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.

Online teaching of inflammatory skin pathology by a French-speaking International University Network

INTRODUCTION: Developments in technology, web-based teaching and whole slide imaging have broadened the teaching horizon in anatomic pathology. Creating online learning material including many types of media such as radiologic images, whole slides, videos, clinical and macroscopic photographs, is now accessible to most universities. Unfortunately, a major limiting factor to maintain and update the learning material is the amount of resources needed. In this perspective, a French-national university network was initiated in 2011 to build joint online teaching modules consisting of clinical cases and tests. The network has since expanded internationally to Québec, Switzerland and Ivory Coast. METHOD: One of the first steps of the project was to build a learning module on inflammatory skin pathology for interns and residents in pathology and dermatology. A pathology resident from Québec spent 6 weeks in France and Switzerland to develop the contents and build the module on an e-learning Moodle platform under the supervision of two dermatopathologists. The learning module contains text, interactive clinical cases, tests with feedback, virtual slides, images and clinical photographs. For that module, the virtual slides are decentralized in 2 universities (Bordeaux and Paris 7). Each university is responsible of its own slide scanning, image storage and online display with virtual slide viewers. RESULTS: The module on inflammatory skin pathology includes more than 50 web pages with French original content, tests and clinical cases, links to over 45 virtual images and more than 50 microscopic and clinical photographs. The whole learning module is being revised by four dermatopathologists and two senior pathologists. It will be accessible to interns and residents in the spring of 2014. The experience and knowledge gained from that work will be transferred to the next international resident whose work will be aimed at creating lung and breast pathology learning modules. CONCLUSION: The challenges of sustaining a project of this scope are numerous. The technical aspect of whole-slide imaging and storage needs to be developed by each university or group. The content needs to be regularly updated and its accuracy reviewed by experts in each individual domain. The learning modules also need to be promoted within the academic community to ensure maximal benefit for trainees. A collateral benefit of the project was the establishment of international partnerships between French-speaking universities and pathologists with the common goal of promoting pathology education through the use of multi-media technology including whole slide imaging.

An international university network for online teaching of pathology in Frenchspeaking countries

Introduction: Building online courses is a highly time consuming task for teachers of a single university. Universities working alone create high-quality courses but often cannot cover all pathological fields. Moreover this often leads to duplication of contents among universities, representing a big waste of teacher time and energy. We initiated in 2011 a French university network for building mutualized online teaching pathology cases, and this network has been extended in 2012 to Quebec and Switzerland. Method: Twenty French universities (see & for details), University Laval in Quebec and University of Lausanne in Switzerland are associated to this project. One e-learning Moodle platform (http://moodle.sorbonne-paris-cite.fr/) contains texts with URL pointing toward virtual slides that are decentralized in several universities. Each university has the responsibility of its own slide scanning, slide storage and online display with virtual slide viewers. The Moodle website is hosted by PRES Sorbonne Paris Cité, and financial supports for hardware have been obtained from UNF3S (http://www.unf3s.org/) and from PRES Sorbonne Paris Cité. Financial support for international fellowships has been obtained from CFQCU (http://www.cfqcu.org/). Results: The Moodle interface has been explained to pathology teachers using web-based conferences with screen sharing. The teachers added then contents such as clinical cases, selfevaluations and other media organized in several sections by student levels and pathological fields. Contents can be used as online learning or online preparation of subsequent courses in classrooms. In autumn 2013, one resident from Quebec spent 6 weeks in France and Switzerland and created original contents in inflammatory skin pathology. These contents are currently being validated by senior teachers and will be opened to pathology residents in spring 2014. All contents of the website can be accessed for free. Most contents just require anonymous connection but some specific fields, especially those containing pictures obtained from patients who agreed for a teaching use only, require personal identification of the students. Also, students have to register to access Moodle tests. All contents are written in French but one case has been translated into English to illustrate this communication (http://moodle.sorbonne-pariscite.fr/mod/page/view.php?id=261) (use "login as a guest"). The Moodle test module allows many types of shared questions, making it easy to create personalized tests. Contents that are opened to students have been validated by an editorial committee composed of colleagues from the participating institutions. Conclusions: Future developments include other international fellowships, the next one being scheduled for one French resident from May to October 2014 in Quebec, with a study program centered on lung and breast pathology. It must be kept in mind that these e-learning programs highly depend on teachers' time, not only at these early steps but also later to update the contents. We believe that funding resident fellowships for developing online pathological teaching contents is a win-win situation, highly beneficial for the resident who will improve his knowledge and way of thinking, highly beneficial for the teachers who will less worry about access rights or image formats, and finally highly beneficial for the students who will get courses fully adapted to their practice.

Online teaching of inflammatory skin pathology by a French-speaking International University Network.

INTRODUCTION: Developments in technology, web-based teaching and whole slide imaging have broadened the teaching horizon in anatomic pathology. Creating online learning material including many types of media such as radiologic images, whole slides, videos, clinical and macroscopic photographs, is now accessible to most universities. Unfortunately, a major limiting factor to maintain and update the learning material is the amount of resources needed. In this perspective, a French-national university network was initiated in 2011 to build joint online teaching modules consisting of clinical cases and tests. The network has since expanded internationally to Québec, Switzerland and Ivory Coast. METHOD: One of the first steps of the project was to build a learning module on inflammatory skin pathology for interns and residents in pathology and dermatology. A pathology resident from Québec spent 6 weeks in France and Switzerland to develop the contents and build the module on an e-learning Moodle platform under the supervision of two dermatopathologists. The learning module contains text, interactive clinical cases, tests with feedback, virtual slides, images and clinical photographs. For that module, the virtual slides are decentralized in 2 universities (Bordeaux and Paris 7). Each university is responsible of its own slide scanning, image storage and online display with virtual slide viewers. RESULTS: The module on inflammatory skin pathology includes more than 50 web pages with French original content, tests and clinical cases, links to over 45 virtual images and more than 50 microscopic and clinical photographs. The whole learning module is being revised by four dermatopathologists and two senior pathologists. It will be accessible to interns and residents in the spring of 2014. The experience and knowledge gained from that work will be transferred to the next international resident whose work will be aimed at creating lung and breast pathology learning modules. CONCLUSION: The challenges of sustaining a project of this scope are numerous. The technical aspect of whole-slide imaging and storage needs to be developed by each university or group. The content needs to be regularly updated and its accuracy reviewed by experts in each individual domain. The learning modules also need to be promoted within the academic community to ensure maximal benefit for trainees. A collateral benefit of the project was the establishment of international partnerships between French-speaking universities and pathologists with the common goal of promoting pathology education through the use of multi-media technology including whole slide imaging.

Scenario-based assessment of future land use change on butterfly species distributions

Species distribution models (SDMs) are increasingly used to predict environmentally induced range shifts of habitats of plant and animal species. Consequently SDMs are valuable tools for scientifically based conservation decisions. The aims of this paper are (1) to identify important drivers of butterfly species persistence or extinction, and (2) to analyse the responses of endangered butterfly species of dry grasslands and wetlands to likely future landscape changes in Switzerland. Future land use was represented by four scenarios describing: (1) ongoing land use changes as observed at the end of the last century; (2) a liberalisation of the agricultural markets; (3) a slightly lowered agricultural production; and (4) a strongly lowered agricultural production. Two model approaches have been applied. The first (logistic regression with principal components) explains what environmental variables have significant impact on species presence (and absence). The second (predictive SDM) is used to project species distribution under current and likely future land uses. The results of the explanatory analyses reveal that four principal components related to urbanisation, abandonment of open land and intensive agricultural practices as well as two climate parameters are primary drivers of species occurrence (decline). The scenario analyses show that lowered agricultural production is likely to favour dry grassland species due to an increase of non-intensively used land, open canopy forests, and overgrown areas. In the liberalisation scenario dry grassland species show a decrease in abundance due to a strong increase of forested patches. Wetland butterfly species would decrease under all four scenarios as their habitats become overgrown

Age-related change in melanin-based coloration of Barn owls (Tyto alba): females that become more female-like and males that become more male-like perform better

Ornament expression fluctuates with age in many organisms. Whether these changes are adaptively plastic is poorly known. In order to understand the ultimate function of melanin-based ornaments, we studied their within-individual fluctuations and their covariation with fitness-related traits. In barn owls (Tyto alba), individuals vary from reddish-brown pheomelanic to white and from immaculate to marked with black eumelanic spots, males being less reddish and less spotted than females. During the first molt, both sexes became less pheomelanic, females displayed larger spots and males fewer spots, but the extent of these changes was not associated with reproduction. At subsequent molts, intra-individual changes in melanin-based traits covaried with simultaneous reproduction changes. Adult females bred earlier in the season and laid larger eggs when they became scattered with larger spots, while adults of both sexes produced larger broods when they became whiter. These results suggest that the production of melanin pigments and fitness-related life history traits are concomitantly regulated in a sex-specific way.

Association between conventional risk factors and different ultrasound-based markers of atherosclerosis at carotid and femoral levels in a middle-aged population.

Ultrasound detection of sub-clinical atherosclerosis (ATS) may help identify individuals at high cardiovascular risk. Most studies evaluated intima-media thickness (IMT) at carotid level. We compared the relationships between main cardiovascular risk factors (CVRF) and five indicators of ATS (IMT, mean and maximal plaque thickness, mean and maximal plaque area) at both carotid and femoral levels. Ultrasound was performed on 496 participants aged 45-64 years randomly selected from the general population of the Republic of Seychelles. 73.4 % participants had ≥ 1 plaque (IMT thickening ≥ 1.2 mm) at carotid level and 67.5 % at femoral level. Variance (adjusted R2) contributed by age, sex and CVRF (smoking, LDL-cholesterol, HDL-cholesterol, blood pressure, diabetes) in predicting any of the ATS markers was larger at femoral than carotid level. At both carotid and femoral levels, the association between CVRF and ATS was stronger based on plaque-based markers than IMT. Our findings show that the associations between CVRF and ATS markers were stronger at femoral than carotid level, and with plaque-based markers rather than IMT. Pending comparison of these markers using harder cardiovascular endpoints, our findings suggest that markers based on plaque morphology assessed at femoral artery level might be useful cardiovascular risk predictors.

Challenging recommended oral and intravenous voriconazole doses for improved efficacy and safety: population pharmacokinetics-based analysis of adult patients with invasive fungal infections.

BACKGROUND: Recommended oral voriconazole (VRC) doses are lower than intravenous doses. Because plasma concentrations impact efficacy and safety of therapy, optimizing individual drug exposure may improve these outcomes. METHODS: A population pharmacokinetic analysis (NONMEM) was performed on 505 plasma concentration measurements involving 55 patients with invasive mycoses who received recommended VRC doses. RESULTS: A 1-compartment model with first-order absorption and elimination best fitted the data. VRC clearance was 5.2 L/h, the volume of distribution was 92 L, the absorption rate constant was 1.1 hour(-1), and oral bioavailability was 0.63. Severe cholestasis decreased VRC elimination by 52%. A large interpatient variability was observed on clearance (coefficient of variation [CV], 40%) and bioavailability (CV 84%), and an interoccasion variability was observed on bioavailability (CV, 93%). Lack of response to therapy occurred in 12 of 55 patients (22%), and grade 3 neurotoxicity occurred in 5 of 55 patients (9%). A logistic multivariate regression analysis revealed an independent association between VRC trough concentrations and probability of response or neurotoxicity by identifying a therapeutic range of 1.5 mg/L (>85% probability of response) to 4.5 mg/L (<15% probability of neurotoxicity). Population-based simulations with the recommended 200 mg oral or 300 mg intravenous twice-daily regimens predicted probabilities of 49% and 87%, respectively, for achievement of 1.5 mg/L and of 8% and 37%, respectively, for achievement of 4.5 mg/L. With 300-400 mg twice-daily oral doses and 200-300 mg twice-daily intravenous doses, the predicted probabilities of achieving the lower target concentration were 68%-78% for the oral regimen and 70%-87% for the intravenous regimen, and the predicted probabilities of achieving the upper target concentration were 19%-29% for the oral regimen and 18%-37% for the intravenous regimen. CONCLUSIONS: Higher oral than intravenous VRC doses, followed by individualized adjustments based on measured plasma concentrations, improve achievement of the therapeutic target that maximizes the probability of therapeutic response and minimizes the probability of neurotoxicity. These findings challenge dose recommendations for VRC.

A cell-based model of extracellular-matrix-guided endothelial cell migration during angiogenesis.

Angiogenesis, the formation of new blood vessels sprouting from existing ones, occurs in several situations like wound healing, tissue remodeling, and near growing tumors. Under hypoxic conditions, tumor cells secrete growth factors, including VEGF. VEGF activates endothelial cells (ECs) in nearby vessels, leading to the migration of ECs out of the vessel and the formation of growing sprouts. A key process in angiogenesis is cellular self-organization, and previous modeling studies have identified mechanisms for producing networks and sprouts. Most theoretical studies of cellular self-organization during angiogenesis have ignored the interactions of ECs with the extra-cellular matrix (ECM), the jelly or hard materials that cells live in. Apart from providing structural support to cells, the ECM may play a key role in the coordination of cellular motility during angiogenesis. For example, by modifying the ECM, ECs can affect the motility of other ECs, long after they have left. Here, we present an explorative study of the cellular self-organization resulting from such ECM-coordinated cell migration. We show that a set of biologically-motivated, cell behavioral rules, including chemotaxis, haptotaxis, haptokinesis, and ECM-guided proliferation suffice for forming sprouts and branching vascular trees.

A cohort-based analysis of the evolution of lifetime prevalence of recourse to prostitution by men in the general population of Switzerland, 1987-2000

Background: Despite their relevance to the prevention of sexually transmitted infections, there are few data on the frequency of recourse to prostitution in the male population in Switzerland. Using data gathered for the evaluation of the Swiss AIDS prevention strategy, we analysed net aggregate change and cohort-based change in lifetime prevalence of recourse to prostitution. Methods: Seven repeated cross-sectional telephone surveys of the general population aged 17-45 years (17-30 years only for the 1987 and 1988 surveys) were undertaken from 1987 to 2000 providing information on sexual behaviour including men's recourse to prostitution (total n¼9318). Age categories were: 17-20, 21-25, 26-30, 31-35, 36-40 and 41-45 years. Prevalence at 17-30 years was available in all surveys and prevalence at 41-45 was available for 1989-2000, though not for the same cohorts. Intra-cohort increase in prevalence over 10 years was analysed using truncated information for cohorts aged 21-25 and 26-30 years in 1987 and 1990. Population estimates were computed with 95% confidence intervals (CI). Results: No net change occurred in the 17-45 years male population prevalence between 1989 (17.6%, CI ¼ 15.4; 20.0) and 2000 (17.7%, CI ¼ 15.6; 20.0). The median starting prevalence of recourse to prostitution at age 17-20 was 4.8% (in 1989, CI ¼ 2.0; 9.7) and the range was from 1.8 (in 1994) to 10.4% (in 1990). The median ending prevalence at age 41-45 was 21.9% (in 1994, CI 16.7; 27.9) and the range was from 17.9 (in 2000) to 26.1% (in 1992). No clear trend was observed in either starting or ending prevalence. Intra-cohort evolution of the 1997 and 1990 cohorts was very similar. Conclusions: Based on available data, there was no net (aggregate) change in the prevalence of recourse to prostitution by males in Switzerland between 1989 and 2000. Within the time frame available, intra-cohort evolution was also very similar.

Laser scanning-based recognition of rotational movements on a deep seated gravitational instability: The Cinque Torri case (North-Eastern Italian Alps)

The Cinque Torri group (Cortina d'Ampezzo, Italy) is an articulated system of unstable carbonatic rock monoliths located in a very important tourism area and therefore characterized by a significant risk. The instability phenomena involved represent an example of lateral spreading developed over a larger deep seated gravitational slope deformation (DSGSD) area. After the recent fall of a monolith of more than 10 000 m3, a scientific study was initiated to monitor the more unstable sectors and to characterize the past movements as a fundamental tool for predicting future movements and hazard assessment. To achieve greater insight on the ongoing lateral spreading process, a method for a quantitative analysis of rotational movements associated with the lateral spreading has been developed, applied and validated. The method is based on: i) detailed geometrical characterization of the area by means of laser scanner techniques; ii) recognition of the discontinuity sets and definition of a reference frame for each set, iii) correlation between the obtained reference frames related to a specific sector and a stable external reference frame, and iv) determination of the 3D rotations in terms of Euler angles to describe the present settlement of the Cinque Torri system with respect to the surrounding stable areas. In this way, significant information on the processes involved in the fragmentation and spreading of a former dolomitic plateau into different rock cliffs has been gained. The method is suitable to be applied to similar case studies.

Externalizing disorders and substance use: empirically derived subtypes in a population-based sample of adults.

PURPOSE: Attention-deficit/hyperactivity disorder (ADHD), conduct disorder (CD), and oppositional defiant disorder (ODD) are common externalizing disorders of childhood. The common effects of these disorders on substance abuse need further investigation. The current study investigated the joint clusters of childhood/adolescence ADHD, CD, and ODD, and their influence on substance abuse/dependence in a population-based sample of adults. METHODS: The data were drawn from the PsyCoLaus study (n = 3,720) conducted in Lausanne, Switzerland. The population-based sample included 238 subjects meeting criteria for ADHD/ODD/CD diagnoses before the age of 15. Latent class analyses (LCA) were performed to derive comorbidity subtypes, which were subsequently characterized with respect to psychosocial correlates and substance use. RESULTS: The best fit in LCAs was achieved with three latent classes: an ADHD subtype (35.7 %); an externalizing multimorbid subtype (33.6 %) involving ODD, ADHD, and CD; and a third subtype with CD (30.7 %). The CD subtype showed the highest association with substance use. Apart from this, the externalizing multimorbid subtype was also significantly linked to substance use. The ADHD subtype had only elevated frequencies for alcohol dependence in comparison with subjects that had no history of ADHD, ODD, and CD during childhood or adolescence. Finally, important interactions between subtypes and sex were observed with regard to substance use. CONCLUSIONS: This study provides evidence showing that subtyping the externalizing disorders, ADHD, ODD and CD, along their comorbidity patterns leads to important differences regarding substance use. This could have implications for the etiology, prevention, and treatment of substance use disorders.