Una Aproximació a la construcció significativa del coneixement matemàtic a l'ESO

This study displays and analyzes the contents of the Mathematics subject in ESO’s second cycle from a constructivist perspective. This analysis has been carried out by contrasting two groups of participants (control group and experimental group). These groups were formed by a sample of 240 students between the ages of 14 and 16 from four different educational centres of the Osona area. Research – Action methodology has been employed, combining quantitative techniques (statistical study with the SPSS package) with qualitative analysis (transcriptions of interviews and discussion group). This study has been carried out after years of classroom observation, reflection and action. The theoretical framework employed is a cognitive one, based on Ausubel’s Significative Learning Theory. Quantitative analysis shows how the researcher’s design improves, on the one hand, the students’ academic motivation and, on the other hand, their comprehensive memory, enabling them to achieve a more significant learning of the subjects’ contents. Furthermore, our analysis shows that the proposed method is more comprehensive than those employed by teachers collaborating with control groups. The main aim of the qualitative analysis is that of identifying the elements which configure the programme and contribute to an improvement of the aspects mentioned above. The key elements here are: co-operation as the basis of group dynamics; the employment, in some cases, of easily handled materials; the type of interaction between teacher and students, where, through open discussion, students are lead by teaching staff towards the course objectives; induction, that is, deducing formulae by initially using examples which are close to the students’ knowledge and experience or taken from everyday life (what we could call “down-top” mathematics). We should add here that the qualitative analysis does not only corroborate the results obtained by quantitative techniques, but also displays an increase of motivation in teaching staff. Teachers did show a positive attitude and welcomed the use and development of these materials in the next academic year. Finally, we discuss possible directions for further research.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

A theoretical and practical study on linear reforms of dual taxes

We extend the linear reforms introduced by Pf¨ahler (1984) to the case of dual taxes. We study the relative effect that linear dual tax cuts have on the inequality of income distribution -a symmetrical study can be made for dual linear tax hikes-. We also introduce measures of the degree of progressivity for dual taxes and show that they can be connected to the Lorenz dominance criterion. Additionally, we study the tax liability elasticity of each of the reforms proposed. Finally, by means of a microsimulation model and a considerably large data set of taxpayers drawn from 2004 Spanish Income Tax Return population, 1) we compare different yield-equivalent tax cuts applied to the Spanish dual income tax and 2) we investigate how much income redistribution the dual tax reform (Act ‘35/2006’) introduced with respect to the previous tax.

Native-like, long synthetic peptides as components of sub-unit vaccines: practical and theoretical considerations for their use in humans.

Vaccines have been used as a successful tool in medicine by way of controlling many major diseases. In spite of this, vaccines today represent only a handful of all infectious diseases. Therefore, there is a pressing demand for improvements of existing vaccines with particular reference to higher efficacy and undisputed safety profiles. To this effect, as an alternative to available vaccine technologies, there has been a drive to develop vaccine candidate polypeptides by chemical synthesis. In our laboratory, we have recently developed a technology to manufacture long synthetic peptides of up to 130 residues, which are correctly folded and biologically active. This paper discusses the advantages of the molecularly defined, long synthetic peptide approach in the context of vaccine design, development and use in human vaccination.

Theoretical study on receptor-G protein recognition: new insights into the mechanisms of the alpha1b-adrenergic recptor activation

This work compares the structural/dynamics features of the wild-type alb-adrenergic receptor (AR) with those of the D142A active mutant and the agonist-bound state. The two active receptor forms were compared in their isolated states as well as in their ability to form homodimers and to recognize the G alpha q beta 1 gamma 2 heterotrimer. The analysis of the isolated structures revealed that, although the mutation- and agonist-induced active states of the alpha 1b-AR are different, they, however, share several structural peculiarities including (a) the release of some constraining interactions found in the wild-type receptor and (b) the opening of a cytosolic crevice formed by the second and third intracellular loops and the cytosolic extensions of helices 5 and 6. Accordingly, also their tendency to form homodimers shows commonalties and differences. In fact, in both the active receptor forms, helix 6 plays a crucial role in mediating homodimerization. However, the homodimeric models result from different interhelical assemblies. On the same line of evidence, in both of the active receptor forms, the cytosolic opened crevice recognizes similar domains on the G protein. However, the docking solutions are differently populated and the receptor-G protein preorientation models suggest that the final complexes should be characterized by different interaction patterns.

Pitàgores: música i matemàtiques

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit cientí­fic del Jovent l'any 2009. L'objectiu general del treball de recerca és estudiar la figura de Pitàgores, així com analitzar la seva filosofia i endinsar-se en les relacions que va establir entre la música i les matemàtiques. El treball consta de dues parts diferenciades, una teòrica i una pràctica. En la part teòrica s'estudien l'Escola Pitagòrica i les seves aportacions al camp musical. Es descriuen les experimentacions de Pitàgores amb el monocordi i es dóna explicació matemàtica a les escales musicals sorgides des de llavors, així com també es comenta la teoria de la música de les esferes. En la part pràctica, l'alumne empra tot el seu bagatge matemàtic i musical, adquirit al llarg de l'elaboració del cos teòric del treball per arribar a la construcció de dos tipus de monocordi.

Testing, not modelling, the impact of cohesion support: a theoretical framework and some preliminary results for the Spanish regions

This paper develops a simple model that can be used to estimate the effectiveness of Cohesion expenditure relative to similar but unsubsidized projects, thereby making it possible to explicitly test an important assumption that is often implicit in estimates of the impact of Cohesion policies. Some preliminary results are reported for the case of infrastructure investment in the Spanish regions.

Theoretical aspects of graph models for MANETs

We survey the main theoretical aspects of models for Mobile Ad Hoc Networks (MANETs). We present theoretical characterizations of mobile network structural properties, different dynamic graph models of MANETs, and finally we give detailed summaries of a few selected articles. In particular, we focus on articles dealing with connectivity of mobile networks, and on articles which show that mobility can be used to propagate information between nodes of the network while at the same time maintaining small transmission distances, and thus saving energy.

Theoretical estimates of consumable food and probability of acquiring food in larvae of Chrysomya putoria (Diptera: Calliphoridae)

An indirect estimate of consumable food and probability of acquiring food in a blowfly species, Chrysomya putoria, is presented. This alternative procedure combines three distinct models to estimate consumable food in the context of the exploitative competition experienced by immature individuals in blowfly populations. The relevant parameters are derived from data for pupal weight and survival and estimates of density-independent larval mortality in twenty different larval densities. As part of this procedure, the probability of acquiring food per unit of time and the time taken to exhaust the food supply are also calculated. The procedure employed here may be valuable for estimations in insects whose immature stages develop inside the food substrate, where it is difficult to partial out confounding effects such as separation of faeces. This procedure also has the advantage of taking into account the population dynamics of immatures living under crowded conditions, which are particularly characteristic of blowflies and other insects as well.

A theoretical model of the tridimensional structure of Bacillus thuringiensis subsp. medellin Cry 11Bb toxin deduced by homology modelling

Cry11Bb is an insecticidal crystal protein produced by Bacillus thuringiensis subsp. medellin during its stationary phase; this ¶-endotoxin is active against dipteran insects and has great potential for mosquito borne disease control. Here, we report the first theoretical model of the tridimensional structure of a Cry11 toxin. The tridimensional structure of the Cry11Bb toxin was obtained by homology modelling on the structures of the Cry1Aa and Cry3Aa toxins. In this work we give a brief description of our model and hypothesize the residues of the Cry11Bb toxin that could be important in receptor recognition and pore formation. This model will serve as a starting point for the design of mutagenesis experiments aimed to the improvement of toxicity, and to provide a new tool for the elucidation of the mechanism of action of these mosquitocidal proteins.

Le conseil génétique: aspects théoriques et pratique en prénatal [Genetic counselling: theoretical aspects and prenatal practice]

Le conseil génétique doit fournir aux individus une information médicale précise et un soutien psychologique. L'importance des principes d'autonomie et de confidentialité, dogmes du conseil génétique, est renforcée par la nouvelle loi suisse (LAGH). Dans certains pays, une grande partie du conseil génétique est assurée par des conseillers en génétique non médecins ayant une formation postgraduée spécifique. Le conseil génétique joue un rôle grandissant dans différents domaines de la médecine. En particulier, il est indispensable dans le contexte du prénatal où les couples reçoivent des informations complexes et doivent bénéficier d’un soutien pour prendre une décision. Genetic counselling provides families with accurate medical information and psychological support. Respect and concern for the emotional well-being should be taken into account while discussing genetics aspects and recurrence risks. The importance of autonomy and confidentiality, central to genetic counselling, is reinforced by the new Swiss law (LAGH). In many countries, most of the genetic counselling is provided by genetic counsellors who have a specialised post-graduate training. Genetic counselling plays an increasing role in different medical specialities. In particular, it is essential in the context of prenatal and pre-conceptual care, where couples are confronted to complex information and should have access to appropriate support during the decision-making process

Theoretical study of the electrostatically driven step of receptor-G protein recognition.

This study proposes a theoretical model describing the electrostatically driven step of the alpha 1 b-adrenergic receptor (AR)-G protein recognition. The comparative analysis of the structural-dynamics features of functionally different receptor forms, i.e., the wild type (ground state) and its constitutively active mutants D142A and A293E, was instrumental to gain insight on the receptor-G protein electrostatic and steric complementarity. Rigid body docking simulations between the different forms of the alpha 1 b-AR and the heterotrimeric G alpha q, G alpha s, G alpha i1, and G alpha t suggest that the cytosolic crevice shared by the active receptor and including the second and the third intracellular loops as well as the cytosolic extension of helices 5 and 6, represents the receptor surface with docking complementarity with the G protein. On the other hand, the G protein solvent-exposed portions that recognize the intracellular loops of the activated receptors are the N-terminal portion of alpha 3, alpha G, the alpha G/alpha 4 loop, alpha 4, the alpha 4/beta 6 loop, alpha 5, and the C-terminus. Docking simulations suggest that the two constitutively active mutants D142A and A293E recognize different G proteins with similar selectivity orders, i.e., G alpha q approximately equal to G alpha s > G alpha i > G alpha t. The theoretical models herein proposed might provide useful suggestions for new experiments aiming at exploring the receptor-G protein interface.