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.

Jevons, Mill and the Private Laboratory of the Mind

In this paper the rift between Jevons and Mill over the method of political economy serves as a prehistory to recent attempts of behavioural economists to once again explain economic behaviour by taking recourse to mankind's physiology. While Mill relied on the association psychology and its introspective method to establish indubitable first principles, Jevons scorned all recourse to introspection. As exemplified for Jevons's theory of labour, psychophysiology gave Jevons the means to think about economic behaviour in terms of functional form, and promised its assessment by means of experiments. Thus levelling down the Victorian distinction between mind and matter, Jevons turned political economy into social physics.

Albuterol delivery in an in vitro pediatric ventilator lung model: comparison of jet, ultrasonic, and mesh nebulizers.

OBJECTIVE: : To determine the influence of nebulizer types and nebulization modes on bronchodilator delivery in a mechanically ventilated pediatric lung model. DESIGN: : In vitro, laboratory study. SETTING: : Research laboratory of a university hospital. INTERVENTIONS: : Using albuterol as a marker, three nebulizer types (jet nebulizer, ultrasonic nebulizer, and vibrating-mesh nebulizer) were tested in three nebulization modes in a nonhumidified bench model mimicking the ventilatory pattern of a 10-kg infant. The amounts of albuterol deposited on the inspiratory filters (inhaled drug) at the end of the endotracheal tube, on the expiratory filters, and remaining in the nebulizers or in the ventilator circuit were determined. Particle size distribution of the nebulizers was also measured. MEASUREMENTS AND MAIN RESULTS: : The inhaled drug was 2.8% ± 0.5% for the jet nebulizer, 10.5% ± 2.3% for the ultrasonic nebulizer, and 5.4% ± 2.7% for the vibrating-mesh nebulizer in intermittent nebulization during the inspiratory phase (p < 0.01). The most efficient nebulizer was the vibrating-mesh nebulizer in continuous nebulization (13.3% ± 4.6%, p < 0.01). Depending on the nebulizers, a variable but important part of albuterol was observed as remaining in the nebulizers (jet and ultrasonic nebulizers), or being expired or lost in the ventilator circuit (all nebulizers). Only small particles (range 2.39-2.70 µm) reached the end of the endotracheal tube. CONCLUSIONS: : Important differences between nebulizer types and nebulization modes were seen for albuterol deposition at the end of the endotracheal tube in an in vitro pediatric ventilator-lung model. New aerosol devices, such as ultrasonic and vibrating-mesh nebulizers, were more efficient than the jet nebulizer.

Evaluation of different POCT devices for glucose measurement in a clinical neonatal setting.

Hypoglycaemia is a major cause of neonatal morbidity and may induce long-term developmental sequelae. Clinical signs of hypoglycaemia in neonatal infants are unspecific or even absent, and therefore, precise and accurate methods for the assessment of glycaemia are needed. Glycaemia measurement in newborns has some particularities like a very low limit of normal glucose concentration compared to adults and a large range of normal haematocrit values. Many bedside point-of-care testing (POCT) systems are available, but literature about their accuracy in newborn infants is scarce and not very convincing. In this retrospective study, we identified over a 1-year study period 1,324 paired glycaemia results, one obtained at bedside with one of three different POCT systems (Elite? XL, Ascensia? Contour? and ABL 735) and the other in the central laboratory of the hospital with the hexokinase reference method. All three POCT systems tended to overestimate glycaemia values, and none of them fulfilled the ISO 15197 accuracy criteria. The Elite XL appeared to be more appropriate than Contour to detect hypoglycaemia, however with a low specificity. Contour additionally showed an important inaccuracy with increasing haematocrit. The bench analyzer ABL 735 was the most accurate of the three tested POCT systems. Both of the tested handheld glucometers have important drawbacks in their use as screening tools for hypoglycaemia in newborn infants. ABL 735 could be a valuable alternative, but the blood volume needed is more than 15 times higher than for handheld glucometers. Before daily use in the newborn population, careful clinical evaluation of each new POCT system for glucose measurement is of utmost importance.

Cytogenetic characterisation of childhood acute lymphoblastic leukemia in Nicaragua

BACKGROUND: Within the frame of a twinning programme with Nicaragua, The La Mascota project, we evaluated in our study the contribution of cytogenetic characterization of acute lymphoblastic leukemia (ALL) as prognostic factor compared to clinical, morphological, and immunohistochemical parameters. METHODS: All patients with ALL treated at the only cancer pediatric hospital in Nicaragua during 2006 were studied prospectively. Diagnostic immunophenotyping was performed locally and bone marrow or blood samples were sent to the cytogenetic laboratory of Zurich for fluorescence in situ hybridization (FISH) analysis and G-banding. RESULTS: Sixty-six patients with ALL were evaluated. Their mean age at diagnosis was 7.3 years, 31.8% were >or=10 years. Thirty-four patients (51.5%) presented with hyperleucocytosis >or=50 x 10(9)/L, 45 (68.2%) had hepatosplenomegaly. Immunophenotypically 63/66 patients (95%) had a B-precursor, 2 (3%) a T- and 1 (1.5%) a B-mature ALL. FISH analysis demonstrated a TEL/AML1 fusion in 9/66 (14%), BCR/ABL fusion in 1 (1.5%), MLL rearrangement in 2 (3.1%), iAMP21 in 2 (3.1%), MYC rearrangement in 1 (1.5%), and high-hyperdiploidy in 16 (24%). All patients but two with TEL/AML1 fusion and high-hyperdiploidy were clinically and hematologically in the standard risk group whereas those with poor cytogenetic factors had clinical high-risk features and were treated intensively. CONCLUSIONS: Compared to Europe, the ALL population in Nicaragua is older, has a higher proportion of poor prognostic clinical and hematological features and receives more intensive treatment, while patients with TEL/AML1 translocations and high-hyperdiploidy are clinically in the standard risk group. Cytogenetics did not contribute as an additional prognostic factor in this setting.

Cyclododecane exposure in the field of conservation and restoration of art objects

PURPOSE: Recent work practices in the conservation and restoration involve the use of cyclododecane (CDD, CAS 294-62-2) to protect fragile artifacts during their handling or transportation. Little is known about its toxicity, and no previous exposure has been reported. A short field investigation was conducted to characterize the exposure conditions to both CDD vapors and aerosols.METHODS: Measurements were conducted in the laboratory of conservation and restoration of the archeological service in Bern (Switzerland). Three indoor and four outdoor typical work situations, either during brush or spray gun applications, were investigated. Measurements were performed on charcoal adsorbent tube and analyzed by a gas chromatograph equipped with a flame ionization detector.RESULTS: Measurements have been conducted during both brush and spray gun applications. Indoor exposures were of 0.75-15.5 mg/m(3), while outdoors exposures were 19.5-53.9 mg/m(3). Exposures appear to be extremely localized due to both physicochemical properties and application methods of the CDD. Vapor exposure increases dramatically with the confinement of the workplace.CONCLUSION: Preventive measures should be undertaken to limit as much as possible these exposures. Field work in confined areas (ditches, underground) is of particular concern. CDD-coated artifacts or materials should be stored in ventilated areas to avoid delayed exposures. [Authors]

Cytogenetic characterization of childhood acute lymphoblastic leukemia in Nicaragua.

BACKGROUND: Within the frame of a twinning programme with Nicaragua, The La Mascota project, we evaluated in our study the contribution of cytogenetic characterization of acute lymphoblastic leukemia (ALL) as prognostic factor compared to clinical, morphological, and immunohistochemical parameters. METHODS: All patients with ALL treated at the only cancer pediatric hospital in Nicaragua during 2006 were studied prospectively. Diagnostic immunophenotyping was performed locally and bone marrow or blood samples were sent to the cytogenetic laboratory of Zurich for fluorescence in situ hybridization (FISH) analysis and G-banding. RESULTS: Sixty-six patients with ALL were evaluated. Their mean age at diagnosis was 7.3 years, 31.8% were >or=10 years. Thirty-four patients (51.5%) presented with hyperleucocytosis >or=50 x 10(9)/L, 45 (68.2%) had hepatosplenomegaly. Immunophenotypically 63/66 patients (95%) had a B-precursor, 2 (3%) a T- and 1 (1.5%) a B-mature ALL. FISH analysis demonstrated a TEL/AML1 fusion in 9/66 (14%), BCR/ABL fusion in 1 (1.5%), MLL rearrangement in 2 (3.1%), iAMP21 in 2 (3.1%), MYC rearrangement in 1 (1.5%), and high-hyperdiploidy in 16 (24%). All patients but two with TEL/AML1 fusion and high-hyperdiploidy were clinically and hematologically in the standard risk group whereas those with poor cytogenetic factors had clinical high-risk features and were treated intensively. CONCLUSIONS: Compared to Europe, the ALL population in Nicaragua is older, has a higher proportion of poor prognostic clinical and hematological features and receives more intensive treatment, while patients with TEL/AML1 translocations and high-hyperdiploidy are clinically in the standard risk group. Cytogenetics did not contribute as an additional prognostic factor in this setting.

Diagnostic and identification in situ of fungal pathogens in superficial mycosis

Fungi are divided in 3 groups in the field of medical mycology. The dermatophytes are filamentous fungi able to grow on keratinized tissues from human or animals. They are the main cause of superficial and cutaneous mycoses of the skin and its appendix (hair and nail). The yeasts, or dimorphic fungi, can be responsible of diverse types of infections (superficial to deep mycoses). The moulds include all Non-dermatophyte Filamentous Fungi (NDF). In medical mycology, the most representative moulds are Aspergillus spp., Fusarium spp. and Mucor spp. Diagnosis of mycosis is currently based on direct mycological examination of biological samples, as well as macroscopic and microscopic identification of the infectious fungus in culture assay. However, culture assays were found to remain sterile in roughly 40% of cases otherwise positive by direct mycological examinations. Additionally, results from culture assays are often difficult to interpret as various NDF are sometimes isolated. This thesis work is composed of three projects focusing on the development of new assays for direct in situ identification of fungi from dermatological samples. Part 1. A Polymerase Chain Reaction - Terminal Restriction Fragment Length Polymorphism assay (PCR-TRFLP) targeting the 28S rDNA was developed to identify dermatophytes and NDF in nails with suspected onychomycosis. This method is faster and more efficient than culture. It further enables the distinction of more than one agent in case of mixed infection. A fast and reliable assay for the identification of dermatophytes and NDF in onychomycosis was found to be highly relevant since onychomycosis with Fusarium spp. or other NDF are weakly responsive or unresponsive to standard onychomycosis treatments with oral terbinafine and itraconazole. Part 2. A nested PCR-sequencing assay targeting the 28S rDNA was developed to identify dermatophyte species in skin and hair samples. This method is especially suitable for tinea capitis where dermatophytes identification is critical for subsequently prescribing the adequate treatment. The challenge presented when performing direct PCR fungi identification in skin and hair differs from that seen in onychomycosis as small amount of material is generally collected, few fungal elements are present in the clinical sample and one dermatophyte among a dozen species must be identified. Part 3. Fusarium spp. is currently isolated from nails with a frequency of 15% of that of dermatophytes in the laboratory of Mycology of the CHUV (2005-2012). The aim of this work was to examine if the intensive use of terbinafine and itraconazole could be a cause of the high incidence of Fusarium nail infections. For that purpose, two different methods, specific PCR and TRFLP, were used to detect both Fusarium spp. and Trichophyton spp. in nails of previously treated or untreated patients. TRFLP assay was found to be less sensitive than classical PCR assays specifically detecting Fusarium spp. or Trichophyton spp. Independently of the detection method used, the prevalence of Fusarium spp. appears not to be higher in patients previously treated by oral standard treatment with terbinafine and azoles which are highly effective to fight Trichophyton spp. in nails. In many cases Fusarium sp. was detected in samples of patients not previously subjected to antifungal therapy. Therefore, these treatments do not appear to favor the establishment of Fusarium spp. after elimination of a dermatophyte in nail infection. - En mycologie médicale, les champignons sont classés en 3 groupes. Les dermatophytes sont des champignons filamenteux capables de se développer dans les tissus kératinisés des hommes et des animaux, ils représentent la principale cause des mycoses superficielles et cutanées de la peau et de ses appendices (ongles et cheveux). Les levures, ou champignons dimorphiques, peuvent être responsables de divers types d'infections (superficielles à profondes). Les moisissures incluent tous les champignons filamenteux non-dermatophytes (NDF), les Aspergillus spp., les Fusarium spp. et les Mucor spp. sont les principales espèces rencontrées. Le diagnostic d'une mycose est basé sur un examen mycologique direct des prélèvements biologiques ainsi que sur l'identification macroscopique et microscopique du champignon infectieux isolé en culture. Cependant, dans environ 40% des cas, l'identification de l'agent pathogène est impossible par cette méthode car la culture reste stérile, bien que l'examen direct soit positif. De plus, la croissance de moisissures et/ou autres contaminants peut rendre l'interprétation de l'examen difficile. Ce travail de thèse est composé de trois projets focalisés sur le développement de nouvelles méthodes d'identification des champignons directement à partir d'échantillons dermatologiques. Projet 1. Une méthode de Réaction en chaîne de polymérase couplée à du polymorphisme de longueur des fragments de restriction terminaux (PCR-TRFLP), en ciblant l'ADN ribosomal 28S, a été développée pour l'identification des dermatophytes et moisissures dans les ongles avec suspicion d'onychomycoses. Cette technique s'est avérée plus rapide et plus efficace que la culture, permettant l'identification de plusieurs champignons en même temps. Posséder une méthode d'identification rapide et fiable des dermatophytes et des NDF dans les onychomycoses a été jugée nécessaire du fait que les Fusarium et d'autres NDF sont peu ou pas sensibles aux traitements oraux standards à la terbinafine et à Γ itraconazole. Projet 2. Une PCR nichée couplée au séquençage d'un fragment de l'ADN ribosomal 28S a été développée afin de différencier les dermatophytes dans la peau et les cheveux. Cette méthode est particulièrement adaptée au cas de tinea capitis, où l'identification du dermatophyte est essentielle afin de prescrire le traitement adéquat. Le problème de l'identification du pathogène fongique dans les cheveux et la peau diffère des onychomycoses car de petites quantités sont prélevées chez les patients, peu d'éléments fongiques sont présents et il faut discriminer un dermatophyte parmi une douzaine d'espèces potentielles. Projet 3. Au laboratoire de Mycologie du CHUV, les Fusarium ont été isolé dans les ongles à une fréquence de 15% pour la période 2005-2012. Le but de ce travail était d'examiner si l'utilisation intensive de terbinafine et d'itraconazole pouvait être une des causes de la forte incidence des infections des ongles par Fusarium. A cet effet, deux méthodes ont été utilisées pour détecter à la fois Fusarium spp. et Trichophyton spp., la PCR spécifique et le TRFLP. Indépendamment de la méthode choisie, il en résulte que la prévalence des Fusarium η'apparaît pas liée à un traitement au préalable des patients avec de la terbinafine ou des azoles, thérapies très efficaces contre les Trichophyton spp. dans les ongles. De plus, il existe de nombreux cas où Fusarium était détecté chez des patients non traités.

Dynamic Modelling of Material Flows and Sustainable Resource Use: Case Studies in Regional Metabolism and Space Life Support Systems

Sustainable resource use is one of the most important environmental issues of our times. It is closely related to discussions on the 'peaking' of various natural resources serving as energy sources, agricultural nutrients, or metals indispensable in high-technology applications. Although the peaking theory remains controversial, it is commonly recognized that a more sustainable use of resources would alleviate negative environmental impacts related to resource use. In this thesis, sustainable resource use is analysed from a practical standpoint, through several different case studies. Four of these case studies relate to resource metabolism in the Canton of Geneva in Switzerland: the aim was to model the evolution of chosen resource stocks and flows in the coming decades. The studied resources were copper (a bulk metal), phosphorus (a vital agricultural nutrient), and wood (a renewable resource). In addition, the case of lithium (a critical metal) was analysed briefly in a qualitative manner and in an electric mobility perspective. In addition to the Geneva case studies, this thesis includes a case study on the sustainability of space life support systems. Space life support systems are systems whose aim is to provide the crew of a spacecraft with the necessary metabolic consumables over the course of a mission. Sustainability was again analysed from a resource use perspective. In this case study, the functioning of two different types of life support systems, ARES and BIORAT, were evaluated and compared; these systems represent, respectively, physico-chemical and biological life support systems. Space life support systems could in fact be used as a kind of 'laboratory of sustainability' given that they represent closed and relatively simple systems compared to complex and open terrestrial systems such as the Canton of Geneva. The chosen analysis method used in the Geneva case studies was dynamic material flow analysis: dynamic material flow models were constructed for the resources copper, phosphorus, and wood. Besides a baseline scenario, various alternative scenarios (notably involving increased recycling) were also examined. In the case of space life support systems, the methodology of material flow analysis was also employed, but as the data available on the dynamic behaviour of the systems was insufficient, only static simulations could be performed. The results of the case studies in the Canton of Geneva show the following: were resource use to follow population growth, resource consumption would be multiplied by nearly 1.2 by 2030 and by 1.5 by 2080. A complete transition to electric mobility would be expected to only slightly (+5%) increase the copper consumption per capita while the lithium demand in cars would increase 350 fold. For example, phosphorus imports could be decreased by recycling sewage sludge or human urine; however, the health and environmental impacts of these options have yet to be studied. Increasing the wood production in the Canton would not significantly decrease the dependence on wood imports as the Canton's production represents only 5% of total consumption. In the comparison of space life support systems ARES and BIORAT, BIORAT outperforms ARES in resource use but not in energy use. However, as the systems are dimensioned very differently, it remains questionable whether they can be compared outright. In conclusion, the use of dynamic material flow analysis can provide useful information for policy makers and strategic decision-making; however, uncertainty in reference data greatly influences the precision of the results. Space life support systems constitute an extreme case of resource-using systems; nevertheless, it is not clear how their example could be of immediate use to terrestrial systems.

Clinicopathological features of eyelid skin tumors. A retrospective study of 5504 cases and review of literature.

Eyelid tumors are the most common neoplasm in daily ophthalmology practice and encompass a wide variety of benign and malignant tumors. In this retrospective study, we report the clinical and histological features of 5504 eyelid skin tumors diagnosed at the Laboratory of Ophthalmopathology of the Hôpital Ophtalmique Jules Gonin, Lausanne, Switzerland, between January 1989 and December 2007. Benign tumors largely predominated over malignant ones, representing 84% of cases in this series, and the 5 most frequent subtypes were squamous cell papilloma (26%), seborrheic keratosis (21%), melanocytic nevus (20%), hidrocystoma (8%), and xanthoma/xanthelasma (6%). Basal cell carcinoma was the most frequent malignant tumor (86%), followed by squamous cell carcinoma (7%) and sebaceous carcinoma (3%). For several tumor subtypes, there was a poor correlation between clinical and histological diagnosis, stressing the numerous pitfalls in the diagnosis of eyelid tumors. We further discuss our results with reference to previously published series.