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.

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.

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.

Transcatheter aortic valve implantation (TAVI): state of the art techniques and future perspectives.

Transcatheter aortic valve therapies are the newest established techniques for the treatment of high risk patients affected by severe symptomatic aortic valve stenosis. The transapical approach requires a left anterolateral mini-thoracotomy, whereas the transfemoral method requires an adequate peripheral vascular access and can be performed fully percutaneously. Alternatively, the trans-subclavian access has been recently proposed as a third promising approach. Depending on the technique, the fine stent-valve positioning can be performed with or without contrast injections. The transapical echo-guided stent-valve implantation without angiography (the Lausanne technique) relies entirely on transoesophageal echocardiogramme imaging for the fine stent-valve positioning and it has been proved that this technique prevents the onset of postoperative contrast-related acute kidney failure. Recent published reports have shown good hospital outcomes and short-term results after transcatheter aortic valve implantation, but there are no proven advantages in using the transfemoral or the transapical technique. In particular, the transapical series have a higher mean logistic Euroscore of 27-35%, a procedural success rate above 95% and a mean 30-day mortality between 7.5 and 17.5%, whereas the transfemoral results show a lower logistic Euroscore of 23-25.5%, a procedural success rate above 90% and a 30-day mortality of 7-10.8%. Nevertheless, further clinical trials and long-term results are mandatory to confirm this positive trend. Future perspectives in transcatheter aortic valve therapies would be the development of intravascular devices for the ablation of the diseased valve leaflets and the launch of new stent-valves with improved haemodynamic, different sizes and smaller delivery systems.

Inhibition of tumor angiogenesis by non-steroidal anti-inflammatory drugs: emerging mechanisms and therapeutic perspectives.

Chronic intake of non steroidal anti-inflammatory drugs (NSAIDs) is associated with a reduced risk of developing gastrointestinal tumors, in particular colon cancer. Increasing evidence indicates that NSAID exert tumor-suppressive activity on pre-malignant lesions (polyps) in humans and on established experimental tumors in mice. Some of the tumor-suppressive effects of NSAIDs depend on the inhibition of cyclooxygenase-2 (COX-2), a key enzyme in the synthesis of prostaglandins and thromboxane, which is highly expressed in inflammation and cancer. Recent findings indicate that NSAIDs exert their anti-tumor effects by suppressing tumor angiogenesis. The availability of COX-2-specific NSAIDs opens the possibility of using this drug class as anti-angiogenic agents in combination with chemotheapy or radiotherapy for the treatment of human cancer. Here we will briefly review recent advances in the understanding of the mechanism by which NSAIDs suppress tumor angiogenesis and discuss their potential clinical application as anti-cancer agents.

Gravure des vues perspectives des ports de France , d'après les tableaux appartenans au Roi, peints par M. Vernet de l'Académie royale de peinture & de sculpture

[Prospectus. Estampes. Cochin, Charles-Nicolas II. 1758]

Inclusive education: exploring teachers' perspectives /

This study explores 5 teachers' perspectives on inclusive education. The literature reviewed gives a historical background of special education as well as discusses a number of current methods and techniques that have been implemented as a means to include exceptional students in regular classroom settings. This is a qualitative study that collected and interpreted data in narrative form. Common themes emerged from the accounts that were shared by the participants. This study found that the understanding of mUltiple intelligences and differentiated instruction might assist a teacher to better meet the needs of exceptional students within inclusive classrooms. Based on this study, it is determined that a range of considerations needs to be weighed when choosing an educational placement for a student with an exceptionality. Each decision needs to be based on the individual student and the options open to himlher. When a decision about class placement is to be made, not only are the student's strengths and needs to be considered, but also the school and community, the teacher, and the parents' desire for their child must be taken into account. More work still needs to be done around inclusive education that is at the practical level, so that the needs of both the student and the teacher can be met. Inclusive education did not mean the same thing to each person. It was individualized, just as each student is an individual and what works best for himlher is individual. In learning about inclusive education, settings and strategies need to be considered to allow for each individual student to achieve hislher personal best.

"Where is the value in education for me?": experiences and perspectives of Ontario secondary students at risk of non-completion of their Ontario Secondary School Diploma /

This study examined students considered at risk of non-completion of their Ontario Secondary School Diploma and aimed to offer insight into the questions, "What factors currently lead to school disconnect" and "How can these factors be addressed?" Eight students currently enrolled in an alternative learning environment participated in the study. Each was asked to take part in two, digitally recorded interviews that were subsequently transcribed by the researcher. The data were then coded and analysed according to specific themes: obstacles, empowerment, goals, views about success, opinions of school, and power of the teacher. From these themes, three broad focus areas emerged that were used to keep the data analysis focused: worldview, school effects, and self-image. Variances between the data collected and ideas presented in the current literature were highlighted as a reminder that when dealing with a human population, we cannot rely on textbook definitions and theory alone.

Spiritual journeys in the classroom: elementary public school teachers' perspectives /

This thesis explored 5 public elementary school teachers ' perceptions of spirituality and its implications for classroom practice. A generic qualitative study was conducted where each teacher shared her experiences and perceptions in one audiotaped semistructured interview. Transcripts were generated and coded for themes which emerged, resulting in the findings of the study. Following this process, the participants verified the accuracy of the transcripts and findings through a member-checking system. The research found that each teacher has her own definition of spirituality. Furthermore, one's personal connection with spirituality can involve a relationship with religion, the self, a higher being, others, and nature. These spiritual relationships were nurtured through a variety of methods outlined by the teachers. This resulted in the creation of a personal spiritual profile for each teacher which contained each teacher's spiritual connections or facets and the methods used to develop these facets. The teachers identified spiritual needs in their students warranting the need for and importance of spiritual education. Given this, a number of classroom practices were identified with the intention of meeting the spiritual needs of students. Among these practices, the teacher as role model was identified as a significant practice for students' spiritual development in the classroom. The teachers further outlined a number of professional development initiatives with the intention to promote greater awareness for spiritual education and to provide resources for educators.