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.

Prenatal Representations of Family in Parents and Coparental Interactions as Predictors of Triadic Interactions During Infancy

In this study, we explored the predictive role of family interactions and family representations in mothers and fathers during pregnancy for postnatal motherfatherinfant interactions during the first 2 years after birth. Families (N = 42) were seen at the fifth month of pregnancy and at 3 and 18 months after birth. During pregnancy, parents were asked to play with their baby at the first meeting by using a doll in accordance with the procedure of the prenatal Lausanne Trilogue Play (LTP; A. Corboz-Warnery & E. Fivaz-Depeursinge, 2001; E. Fivaz-Depeursinge, F. Frascarolo-Moutinot, & A. Corboz-Warnery, 2010). Family representations were assessed by administering the Family System Test (T. Gehring, 1998). Marital satisfaction and the history of the couple were assessed through self-reported questionnaires. At 3 and 18 months, family interactions were assessed in the postnatal LTP. Infant temperament was assessed through parent reports. Results show that (a) prenatal interactions and child temperament are the most important predictors of family interactions and (b) paternal representations are predictive of family interactions at 3 months. These results show that observational assessment of nascent family interactions is possible during pregnancy, which would allow early screening of family maladjustment. The findings also highlight the necessity of taking into account paternal representations as a significant variable in the development of family interactions.

Efficacité du counseling d'orientation: impacts de l'alliance de travail et du contexte psychosocial

La problématique centrale de cette thèse de doctorat est l'efficacité de l'accompagnement à l'orientation. Elle renvoie en particulier à la multiplicité des types d'interventions ainsi qu'aux tensions entre les finalités de l'orientation qui rendent improbable une mesure univoque et objective de l'efficacité des pratiques. Le «mythe » de l'efficacité trouve notamment sa source dans le persistent monopole du modèle de l'appariement qui a largement influencé le développement de la discipline. Le manuscrit est basé sur deux études empiriques. Premièrement, « voies professionnelles » est une étude longitudinale visant l'évaluation de l'efficacité d'un service de counseling d'orientation au travers de mesures intraindividuelles. Les résultats immédiats (pre-post) indiquent une forte diminution de l'indécision vocationnelle des consultants ainsi qu'une augmentation de leur bien-être. Les résultats longitudinaux sur un an indiquent une évolution positive des difficultés plus ancrées ainsi qu'un fort taux d'implémentation des projets professionnels. La qualité de l'alliance de travail démontre un impact positif sur l'efficacité de la démarche. Deuxièmement, l'étude « orientation et genre » a permis de mettre en évidence un effet d'interaction entre le sexe et le niveau scolaire d'élèves en fin de scolarité sur leurs profils d'intérêts professionnels. Ce résultat affecte en particulier les jeunes filles dans une filière à exigences élémentaires car ces deux identités psychosociales semblent restreindre doublement les options professionnelles envisageables. Les deux études ont permis de soulever cinq implications centrales : (1) La distinction entre les aspects cognitifs et émotionnels de l'indécision vocationnelle est importante. En particulier, la préparation au choix est un construit qui nécessite clarification ; (2) Les processus de transitions professionnelles ainsi que leur accompagnement doivent être considérés dans leur dimension temporelle ; (3) L'interconnexion des différentes sphères de vie est centrale dans les processus d'orientation et leur accompagnement ; (4) L'efficacité du conseil en orientation est affectée par la qualité des aspects relationnels ; (5) La complexité des pratiques et de leurs finalités confronte l'orientation à son rôle envers des identités psychosociales fragilisées. - The central issue of this doctoral thesis is the effectiveness of career counseling and guidance. In particular, this refers to the many types of career interventions as well as the tensions between their objectives. Those aspects make it unlikely to get an unambiguous and objective measure of the effectiveness of career practices. The "myth of efficiency" is particularly rooted in the persistent monopoly of person-environment fit models, which greatly influenced the development of the discipline. This manuscript is based on two empirical studies. First, "career paths" is a longitudinal study looking at the effectiveness of a career counseling service through intraindividual measures. Pre-post impacts showed a significant decrease in clients' vocational indecision as well as a moderate increase in their well-being. The one year-longitudinal results highlighted significant decreases in more constant decision-making difficulties with a high proportion of clients having implemented their professional projects. The quality of the working alliance had a positive impact on the effectiveness of the intervention. The second study, "vocational development and gender" highlighted an interaction effect between late schoolchildren's gender and school level on their professional interests profile. This result particularly affected girls at a low school level, because these psychosocial identities were a double restraint in restricting career options. The two studies raised five central implications: (1) The distinction between cognitive and emotional aspects of vocational indecision is important. In particular, readiness to make a choice is a construct that requires clarification; (2) career transitions processes as well as supporting these transitions, should be considered in their temporal dimension (3) the interconnection of different spheres of life is central to vocational development and career guidance and counseling; (4) the effectiveness of career counseling is affected by the quality of the relational aspects in the intervention; (5) and the complexity of career interventions and their objectives forces practitioners to consider their role and responsibilities towards clients with marginalized psychosocial identities.

Significant correction of disease after postnatal administration of recombinant ectodysplasin A in canine X-linked ectodermal dysplasia.

Patients with defective ectodysplasin A (EDA) are affected by X-linked hypohidrotic ectodermal dysplasia (XLHED), a condition characterized by sparse hair, inability to sweat, decreased lacrimation, frequent pulmonary infections, and missing and malformed teeth. The canine model of XLHED was used to study the developmental impact of EDA on secondary dentition, since dogs have an entirely brachyodont, diphyodont dentition similar to that in humans, as opposed to mice, which have only permanent teeth (monophyodont dentition), some of which are very different (aradicular hypsodont) than brachyodont human teeth. Also, clinical signs in humans and dogs with XLHED are virtually identical, whereas several are missing in the murine equivalent. In our model, the genetically missing EDA was compensated for by postnatal intravenous administration of soluble recombinant EDA. Untreated XLHED dogs have an incomplete set of conically shaped teeth similar to those seen in human patients with XLHED. After treatment with EDA, significant normalization of adult teeth was achieved in four of five XLHED dogs. Moreover, treatment restored normal lacrimation and resistance to eye and airway infections and improved sweating ability. These results not only provide proof of concept for a potential treatment of this orphan disease but also demonstrate an essential role of EDA in the development of secondary dentition.

Noninvasive imaging of 5-HT3 receptor trafficking in live cells: from biosynthesis to endocytosis.

Sequential stages in the life cycle of the ionotropic 5-HT(3) receptor (5-HT(3)R) were resolved temporally and spatially in live cells by multicolor fluorescence confocal microscopy. The insertion of the enhanced cyan fluorescent protein into the large intracellular loop delivered a fluorescent 5-HT(3)R fully functional in terms of ligand binding specificity and channel activity, which allowed for the first time a complete real-time visualization and documentation of intracellular biogenesis, membrane targeting, and ligand-mediated internalization of a receptor belonging to the ligand-gated ion channel superfamily. Fluorescence signals of newly expressed receptors were detectable in the endoplasmic reticulum about 3 h after transfection onset. At this stage receptor subunits assembled to form active ligand binding sites as demonstrated in situ by binding of a fluorescent 5-HT(3)R-specific antagonist. After novel protein synthesis was chemically blocked, the 5-HT(3) R populations in the endoplasmic reticulum and Golgi cisternae moved virtually quantitatively to the cell surface, indicating efficient receptor folding and assembly. Intracellular 5-HT(3) receptors were trafficking in vesicle-like structures along microtubules to the cell surface at a velocity generally below 1 mum/s and were inserted into the plasma membrane in a characteristic cluster distribution overlapping with actin-rich domains. Internalization of cell surface 5-HT(3) receptors was observed within minutes after exposure to an extracellular agonist. Our orchestrated use of spectrally distinguishable fluorescent labels for the receptor, its cognate ligand, and specific organelle markers can be regarded as a general approach allowing subcellular insights into dynamic processes of membrane receptor trafficking.

Cell surface expression of a functional rubella virus E1 glycoprotein by addition of a GPI anchor.

Rubella virus (RV) envelope glycoproteins E1 and E2 are targeted to the Golgi as heterodimers. While E2 contains a transmembrane Golgi retention signal, E1 is arrested in a pre-Golgi compartment in the absence of E2, and appears to require heterodimerization in order to reach the Golgi. Various forms of E1 with deletions in the ectodomain or lacking the cytoplasmic (CT) and transmembrane (TM) domains, as well as the 29 C-terminal amino acid residues of the ectodomain were also retained intracellularly. We therefore investigated the possibility of targetting E1 to the plasma membrane by addition of a glycosylphosphatidylinositol (GPI) anchor. We found that E1GPI was transported to the cell surface where it retained the hemadsorption activity characteristic of the wild-type E1/E2 heterodimer. Furthermore, coexpression of a mammalian GPI-specific phospholipase D (GPI-PLD) resulted in the release of E1GPI and in constitutive expression of a soluble form of E1. This study thus demonstrates that the GPI anchor has a dominant effect over the E1 pre-Golgi retention signal and that E1 is sufficient for hemadsorption.

Liquid line of descent of a basanitic liquid at 1.5 GPa: Constraints for metasomatic vein formation

The metasomatism observed in the oceanic and continental lithosphere is generally interpreted to represent a continuous differentiation process forming anhydrous and hydrous veins plus a cryptic enrichment in the surrounding peridotite. In order to constrain the mechanisms of vein formation and potentially clarify the nature and origin of the initial metasomatic agent, we performed a series of high-pressure experiments simulating the liquid line of descent of a basanitic magma differentiating within continental or mature oceanic lithosphere. This series of experiments has been conducted in an end-loaded piston cylinder apparatus starting from an initial hydrous ne-normative basanite at 1.5 GPa and temperature varying between 1,250 and 980°C. Near-pure fractional crystallization process was achieved in a stepwise manner in 30°C temperature steps and starting compositions corresponding to the liquid composition of the previous, higher-temperature glass composition. Liquids evolve progressively from basanite to peralkaline, aluminum-rich compositions without significant SiO2 variation. The resulting cumulates are characterized by an anhydrous clinopyroxene + olivine assemblage at high temperature (1,250-1,160°C), while at lower temperature (1,130-980°C), hydrous cumulates with dominantly amphibole + minor clinopyroxene, spinel, ilmenite, titanomagnetite and apatite (1,130-980°C) are formed. This new data set supports the interpretation that anhydrous and hydrous metasomatic veins could be produced during continuous differentiation processes of primary, hydrous alkaline magmas at high pressure. However, the comparison between the cumulates generated by the fractional crystallization from an initial ne-normative liquid or from hy-normative initial compositions (hawaiite or picrobasalt) indicates that for all hydrous liquids, the different phases formed upon differentiation are mostly similar even though the proportions of hydrous versus anhydrous minerals could vary significantly. This suggests that the formation of amphibole-bearing metasomatic veins observed in the lithospheric mantle could be linked to the differentiation of initial liquids ranging from ne-normative to hy-normative in composition. The present study does not resolve the question whether the metasomatism observed in lithospheric mantle is a precursor or a consequence of alkaline magmatism; however, it confirms that the percolation and differentiation of a liquid produced by a low degree of partial melting of a source similar or slightly more enriched than depleted MORB mantle could generate hydrous metasomatic veins interpreted as a potential source for alkaline magmatism by various authors.

Amplification efficiency: linking baseline and bias in the analysis of quantitative PCR data.

Despite the central role of quantitative PCR (qPCR) in the quantification of mRNA transcripts, most analyses of qPCR data are still delegated to the software that comes with the qPCR apparatus. This is especially true for the handling of the fluorescence baseline. This article shows that baseline estimation errors are directly reflected in the observed PCR efficiency values and are thus propagated exponentially in the estimated starting concentrations as well as 'fold-difference' results. Because of the unknown origin and kinetics of the baseline fluorescence, the fluorescence values monitored in the initial cycles of the PCR reaction cannot be used to estimate a useful baseline value. An algorithm that estimates the baseline by reconstructing the log-linear phase downward from the early plateau phase of the PCR reaction was developed and shown to lead to very reproducible PCR efficiency values. PCR efficiency values were determined per sample by fitting a regression line to a subset of data points in the log-linear phase. The variability, as well as the bias, in qPCR results was significantly reduced when the mean of these PCR efficiencies per amplicon was used in the calculation of an estimate of the starting concentration per sample.

Regulation of membrane trafficking and organ separation by the NEVERSHED ARF-GAP protein.

Cell separation, or abscission, is a highly specialized process in plants that facilitates remodeling of their architecture and reproductive success. Because few genes are known to be essential for organ abscission, we conducted a screen for mutations that alter floral organ shedding in Arabidopsis. Nine recessive mutations that block shedding were found to disrupt the function of an ADP-ribosylation factor-GTPase-activating protein (ARF-GAP) we have named NEVERSHED (NEV). As predicted by its homology to the yeast Age2 ARF-GAP and transcriptional profile, NEV influences other aspects of plant development, including fruit growth. Co-localization experiments carried out with NEV-specific antiserum and a set of plant endomembrane markers revealed that NEV localizes to the trans-Golgi network and endosomes in Arabidopsis root epidermal cells. Interestingly, transmission electron micrographs of abscission zone regions from wild-type and nev flowers reveal defects in the structure of the Golgi apparatus and extensive accumulation of vesicles adjacent to the cell walls. Our results suggest that NEV ARF-GAP activity at the trans-Golgi network and distinct endosomal compartments is required for the proper trafficking of cargo molecules required for cell separation.

The kidney during hibernation and arousal from hibernation. A natural model of organ preservation during cold ischaemia and reperfusion.

BACKGROUND: During hibernation the kidney is in a hypothermic condition where renal blood flow is minimal and urine production is much reduced. Periodical arousal from hibernation is associated with kidney reperfusion at increasing body temperature, and restored urine production rate. METHODS: To assess the degree of structural preservation during such extreme conditions, the kidney cortex was investigated by means of electron microscopy in the dormouse Muscardinus avellanarius during winter hibernation, arousal from hibernation and the summer active period. RESULTS: Results show that the fine structure of the kidney cortex is well preserved during hibernation. In the renal corpuscle, a sign of slight lesion was the focal presence of oedematous endothelial cells and/or podocytes. Proximal convoluted tubule cells showed fully preserved ultrastructure and polarity, and hypertrophic apical endocytic apparatus. Structural changes were associated with increased plasma electrolytes, creatinine and urea nitrogen, and proteinuria. During the process of arousal the fine structure of the kidney cortex was also well maintained. CONCLUSION: These results demonstrate that dormice are able to fully preserve kidney cortex structure under extreme conditions resembling e.g. severe ischaemia or hypothermic organ storage for transplantation, and reperfusion. Elucidation of the mechanisms involved in such a natural model of organ preservation could be relevant to human medicine.

Militarism and Melodrama: The Cultural Work of Combat Death

This essay examines the role of melodrama in the American war film, focusing on three post-WWII examples. The main argument centers on the natural alliance between melodrama and militarism based on a shared intolerance for the notion of death as meaningless and in vain. Both melodrama and military ideology employ elaborate rhetorical and narrative strategies to enfold deaths into larger systems of meaning, such as the nation, or in more personal terms, as a rite of passage. One of the most common narrative devices present in the military melodrama is the death that converts survivors to the values of the virtuous victim. The essay examines the shared conventions and different strategies of the following three films: Sands of Iwo Jima (1949), Platoon (1986), and Top Gun (1986).

Effects of motive-oriented therapeutic relationship in early-phase treatment of borderline personality disorder: a pilot study of a randomized trial.

Motive-oriented therapeutic relationship (MOTR, also called complementary therapeutic relationship) was postulated to be a particularly helpful therapeutic ingredient in the early-phase treatment of patients with personality disorders, in particular borderline personality disorder (BPD). The present pilot study of randomized controlled trial using an add-on design aims to investigate the effects of MOTR in early-phase treatment (up to session 10), with BPD patients on therapeutic alliance, session impact, and outcome. In total, N = 25 patients participated in the study. BPD patients were randomly allocated to a manual-based investigation process in 10 sessions or to the same investigation process infused with MOTR. Adherence ratings were performed and yielded satisfactory results. The results suggested a specific effectiveness of MOTR on the interpersonal problem area, on the quality of the therapeutic alliance and the quality of the therapeutic relationship, as rated by the patient. These results may have important clinical implications for the early-phase treatment of patients presenting with BPD.

Coping specificities in bipolar affective disorder: relations with symptoms and therapeutic alliance

Ways to enhance research into coping have been suggested by Lazarus (2000). The issues of adaptiveness and conceptual structure of coping (Cramer, 1998; Skinner et al., 2003) are particularly relevant; thus, this study addresses them in a clinical research setting. A total of 30 inpatients presenting with Bipolar Affective Disorder (BD) have been interviewed twice, as well as the participants of a matched control group (N = 30). Self-report (CISS) and observerrater methods (CAP) of coping have been applied: low correlations were found between the instruments. Coping specificities in BD have been identified: opposition and support-seeking are most frequently practiced by BD patients, in comparison with controls. No significant link has been found between coping processes, symptom level and the therapeutic alliance. This study lends support for a quantitative definition of coping adaptiveness which is discussed, along with clinical implications on psychological treatments of BD (German J Psychiatry 2009; 12: 19-27).

Tibial component positioning in total knee arthroplasty: bone coverage and extensor apparatus alignment.

Correct positioning of the tibial component in total knee arthroplasty (TKA) must take into account both an optimal bone coverage (defined by a maximal cortical bearing with posteromedial and anterolateral support) and satisfactory patellofemoral tracking. Consequently, a compromise position must be found by the surgeon during the operation to simultaneously meet these two requirements. Moreover, tibial tray positioning depends upon the tibial torsion, which has been shown to act mainly in the proximal quarter of the tibia. Therefore, the correct application of the tibial tray is also theoretically related to the level of bone resection. In this study, we first quantified the torsional profile given by an optimal bone coverage for a symmetrical tibial tray design and for an asymmetrical one. Then, for the two types of tibial trays, we measured the angle difference between optimal bone coverage and an alignment on the middle of the tibial tubercule. Results showed that the values of the torsional profile given by the symmetrical tray were more scattered than those from the asymmetrical one. However, determination of the mean differential angle between the position providing optimal bone coverage and the one providing the best patellofemoral tracking indicated that the symmetrical prosthetic tray offered the best compromise between these two requirements. Although the tibiofemoral joint is known to be asymmetric in both shape and dimension, the asymmetrical tray chosen in this study was found to fulfill this compromise with more difficulty.