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.

A First Order Predicate Logic Formulation of the 3D Reconstruction Problem and its Solution Space

This paper defines the 3D reconstruction problem as the process of reconstructing a 3D scene from numerous 2D visual images of that scene. It is well known that this problem is ill-posed, and numerous constraints and assumptions are used in 3D reconstruction algorithms in order to reduce the solution space. Unfortunately, most constraints only work in a certain range of situations and often constraints are built into the most fundamental methods (e.g. Area Based Matching assumes that all the pixels in the window belong to the same object). This paper presents a novel formulation of the 3D reconstruction problem, using a voxel framework and first order logic equations, which does not contain any additional constraints or assumptions. Solving this formulation for a set of input images gives all the possible solutions for that set, rather than picking a solution that is deemed most likely. Using this formulation, this paper studies the problem of uniqueness in 3D reconstruction and how the solution space changes for different configurations of input images. It is found that it is not possible to guarantee a unique solution, no matter how many images are taken of the scene, their orientation or even how much color variation is in the scene itself. Results of using the formulation to reconstruct a few small voxel spaces are also presented. They show that the number of solutions is extremely large for even very small voxel spaces (5 x 5 voxel space gives 10 to 10(7) solutions). This shows the need for constraints to reduce the solution space to a reasonable size. Finally, it is noted that because of the discrete nature of the formulation, the solution space size can be easily calculated, making the formulation a useful tool to numerically evaluate the usefulness of any constraints that are added.

Analysis of trigonometric implicit Runge-Kutta methods

Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge-Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. (c) 2006 Elsevier B.V. All rights reserved.

Modern methods for traditional tasks: Developing an electronic version of student fieldwork assessment at The University of Queensland.

Fieldwork placements are an integral part of many professional tertiary programmes. At The University of Queensland, Occupational Therapy students undertake block fieldwork affiliations off campus at a wide range of sites as part of their studies. Students’ fieldwork performance has traditionally been assessed using a hard copy format of the Student Placement Evaluation Form (SPEF), which is posted to the university on completion by the clinical supervisor. This project aimed to develop an electronic version of the UQ Occupational Therapy Student Placement Evaluation Form (SPEF), to allow the assessment to be completed and returned in an on line format. Practitioners had become very comfortable with using the existing print based form so in order to encourage and assist users to extend beyond their comfort zones, numerous steps were taken to ease the learning process including incorporating the existing page layout, consistent colour coding, considerable user instruction, testing and software enhancement cycles. Additionally, the e-version of the SPEF aimed to provide a range of benefits such as on screen assistance in the form of instructions, roll overs and feedback to supervisors, increased accuracy, faster completion, cost savings to the School, up to date design, improved security and confidential and anonymous storage of fieldwork results for potential future research.

Evaluation and comparison of mammalian subcellular localization prediction methods

Background: Determination of the subcellular location of a protein is essential to understanding its biochemical function. This information can provide insight into the function of hypothetical or novel proteins. These data are difficult to obtain experimentally but have become especially important since many whole genome sequencing projects have been finished and many resulting protein sequences are still lacking detailed functional information. In order to address this paucity of data, many computational prediction methods have been developed. However, these methods have varying levels of accuracy and perform differently based on the sequences that are presented to the underlying algorithm. It is therefore useful to compare these methods and monitor their performance. Results: In order to perform a comprehensive survey of prediction methods, we selected only methods that accepted large batches of protein sequences, were publicly available, and were able to predict localization to at least nine of the major subcellular locations (nucleus, cytosol, mitochondrion, extracellular region, plasma membrane, Golgi apparatus, endoplasmic reticulum (ER), peroxisome, and lysosome). The selected methods were CELLO, MultiLoc, Proteome Analyst, pTarget and WoLF PSORT. These methods were evaluated using 3763 mouse proteins from SwissProt that represent the source of the training sets used in development of the individual methods. In addition, an independent evaluation set of 2145 mouse proteins from LOCATE with a bias towards the subcellular localization underrepresented in SwissProt was used. The sensitivity and specificity were calculated for each method and compared to a theoretical value based on what might be observed by random chance. Conclusion: No individual method had a sufficient level of sensitivity across both evaluation sets that would enable reliable application to hypothetical proteins. All methods showed lower performance on the LOCATE dataset and variable performance on individual subcellular localizations was observed. Proteins localized to the secretory pathway were the most difficult to predict, while nuclear and extracellular proteins were predicted with the highest sensitivity.