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.

Genotype-level interactions determine the degree of reduction of leaf rust on wheat by seed application of beneficial Pseudomonas spp.

Some bacteria have the capacity to reduce incidence and severity of plant diseases either by inhibiting the pathogen or by modulating the resistance response of the plant. Plants dispose of different resistance mechanisms that are influenced by the biotic and abiotic environment. The present experiments explored the effects of biocontrol strains of Pseudomonas fluorescens on the resistance of wheat varieties against brown rust disease caused by Puccinia triticina. Root inoculation with biocontrol pseudomonads reduced the disease severity on the leaves. The plant response depended on the genotype of both the microbes and the wheat varieties, suggesting a straight interaction at the molecular level.

Confounding effects of heart rate on pulse wave velocity in paced patients with a low degree of atherosclerosis.

BACKGROUND: Pulse wave velocity (PWV), an index of arterial wall stiffness, is modulated by blood pressure (BP). Whether heart rate (HR) is also a modulator of PWV is controversial. Recent research involving mainly patients with high aortic PWV have found either no change or a positive correlation between the two. Given that PWV is increasingly being measured in cardiovascular studies, the relationship between HR and PWV should be known in patients with preserved arterial wall elasticity. OBJECTIVE: The aim of this study was to evaluate the importance of HR as a determinant of the variability in PWV in patients with a low degree of atherosclerosis. DESIGN AND METHODS: Fourteen patients (five female, nine male; aged 68 +/- 8 years) were evaluated post pacemaker implantation due to sick sinus or carotid hypersensitivity syndromes. Carotid-femoral PWV was measured at rest and during atrial pacing at 80, 90 and 100 bpm (paced HR). Arterial femoral blood flow (AFBF) was measured by echodoppler. RESULTS: PWV increased from 6.2 +/- 1.5 m/s (mean +/- SD) during resting sinus rhythm (HR 62 +/- 8 bpm; mean +/- SD) to 6.8 +/- 1.0, 7.0 +/- 0.9, and 7.6 +/- 1.1 m/s at pacing rates of 80, 90 and 100 bpm, respectively (P < 0.0001). Systolic (SBP) and mean blood pressure (MBP) remained constant at all HR levels, whereas AFBF increased in a linear fashion. CONCLUSIONS: These results demonstrate that even in patients with a low degree of atherosclerosis, HR is a potential modulator of carotid-femoral PWV.

Insuffisance veineuse chronique stade III: Prise en charge physio- thérapeutique [3rd degree chronic venous insufficiency: physiotherapy treatment]

A venous ulcer is the end result of a long pathological process where venous hypertension represents the principal cause of a number of complications. The physiotherapist by adapting various different therapeutic approaches improves the vascular, joint and respiratory problems of these patients.

Severity of endoscopically detected esophageal inflammatory and fibrostenotic features correlates with degree of esophageal eosinophilia in adults with eosinophilic esophagitis

Background: Eosinophilic esophagitis (EoE) has emerged as a leading cause of dysphagia in adults. Characteristic esophageal features on endoscopy include structural/fibrostenotic (rings, narrow caliber, strictures) and inflammatory manifestations (longitudinal furrows, exudates, edema). Aim: The purpose of this study was to correlate the clinical, endoscopic and histopathologic features in adult EoE patients. Methods: A total of 106 encounters of 81 patients with EoE were analyzed. Data included an EoE-directed symptom-severity patient questionnaire evaluating symptoms of dysphagia (frequency, intensity, duration), meal duration, chest pain, and overall symptom severity. Video recordings of endoscopies were reviewed in a blinded manner using a classification and grading scheme for the esophageal features of EoE. Histopathology was reviewed for peak eosinophil count/high power field by pathologists blinded to the patients' clinical status. Associations between endoscopic features, histology and symptoms were evaluated using the Spearman rank correlation analysis. Results: The endoscopic severity of both structural and inflammatory esophageal features of EoE, including rings, exudates, longitudinal furrows, and edema, correlated significantly with peak eosinophil counts (see Table 1). Presence of "crepe paper mucosa" did not demonstrate significant association with peak eosinophil counts. Both structural (rings, narrow-caliber esophagus and strictures) and inflammatory (furrows, exudates and edema) composite endoscopic scores demonstrated a strong correlation with peak eosinophil counts. The strongest association with the degree of esophageal eosinophilia was found with a combination of both structural and inflammatory findings (p < 0.0001). The esophageal diameter (in mm) was negatively correlated with overall symptom severity (Spearman's rho = -0.4883, P = 0.0339). None of the individual or combined patient reported symptoms correlated significantly with either endoscopic or histopathologic findings. Conclusion: The severity of both structural and inflammatory endoscopic features associated with EoE is significantly associated with the degree of esophageal eosinophilia. Patient reported symptom severity was not associated with the degree of esophageal eosinophilia. Esophageal stricture diameter was inversely correlated with EoE symptom severity. The prognostic and therapeutic implications of these observations need to be determined.

Inferring the degree of incipient speciation in secondary contact zones of closely related lineages of Palearctic green toads (Bufo viridis subgroup).

Reproductive isolation between lineages is expected to accumulate with divergence time, but the time taken to speciate may strongly vary between different groups of organisms. In anuran amphibians, laboratory crosses can still produce viable hybrid offspring >20 My after separation, but the speed of speciation in closely related anuran lineages under natural conditions is poorly studied. Palearctic green toads (Bufo viridis subgroup) offer an excellent system to address this question, comprising several lineages that arose at different times and form secondary contact zones. Using mitochondrial and nuclear markers, we previously demonstrated that in Sicily, B. siculus and B. balearicus developed advanced reproductive isolation after Plio-Pleistocene divergence (2.6 My, 3.3-1.9), with limited historic mtDNA introgression, scarce nuclear admixture, but low, if any, current gene flow. Here, we study genetic interactions between younger lineages of early Pleistocene divergence (1.9 My, 2.5-1.3) in northeastern Italy (B. balearicus, B. viridis). We find significantly more, asymmetric nuclear and wider, differential mtDNA introgression. The population structure seems to be molded by geographic distance and barriers (rivers), much more than by intrinsic genomic incompatibilities. These differences of hybridization between zones may be partly explained by differences in the duration of previous isolation. Scattered research on other anurans suggests that wide hybrid zones with strong introgression may develop when secondary contacts occur <2 My after divergence, whereas narrower zones with restricted gene flow form when divergence exceeds 3 My. Our study strengthens support for this rule of thumb by comparing lineages with different divergence times within the same radiation.

An attempt to refine rockfall hazard zoning based on the kinetic energy, frequency and fragmentation degree

Rockfall hazard zoning is usually achieved using a qualitative estimate of hazard, and not an absolute scale. In Switzerland, danger maps, which correspond to a hazard zoning depending on the intensity of the considered phenomenon (e.g. kinetic energy for rockfalls), are replacing hazard maps. Basically, the danger grows with the mean frequency and with the intensity of the rockfall. This principle based on intensity thresholds may also be applied to other intensity threshold values than those used in Switzerland for rockfall hazard zoning method, i.e. danger mapping. In this paper, we explore the effect of slope geometry and rockfall frequency on the rockfall hazard zoning. First, the transition from 2D zoning to 3D zoning based on rockfall trajectory simulation is examined; then, its dependency on slope geometry is emphasized. The spatial extent of hazard zones is examined, showing that limits may vary widely depending on the rockfall frequency. This approach is especially dedicated to highly populated regions, because the hazard zoning has to be very fine in order to delineate the greatest possible territory containing acceptable risks.

High prevalence of major cardiovascular risk factors in first-degree relatives of individuals with familial premature coronary artery disease--the GENECARD project.

BACKGROUND: Hypertension, hypercholesterolemia, obesity and smoking are highly prevalent among patients with familial premature coronary artery disease (FP-CAD). Whether these risk factors equally affect other family members remains unknown. METHODS: We examined 222 FP-CAD patients, 158 unaffected sibs, 197 offspring and 94 spouses in 108 FP-CAD families (> or = 2 sibs having survived CAD diagnosed before age 51 (M)/56 (F)), and compared them to population controls. RESULTS: Unaffected sibs had a higher prevalence of hypertension (49% versus 24%, p<0.001), hypercholesterolemia (47% versus 34%, p=0.002), abdominal obesity (35% versus 24%, p=0.006) and smoking (39% versus 24%, p=0.001) than population controls. Offspring had a higher prevalence of hypertension (females), hypercholesterolemia and abdominal obesity than population controls. No difference was observed between spouses and controls. Compared to unaffected sibs, FP-CAD affected sibs had a similar risk factor profile, except for smoking, which was more prevalent (76% versus 39%, p=0.008). CONCLUSIONS: Hypertension, obesity and hypercholesterolemia are highly prevalent among first-degree relatives, but not spouses, of patients with FP-CAD. These persons deserve special medical attention due to their familial/genetic susceptibility to atherogenic metabolic abnormalities. In these families, smoking may be the trigger for FP-CAD.

Emergence of Cooperation on Static and Dynamic Networks

Game theory is a branch of applied mathematics used to analyze situation where two or more agents are interacting. Originally it was developed as a model for conflicts and collaborations between rational and intelligent individuals. Now it finds applications in social sciences, eco- nomics, biology (particularly evolutionary biology and ecology), engineering, political science, international relations, computer science, and philosophy. Networks are an abstract representation of interactions, dependencies or relationships. Net- works are extensively used in all the fields mentioned above and in many more. Many useful informations about a system can be discovered by analyzing the current state of a network representation of such system. In this work we will apply some of the methods of game theory to populations of agents that are interconnected. A population is in fact represented by a network of players where one can only interact with another if there is a connection between them. In the first part of this work we will show that the structure of the underlying network has a strong influence on the strategies that the players will decide to adopt to maximize their utility. We will then introduce a supplementary degree of freedom by allowing the structure of the population to be modified along the simulations. This modification allows the players to modify the structure of their environment to optimize the utility that they can obtain.

Pseudo-pacemaker syndrome in a young woman with first-degree atrio-ventricular block.

First-degree atrio-ventricular (AV) block is defined as a PR interval longer than 200 ms. If too long, it can become clinically relevant and may mimic a pacemaker syndrome. We report the case of a young woman with a long PR interval, probably congenital, with episodes of syncope and dizziness since childhood. Pseudo-pacemaker syndrome is rare and is a Class IIa recommendation for a pacemaker implantation. A dual-chamber pacemaker was implanted and short AV delay was programmed, with rapid clinical improvement.

High prevalence of major cardiovascular risk factors in first-degree relatives of individuals with familial premature coronary artery disease : the GENECARD project

Rapport de synthèse La prévalence de l'hypertension artérielle, d'une dyslipidémie, d'une obésité et d'un tabagisme est élevée chez les patients qui souffrent d' une maladie coronarienne familiale précoce (MC-FP). L? e but de cette étude fut d'investiguer la prévalence de ces facteurs de risque cardiovasculaires au sein des membres d'une famille dont un patient est affecté d'une MC-FP. Nous avons étudié 108 familles différentes dont au minimum 2 frères/soeurs ont survécu à une maladie coronarienne précoce. Cette dernière fut définie par la survenue d'un événement coronarien avant l'âge de 51 ans pour les hommes et 56 ans pour les femmes. Au total, nous avons identifié 222 patients atteints de MC-FP chez qui 158 frères/soeurs, 197 enfants et 94 époux/épouses ne souffraient pas de maladie coronarienne. Ces parents proches furent comparés à un collectif d'individus "contrôles" issus de la population générale. Les frères/soeurs non affectés avaient une prévalence plus élevée d'hypertension artérielle (49% versus 24%, p<0.001), d'hypercholestérolémie (47% versus 34%, p=0.002), d'obésité abdominale (35% versus 24%, p=0.006) et de tabagisme (39% versus 24%, p=0.001) par rapport aux individus issus de la population générale. Parmi les enfants, une prévalence plus élevée d'hypertension artérielle fut identifiée chez les femmes, et une prévalence plus élevée d'hypercholestérolémie et d'obésité abdominale dans les deux sexes par rapport aux contrôles de la population générale. Aucune différence parmi les facteurs de risque cardiovasculaire n'a été observée entre les époux/ épouses et les contrôles. Les frères/soeurs affectés et non affectés par la MC-FP ont également été comparés entre eux. La prévalence des facteurs de risque était similaire dans les 2 groupes, sauf pour le tabagisme, qui avait une prévalence plus élevée chez les frères/sueurs affectés (76% versus 39%, p=0.008). La prévalence de l'hypertension artérielle, de l'obésité, et de la dyslipidémie est également élevée chez les parents de premier degré de patients atteints de MC-FP, mais pas chez leurs époux/épouses. Ces personnes-là requièrent donc une attention médicale particulière en raison d'une vulnérabilité familiale et/ou génétique augmentée aux anomalies métaboliques athérogènes. Dans ces familles, le tabagisme pourrait être le facteur déclenchant de la MC-FP.