Mean and variance of estimates of the bispectrum of a harmonic random process-an analysis including leakage effects

Analytical expressions are derived for the mean and variance, of estimates of the bispectrum of a real-time series assuming a cosinusoidal model. The effects of spectral leakage, inherent in discrete Fourier transform operation when the modes present in the signal have a nonintegral number of wavelengths in the record, are included in the analysis. A single phase-coupled triad of modes can cause the bispectrum to have a nonzero mean value over the entire region of computation owing to leakage. The variance of bispectral estimates in the presence of leakage has contributions from individual modes and from triads of phase-coupled modes. Time-domain windowing reduces the leakage. The theoretical expressions for the mean and variance of bispectral estimates are derived in terms of a function dependent on an arbitrary symmetric time-domain window applied to the record. the number of data, and the statistics of the phase coupling among triads of modes. The theoretical results are verified by numerical simulations for simple test cases and applied to laboratory data to examine phase coupling in a hypothesis testing framework

Compilation of somatic mutations of the CDKN2 gene in human cancers : non-random distribution of base substitutions

The CDKN2 gene, encoding the cyclin-dependent kinase inhibitor p16, is a tumour suppressor gene that maps to chromosome band 9p21-p22. The most common mechanism of inactivation of this gene in human cancers is through homozygous deletion; however, in a smaller proportion of tumours and tumour cell lines intragenic mutations occur. In this study we have compiled a database of over 120 published point mutations in the CDKN2 gene from a wide variety of tumour types. A further 50 deletions, insertions, and splice mutations in CDKN2 have also been compiled. Furthermore, we have standardised the numbering of all mutations according to the full-length 156 amino acid form of p16. From this study we are able to define several hot spots, some of which occur at conserved residues within the ankyrin domains of p16. While many of the hotspots are shared by a number of cancers, the relative importance of each position varies, possibly reflecting the role of different carcinogens in the development of certain tumours. As reported previously, the mutational spectrum of CDKN2 in melanomas differs from that of internal malignancies and supports the involvement of UV in melanoma tumorigenesis. Notably, 52% of all substitutions in melanoma-derived samples occurred at just six nucleotide positions. Nonsense mutations comprise a comparatively high proportion of mutations present in the CDKN2 gene, and possible explanations for this are discussed.

Modelling travelling waves in spatially constrained environment solutions

In this study, we consider how Fractional Differential Equations (FDEs) can be used to study the travelling wave phenomena in parabolic equations. As our method is conducted under intracellular environments that are highly crowded, it was discovered that there is a simple relationship between the travelling wave speed and obstacle density.

Floods, earthquakes and insurance coverage : issues, problems and solutions

The recent floods in Queensland and elsewhere in Australia as well as the recent earthquakes in New Zealand have again given rise to very significant uninsured losses. This article looks at the issue of cover protection against catastrophes such as floods and earthquakes affecting home buildings and contents insurance and the standard cover provisions of the Insurance Contracts Act 1984 (Cth). It points also to the possibility of a national scheme to cover natural disasters including floods.

An examination of the applicability of hydrotalcite for removing oxalate anions from Bayer process solutions

Hydrotalcite and thermally activated hydrotalcites were examined for their potential as methods for the removal of oxalate anions from Bayer Process liquors. Hydrotalcite was prepared and characterised by a number of methods, including X-ray diffraction, thermogravimetric analysis, nitrogen adsorption analysis and vibrational spectroscopy. Thermally activated hydrotalcites were prepared by a low temperature method and characterised using X-ray diffraction, nitrogen adsorption analysis and vibrational spectroscopy. Oxalate intercalated hydrotalcite was prepared by two methods and analysed with X-ray diffraction and for the first time thermogravimetric analysis, Raman spectroscopy and infrared emission spectroscopy. The adsorption of oxalate anions by hydrotalcite and thermally activated hydrotalcite was tested in a range of solutions using both batch and kinetic adsorption models.

New exact solutions for Hele-Shaw flow in doubly connected regions

Radial Hele-Shaw flows are treated analytically using conformal mapping techniques. The geometry of interest has a doubly-connected annular region of viscous fluid surrounding an inviscid bubble that is either expanding or contracting due to a pressure difference caused by injection or suction of the inviscid fluid. The zero-surface-tension problem is ill-posed for both bubble expansion and contraction, as both scenarios involve viscous fluid displacing inviscid fluid. Exact solutions are derived by tracking the location of singularities and critical points in the analytic continuation of the mapping function. We show that by treating the critical points, it is easy to observe finite-time blow-up, and the evolution equations may be written in exact form using complex residues. We present solutions that start with cusps on one interface and end with cusps on the other, as well as solutions that have the bubble contracting to a point. For the latter solutions, the bubble approaches an ellipse in shape at extinction.

Zinc aluminium layered double hydroxides for the removal of iodine and iodide from aqueous solutions

129I is a radioactive isotope of iodine that is readily absorbed by the body. In this paper we investigated the potential of a 3:1 Zn/Al layered double hydroxide (LDH) as a sorbent for the removal of iodine and iodide from water. Synthetic Zn6Al2(OH)16(CO3)∙4H2O was prepared by the co-precipitation before thermal activation. The LDH was treated with solutions containing iodide and iodine. It was found that iodine could be more easily removed from solution than iodide. Powder X-ray diffraction revealed the destruction of the LDH structure during thermal activation and the successful reformation of a similar LDH material after treatment with the iodide or iodine solution. Thermal decomposition of all samples studied by thermogravimetry appeared to be similar. A new decomposition mechanism similar to one previously described in the literature was proposed for the Zn/Al LDH. The total mass loss of samples treated with iodide and iodine was significantly lower than that of the original LDH indicating that iodine species may form non-removable anions when intercalated into the LDH structure. Evolved gas mass spectrometry failed to detect any iodine species lost as gases during the decomposition of iodide treated LDH however, small quantities of iodine species were observed during decomposition of samples treated with iodine solution.

Optimisation of process parameters for the removal of hydroxycinnamic acids in sugar solutions

Colour is one of the most important parameters in sugar quality and its presence in raw sugar plays a key role in the marketing strategy of sugar industries worldwide. This study investigated the degradation of a mixture of colour precursors using the Fenton oxidation process. These colour precursors are caffeic acid, p–coumaric acid and ferulic acid, which are present in cane juice. Results showed that with a Fe(II) to H2O2 molar ratio of 1:15 in an aqueous system at 25 °C, 77% of the total phenolic acid content was removed at pH 4.72. However, in a synthetic juice solution which contained 13 mass % sucrose (35 °C, pH 5.4), only 60% of the total phenolic acid content was removed.

Sequential fusion of decisions from adaptive and random samples for controlled verification of errors

Fusion techniques have received considerable attention for achieving performance improvement with biometrics. While a multi-sample fusion architecture reduces false rejects, it also increases false accepts. This impact on performance also depends on the nature of subsequent attempts, i.e., random or adaptive. Expressions for error rates are presented and experimentally evaluated in this work by considering the multi-sample fusion architecture for text-dependent speaker verification using HMM based digit dependent speaker models. Analysis incorporating correlation modeling demonstrates that the use of adaptive samples improves overall fusion performance compared to randomly repeated samples. For a text dependent speaker verification system using digit strings, sequential decision fusion of seven instances with three random samples is shown to reduce the overall error of the verification system by 26% which can be further reduced by 6% for adaptive samples. This analysis novel in its treatment of random and adaptive multiple presentations within a sequential fused decision architecture, is also applicable to other biometric modalities such as finger prints and handwriting samples.

Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

Co-management to solve homelessness : wicked solutions to wicked problems

While governments are engaged in developing social policy responses to address wicked issues such as poverty, homelessness, drug addiction and crime, long term resolution of these issues through government policy making and state-based programmatic action has remained elusive. The use of vehicles for joint action and partnership between government and the community sector such as co-management has been offered as a way of harnessing productive capability and innovative capacity of both these sectors to resolve these complex problems. However, it is suggested that while there is a well advanced agenda with the intent for collaboration and partnership, working with the models for undertaking this joint action are not well understood and have not been fully developed or evaluated. This chapter examines new approaches to resolving the wicked issue of homelessness through applying the lens of co-management to understand the complexities of this issue and its resolution. The chapter analyses an attempt to move away from traditional bureaucratic structures of welfare departments, operating through single functional ‘silos’ to a new horizontal ‘hub-based’ model of service delivery that seeks to integrate actors across many different service areas and organizations. The chapter explores case studies of co-management in the establishment, development and operation of service hubs to address homelessness. We argue that the response to homelessness needs a ‘wicked solution’ that goes beyond simply providing shelter to those in need. The case of the hub models of community sector organizations working across organizational boundaries is evaluated to determine whether this approach can be considered successful co-managing of an innovative initiative, and understanding the requirements for developing, improving and extending this model. The role of the third sector in co-managing public services is examined through the in-depth case studies and the results are presented together with an assessment of how co-management can contribute to service quality and service management in public services.

Modeling random effect and excess zeros in road traffic accident prediction

Poisson distribution has often been used for count like accident data. Negative Binomial (NB) distribution has been adopted in the count data to take care of the over-dispersion problem. However, Poisson and NB distributions are incapable of taking into account some unobserved heterogeneities due to spatial and temporal effects of accident data. To overcome this problem, Random Effect models have been developed. Again another challenge with existing traffic accident prediction models is the distribution of excess zero accident observations in some accident data. Although Zero-Inflated Poisson (ZIP) model is capable of handling the dual-state system in accident data with excess zero observations, it does not accommodate the within-location correlation and between-location correlation heterogeneities which are the basic motivations for the need of the Random Effect models. This paper proposes an effective way of fitting ZIP model with location specific random effects and for model calibration and assessment the Bayesian analysis is recommended.

Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

Analytical solutions for the two- and three-dimensional time-fractional telegraph equations by the method of separating variables

In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE) in two and three dimensions. We discuss and derive the analytical solution of the TFTE in two and three dimensions with nonhomogeneous Dirichlet boundary condition. This method can be extended to other kinds of the boundary conditions.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.