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Item type: Item , Access status: Metadata only , Generalized soft finite element method for elliptic eigenvalue problems(2025-04-15) Chen, Jipei; Calo, Victor M.; Deng, Quanling; School of Computing; School of ComputingThe recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps across mesh interfaces from the FEM stiffness bilinear form while maintaining the system's coercivity. Herein, we present two generalizations for SoftFEM that aim to improve the approximation accuracy and further reduce the discrete systems' stiffness. Firstly and most naturally, we generalize SoftFEM by adding a least-square term to the mass bilinear form. Superconvergent results of rates h6 and h8 for eigenvalues are established for linear uniform elements; h8 is the highest order of convergence known in the literature. Secondly, we generalize SoftFEM by applying the blended Gaussian-type quadratures. We demonstrate further reductions in stiffness compared to traditional FEM and SoftFEM. The coercivity and analysis of the optimal error convergences follow the work of SoftFEM. Thus, this paper focuses on the numerical study of these generalizations. For linear and uniform elements, analytical eigenpairs, exact eigenvalue errors, and superconvergent error analysis are established. Various numerical examples demonstrate the potential of generalized SoftFEMs for spectral approximation, particularly in high-frequency regimes.Item type: Item , Access status: Metadata only , Circular viewpoint of higher-order rogue wave structures of the nonlinear Schrödinger equation(2025-04-01) Ankiewicz, A.; Department of Fundamental & Theoretical Physics; Department of Fundamental & Theoretical PhysicsWe analyze rogue wave patterns for various orders of the nonlinear Schr & ouml;dinger equation for large values of solution parameters. We use a combination of exact solutions, geometric constructions and polynomial approximations for analysis, and introduce a new way of viewing the formations of rogue waves, including the triangular ones, by showing that they all can be represented as occupying circular shells, some of which contain 'nuclei'.Item type: Publication , Access status: Metadata only , Chapter 10: Italian immigrants and the built environment in rural Australia(2010) Jordan, Kirrily; Krivokapic-Skoko, Branka; Collins, JockNon-Anglo-Celtic immigrants have transformed Australian rural landscape through the construction of public and private spaces expressing their cultural heritage. These sites can also significantly impact the dynamics of social cohesion and intercultural relations in multicultural rural communities. This chapter links heritage and multiculturalism in rural settings and explores the potential role of the sites built by rural ethnic minorities in facilitating intra- and intergroup social networks. The chapter is divided into two parts. The first part briefly explores the literature on immigration and heritage, place, belonging and social cohesion, and the relationship between social capital and the built environment. The second part outlines preliminary empirical findings from Griffith in New South Wales. Using the concepts of intercultural dialogue and bonding and bridging social capital, the chapter explores the role of the places built by Italian immigrants in facilitating social networks and improved relations within and between Griffith's ethnic communities.Item type: Publication , Access status: Metadata only , Tracking by detection for interactive image augmentation in laparoscopy(2012) Kim, Jae Hak; Bartoli, Adrien; Collins, Toby; Hartley, RichardWe present a system for marking, tracking and visually augmenting a deformable surgical site by the robust automatic detection of natural landmarks (image features) in laparoscopic surgery. In our system, the surgeon first selects a frame containing an organ of interest, and this is used by our system both to detect every instance of the organ in a laparoscopic video feed, and to recover the nonrigid deformations. The system then augments the video with customizable visual information such as the location of hidden or weakly visible structures (cysts, vessels, etc), or planned incision points, acquired from pre-operative or intra-operative data. Frame-rate organ detection is performed via a novel procedure that matches the current frame to the reference frame. Because laparoscopic images are known to be extremely difficult to match, we propose to use Shape-from-Shading and conformal flattening to cancel out much of the variation in appearance due to perspective foreshortening, and we then apply robust matching to the flattened surfaces. Experiments show robust tracking and detection results on a laparoscopic procedure with the uterus as target organ. As our system detects the organ in every frame, it is not impaired by target loss, contrary to most previous methods.Item type: Publication , Access status: Metadata only , Elicitation and identification of properties(2014) Steinwart, Ingo; Pasin, Chloé; Williamson, Robert C.; Zhang, SiyuProperties of distributions are real-valued functionals such as the mean, quantile or conditional value at risk. A property is elicitable if there exists a scoring function such that minimization of the associated risks recovers the property. We extend existing results to characterize the elicitability of properties in a general setting. We further relate elicitability to identifiability (a notion introduced by Osband) and provide a general formula describing all scoring functions for an elicitable property. Finally, we draw some connections to the theory of coherent risk measures.