A note on bifurcation from an interval

We study the global bifurcation of nonlinear Sturm-Liouville problems of the form -(pu')' + qu = lambda a(x)f(u), b(0)u(0) - c(0)u' (0) = 0, b(1)u(1) + c(1)u'(1) = 0 which are not linearizable in any neighborhood of the origin. (c) 2005 Published by Elsevier Ltd.

Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Crosstalk between developmental and tumour-specific signalling pathways : kallikrein-related serine peptidases and nodal in prostrate cancer

Prostate cancer is an important male health issue. The strategies used to diagnose and treat prostate cancer underscore the cell and molecular interactions that promote disease progression. Prostate cancer is histologically defined by increasingly undifferentiated tumour cells and therapeutically targeted by androgen ablation. Even as the normal glandular architecture of the adult prostate is lost, prostate cancer cells remain dependent on the androgen receptor (AR) for growth and survival. This project focused on androgen-regulated gene expression, altered cellular differentiation, and the nexus between these two concepts. The AR controls prostate development, homeostasis and cancer progression by regulating the expression of downstream genes. Kallikrein-related serine peptidases are prominent transcriptional targets of AR in the adult prostate. Kallikrein 3 (KLK3), which is commonly referred to as prostate-specific antigen, is the current serum biomarker for prostate cancer. Other kallikreins are potential adjunct biomarkers. As secreted proteases, kallikreins act through enzyme cascades that may modulate the prostate cancer microenvironment. Both as a panel of biomarkers and cascade of proteases, the roles of kallikreins are interconnected. Yet the expression and regulation of different kallikreins in prostate cancer has not been compared. In this study, a spectrum of prostate cell lines was used to evaluate the expression profile of all 15 members of the kallikrein family. A cluster of genes was co-ordinately expressed in androgenresponsive cell lines. This group of kallikreins included KLK2, 3, 4 and 15, which are located adjacent to one another at the centromeric end of the kallikrein locus. KLK14 was also of interest, because it was ubiquitously expressed among the prostate cell lines. Immunohistochemistry showed that these 5 kallikreins are co-expressed in benign and malignant prostate tissue. The androgen-regulated expression of KLK2 and KLK3 is well-characterised, but has not been compared with other kallikreins. Therefore, KLK2, 3, 4, 14 and 15 expression were all measured in time course and dose response experiments with androgens, AR-antagonist treatments, hormone deprivation experiments and cells transfected with AR siRNA. Collectively, these experiments demonstrated that prostatic kallikreins are specifically and directly regulated by the AR. The data also revealed that kallikrein genes are differentially regulated by androgens; KLK2 and KLK3 were strongly up-regulated, KLK4 and KLK15 were modestly up-regulated, and KLK14 was repressed. Notably, KLK14 is located at the telomeric end of the kallikrein locus, far away from the centromeric cluster of kallikreins that are stimulated by androgens. These results show that the expression of KLK2, 3, 4, 14 and 15 is maintained in prostate cancer, but that these genes exhibit different responses to androgens. This makes the kallikrein locus an ideal model to investigate AR signalling. The increasingly dedifferentiated phenotype of aggressive prostate cancer cells is accompanied by the re-expression of signalling molecules that are usually expressed during embryogenesis and foetal tissue development. The Wnt pathway is one developmental cascade that is reactivated in prostate cancer. The canonical Wnt cascade regulates the intracellular levels of β-catenin, a potent transcriptional co-activator of T-cell factor (TCF) transcription factors. Notably, β-catenin can also bind to the AR and synergistically stimulate androgen-mediated gene expression. This is at the expense of typical Wnt/TCF target genes, because the AR:β-catenin and TCF:β-catenin interactions are mutually exclusive. The effect of β-catenin on kallikrein expression was examined to further investigate the role of β-catenin in prostate cancer. Stable knockdown of β-catenin in LNCaP prostate cancer cells attenuated the androgen-regulated expression of KLK2, 3, 4 and 15, but not KLK14. To test whether KLK14 is instead a TCF:β-catenin target gene, the endogenous levels of β-catenin were increased by inhibiting its degradation. Although KLK14 expression was up-regulated by these treatments, siRNA knockdown of β-catenin demonstrated that this effect was independent of β-catenin. These results show that β-catenin is required for maximal expression of KLK2, 3, 4 and 15, but not KLK14. Developmental cells and tumour cells express a similar repertoire of signalling molecules, which means that these different cell types are responsive to one another. Previous reports have shown that stem cells and foetal tissues can reprogram aggressive cancer cells to less aggressive phenotypes by restoring the balance to developmental signalling pathways that are highly dysregulated in cancer. To investigate this phenomenon in prostate cancer, DU145 and PC-3 prostate cancer cells were cultured on matrices pre-conditioned with human embryonic stem cells (hESCs). Soft agar assays showed that prostate cancer cells exposed to hESC conditioned matrices had reduced clonogenicity compared with cells harvested from control matrices. A recent study demonstrated that this effect was partially due to hESC-derived Lefty, an antagonist of Nodal. A member of the transforming growth factor β (TGFβ) superfamily, Nodal regulates embryogenesis and is re-expressed in cancer. The role of Nodal in prostate cancer has not previously been reported. Therefore, the expression and function of the Nodal signalling pathway in prostate cancer was investigated. Western blots confirmed that Nodal is expressed in DU145 and PC-3 cells. Immunohistochemistry revealed greater expression of Nodal in malignant versus benign glands. Notably, the Nodal inhibitor, Lefty, was not expressed at the mRNA level in any prostate cell lines tested. The Nodal signalling pathway is functionally active in prostate cancer cells. Recombinant Nodal treatments triggered downstream phosphorylation of Smad2 in DU145 and LNCaP cells, and stably-transfected Nodal increased the clonogencity of LNCaP cells. Nodal was also found to modulate AR signalling. Nodal reduced the activity of an androgen-regulated KLK3 promoter construct in luciferase assays and attenuated the endogenous expression of AR target genes including prostatic kallikreins. These results demonstrate that Nodal is a novel example of a developmental signalling molecule that is reexpressed in prostate cancer and may have a functional role in prostate cancer progression. In summary, this project clarifies the role of androgens and changing cellular differentiation in prostate cancer by characterising the expression and function of the downstream genes encoding kallikrein-related serine proteases and Nodal. Furthermore, this study emphasises the similarities between prostate cancer and early development, and the crosstalk between developmental signalling pathways and the AR axis. The outcomes of this project also affirm the utility of the kallikrein locus as a model system to monitor tumour progression and the phenotype of prostate cancer cells.

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.

The development of a simple multi-nodal tool to identify performance issues in existing commercial buildings

Australia’s building stock includes many older commercial buildings with numerous factors that impact energy performance and indoor environment quality. The built environment industry has generally focused heavily on improving physical building design elements for greater energy efficiency (such as retrofits and environmental upgrades), however there are noticeable ‘upper limits’ to performance improvements in these areas. To achieve a stepchange improvement in building performance, the authors propose that additional components need to be addressed in a whole of building approach, including the way building design elements are managed and the level of stakeholder engagement between owners, tenants and building managers. This paper focuses on the opportunities provided by this whole-of-building approach, presenting the findings of a research project undertaken through the Sustainable Built Environment National Research Centre (SBEnrc) in Australia. Researchers worked with a number of industry partners over two years to investigate issues facing stakeholders at base building and tenancy levels, and the barriers to improving building performance. Through a mixed-method, industry-led research approach, five ‘nodes’ were identified in whole-of-building performance evaluation, each with interlinking and overlapping complexities that can influence performance. The nodes cover building management, occupant experience, indoor environment quality, agreements and culture, and design elements. This paper outlines the development and testing of these nodes and their interactions, and the resultant multi-nodal tool, called the ‘Performance Nexus’ tool. The tool is intended to be of most benefit in evaluating opportunities for performance improvement in the vast number of existing low-performing building stock.

Analysis of recreational fish catches – dealing with highly skewed distributions with many zeros

Data from surveys of recreational anglers fishing on three estuaries in eastern Australia reveal highly skewed distributions of catches with many zeros. Such data may be analysed using a two component approach involving a binary (zero/non-zero catch) response and the non-zero catches. A truncated regression model was effective in analysing the non-zero catches. Covariates were incorporated in the modelling, and their critical assessment has led to improved measures of fishing effort for this recreational fishery.

QTL for nodal root angle in sorghum (Sorghum bicolor L. Moench) co-locate with QTL for traits associated with drought adaptation.

Nodal root angle in sorghum influences vertical and horizontal root distribution in the soil profile and is thus relevant to drought adaptation. In this study, we report for the first time on the mapping of four QTL for nodal root angle (qRA) in sorghum, in addition to three QTL for root dry weight, two for shoot dry weight, and three for plant leaf area. Phenotyping was done at the six leaf stage for a mapping population (n = 141) developed by crossing two inbred sorghum lines with contrasting root angle. Nodal root angle QTL explained 58.2% of the phenotypic variance and were validated across a range of diverse inbred lines. Three of the four nodal root angle QTL showed homology to previously identified root angle QTL in rice and maize, whereas all four QTL co-located with previously identified QTL for stay-green in sorghum. A putative association between nodal root angle QTL and grain yield was identified through single marker analysis on field testing data from a subset of the mapping population grown in hybrid combination with three different tester lines. Furthermore, a putative association between nodal root angle QTL and stay-green was identified using data sets from selected sorghum nested association mapping populations segregating for root angle. The identification of nodal root angle QTL presents new opportunities for improving drought adaptation mechanisms via molecular breeding to manipulate a trait for which selection has previously been very difficult.

A parallel wilf algorithm for complex zeros of a polynomial

A global recursive bisection algorithm is described for computing the complex zeros of a polynomial. It has complexityO(n 3 p) wheren is the degree of the polynomial andp the bit precision requirement. Ifn processors are available, it can be realized in parallel with complexityO(n 2 p); also it can be implemented using exact arithmetic. A combined Wilf-Hansen algorithm is suggested for reduction in complexity.

Genetic control of nodal root angle in sorghum and its implications on water extraction

Genotypic variability in root system architecture has been associated with root angle of seedlings and water extraction patterns of mature plants in a range of crops. The potential inclusion of root angle as a selection criterion in a sorghum breeding program requires (1) availability of an efficient screening method, (2) presence of genotypic variation with high heritability, and (3) an association with water extraction pattern. The aim of this study was to determine the feasibility for inclusion of nodal root angle as a selection criterion in sorghum breeding programs. A high-throughput phenotypic screen for nodal root angle in young sorghum plants has recently been developed and has been used successfully to identify significant variation in nodal root angle across a diverse range of inbred lines and a mapping population. In both cases, heritabilities for nodal root angle were high. No association between nodal root angle and plant size was detected. This implies that parental inbred lines could potentially be used to asses nodal root angle of their hybrids, although such predictability is compromised by significant interactions. To study effects of nodal root angle on water extraction patterns of mature plants, four inbred lines with contrasting nodal root angle at seedling stage were grown until at least anthesis in large rhizotrons. A consistent trend was observed that nodal root angle may affect the spatial distribution of root mass of mature plants and hence their ability to extract soil water, although genotypic differences were not significant. The potential implications of this for specific adaptation to drought stress are discussed. Results suggest that nodal root angle of young plants can be a useful selection criterion for specific drought adaptation, and could potentially be used in molecular breeding programs if QTLs for root angle can be identified. (C) 2012 Elsevier B.V. All rights reserved.

Alginate encapsulation of shoot tips and nodal segments for short-term storage and distribution of the eucalypt Corymbia torelliana × C. citriodora

A protocol was developed for short-term preservation and distribution of the plantation eucalypt, Corymbia torelliana × C. citriodora, using alginate-encapsulated shoot tips and nodes as synthetic seeds. Effects of sowing medium, auxin concentration, storage temperature and planting substrate on shoot regrowth or conversion into plantlets were assessed for four different clones. High frequencies of shoot regrowth (76–100%) from encapsulated explants were consistently obtained in hormone-free half- and full-strength Murashige and Skoog (MS) sowing media. Conversion into plantlets from synthetic seeds was achieved on half-strength MS medium by treating shoot tips or nodes with 4.9–78.4 μM IBA prior to encapsulation. Pre-treatment with 19.6 μM IBA provided 62–100% conversion, and 95–100% of plantlets survived after acclimatisation under nursery conditions. Synthetic seeds containing explants pre-treated with IBA were stored for 8 weeks much more effectively at 25°C than at 4°C, with regrowth frequencies of 50–84% at 25°C compared with 0–4% at 4°C. To eliminate the in vitro culture step after encapsulation, synthetic seeds were allowed to pre-convert before sowing directly onto a range of ex vitro non-sterile planting substrates. Highest frequencies (46–90%) of plantlet formation from pre-converted synthetic seeds were obtained by transferring shoot tip-derived synthetic seeds onto an organic compost substrate. These plantlets exhibited almost 100% survival in the nursery without mist irrigation. Pre-conversion of non-embryonic synthetic seeds is a novel technique that provides a convenient alternative to somatic embryo-derived artificial seeds.

Nodal length fluctuations for arithmetic random waves

Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus (''arithmetic random waves''). We study the distribution of the nodal length of random eigenfunctions for large eigenvalues, and our primary result is that the asymptotics for the variance is nonuniversal. Our result is intimately related to the arithmetic of lattice points lying on a circle with radius corresponding to the energy.

Nodal domains of the equilateral triangle billiard

We characterize the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns of the eigenfunctions follow a group-theoretic connection in a way that makes them predictable as one goes from one state to another. Extensive numerical investigations bring out the distribution functions of the mode number and signed areas. The statistics of the boundary intersections is also treated analytically. Finally, the distribution functions of the nodal loop count and the nodal counting function are shown to contain information about the classical periodic orbits using the semiclassical trace formula. We believe that the results belong generically to non-separable systems, thus extending the previous works which are concentrated on separable and chaotic systems.