69 resultados para Degenerate Hopf bifurcation


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Research on expertise, talent identification and development has tended to be mono-disciplinary, typically adopting geno-centric or environmentalist positions, with an overriding focus on operational issues. In this thesis, the validity of dualist positions on sport expertise is evaluated. It is argued that, to advance understanding of expertise and talent development, a shift towards a multidisciplinary and integrative science focus is necessary, along with the development of a comprehensive multidisciplinary theoretical rationale. Dynamical systems theory is utilised as a multidisciplinary theoretical rationale for the succession of studies, capturing how multiple interacting constraints can shape the development of expert performers. Phase I of the research examines experiential knowledge of coaches and players on the development of fast bowling talent utilising qualitative research methodology. It provides insights into the developmental histories of expert fast bowlers, as well as coaching philosophies on the constraints of fast bowling expertise. Results suggest talent development programmes should eschew the notion of common optimal performance models and emphasize the individual nature of pathways to expertise. Coaching and talent development programmes should identify the range of interacting constraints that impinge on the performance potential of individual athletes, rather than evaluating current performance on physical tests referenced to group norms. Phase II of this research comprises three further studies that investigate several of the key components identified as important for fast bowling expertise, talent identification and development extrapolated from Phase I of this research. This multidisciplinary programme of work involves a comprehensive analysis of fast bowling performance in a cross-section of the Cricket Australia high performance pathways, from the junior, emerging and national elite fast bowling squads. Briefly, differences were found in trunk kinematics associated with the generation of ball speed across the three groups. These differences in release mechanics indicated the functional adaptations in movement patterns as bowlers’ physical and anatomical characteristics changed during maturation. Second to the generation of ball speed, the ability to produce a range of delivery types was highlighted as a key component of expertise in the qualitative phase. The ability of athletes to produce consistent results on different surfaces and in different environments has drawn attention to the challenge of measuring consistency and flexibility in skill assessments. Examination of fast bowlers in Phase II demonstrated that national bowlers can make adjustments to the accuracy of subsequent deliveries during performance of a cricket bowling skills test, and perform a range of delivery types with increased accuracy and consistency. Finally, variability in selected delivery stride ground reaction force components in fast bowling revealed the degenerate nature of this complex multi-articular skill where the same performance outcome can be achieved with unique movement strategies. Utilising qualitative and quantitative methodologies to examine fast bowling expertise, the importance of degeneracy and adaptability in fast bowling has been highlighted alongside learning design that promotes dynamic learning environments.

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Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

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Vitamin A deficiency (VAD) is a serious problem in developing countries, affecting approximately 127 million children of preschool age and 7.2 million pregnant women each year. However, this deficiency is readily treated and prevented through adequate nutrition. This can potentially be achieved through genetically engineered biofortification of staple food crops to enhance provitamin A (pVA) carotenoid content. Bananas are the fourth most important food crop with an annual production of 100 million tonnes and are widely consumed in areas affected by VAD. However, the fruit pVA content of most widely consumed banana cultivars is low (~ 0.2 to 0.5 ìg/g dry weight). This includes cultivars such as the East African highland banana (EAHB), the staple crop in countries such as Uganda, where annual banana consumption is approximately 250 kg per person. This fact, in addition to the agronomic properties of staple banana cultivars such as vegetative reproduction and continuous cropping, make bananas an ideal target for pVA enhancement through genetic engineering. Interestingly, there are banana varieties known with high fruit pVA content (up to 27.8 ìg/g dry weight), although they are not widely consumed due to factors such as cultural preference and availability. The genes involved in carotenoid accumulation during banana fruit ripening have not been well studied and an understanding of the molecular basis for the differential capacity of bananas to accumulate carotenoids may impact on the effective production of genetically engineered high pVA bananas. The production of phytoene by the enzyme phytoene synthase (PSY) has been shown to be an important rate limiting determinant of pVA accumulation in crop systems such as maize and rice. Manipulation of this gene in rice has been used successfully to produce Golden Rice, which exhibits higher seed endosperm pVA levels than wild type plants. Therefore, it was hypothesised that differences between high and low pVA accumulating bananas could be due either to differences in PSY enzyme activity or factors regulating the expression of the psy gene. Therefore, the aim of this thesis was to investigate the role of PSY in accumulation of pVA in banana fruit of representative high (Asupina) and low (Cavendish) pVA banana cultivars by comparing the nucleic acid and encoded amino acid sequences of the banana psy genes, in vivo enzyme activity of PSY in rice callus and expression of PSY through analysis of promoter activity and mRNA levels. Initially, partial sequences of the psy coding region from five banana cultivars were obtained using reverse transcriptase (RT)-PCR with degenerate primers designed to conserved amino acids in the coding region of available psy sequences from other plants. Based on phylogenetic analysis and comparison to maize psy sequences, it was found that in banana, psy occurs as a gene family of at least three members (psy1, psy2a and psy2b). Subsequent analysis of the complete coding regions of these genes from Asupina and Cavendish suggested that they were all capable of producing functional proteins due to high conservation in the catalytic domain. However, inability to obtain the complete mRNA sequences of Cavendish psy2a, and isolation of two non-functional Cavendish psy2a coding region variants, suggested that psy2a expression may be impaired in Cavendish. Sequence analysis indicated that these Cavendish psy2a coding region variants may have resulted from alternate splicing. Evidence of alternate splicing was also observed in one Asupina psy1 coding region variant, which was predicted to produce a functional PSY1 isoform. The complete mRNA sequence of the psy2b coding regions could not be isolated from either cultivar. Interestingly, psy1 was cloned predominantly from leaf while psy2 was obtained preferentially from fruit, suggesting some level of tissue-specific expression. The Asupina and Cavendish psy1 and psy2a coding regions were subsequently expressed in rice callus and the activity of the enzymes compared in vivo through visual observation and quantitative measurement of carotenoid accumulation. The maize B73 psy1 coding region was included as a positive control. After several weeks on selection, regenerating calli showed a range of colours from white to dark orange representing various levels of carotenoid accumulation. These results confirmed that the banana psy coding regions were all capable of producing functional enzymes. No statistically significant differences in levels of activity were observed between banana PSYs, suggesting that differences in PSY activity were not responsible for differences in the fruit pVA content of Asupina and Cavendish. The psy1 and psy2a promoter sequences were isolated from Asupina and Cavendish gDNA using a PCR-based genome walking strategy. Interestingly, three Cavendish psy2a promoter clones of different sizes, representing possible allelic variants, were identified while only single promoter sequences were obtained for the other Asupina and Cavendish psy genes. Bioinformatic analysis of these sequences identified motifs that were previously characterised in the Arabidopsis psy promoter. Notably, an ATCTA motif associated with basal expression in Arabidopsis was identified in all promoters with the exception of two of the Cavendish psy2a promoter clones (Cpsy2apr2 and Cpsy2apr3). G1 and G2 motifs, linked to light-regulated responses in Arabidopsis, appeared to be differentially distributed between psy1 and psy2a promoters. In the untranscribed regulatory regions, the G1 motifs were found only in psy1 promoters, while the G2 motifs were found only in psy2a. Interestingly, both ATCTA and G2 motifs were identified in the 5’ UTRs of Asupina and Cavendish psy1. Consistent with other monocot promoters, introns were present in the Asupina and Cavendish psy1 5’ UTRs, while none were observed in the psy2a 5’ UTRs. Promoters were cloned into expression constructs, driving the â-glucuronidase (GUS) reporter gene. Transient expression of the Asupina and Cavendish psy1 and psy2a promoters in both Cavendish embryogenic cells and Cavendish fruit demonstrated that all promoters were active, except Cpsy2apr2 and Cpsy2apr3. The functional Cavendish psy2a promoter (Cpsy2apr1) appeared to have activity similar to the Asupina psy2a promoter. The activities of the Asupina and Cavendish psy1 promoters were similar to each other, and comparable to those of the functional psy2a promoters. Semi-quantitative PCR analysis of Asupina and Cavendish psy1 and psy2a transcripts showed that psy2a levels were high in green fruit and decreased during ripening, reinforcing the hypothesis that fruit pVA levels were largely dependent on levels of psy2a expression. Additionally, semi-quantitative PCR using intron-spanning primers indicated that high levels of unprocessed psy2a and psy2b mRNA were present in the ripe fruit of Cavendish but not in Asupina. This raised the possibility that differences in intron processing may influence pVA accumulation in Asupina and Cavendish. In this study the role of PSY in banana pVA accumulation was analysed at a number of different levels. Both mRNA accumulation and promoter activity of psy genes studied were very similar between Asupina and Cavendish. However, in several experiments there was evidence of cryptic or alternate splicing that differed in Cavendish compared to Asupina, although these differences were not conclusively linked to the differences in fruit pVA accumulation between Asupina and Cavendish. Therefore, other carotenoid biosynthetic genes or regulatory mechanisms may be involved in determining pVA levels in these cultivars. This study has contributed to an increased understanding of the role of PSY in the production of pVA carotenoids in banana fruit, corroborating the importance of this enzyme in regulating carotenoid production. Ultimately, this work may serve to inform future research into pVA accumulation in important crop varieties such as the EAHB and the discovery of avenues to improve such crops through genetic modification.

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This paper presents an approach for the automatic calibration of low-cost cameras which are assumed to be restricted in their freedom of movement to either pan or tilt movements. Camera parameters, including focal length, principal point, lens distortion parameter and the angle and axis of rotation, can be recovered from a minimum set of two images of the camera, provided that the axis of rotation between the two images goes through the camera’s optical center and is parallel to either the vertical (panning) or horizontal (tilting) axis of the image. Previous methods for auto-calibration of cameras based on pure rotations fail to work in these two degenerate cases. In addition, our approach includes a modified RANdom SAmple Consensus (RANSAC) algorithm, as well as improved integration of the radial distortion coefficient in the computation of inter-image homographies. We show that these modifications are able to increase the overall efficiency, reliability and accuracy of the homography computation and calibration procedure using both synthetic and real image sequences

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Recent studies have implicated the hypocretin/orexinergic system in reward-seeking behavior. Almorexant, a dual orexin/hypocretin R1 and R2 receptor antagonist, has proven effective in preclinical studies in promoting sleep in animal models and was in Phase III clinical trials for sleep disorders. The present study combines behavioral assays with in vitro biochemical and electrophysiological techniques to elucidate the role of almorexant in ethanol and sucrose intake. Using an operant self-administration paradigm, we demonstrate that systemic administration of almorexant decreased operant selfadministration of both 20% ethanol and 5% sucrose. We further demonstrate that intraventral tegmental area (VTA) infusions, but not intra substantia nigra infusions, of almorexant reduced ethanol self-administration. Extracellular recordings performed in VTA neurons revealed that orexin-A increased firing and this enhancement of firing was blocked by almorexant. The results demonstrate that orexin/hypocretin receptors in distinct brain regions regulate ethanol and sucrose mediated behaviors.

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Localized planar patterns arise in many reaction-diffusion models. Most of the paradigm equations that have been studied so far are two-component models. While stationary localized structures are often found to be stable in such systems, travelling patterns either do not exist or are found to be unstable. In contrast, numerical simulations indicate that localized travelling structures can be stable in three-component systems. As a first step towards explaining this phenomenon, a planar singularly perturbed three-component reaction-diffusion system that arises in the context of gas-discharge systems is analysed in this paper. Using geometric singular perturbation theory, the existence and stability regions of radially symmetric stationary spot solutions are delineated and, in particular, stable spots are shown to exist in appropriate parameter regimes. This result opens up the possibility of identifying and analysing drift and Hopf bifurcations, and their criticality, from the stationary spots described here.

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In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others.

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In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction-diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction-diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.

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Some minerals are colloidal and show no X-ray diffraction patterns. Vibrational spectroscopy offers one of the few methods for the assessment of the structure of these types of mineral. Among this group of minerals is kemmlitzite (Sr,Ce)Al3(AsO4)(SO4)(OH)6. The objective of this research is to determine the molecular structure of the mineral kemmlitzite using vibrational spectroscopy. Raman microscopy offers a useful method for the analysis of such colloidal minerals. Raman and infrared bands are attributed to the AsO43- , SO42- and water stretching vibrations. The Raman spectrum is dominated by a very intense sharp band at 984 cm-1 assigned to the SO42- symmetric stretching mode. Raman bands at 690, 772 and 825 cm-1 may be assigned to the AsO43- antisymmetric and symmetric stretching modes. Raman bands observed at 432 and 465 cm-1 are attributable to the doubly degenerate 2 (SO4)2- bending mode. Vibrational spectroscopy is important in the assessment of the molecular structure of the kemmlitzite, especially when the mineral is non-diffracting or poorly diffracting.

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We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.

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We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.

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Vibrational spectroscopy has been used to characterize the sulphate mineral khademite Al(SO4)F∙5(H2O). Raman band at 991 cm-1 with a shoulder at 975 cm-1 is assigned to the ν1 (SO4)2- symmetric stretching mode. The observation of two symmetric stretching modes suggests that the sulphate units are not equivalent. Two low intensity Raman bands at 1104 and 1132 cm-1 are assigned to the ν3 (SO4)2- antisymmetric stretching mode. The broad Raman band at 618 cm-1 is assigned to the v4 (SO4)2- bending modes. Raman bands at 455, 505 and 534 cm-1 are attributable to the doubly degenerate v2 (SO4)2- bending modes. Raman bands at 2991, 3146 and 3380 cm-1 are assigned to the OH stretching bands of water. Five infrared bands are noted at 2458, 2896, 3203, 3348 and 3489 cm-1 are also due to water stretching bands. The observation of multiple water stretching vibrations gives credence to the non-equivalence of water units in the khademite structure. Vibrational spectroscopy enables an assessment of the structure of khademite.

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The molecular structure of the arsenate mineral ceruleite has been assessed using a combination of Raman and infrared spectroscopy. The most intense band observed at 903 cm-1 is assigned to the (AsO4)3- symmetric stretching vibrational mode. The infrared spectrum shows intense bands at 787, 827 and 886 cm-1, ascribed to the triply degenerate m3 antisymmetric stretching vibration. Raman bands observed at 373, 400, 417 and 430 cm-1 are attributed to the m2 vibrational mode. Three broad bands for ceruleite found at 3056, 3198 and 3384 cm-1 are assigned to water OH stretching bands. By using a Libowitzky empirical equation, hydrogen bond distances of 2.65 and 2.75 Å are calculated. Vibrational spectra enable the molecular structure of the ceruleite mineral to be determined and whilst similarities exist in the spectral patterns with the roselite mineral group, sufficient differences exist to be able to determine the identification of the minerals.

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In an attempt to define genomic copy number changes associated with the development of basal cell carcinoma, we investigated 15 sporadic tumors by comparative genomic hybridization. With the incorporation of tissue microdissection and degenerate oligonucleotide primed-polymerase chain reaction we were able to isolate, and then universally amplify, DNA from the tumor type. This combined approach allows the investigation of chromosomal imbalances within a histologically distinct region of tissue. Using comparative genomic hybridization we have observed novel and recurrent chromosomal gains at 6p (47%), 6q (20%), 9p (20%), 7 (13%), and X (13%). In addition comparative genomic hybridization revealed regional loss on 9q in 33% of tested tumors encompassing 9q22.3 to which the putative tumor suppressor gene, Patched, has been mapped. The deletion of Patched has been indicated in the development of hereditary and sporadic basal cell carcinomas. The identification of these recurrent genetic aberrations suggests that basal cell carcinomas may not be as genetically stable as previously thought. Further investigation of these regions may lead to the identification of other genes responsible for basal cell carcinoma formation.

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Comparison of well-determined single crystal data for stoichiometric, or near-stoichiometric, metal hexaborides con-firm previously identified lattice parameter trends using powder diffraction. Trends for both divalent and trivalent forms suggest that potential new forms for synthesis include Sc and Mn hexaborides. Density Functional Theory (DFT) calculations for KB6, CaB6, YB6, LaB6, boron octahedral clusters and Sc and Mn forms, show that the shapes of bonding orbitals are defined by the boron framework. Inclusion of metal into the boron framework induces a reduction in energy ranging from 1 eV to 6 eV increasing with ionic charge. For metals with d1 character, such a shift in energy brings a doubly degenerate band section along the G-M reciprocal space direction within the conduction bands tangential to the Fermi surface. ScB6 band structure and density of states calculations show directional and gap characteristics similar to those of YB6 and LaB6. These calculations for ScB6 suggest it may be possible to realize superconductivity in this compound if synthesized.