A Recommender System based on Idiotypic Artificial Immune Networks

The immune system is a complex biological system with a highly distributed, adaptive and self-organising nature. This paper presents an Artificial Immune System (AIS) that exploits some of these characteristics and is applied to the task of film recommendation by Collaborative Filtering (CF). Natural evolution and in particular the immune system have not been designed for classical optimisation. However, for this problem, we are not interested in finding a single optimum. Rather we intend to identify a sub-set of good matches on which recommendations can be based. It is our hypothesis that an AIS built on two central aspects of the biological immune system will be an ideal candidate to achieve this: Antigen-antibody interaction for matching and idiotypic antibody-antibody interaction for diversity. Computational results are presented in support of this conjecture and compared to those found by other CF techniques.

A modelação matemática com recurso a tecnologia: Um estudo em contexto de colaboração entre professoras de matemática e de física-química

Este estudo teve como objectivo compreender o desenvolvimento de tarefas de modelação, por parte de uma professora de Matemática e de uma professora de Física­ Química, no âmbito de trabalho colaborativo. Para tal foram formuladas três questões orientadoras: 1. Como é que os professores seleccionam e preparam as tarefas de modelação a colocar aos alunos em situação de sala de aula? Que características das tarefas de modelação se mostram fundamentais para a sua selecção? 2. como desenvolvem os professores as tarefas de modelação na sala de aula? Como gerem e dinamizam as aulas onde colocam tarefas de modelação aos alunos? Que papel reservam ao professor e ao aluno? 3. como exploram os professores as potencialidades das calculadoras gráficas no desenvolvimento das tarefas de modelação? Que questões se colocam à utilização de sensores? O estudo decorreu numa escola secundária, durante o ano lectivo de 2005/06, sob proposta e com a participação da investigadora, envolvendo uma professora de Matemática e uma professora de Física-Química de uma mesma turma de 100 ano. O grupo colaborativo reuniu regularmente e preparou e leccionou aulas com tarefas de modelação matemática, recorrendo a calculadoras gráficas e sensores, tarefas e tecnologias novas para ambas as professoras. A metodologia utilizada na investigação tem natureza qualitativa, tendo sido realizadas duas entrevistas longas a cada professora, uma no início e outra no fim do estudo, bem como entrevistas de curta duração às professoras após cada uma das aulas onde foram desenvolvidas as tarefas. Foram também recolhidos registos das sessões colectivas de trabalho e elaborado um "diário de bordo". O estudo permitiu formular as seguintes conclusões: - Quando as professoras seleccionavam as tarefas de modelação a propor aos seus alunos tinham em consideração o cumprimento dos programas, os conteúdos a abordar e a diversidade de questões que se podem formular sobre os mesmos e o interesse e significado da experiência para os alunos. - O tempo que é necessário para a preparação e execução das tarefas de modelação pareceu ser factor de grande peso na sua selecção. - O elevado número de alunos por turma pode ser factor um negativo para o desenvolvimento de tarefas de modelação na sala de aula. -Na opinião das professoras, o recurso à calculadora gráfica e aos sensores para realizar a recolha de dados relativos a uma tarefa de modelação tomou-as mais apelativas e ajudou os alunos a compreender a situação em causa assim como permitiu tomar mais nítida a relação entre a Matemática e a Física. ABSTRACT: This study aimed to understand the development of modelling tasks, by a Mathematics teacher and a Physics-Chemistry teacher, as part of collaborative work. For this study were formulated three guidelines: 1. How do teachers select and prepare the modelling tasks to present to the students in a classroom situation? What characteristics of these tasks are essential for their selection? 2. How do teachers develop the modelling tasks in the classroom? How do they manage and dynamize the classes where the modelling tasks took place? What role it's reserd to the teacher and the student? 3. How do teachers exploit the potential of graphics calculator in the development of the modelling tasks? What issues arise for the use of sensors? This study took place at a secundary school during the academic year 2005/06, as a suggestion and with the participation of the researcher, involving a Mathematics teacher and a Physics-Chemistry teacher of the same class (10th grade). The collaborative group had regular meetings and prepared and developed modellin tasks in the classroom using graphics calculator and sensors, which was a new activity for all the teachears. The methodology used has a qualitative nature. Two interviews were made to each teacher, one at baseline and another at the end of the study, fourteen work sections and three modelling tasks were explored in classroom context after which followed small interviews to the teacher that gave the class. ln addition records were also made in a small "log-book". This study allowed to reach the following conclusions: - When the teachers select the modelling tasks to offer its students they take into account the programs, the contents and the diversity of questions that can be made on it and the interest and significance of the experience for students. - The time needed for preparation and implementation of the modelling tasks is another factor of great weight in its selection. - The high number of student per class can be a negative factor for the development of modelling tasks in the classroom. Iii - ln the teacher’s opinion, the use of the graphics calculator and sensors to collect data on a modelling tasks makes its more attractive and helps students to understand the situation and makes clearer the link between Mathematics and Physics.

A two-fluid model for tissue growth within a dynamic flow environment

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89). The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a chanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct. The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population.

Teaching Through Technology – the Experience of Bulgarian Teachers

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

Modelling socially optimal land allocations for sugar cane growing in North Queensland: a linked mathematical programming and choice modelling study

A modelling framework is developed to determine the joint economic and environmental net benefits of alternative land allocation strategies. Estimates of community preferences for preservation of natural land, derived from a choice modelling study, are used as input to a model of agricultural production in an optimisation framework. The trade-offs between agricultural production and environmental protection are analysed using the sugar industry of the Herbert River district of north Queensland as an example. Spatially-differentiated resource attributes and the opportunity costs of natural land determine the optimal tradeoffs between production and conservation for a range of sugar prices.

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

Mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Modelling oil absorption during post-frying cooling - II: solution of the mathematical model, model testing and simulations

The mathematical models that describe the immersion-frying period and the post-frying cooling period of an infinite slab or an infinite cylinder were solved and tested. Results were successfully compared with those found in the literature or obtained experimentally, and were discussed in terms of the hypotheses and simplifications made. The models were used as the basis of a sensitivity analysis. Simulations showed that a decrease in slab thickness and core heat capacity resulted in faster crust development. On the other hand, an increase in oil temperature and boiling heat transfer coefficient between the oil and the surface of the food accelerated crust formation. The model for oil absorption during cooling was analysed using the tested post-frying cooling equation to determine the moment in which a positive pressure driving force, allowing oil suction within the pore, originated. It was found that as crust layer thickness, pore radius and ambient temperature decreased so did the time needed to start the absorption. On the other hand, as the effective convective heat transfer coefficient between the air and the surface of the slab increased the required cooling time decreased. In addition, it was found that the time needed to allow oil absorption during cooling was extremely sensitive to pore radius, indicating the importance of an accurate pore size determination in future studies.

Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Mathematical and numerical modelling of dispersion-managed solitons, autosolitons and self-similar optical pulses

This thesis presents theoretical investigation of three topics concerned with nonlinear optical pulse propagation in optical fibres. The techniques used are mathematical analysis and numerical modelling. Firstly, dispersion-managed (DM) solitons in fibre lines employing a weak dispersion map are analysed by means of a perturbation approach. In the case of small dispersion map strengths the average pulse dynamics is described by a perturbation approach (NLS) equation. Applying a perturbation theory, based on the Inverse Scattering Transform method, an analytic expression for the envelope of the DM soliton is derived. This expression correctly predicts the power enhancement arising from the dispersion management.Secondly, autosoliton transmission in DM fibre systems with periodical in-line deployment of nonlinear optical loop mirrors (NOLMs) is investigated. The use of in-line NOLMs is addressed as a general technique for all-optical passive 2R regeneration of return-to-zero data in high speed transmission system with strong dispersion management. By system optimisation, the feasibility of ultra-long single-channel and wavelength-division multiplexed data transmission at bit-rates ³ 40 Gbit s-1 in standard fibre-based systems is demonstrated. The tolerance limits of the results are defined.Thirdly, solutions of the NLS equation with gain and normal dispersion, that describes optical pulse propagation in an amplifying medium, are examined. A self-similar parabolic solution in the energy-containing core of the pulse is matched through Painlevé functions to the linear low-amplitude tails. The analysis provides a full description of the features of high-power pulses generated in an amplifying medium.

An Overview of Modelling Bulgarian Wildland Fire Behaviour by Application of a Mathematical Game Method and WRF-Fire Models

This paper presents the main achievements of the author’s PhD dissertation. The work is dedicated to mathematical and semi-empirical approaches applied to the case of Bulgarian wildland fires. After the introductory explanations, short information from every chapter is extracted to cover the main parts of the obtained results. The methods used are described in brief and main outcomes are listed. ACM Computing Classification System (1998): D.1.3, D.2.0, K.5.1.

A contribution for thermoeconomic modelling: A methodology proposal

This work presents a thermoeconomic optimization methodology for the analysis and design of energy systems. This methodology involves economic aspects related to the exergy conception, in order to develop a tool to assist the equipment selection, operation mode choice as well as to optimize the thermal plants design. It also presents the concepts related to exergy in a general scope and in thermoeconomics which combines the thermal sciences principles (thermodynamics, heat transfer, and fluid mechanics) and the economic engineering in order to rationalize energy systems investment decisions, development and operation. Even in this paper, it develops a thermoeconomic methodology through the use of a simple mathematical model, involving thermodynamics parameters and costs evaluation, also defining the objective function as the exergetic production cost. The optimization problem evaluation is developed for two energy systems. First is applied to a steam compression refrigeration system and then to a cogeneration system using backpressure steam turbine. (C) 2010 Elsevier Ltd. All rights reserved.

Modelling grain boundary migration during geometric dynamic recrystallization

High-angle grain boundary migration is predicted during geometric dynamic recrystallization (GDRX) by two types of mathematical models. Both models consider the driving pressure due to curvature and a sinusoidal driving pressure owing to subgrain walls connected to the grain boundary. One model is based on the finite difference solution of a kinetic equation, and the other, on a numerical technique in which the boundary is subdivided into linear segments. The models show that an initially flat boundary becomes serrated, with the peak and valley migrating into both adjacent grains, as observed during GDRX. When the sinusoidal driving pressure amplitude is smaller than 2 pi, the boundary stops migrating, reaching an equilibrium shape. Otherwise, when the amplitude is larger than 2 pi, equilibrium is never reached and the boundary migrates indefinitely, which would cause the protrusions of two serrated parallel boundaries to impinge on each other, creating smaller equiaxed grains.