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.

Linking Global Youth Tobacco Survey (GYTS) data to the WHO Framework Convention on Tobacco Control (FCTC): the case for the Seychelles

Tobacco control has been recognized as a main public health concern in Seychelles for the past two decades. Tobacco advertising, sponsoring and promotion has been banned for years, tobacco products are submitted to high taxes, high-profile awareness programs are organized regularly, and several other control measures have been implemented. The Republic of Seychelles was the first country to ratify the WHO Framework Convention on Tobacco Control (FCTC) in the African region. Three population-based surveys have been conducted in adults in Seychelles and results showed a substantial decrease in the prevalence of smoking among adults between 1989 and 2004. A first survey in adolescents was conducted in Seychelles in 2002 (the Global Youth Tobacco Survey, GYTS) in a representative sample of 1321 girls and boys aged 13-15 years. The results show that approximately half of students had tried smoking and a quarter of both boys and girls had smoked at least one cigarette during the past 30 days. Although "current smoking" is defined differently in adolescents (>or=1 cigarette during the past 30 days) and in adults (>or=1 cigarette per day), which precludes direct comparison, the high smoking prevalence in youth in Seychelles likely predicts an increasing prevalence of tobacco use in the next adult generation, particularly in women. GYTS 2002 also provides important data on a wide range of specific individual and societal factors influencing tobacco use. Hence, GYTS can be a powerful tool for monitoring the situation of tobacco use in adolescents, for highlighting the need for new policy and programs, and for evaluating the impact of current and future programs.

Modeling resting-state functional networks when the cortex falls asleep: local and global changes.

The transition from wakefulness to sleep represents the most conspicuous change in behavior and the level of consciousness occurring in the healthy brain. It is accompanied by similarly conspicuous changes in neural dynamics, traditionally exemplified by the change from "desynchronized" electroencephalogram activity in wake to globally synchronized slow wave activity of early sleep. However, unit and local field recordings indicate that the transition is more gradual than it might appear: On one hand, local slow waves already appear during wake; on the other hand, slow sleep waves are only rarely global. Studies with functional magnetic resonance imaging also reveal changes in resting-state functional connectivity (FC) between wake and slow wave sleep. However, it remains unclear how resting-state networks may change during this transition period. Here, we employ large-scale modeling of the human cortico-cortical anatomical connectivity to evaluate changes in resting-state FC when the model "falls asleep" due to the progressive decrease in arousal-promoting neuromodulation. When cholinergic neuromodulation is parametrically decreased, local slow waves appear, while the overall organization of resting-state networks does not change. Furthermore, we show that these local slow waves are structured macroscopically in networks that resemble the resting-state networks. In contrast, when the neuromodulator decrease further to very low levels, slow waves become global and resting-state networks merge into a single undifferentiated, broadly synchronized network.

Nouvelles pistes pour la réhabilitation respiratoire dons la bronchopneumopathie chronique obstructive (BPCO) [New perspectives for respiratory rehabilitation in COPD].

COPD is associated with some skeletal muscle dysfunction which contributes to a poor exercise tolerance. This dysfunction results from multiple factors: physical inactivity, corticosteroids, smoking, malnutrition, anabolic deficiency, systemic inflammation, hypoxia, oxidative stress. Respiratory rehabilitation is based on exercise training and allows patients with COPD to experience less dyspnoea, and to improve their exercise tolerance and quality of life. Not all patients, however, benefit from rehabilitation. Acknowledging the different factors leading to muscular dysfunction allows one to foresee new avenues to improve efficacy of exercise training in COPD.

The United Nations Educational, Scientific and Cultural Organisation: Pawn or Global Player?,

This contribution aims at exploring the significance of the new generation of UNESCO conventions for the recognition of higher education qualifications. It discusses three possible scenarios and links them to the empirical findings of a study that compares the enabling conditions of the first generation of recognition conventions established in the 1970s and 1980s with the ones establishing the second generation today. Taking an interdisciplinary approach, the paper argues that the changes illustrate a more general shift in the architecture of the global order and highlights a new role of UNESCO.

New perspectives in the use of ink evidence in forensic science: Part I. Development of a quality assurance process for forensic ink analysis by HPTLC

The level of information provided by ink evidence to the criminal and civil justice system is limited. The limitations arise from the weakness of the interpretative framework currently used, as proposed in the ASTM 1422-05 and 1789-04 on ink analysis. It is proposed to use the likelihood ratio from the Bayes theorem to interpret ink evidence. Unfortunately, when considering the analytical practices, as defined in the ASTM standards on ink analysis, it appears that current ink analytical practices do not allow for the level of reproducibility and accuracy required by a probabilistic framework. Such framework relies on the evaluation of the statistics of the ink characteristics using an ink reference database and the objective measurement of similarities between ink samples. A complete research programme was designed to (a) develop a standard methodology for analysing ink samples in a more reproducible way, (b) comparing automatically and objectively ink samples and (c) evaluate the proposed methodology in a forensic context. This report focuses on the first of the three stages. A calibration process, based on a standard dye ladder, is proposed to improve the reproducibility of ink analysis by HPTLC, when these inks are analysed at different times and/or by different examiners. The impact of this process on the variability between the repetitive analyses of ink samples in various conditions is studied. The results show significant improvements in the reproducibility of ink analysis compared to traditional calibration methods.

ATP-competitive inhibitors of mTOR: new perspectives in the treatment of renal cell carcinoma.

Targeting mTOR (mammalian target of rapamycin) is an effective approach in the treatment of advanced RCC (renal cell carcinoma). Rapamycin-like drugs (rapalogues) have shown clinical activities and have been approved for the treatment of RCC. Recently, with the development of ATP-competitive inhibitors of mTOR, therapies targeting mTOR have entered a new era. Here, we discuss the biological relevance of blocking mTOR in RCC and review the mechanisms of action of rapalogues in RCC. We also advance some perspectives on the use of ATP-competitive inhibitors of mTOR in RCC.