Interdisciplinary experience in the Teacher Training College of Vitoria-Gasteiz: teaching profession module

[EN] The higher education regulation process in Europe, known as the Bologna Process, has involved many changes, mainly in relation to methodology and assessment. The paper given below relates to implementing the new EU study plans into the Teacher Training College of Vitoria-Gasteiz; it is the first interdisciplinary paper written involving teaching staff and related to the Teaching Profession module, the first contained in the structure of the new plans. The coordination of teaching staff is one of the main lines of work in the Bologna Process, which is also essential to develop the right skills and maximise the role of students as an active learning component. The use of active, interdisciplinary methodologies has opened up a new dimension in universities, requiring the elimination of the once componential, individual structure, making us look for new areas of exchange that make it possible for students' training to be developed jointly.

Using the system dynamics paradigm in teaching and learning technological university subjets

2nd International Conference on Education and New Learning Technologies

Indication of pollution in a teaching and research farm reservoir

The production and productivity of a water body is largely dependent on its quality. One major source of water pollution is from the agrochemicals from nearby farmlands. The quality of water in the Obafemi Awolowo University Teaching and Research Farm Reservoir (Ile-Ife, Nigeria) was monitored between October, 1993 and March, 1994. Structured questionnaires were administered to obtain information on the types of agrochemicals in use on the farm. Water samples were collected fortnightly for analyses of the physico-chemical parameters and ionic content of the water. Investigation revealed that 21 agrochemicals had been in use on the farm. The physico-chemical parameters of the water showed that the water was very poor in nutrient. The high concentration of ammonium ion contents of the water shows an indication that the residues of certain agrochemicals got into the water to pollute it. Agrochemicals should be used with great caution on farmlands especially in areas close to water bodies from which man obtains fish and other proteinous foods. This paper also suggests a regular monitoring of water quality of reservoirs in order to pick the earliest signs of pollution

On reconstruction theorems in noncommutative Riemannian geometry

We present a novel account of the theory of commutative spectral triples and their two closest noncommutative generalisations, almost-commutative spectral triples and toric noncommutative manifolds, with a focus on reconstruction theorems, viz, abstract, functional-analytic characterisations of global-analytically defined classes of spectral triples. We begin by reinterpreting Connes's reconstruction theorem for commutative spectral triples as a complete noncommutative-geometric characterisation of Dirac-type operators on compact oriented Riemannian manifolds, and in the process clarify folklore concerning stability of properties of spectral triples under suitable perturbation of the Dirac operator. Next, we apply this reinterpretation of the commutative reconstruction theorem to obtain a reconstruction theorem for almost-commutative spectral triples. In particular, we propose a revised, manifestly global-analytic definition of almost-commutative spectral triple, and, as an application of this global-analytic perspective, obtain a general result relating the spectral action on the total space of a finite normal compact oriented Riemannian cover to that on the base space. Throughout, we discuss the relevant refinements of these definitions and results to the case of real commutative and almost-commutative spectral triples. Finally, we outline progess towards a reconstruction theorem for toric noncommutative manifolds.

Conformal geometry processing

This thesis introduces fundamental equations and numerical methods for manipulating surfaces in three dimensions via conformal transformations. Conformal transformations are valuable in applications because they naturally preserve the integrity of geometric data. To date, however, there has been no clearly stated and consistent theory of conformal transformations that can be used to develop general-purpose geometry processing algorithms: previous methods for computing conformal maps have been restricted to the flat two-dimensional plane, or other spaces of constant curvature. In contrast, our formulation can be used to produce---for the first time---general surface deformations that are perfectly conformal in the limit of refinement. It is for this reason that we commandeer the title Conformal Geometry Processing.

The main contribution of this thesis is analysis and discretization of a certain time-independent Dirac equation, which plays a central role in our theory. Given an immersed surface, we wish to construct new immersions that (i) induce a conformally equivalent metric and (ii) exhibit a prescribed change in extrinsic curvature. Curvature determines the potential in the Dirac equation; the solution of this equation determines the geometry of the new surface. We derive the precise conditions under which curvature is allowed to evolve, and develop efficient numerical algorithms for solving the Dirac equation on triangulated surfaces.

From a practical perspective, this theory has a variety of benefits: conformal maps are desirable in geometry processing because they do not exhibit shear, and therefore preserve textures as well as the quality of the mesh itself. Our discretization yields a sparse linear system that is simple to build and can be used to efficiently edit surfaces by manipulating curvature and boundary data, as demonstrated via several mesh processing applications. We also present a formulation of Willmore flow for triangulated surfaces that permits extraordinarily large time steps and apply this algorithm to surface fairing, geometric modeling, and construction of constant mean curvature (CMC) surfaces.

Coupled effects of mechanics, geometry, and chemistry on bio-membrane behavior

Lipid bilayer membranes are models for cell membranes--the structure that helps regulate cell function. Cell membranes are heterogeneous, and the coupling between composition and shape gives rise to complex behaviors that are important to regulation. This thesis seeks to systematically build and analyze complete models to understand the behavior of multi-component membranes.

We propose a model and use it to derive the equilibrium and stability conditions for a general class of closed multi-component biological membranes. Our analysis shows that the critical modes of these membranes have high frequencies, unlike single-component vesicles, and their stability depends on system size, unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We compare these results with experimental observations.

We also study open membranes to gain insight into long tubular membranes that arise for example in nerve cells. We derive a complete system of equations for open membranes by using the principle of virtual work. Our linear stability analysis predicts that the tubular membranes tend to have coiling shapes if the tension is small, cylindrical shapes if the tension is moderate, and beading shapes if the tension is large. This is consistent with experimental observations reported in the literature in nerve fibers. Further, we provide numerical solutions to the fully nonlinear equilibrium equations in some problems, and show that the observed mode shapes are consistent with those suggested by linear stability. Our work also proves that beadings of nerve fibers can appear purely as a mechanical response of the membrane.