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.

Mise en place d'un programme de prévention et de prise en charge du diabète en Suisse: le point de vue des patients et des professionnels de la santé [Implementation of a diabetes disease management program in Switzerland: patients' and healthcare professionals' point of view].

BACKGROUND: A reorganization of healthcare systems is required to meet the challenge of the increasing prevalence of chronic diseases, e.g. diabetes. In North-America and Europe, several countries have thus developed national or regional chronic disease management programs. In Switzerland, such initiatives have only emerged recently. In 2010, the canton of Vaud set up the "Diabetes Cantonal Program", within the framework of which we conducted a study designed to ascertain the opinions of both diabetic patients and healthcare professionals on the elements that could be integrated into this program, the barriers and facilitators to its development, and the incentives that could motivate these actors to participate. METHODS: We organized eight focus-groups: one with diabetic patients and one with healthcare professionals in the four sanitary areas of the canton of Vaud. The discussions were recorded, transcribed and submitted to a thematic content analysis. RESULTS: Patients and healthcare professionals were rather in favour of the implementation of a cantonal program, although patients were more cautious concerning its necessity. All participants envisioned a set of elements that could be integrated to this program. They also considered that the program could be developed more easily if it were adapted to patients' and professionals' needs and if it used existing structures and professionals. The difficulty to motivate both patients and professionals to participate was mentioned as a barrier to the development of this program however. Quality or financial incentives could therefore be created to overcome this potential problem. CONCLUSION: The identification of the elements to consider, barriers, facilitators and incentives to participate to a chronic disease management program, obtained by exploring the opinions of patients and healthcare professionals, should favour its further development and implementation.

The generic Hanna Neumann conjecture and post correspondence problem

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Heterogeneity of atherosclerotic plaque phenotypes and composition in four different arterial beds: an intravascular ultrasound virtual histology study

Purpose: The purpose of this study was to compare the plaque morphology between coronary and peripheral arteries using intravascular ultrasound (IVUS). Methods: IVUS was performed in 68 patients with coronary and 93 with peripheral artery lesions (29 carotid, 50 renal, and 14 iliac). Plaques were classified as fibroatheroma (VH-FA) (further subclassified as thin-capped [VH-TCFA] and thick-capped [VH-ThCFA]), fibrocalcific plaque (VH-FC) and pathological intimal thickening (VH-PIT). Results: Plaque rupture (13% of coronary, 7% of carotid, 6% of renal, and 7% of iliac arteries; P=NS) and VH-TCFA (37% of coronary, 24% of carotid, 16% of renal, and 7% of iliac arteries; P=0.02) was observed in all arteries. Compared to coronary arteries, VH-FA was less frequently observed in renal (P<0.001) and iliac arteries (P<0.006), while VH-PIT and VH-FC were prevalent in both of these peripheral arteries. Lesions with positive remodeling demonstrated more characteristics of VH-FA in coronary, carotid, and renal arteries compared to those with intermediate/negative remodeling (all P<0.01). There was positive relationship between RI and percent necrotic core area in all four arteries. Conclusions: Atherosclerotic plaque phenotypes were heterogeneous among four different arteries. In contrast, the associations of remodeling mode with plaque phenotype and composition were similar among the various arterial beds.

On Emblemasomini (Dipitera-Sarcophagidae), with descriptions of four new species

Two new species of Pessomyia from Peru and two species of Emblemasoma from Mexico and Costa rica are proposed; key to species of Emblemasomini is given.

Superior outcome of women with stage I/II cutaneous melanoma: pooled analysis of four European Organisation for Research and Treatment of Cancer phase III trials.

PURPOSE: Several studies observed a female advantage in the prognosis of cutaneous melanoma, for which behavioral factors or an underlying biologic mechanism might be responsible. Using complete and reliable follow-up data from four phase III trials of the European Organisation for Research and Treatment of Cancer (EORTC) Melanoma Group, we explored the female advantage across multiple end points and in relation to other important prognostic indicators. PATIENTS AND METHODS: Patients diagnosed with localized melanoma were included in EORTC adjuvant treatment trials 18832, 18871, 18952, and 18961 and randomly assigned during the period of 1984 to 2005. Cox proportional hazard models were used to calculate hazard ratios (HRs) and 95% CIs for women compared with men, adjusted for age, Breslow thickness, body site, ulceration, performed lymph node dissection, and treatment. RESULTS: A total of 2,672 patients with stage I/II melanoma were included. Women had a highly consistent and independent advantage in overall survival (adjusted HR, 0.70; 95% CI, 0.59 to 0.83), disease-specific survival (adjusted HR, 0.74; 95% CI, 0.62 to 0.88), time to lymph node metastasis (adjusted HR, 0.70; 95% CI, 0.51 to 0.96), and time to distant metastasis (adjusted HR, 0.69; 95% CI, 0.59 to 0.81). Subgroup analysis showed that the female advantage was consistent across all prognostic subgroups (with the possible exception of head and neck melanomas) and in pre- and postmenopausal age groups. CONCLUSION: Women have a consistent and independent relative advantage in all aspects of the progression of localized melanoma of approximately 30%, most likely caused by an underlying biologic sex difference.

Four-month-olds make triangular bids to father and mother during trilogue play with still-face

(from the journal abstract) A new observational procedure, Trilogue Play with Still-face, revealed 4-month-olds' capacities to address both their fathers and mothers, by rapidly shifting gaze and affect between them. Infants were observed in four interactive contexts: (1) '3-together' play with both parents; (2) '2 + 1' play with one parent engaging and the other as third party; (3) the same, with one parent posing a still-face; (4) '3-together' play. Infants were able to discriminate between the four contexts. They coordinated three social poles of attention in each one. Their affect configurations were context sensitive. These findings demonstrate the infant's social capacities for triangular, three-person interactions, in addition to dyadic, two-person, and triadic, two-person plus object, ones. They support a view of intersubjectivity as primary and point to a promising field of investigation for the study of family process. (PsycINFO Database Record (c) 2005 APA, all rights reserved)

Model based fault diagnosis with application to an automotive engine

Report for the scientific sojourn at the University of Linköping between April to July 2007. Monitoring of the air intake system of an automotive engine is important to meet emission related legislative diagnosis requirements. During the research the problem of fault detection in the air intake system was stated as a constraint satisfaction problem over continuous domains with a big number of variables and constraints. This problem was solved using Interval-based Consistency Techniques. Interval-based consistency techniques are shown to be particularly efficient for checking the consistency of the Analytical Redundancy Relations (ARRs), dealing with uncertain measurements and parameters, and using experimental data. All experiments were performed on a four-cylinder turbo-charged spark-ignited SAAB engine located in the research laboratory at Vehicular System Group - University of Linköping.

Periodic Sequences of Arbitrage: A Tale of Four Currencies

This paper investigates arbitrage chains involving four currencies and four foreign exchange trader-arbitrageurs. In contrast with the three-currency case, we fi nd that arbitrage operations when four currencies are present may appear periodic in nature, and not involve smooth convergence to a \balanced" ensemble of exchange rates in which the law of one price holds. The goal of this article is to understand some interesting features of sequences of arbitrage operations, features which might well be relevant in other contexts in finance and economics.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Gas emission during laparoscopic colorectal surgery using a bipolar vessel sealing device: A pilot study on four patients.

BACKGROUND: Dissection during laparoscopic surgery produces smoke containing potentially toxic substances. The aim of the present study was to analyze smoke samples produced during laparoscopic colon surgery using a bipolar vessel sealing device (LigaSuretrade mark). METHODS: Four consecutive patients undergoing left-sided colectomy were enrolled in this pilot study. Smoke was produced by the use of LigaSuretrade mark. Samples (5,5l) were evacuated from the pneumoperitoneum in a closed system into a reservoir. Analysis was performed with CO2-laser-based photoacoustic spectroscopy and confirmed by a Fourier-transform infrared spectrum. The detected spectra were compared to the available spectra of known toxins. RESULTS: Samples from four laparoscopic sigmoid resections were analyzed. No relevant differences were noted regarding patient and operation characteristics. The gas samples were stable over time proven by congruent control measurements as late as 24 h after sampling. The absorption spectra differed considerably between the patients. One broad absorption line at 100 ppm indicating H2O and several unknown molecules were detected. With a sensitivity of alpha min ca 10-5 cm-1 no known toxic substances like phenol or indole were identified. CONCLUSION: The use of a vessel sealing device during laparoscopic surgery does not produce known toxic substances in relevant quantity. Further studies are needed to identify unknown molecules and to analyze gas emission under various conditions.

An Empirical Examination of the R&D Boundaries of the Firm - A Problem-Solving Perspective

We consider, both theoretically and empirically, how different organization modes are aligned to govern the efficient solving of technological problems. The data set is a sample from the Chinese consumer electronics industry. Following mainly the problem solving perspective (PSP) within the knowledge based view (KBV), we develop and test several PSP and KBV hypotheses, in conjunction with competing transaction cost economics (TCE) alternatives, in an examination of the determinants of the R&D organization mode. The results show that a firm’s existing knowledge base is the single most important explanatory variable. Problem complexity and decomposability are also found to be important, consistent with the theoretical predictions of the PSP, but it is suggested that these two dimensions need to be treated as separate variables. TCE hypotheses also receive some support, but the estimation results seem more supportive of the PSP and the KBV than the TCE.

Agronomic and commercial performance of four Spanish carob cultivars

The carob tree (Ceratonia siliqua) shows interesting prospects for some coastal Mediterranean growing areas and is widely used for industrial, agricultural, and ornamental purposes. It can be an alternative crop adapted to part-time farming and can also be used to regenerate vegetation in areas with a mild climate and erosion problems. Four Spanish carob cultivars were examined (Banya de Cabra, Duraio, Matalafera, and Rojal) to determine the one that performed the best for planting new orchards in northeastern Spain (Catalonia). The trees in this rain-fed trial (average rainfall of 500 mm) were planted in 1986 using seedling rootstocks that were budded in 1987. The trees were trained using the free-vase system and were spaced 8 x 9 m (138 trees/ha including 12% pollinators). The results showed that ‘Rojal’ was the earliest bearing cultivar. However, no significant differences were observed for cumulative pod production 18 years after budding. With respect to cumulative seed yield, ‘Duraio’ had the highest production (95 kg/tree). The lowest tree vigor (trunk cross-section) was observed in ‘Matalafera’. ‘Rojal’ trees produced the largest pods (average fruit weight of 18.9 g) and lowest seed content (11.8%), while ‘Banya de Cabra’ and ‘Duraio’ produced the smallest fruit (weighing 15.3 and 16.2 g, respectively) with the highest seed content (15.2% and 17.3%, respectively). Gum content, expressed as a percentage of the dry weight, was highest in ‘Duraio’ (56.9%) and was lowest in ‘Rojal’ (54.1%). Thus, in terms of kernel and pod production, ‘Duraio’ appeared to be the best-performing female cultivar for planting new carob orchards

Symmetry for a Dirichlet-Neumann problem arising in water waves

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