Application of real and functional analysis to solve boundary value problems

This thesis is about using appropriate tools in functional analysis arid classical analysis to tackle the problem of existence and uniqueness of nonlinear partial differential equations. There being no unified strategy to deal with these equations, one approaches each equation with an appropriate method, depending on the characteristics of the equation. The correct setting of the problem in appropriate function spaces is the first important part on the road to the solution. Here, we choose the setting of Sobolev spaces. The second essential part is to choose the correct tool for each equation. In the first part of this thesis (Chapters 3 and 4) we consider a variety of nonlinear hyperbolic partial differential equations with mixed boundary and initial conditions. The methods of compactness and monotonicity are used to prove existence and uniqueness of the solution (Chapter 3). Finding a priori estimates is the main task in this analysis. For some types of nonlinearity, these estimates cannot be easily obtained, arid so these two methods cannot be applied directly. In this case, we first linearise the equation, using linear recurrence (Chapter 4). In the second part of the thesis (Chapter 5), by using an appropriate tool in functional analysis (the Sobolev Imbedding Theorem), we are able to improve previous results on a posteriori error estimates for the finite element method of lines applied to nonlinear parabolic equations. These estimates are crucial in the design of adaptive algorithms for the method, and previous analysis relies on, what we show to be, unnecessary assumptions which limit the application of the algorithms. Our analysis does not require these assumptions. In the last part of the thesis (Chapter 6), staying with the theme of choosing the most suitable tools, we show that using classical analysis in a proper way is in some cases sufficient to obtain considerable results. We study in this chapter nonexistence of positive solutions to Laplace's equation with nonlinear Neumann boundary condition. This problem arises when one wants to study the blow-up at finite time of the solution of the corresponding parabolic problem, which models the heating of a substance by radiation. We generalise known results which were obtained by using more abstract methods.

Data-driven computation of contact dynamics during two-point manipulation of deformable objects

This study represents a preliminary step towards data-driven computation of contact dynamics during manipulation of deformable objects at two points of contact. A modeling approach is proposed that characterizes the individual interaction at both points and the mutual effects of the two interactions on each other via a set of parameters. Both global as well as local coordinate systems are tested for encoding the contact mechanics. Artificial neural networks are trained on simulated data to capture the object behavior. A comparison of test data with the output of the trained system reveals a mean squared error percentage between 1% and 3% for simple interactions.

Challenges in designing culturally-adaptive ICT-based learning environments

This paper argues that two of the major problems facing local courseware developers and educators in creating culturally-sensitive lCT-based learning environments are the difficulties of representing cultural artefacts in courseware and of having a model of 'culture' that can be implemented in lCT-based systems. A developing learning-object model is presented; one that can be adopted to address aspects of this problem by providing a systematic way to approach implementing and representing cultural artefacts in courseware. This also provides a basis for some aspects of computer-based cultural preservation initiatives. While this approach may have higher short term development costs, the potential long term cultural benefits to the society far outweigh short term considerations.

Personality : social issues and personal growth

In this chapter, we will look at the application of personality to social problems and personal growth.  we have chosen two examples of social problems, anger (and aggression) and crime, to illustrate areas where personality has had an impact.

A hybrid approach for multiple particle tracking microrheology

Geometric object detection has many applications, such as in tracking. Particle tracking microrheology is a technique for studying mechanical properties by accurately tracking the motion of the immersed particles undergoing Brownian motion. Since particles are carried along by these random undulations of the medium, they can move in and out of the microscope's depth of focus, which results in halos (lower intensity). Two-point particle tracking microrheology (TPM) uses a threshold to find those particles with peak, which leads to the broken trajectory of the particles. The halos of those particles which are out of focus are circles and the centres can be accurately tracked in most cases. When the particles are sparse, TPM will lose certain useful information. Thus, it may cause inaccurate microrheology. An efficient algorithm to detect the centre of those particles will increase the accuracy of the Brownian motion. In this paper, a hybrid approach is proposed which combines the steps of TPM for particles in focus with a circle detection step using circular Hough transform for particles with halos. As a consequence, it not only detects more particles in each frame but also dramatically extends the trajectories with satisfactory accuracy. Experiments over a video microscope data set of polystyrene spheres suspended in water undergoing Brownian motion confirmed the efficiency of the algorithm.

A novel Physarum-Based ant colony system for solving the real-world traveling salesman problem

The solutions to Traveling Salesman Problem can be widely applied in many real-world problems. Ant colony optimization algorithms can provide an approximate solution to a Traveling Salesman Problem. However, most ant colony optimization algorithms suffer premature convergence and low convergence rate. With these observations in mind, a novel ant colony system is proposed, which employs the unique feature of critical tubes reserved in the Physaurm-inspired mathematical model. A series of experiments are conducted, which are consolidated by two realworld Traveling Salesman Problems. The experimental results show that the proposed new ant colony system outperforms classical ant colony system, genetic algorithm, and particle swarm optimization algorithm in efficiency and robustness.

Tree-based iterated local search for Markov random fields with applications in image analysis

The maximum a posteriori assignment for general structure Markov random fields is computationally intractable. In this paper, we exploit tree-based methods to efficiently address this problem. Our novel method, named Tree-based Iterated Local Search (T-ILS), takes advantage of the tractability of tree-structures embedded within MRFs to derive strong local search in an ILS framework. The method efficiently explores exponentially large neighborhoods using a limited memory without any requirement on the cost functions. We evaluate the T-ILS on a simulated Ising model and two real-world vision problems: stereo matching and image denoising. Experimental results demonstrate that our methods are competitive against state-of-the-art rivals with significant computational gain.

Cross-cultural examination of the structure of the Revised American Pain Society Patient Outcome Questionnaire (APS-POQ-R)

This study investigated the cross-cultural factor stability and internal consistency of the Revised American Pain Society Patient Outcome Questionnaire (APS-POQ-R); a measure of the quality of postoperative pain management employed internationally. We conducted exploratory factor analysis (EFA) of APS-POQ-R data from two point-prevalence studies comprising 268 and 311 surveys of Danish and Australian medical-surgical patients. Parallel analysis indicated four and three factor solutions for Danish and Australian patients respectively, which accounted for 58.1% and 52.9% of variance. Internal consistency was unsatisfactory among both Danish (Cronbach α=.54) and Australian (Cronbach α=.63) cohorts. There was a high degree of between-group similarity in item-factor loadings of variables coded as "pain experience", but not "pain management". This reflected cross-cultural differences in ratings of treatment satisfaction. For Danish patients, satisfaction was associated with the degree of pain severity and activity interference whereas for Australian patients, satisfaction was associated with their perceived ability to participate in treatment. To facilitate further cross-cultural comparison, we compared our findings to past research conducted in the U.S. and Iceland. EFA supported the construct validity of the APS-POQ-R as a measure of "pain experience", but indicated that items measuring "pain management" may vary cross-culturally. Findings highlighted the need for further validation of the APS-POQ-R internationally. PERSPECTIVE: This study revealed the APS-POQ-R as a valid measure of postoperative pain experience for Danish and Australian patients. Measures of patients' perception of pain management were not robust to group differences in treatment expectations and demonstrated cross-cultural instability. Results highlighted difficulties in establishing stable cross-cultural, cross-population subscales for the APS-POQ-R.

The influence of follower cultural orientation on attitudinal responses towards transformational leadership: evidence from the Chinese hospitality industry

In addition to extending the empirical investigation of the relationship between transformational leadership and follower affective commitment to the Chinese hospitality industry, this study makes a theoretical contribution by investigating the influence of individually held cultural values on this relationship. Building on previous research which has examined whether collectivism moderates the transformational leadership/affective commitment relationship, this study investigates the moderating effects of two additional cultural value orientations, namely power distance and uncertainty avoidance. Hierarchical regression analysis was utilized to analyse survey data from 398 employees of four Chinese hotels in Zhejiang Province. In addition to finding a positive relationship between transformational leadership and affective commitment, data analysis revealed that followers low in power distance exhibited higher levels of affective commitment when working under a transformational leader than those high in power distance. In addition, followers high in uncertainty avoidance and collectivism exhibited greater commitment when working under a transformational leader than those low in uncertainty avoidance and collectivism. These findings clearly indicate the importance of within-country cultural differences to the effectiveness of leaders in the workplace. © 2014 © 2013 Taylor & Francis.

Polyhedral results for the Cardinality Constrained Multi-cycle Problem (CCMcP) and the Cardinality Constrained Cycles and Chains Problem (CCCCP)

In recent years, there has been studies on the cardinality constrained multi-cycle problems on directed graphs, some of which considered chains co-existing on the same digraph whilst others did not. These studies were inspired by the optimal matching of kidneys known as the Kidney Exchange Problem (KEP). In a KEP, a vertex on the digraph represents a donor-patient pair who are related, though the kidney of the donor is incompatible to the patient. When there are multiple such incompatible pairs in the kidney exchange pool, the kidney of the donor of one incompatible pair may in fact be compatible to the patient of another incompatible pair. If Donor A’s kidney is suitable for Patient B, and vice versa, then there will be arcs in both directions between Vertex A to Vertex B. Such exchanges form a 2-cycle. There may also be cycles involving 3 or more vertices. As all exchanges in a kidney exchange cycle must take place simultaneously, (otherwise a donor can drop out from the program once his/her partner has received a kidney from another donor), due to logistic and human resource reasons, only a limited number of kidney exchanges can occur simultaneously, hence the cardinality of these cycles are constrained. In recent years, kidney exchange programs around the world have altruistic donors in the pool. A sequence of exchanges that starts from an altruistic donor forms a chain instead of a cycle. We therefore have two underlying combinatorial optimization problems: Cardinality Constrained Multi-cycle Problem (CCMcP) and the Cardinality Constrained Cycles and Chains Problem (CCCCP). The objective of the KEP is either to maximize the number of kidney matches, or to maximize a certain weighted function of kidney matches. In a CCMcP, a vertex can be in at most one cycle whereas in a CCCCP, a vertex can be part of (but in no more than) a cycle or a chain. The cardinality of the cycles are constrained in all studies. The cardinality of the chains, however, are considered unconstrained in some studies, constrained but larger than that of cycles, or the same as that of cycles in others. Although the CCMcP has some similarities to the ATSP- and VRP-family of problems, there is a major difference: strong subtour elimination constraints are mostly invalid for the CCMcP, as we do allow smaller subtours as long as they do not exceed the size limit. The CCCCP has its distinctive feature that allows chains as well as cycles on the same directed graph. Hence, both the CCMcP and the CCCCP are interesting and challenging combinatorial optimization problems in their own rights. Most existing studies focused on solution methodologies, and as far as we aware, there is no polyhedral studies so far. In this paper, we will study the polyhedral structure of the natural arc-based integer programming models of the CCMcP and the CCCCP, both containing exponentially many constraints. We do so to pave the way for studying strong valid cuts we have found that can be applied in a Lagrangean relaxation-based branch-and-bound framework where at each node of the branch-and-bound tree, we may be able to obtain a relaxation that can be solved in polynomial time, with strong valid cuts dualized into the objective function and the dual multipliers optimised by subgradient optimisation.

Widespread convergence in toxin resistance by predictable molecular evolution

The question about whether evolution is unpredictable and stochastic or intermittently constrained along predictable pathways is the subject of a fundamental debate in biology, in which understanding convergent evolution plays a central role. At the molecular level, documented examples of convergence are rare and limited to occurring within specific taxonomic groups. Here we provide evidence of constrained convergent molecular evolution across the metazoan tree of life. We show that resistance to toxic cardiac glycosides produced by plants and bufonid toads is mediated by similar molecular changes to the sodium-potassium-pump (Na(+)/K(+)-ATPase) in insects, amphibians, reptiles, and mammals. In toad-feeding reptiles, resistance is conferred by two point mutations that have evolved convergently on four occasions, whereas evidence of a molecular reversal back to the susceptible state in varanid lizards migrating to toad-free areas suggests that toxin resistance is maladaptive in the absence of selection. Importantly, resistance in all taxa is mediated by replacements of 2 of the 12 amino acids comprising the Na(+)/K(+)-ATPase H1-H2 extracellular domain that constitutes a core part of the cardiac glycoside binding site. We provide mechanistic insight into the basis of resistance by showing that these alterations perturb the interaction between the cardiac glycoside bufalin and the Na(+)/K(+)-ATPase. Thus, similar selection pressures have resulted in convergent evolution of the same molecular solution across the breadth of the animal kingdom, demonstrating how a scarcity of possible solutions to a selective challenge can lead to highly predictable evolutionary responses.

Exempt treatment of financial intermediation services under a value-added tax: an assessment of alternatives

Most countries with a value-added tax (VAT) exempt financial intermediation services from the tax. While exemption is generally perceived to be undesirable, it is also widely regarded as unavoidable because of technical difficulties in applying VAT to these services. This article reviews the standard rationale for exempt treatment and then considers the relative merits of two recent challenges raised in the tax literature. The first challenge involves the application of cash flow taxation to financial intermediation services in a manner that is consistent with an invoice/credit VAT (which is the dominant form). The second challenge proposes a comprehensive system of zero-rating of financial intermediation services, which is supported by a characterization of the household consumption of such services as non-taxable. The author argues that each of these alternatives to an exemption system suffers from both theoretical and practical implementation difficulties that make maintenance of exempt treatment the preferred approach, at least in the short term. There is, however, a simpler alternative to these fundamental reform options, involving modification of just one aspect of an exemption system to relieve some of its more problematic aspects. Many of the interpretative problems and associated inefficiencies that plague an exemption system arise from the need to distinguish between taxable and exempt financial services. The author argues that these difficulties can be eliminated, to a large extent, by basing the distinction on the form of prices. In support of this approach, he points out that it is consistent with the underlying reasons for the application of exempt treatment. The author considers a number of other possible modifications, but these are either rejected outright or viewed with a healthy skepticism. For example, the author is critical of the apparent rationale for the application of cash flow taxation to property and casualty insurers. He also rejects proposals that accept some looseness in the formulaic allocation by financial intermediaries of the costs of business inputs between exempt and taxable services for input credit purposes. In his view, an explicit reliance on pricing structures to draw the boundary between exempt and taxable services is preferable to the provision of relief for blocked input tax credits of financial intermediaries. Finally, the author is skeptical of the case for a policy response intended to address the tax bias under an exemption system for financial intermediaries to insource supplies.

Two-stage sequential procedure for nonparametric regression estimation

In nonparametric statistics the functional form of the relationship between the response variable and its associated predictor variables is unspecified but it is assumed to be a smooth function. We develop a procedure for constructing a fixed width confidence interval for the predicted value at a specified point of the independent variable. The optimal sample size for constructing this interval is obtained using a two stage sequential procedure which relies on some asymptotic properties of the Nadaraya--Watson and local linear estimators. Finally, a large scale simulation study demonstrates the applicability of the developed procedure for small and moderate sample sizes. The procedure developed here should find wide applicability since many practical problems which arise in industry involve estimating an unknown function.