A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed. © 2014 IMACS.

I don't see me like you see me, but is that a problem? Cultural influences on rating discrepancy in 360-degree feedback instruments

360-degree feedback from a variety of rater sources yields important information about leaders' styles, strengths and weaknesses for development. Results where observer ratings are discrepant (i.e., different) from self-ratings are often seen as indicators of problematic leadership relationships, skills, or lack of self-awareness. Yet research into the antecedents of such self-observer rating discrepancy suggests the presence of systematic influences, such as cultural values. The present study investigates the variation of rating discrepancies on three leadership skills (decision making, leading employees, and composure) in dependence of one exemplary culture dimension (power distance) on data from 31 countries using multilevel structural equation modelling. Results show that cultural values indeed predict self-observer rating discrepancies. Thus, systemic and contextual influences such as culture need to be taken into consideration when interpreting the importance and meaning of self-observer rating discrepancies in 360-degree instruments.

Minimum description length, regularisation and multi-modal data

Relationships between clustering, description length, and regularisation are pointed out, motivating the introduction of a cost function with a description length interpretation and the unusual and useful property of having its minimum approximated by the densest mode of a distribution. A simple inverse kinematics example is used to demonstrate that this property can be used to select and learn one branch of a multi-valued mapping. This property is also used to develop a method for setting regularisation parameters according to the scale on which structure is exhibited in the training data. The regularisation technique is demonstrated on two real data sets, a classification problem and a regression problem.

Minimum description length, regularisation and multi-modal data

Conventional feed forward Neural Networks have used the sum-of-squares cost function for training. A new cost function is presented here with a description length interpretation based on Rissanen's Minimum Description Length principle. It is a heuristic that has a rough interpretation as the number of data points fit by the model. Not concerned with finding optimal descriptions, the cost function prefers to form minimum descriptions in a naive way for computational convenience. The cost function is called the Naive Description Length cost function. Finding minimum description models will be shown to be closely related to the identification of clusters in the data. As a consequence the minimum of this cost function approximates the most probable mode of the data rather than the sum-of-squares cost function that approximates the mean. The new cost function is shown to provide information about the structure of the data. This is done by inspecting the dependence of the error to the amount of regularisation. This structure provides a method of selecting regularisation parameters as an alternative or supplement to Bayesian methods. The new cost function is tested on a number of multi-valued problems such as a simple inverse kinematics problem. It is also tested on a number of classification and regression problems. The mode-seeking property of this cost function is shown to improve prediction in time series problems. Description length principles are used in a similar fashion to derive a regulariser to control network complexity.

e-CAF: flexible marking schemes for electronic coursework assessment and feedback

Recent surveys reveal that many university students in the U.K. are not satisfied with the timeliness and usefulness of the feedback given by their tutors. Ensuring timeliness in marking can result in a reduction in the quality of feedback. Though suitable use of Information and Communication Technology should alleviate this problem, existing Virtual Learning Environments are inadequate to support detailed marking scheme creation and they provide little support for giving detailed feedback. This paper describes a unique new web-based tool called e-CAF for facilitating coursework assessment and feedback management directed by marking schemes. Using e-CAF, tutors can create or reuse detailed marking schemes efficiently without sacrificing the accuracy or thoroughness in marking. The flexibility in marking scheme design also makes it possible for tutors to modify a marking scheme during the marking process without having to reassess the students’ submissions. The resulting marking process will become more transparent to students.

Enhancing creativity in a general work environment : the role of problem-solving demand

Prior research suggests management can employ cognitively demanding job attributes to promote employee creativity. However, it is not clear what specific type of cognitive demand is particularly important for creativity, what processes underpin the relationship between demanding job conditions and creativity and what factors lead to employee perceptions of demanding job attributes. This research sets out to address the aforementioned issues by examining: (i) problem-solving demand (PDS), a specific type of cognitive demand, and the processes that link PSD to creativity, and (ii) antecedents to PSD. Based on social cognitive theory, PSD was hypothesized to be positively related to creativity through the motivational mechanism of creative self-efficacy. However, the relationship between PSD and creative self-efficacy was hypothesized to be contingent on levels of intrinsic motivation. Social information processing perspective and the job crafting model were used to identify antecedents of PSD. Consequently, two social-contextual factors (supervisor developmental feedback and job autonomy) and one individual factor (proactive personality) were hypothesized to be precursors to PSD perceptions. The theorized model was tested with data obtained from a sample of 270 employees and their supervisors from 3 organisations in the People’s Republic of China. Regression results revealed that PSD was positively related to creativity but this relationship was partially mediated by creative self-efficacy. Additionally, intrinsic motivation moderated the relationship between PSD and creative self-efficacy such that the relationship was stronger for individuals high rather than low in intrinsic motivation. The findings represent a productive first step in identifying a specific cognitive demand that is conducive to employee creativity. In addition, the findings contribute to the literature by identifying a psychological mechanism that may link cognitively demanding job attributes and creativity.

Enhancing student learning experience through a novel electronic coursework assessment and feedback management system

Recent National Student Surveys revealed that many U.K. university students are dissatisfied with the timeliness and usefulness of the feedback received from their tutors. Ensuring timeliness in marking often results in a reduction in the quality of feedback. In Computer Science where learning relies on practising and learning from mistakes, feedback that pin-points errors and explains means of improvement is important to achieve a good student learning experience. Though suitable use of Information and Communication Technology should alleviate this problem, existing Virtual Learning Environments and e-Assessment applications such as Blackboard/WebCT, BOSS, MarkTool and GradeMark are inadequate to support a coursework assessment process that promotes timeliness and usefulness of feedback while maintaining consistency in marking involving multiple tutors. We have developed a novel Internet application, called eCAF, for facilitating an efficient and transparent coursework assessment and feedback process. The eCAF system supports detailed marking scheme editing and enables tutors to use such schemes to pin-point errors in students' work so as to provide helpful feedback efficiently. Tutors can also highlight areas in a submitted work and associate helpful feedback that clearly links to the identified mistakes and the respective marking criteria. In light of the results obtained from a recent trial of eCAF, we discuss how the key features of eCAF may facilitate an effective and efficient coursework assessment and feedback process.

Design and analysis of distributed utility maximization algorithm for multihop wireless network with inaccurate feedback

Distributed network utility maximization (NUM) is receiving increasing interests for cross-layer optimization problems in multihop wireless networks. Traditional distributed NUM algorithms rely heavily on feedback information between different network elements, such as traffic sources and routers. Because of the distinct features of multihop wireless networks such as time-varying channels and dynamic network topology, the feedback information is usually inaccurate, which represents as a major obstacle for distributed NUM application to wireless networks. The questions to be answered include if distributed NUM algorithm can converge with inaccurate feedback and how to design effective distributed NUM algorithm for wireless networks. In this paper, we first use the infinitesimal perturbation analysis technique to provide an unbiased gradient estimation on the aggregate rate of traffic sources at the routers based on locally available information. On the basis of that, we propose a stochastic approximation algorithm to solve the distributed NUM problem with inaccurate feedback. We then prove that the proposed algorithm can converge to the optimum solution of distributed NUM with perfect feedback under certain conditions. The proposed algorithm is applied to the joint rate and media access control problem for wireless networks. Numerical results demonstrate the convergence of the proposed algorithm. © 2013 John Wiley & Sons, Ltd.

On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach

We investigate the problem of determining the stationary temperature field on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the temperature (or the heat flux) is known, and, additionally, on a portion of this exterior boundary the heat flux (or temperature) is also given. We propose a direct boundary integral approach in combination with Tikhonov regularization for the stable determination of the temperature and flux on the inclusion. To determine these quantities on the inclusion, boundary integral equations are derived using Green’s functions, and properties of these equations are shown in an L2-setting. An effective way of discretizing these boundary integral equations based on the Nystr¨om method and trigonometric approximations, is outlined. Numerical examples are included, both with exact and noisy data, showing that accurate approximations can be obtained with small computational effort, and the accuracy is increasing with the length of the portion of the boundary where the additionally data is given.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

Design and analysis of distributed utility maximization algorithm for multihop wireless network with inaccurate feedback

Distributed network utility maximization (NUM) is receiving increasing interests for cross-layer optimization problems in multihop wireless networks. Traditional distributed NUM algorithms rely heavily on feedback information between different network elements, such as traffic sources and routers. Because of the distinct features of multihop wireless networks such as time-varying channels and dynamic network topology, the feedback information is usually inaccurate, which represents as a major obstacle for distributed NUM application to wireless networks. The questions to be answered include if distributed NUM algorithm can converge with inaccurate feedback and how to design effective distributed NUM algorithm for wireless networks. In this paper, we first use the infinitesimal perturbation analysis technique to provide an unbiased gradient estimation on the aggregate rate of traffic sources at the routers based on locally available information. On the basis of that, we propose a stochastic approximation algorithm to solve the distributed NUM problem with inaccurate feedback. We then prove that the proposed algorithm can converge to the optimum solution of distributed NUM with perfect feedback under certain conditions. The proposed algorithm is applied to the joint rate and media access control problem for wireless networks. Numerical results demonstrate the convergence of the proposed algorithm. © 2013 John Wiley & Sons, Ltd.

Topological versus chemical ordering in network glasses at intermediate and extended length scales

Atomic ordering in network glasses on length scales longer than nearest-neighbour length scales has long been a source of controversy(1-6). Detailed experimental information is therefore necessary to understand both the network properties and the fundamentals of glass formation. Here we address the problem by investigating topological and chemical ordering in structurally disordered AX2 systems by applying the method of isotopic substitution in neutron diffraction to glassy ZnCl2. This system may be regarded as a prototypical ionic network forming glass, provided that ion polarization effects are taken into account(7), and has thus been the focus of much attention(8-14). By experiment, we show that both the topological and chemical ordering are described by two length scales at distances greater than nearest-neighbour length scales. One of these is associated with the intermediate range, as manifested by the appearance in the measured diffraction patterns of a first sharp diffraction peak at 1.09( 3) angstrom(-1); the other is associated with an extended range, which shows ordering in the glass out to 62( 4) angstrom. We also find that these general features are characteristic of glassy GeSe2, a prototypical covalently bonded network material(15,16). The results therefore offer structural insight into those length scales that determine many important aspects of supercooled liquid and glass phenomenology(11).

Modeling of the spectrum in a random distributed feedback fiber laser within the power balance modes

The simplest model for a description of the random distributed feedback (RDFB) Raman fiber laser is a power balance model describing the evolution of the intensities of the waves over the fiber length. The model predicts well the power performances of the RDFB fiber laser including the generation threshold, the output power and pump and generation wave intensity distributions along the fiber. In the present work, we extend the power balance model and modify equations in such a way that they describe now frequency dependent spectral power density instead of integral over the spectrum intensities. We calculate the generation spectrum by using the depleted pump wave longitudinal distribution derived from the conventional power balance model. We found the spectral balance model to be sufficient to account for the spectral narrowing in the RDFB laser above the threshold of the generation. © 2014 SPIE.

Raman gain and random distributed feedback generation in nitrogen doped silica core fiber

Recently, the concept of a random distributed feedback (DFB) lasing in optical fibers has been demonstrated [1], A number of different random DFB fiber lasers has been demonstrated so far including tunable, multiwalength, cascaded generation, generation in different spectral bands etc [2-7]. All systems are based on standard low-loss germanium doped silica core fibres having relatively low Rayleigh scattering coefficient. Thus, the typical length of random DFB fiber lasers is in the range from several kilometres to tens of kilometres to accumulate enough random feedback. Here we demonstrate for the first time to our knowledge the random DFB fiber laser based on a nitrogen doped silica core (N-doped) fiber. The fiber has several times higher Rayleigh scattering coefficient compared to standard telecommunication fibres. Thus, the generation is achieved in 500 meters long fiber only. © 2013 IEEE.

Raman fiber lasers with a random distributed feedback based on Rayleigh scattering

We demonstrate lasing based on a random distributed feedback due to the Raman amplified Rayleigh backscattering in different types of cavities with and without conventional point-action reflectors. Quasistationary generation of a narrowband spectrum is achieved despite the random nature of the feedback. The generated spectrum is localized at the reflection or gain spectral maxima in schemes with and without point reflectors, respectively. The length limit for a conventional cavity and the minimal pump power required for the lasing based purely on a random distributed feedback are determined. © 2010 The American Physical Society.