data assimilation on the vast range of length and time scales encountered in the Earth. We identify key length scales for Earth systems processes and find a substantial scale separation between chemical, hydrous and thermal diffusion. We propose that this allows a simplified two-scale analysis where the outputs from the micro-scale model can be used as inputs for meso-scale simulations, which then in turn becomes the micro-model for the next scale up. We present two fundamental theoretical approaches to link the scales through asymptotic homogenisation from a macroscopic thermodynamic view and percolation renormalisation from a microscopic, statistical mechanics view.

Statistical analysis of reduction in tensile strength of cotton strips as a measure of soil microbial activity

The cotton strip assay (CSA) is an established technique for measuring soil microbial activity. The technique involves burying cotton strips and measuring their tensile strength after a certain time. This gives a measure of the rotting rate, R, of the cotton strips. R is then a measure of soil microbial activity. This paper examines properties of the technique and indicates how the assay can be optimised. Humidity conditioning of the cotton strips before measuring their tensile strength reduced the within and between day variance and enabled the distribution of the tensile strength measurements to approximate normality. The test data came from a three-way factorial experiment (two soils, two temperatures, three moisture levels). The cotton strips were buried in the soil for intervals of time ranging up to 6 weeks. This enabled the rate of loss of cotton tensile strength with time to be studied under a range of conditions. An inverse cubic model accounted for greater than 90% of the total variation within each treatment combination. This offers support for summarising the decomposition process by a single parameter R. The approximate variance of the decomposition rate was estimated from a function incorporating the variance of tensile strength and the differential of the function for the rate of decomposition, R, with respect to tensile strength. This variance function has a minimum when the measured strength is approximately 2/3 that of the original strength. The estimates of R are almost unbiased and relatively robust against the cotton strips being left in the soil for more or less than the optimal time. We conclude that the rotting rate X should be measured using the inverse cubic equation, and that the cotton strips should be left in the soil until their strength has been reduced to about 2/3.

Field validation of controlled Monte Carlo data generation for statistical damage identification employing Mahalanobis squared distance

This article presents the field applications and validations for the controlled Monte Carlo data generation scheme. This scheme was previously derived to assist the Mahalanobis squared distance–based damage identification method to cope with data-shortage problems which often cause inadequate data multinormality and unreliable identification outcome. To do so, real-vibration datasets from two actual civil engineering structures with such data (and identification) problems are selected as the test objects which are then shown to be in need of enhancement to consolidate their conditions. By utilizing the robust probability measures of the data condition indices in controlled Monte Carlo data generation and statistical sensitivity analysis of the Mahalanobis squared distance computational system, well-conditioned synthetic data generated by an optimal controlled Monte Carlo data generation configurations can be unbiasedly evaluated against those generated by other set-ups and against the original data. The analysis results reconfirm that controlled Monte Carlo data generation is able to overcome the shortage of observations, improve the data multinormality and enhance the reliability of the Mahalanobis squared distance–based damage identification method particularly with respect to false-positive errors. The results also highlight the dynamic structure of controlled Monte Carlo data generation that makes this scheme well adaptive to any type of input data with any (original) distributional condition.

Multivariate statistical analysis of hydrochemical data to assess alluvial aquifer–stream connectivity during drought and flood : Cressbrook Creek, southeast Queensland, Australia

A catchment-scale multivariate statistical analysis of hydrochemistry enabled assessment of interactions between alluvial groundwater and Cressbrook Creek, an intermittent drainage system in southeast Queensland, Australia. Hierarchical cluster analyses and principal component analysis were applied to time-series data to evaluate the hydrochemical evolution of groundwater during periods of extreme drought and severe flooding. A simple three-dimensional geological model was developed to conceptualise the catchment morphology and the stratigraphic framework of the alluvium. The alluvium forms a two-layer system with a basal coarse-grained layer overlain by a clay-rich low-permeability unit. In the upper and middle catchment, alluvial groundwater is chemically similar to streamwater, particularly near the creek (reflected by high HCO3/Cl and K/Na ratios and low salinities), indicating a high degree of connectivity. In the lower catchment, groundwater is more saline with lower HCO3/Cl and K/Na ratios, notably during dry periods. Groundwater salinity substantially decreased following severe flooding in 2011, notably in the lower catchment, confirming that flooding is an important mechanism for both recharge and maintaining groundwater quality. The integrated approach used in this study enabled effective interpretation of hydrological processes and can be applied to a variety of hydrological settings to synthesise and evaluate large hydrochemical datasets.

A statistical approach to quantify the impact on voltage quality caused by PV generators

A probabilistic method is proposed to evaluate voltage quality of grid-connected photovoltaic (PV) power systems. The random behavior of solar irradiation is described in statistical terms and the resulting voltage fluctuation probability distribution is then derived. Reactive power capabilities of the PV generators are then analyzed and their operation under constant power factor mode is examined. By utilizing the reactive power capability of the PV-generators to the full, it is shown that network voltage quality can be greatly enhanced.

Including nonequilibrium interface kinetics in a continuum model for melting nanoscaled particles

The melting temperature of a nanoscaled particle is known to decrease as the curvature of the solid-melt interface increases. This relationship is most often modelled by a Gibbs--Thomson law, with the decrease in melting temperature proposed to be a product of the curvature of the solid-melt interface and the surface tension. Such a law must break down for sufficiently small particles, since the curvature becomes singular in the limit that the particle radius vanishes. Furthermore, the use of this law as a boundary condition for a Stefan-type continuum model is problematic because it leads to a physically unrealistic form of mathematical blow-up at a finite particle radius. By numerical simulation, we show that the inclusion of nonequilibrium interface kinetics in the Gibbs--Thomson law regularises the continuum model, so that the mathematical blow up is suppressed. As a result, the solution continues until complete melting, and the corresponding melting temperature remains finite for all time. The results of the adjusted model are consistent with experimental findings of abrupt melting of nanoscaled particles. This small-particle regime appears to be closely related to the problem of melting a superheated particle.

Adsorption thermodynamics and kinetics study for the self-assembly of 1,8,15,22-tetraaminophthalocyanatocobalt(II) on glassy carbon surface

Spontaneous adsorption of 1,8,15,22-tetraaminophthalocyanatocobalt(II) (4α-CoIITAPc) on glassy carbon (GC) electrode leads to the formation of a stable self-assembled monolayer (SAM). Since the SAM of 4α-CoIITAPc is redox active, its adsorption on GC electrode was followed by cyclic voltammetry. SAM of 4α-CoIITAPc on GC electrode shows two pairs of well-defined redox peaks corresponding to CoIII/CoII and CoIIIPc−1/CoIIIPc−2. The surface coverage (Γ) value, calculated by integrating the charge under CoII oxidation, was used to study the adsorption thermodynamics and kinetics of 4α-CoIITAPc on GC surface. Cyclic voltammetric studies show that the adsorption of 4α-CoIITAPc on GC electrode has reached the saturation coverage (Γs) within 3 h. The Γs value for the SAM of 4α-CoIITAPc on GC electrode was found to be 2.37 × 10−10 mol cm−2. Gibbs free energy (ΔGads) and adsorption rate constant (kad) for the adsorption of 4α-CoIITAPc on GC surface were found to be −16.76 kJ mol−1 and 7.1 M−1 s−1, respectively. The possible mechanism for the self-assembly of 4α-CoIITAPc on GC surface is through the addition of nucleophilic amines to the olefinic bond on the GC surface in addition to a meager contribution from π stacking. The contribution of π stacking was confirmed from the adsorption of unsubstituted phthalocyanatocobalt(II) (CoPc) on GC electrode. Raman spectra for the SAM of 4α-CoIITAPc on carbon surface shows strong stretching and breathing bands of Pc macrocycle, pyrrole ring and isoindole ring. Raman and CV studies suggest that 4α-CoIITAPc is adopting nearly a flat orientation or little bit tilted orientation.