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.

Comparing Multilevel Clustering Methods on Weighted Graphs : The Case of Worldwide Air Passenger Traffic 2000-2004

Specific properties emerge from the structure of large networks, such as that of worldwide air traffic, including a highly hierarchical node structure and multi-level small world sub-groups that strongly influence future dynamics. We have developed clustering methods to understand the form of these structures, to identify structural properties, and to evaluate the effects of these properties. Graph clustering methods are often constructed from different components: a metric, a clustering index, and a modularity measure to assess the quality of a clustering method. To understand the impact of each of these components on the clustering method, we explore and compare different combinations. These different combinations are used to compare multilevel clustering methods to delineate the effects of geographical distance, hubs, network densities, and bridges on worldwide air passenger traffic. The ultimate goal of this methodological research is to demonstrate evidence of combined effects in the development of an air traffic network. In fact, the network can be divided into different levels of âeurooecohesionâeuro, which can be qualified and measured by comparative studies (Newman, 2002; Guimera et al., 2005; Sales-Pardo et al., 2007).

Sawhorse-type diruthenium tetracarbonyl complexes containing porphyrin-derived ligands as highly selective photosensitizers for female reproductive cancer cells.

Diruthenium tetracarbonyl complexes of the type [Ru2(CO)4(l2-g2-O2CR)2L2] containing a Ru-Ru backbone with four equatorial carbonyl ligands, two carboxylato bridges, and two axial two-electron ligands in a sawhorse-like geometry have been synthesized with porphyrin-derived substituents in the axial ligands [1: R is CH3, L is 5-(4-pyridyl)-10,15,20-triphenyl-21,23H-porphyrin], in the bridging carboxylato ligands [2: RCO2H is 5-(4-carboxyphenyl)-10,15,20-triphenyl-21,23H-porphyrin, L is PPh3; 3: RCO2H is 5-(4-carboxyphenyl)-10,15,20-triphenyl-21,23H-porphyrin, L is 1,3,5-triaza-7-phosphatricyclo [3.3.1.1]decane], or in both positions [4: RCO2H is 5-(4-carboxyphenyl)-10,15,20-triphenyl-21,23H-porphyrin, L is 5-(4-pyridyl)-10,15,20-triphenyl-21,23H-porphyrin]. Compounds 1-3 were assessed on different types of human cancer cells and normal cells. Their uptake by cells was quantified by fluorescence and checked by fluorescence microscopy. These compounds were taken up by human HeLa cervix and A2780 and Ovcar ovarian carcinoma cells but not by normal cells and other cancer cell lines (A549 pulmonary, Me300 melanoma, PC3 and LnCap prostate, KB head and neck, MDAMB231 and MCF7 breast, or HT29 colon cancer cells). The compounds demonstrated no cytotoxicity in the absence of laser irradiation but exhibited good phototoxicities in HeLa and A2780 cells when exposed to laser light at 652 nm, displaying an LD50 between 1.5 and 6.5 J/cm2 in these two cell lines and more than 15 J/cm2 for the others. Thus, these types of porphyric compound present specificity for cancer cell lines of the female reproductive system and not for normal cells; thus being promising new organometallic photosensitizers.

Nosology and classification of genetic skeletal disorders: 2010 revision.

Genetic disorders involving the skeletal system arise through disturbances in the complex processes of skeletal development, growth and homeostasis and remain a diagnostic challenge because of their variety. The Nosology and Classification of Genetic Skeletal Disorders provides an overview of recognized diagnostic entities and groups them by clinical and radiographic features and molecular pathogenesis. The aim is to provide the Genetics, Pediatrics and Radiology community with a list of recognized genetic skeletal disorders that can be of help in the diagnosis of individual cases, in the delineation of novel disorders, and in building bridges between clinicians and scientists interested in skeletal biology. In the 2010 revision, 456 conditions were included and placed in 40 groups defined by molecular, biochemical, and/or radiographic criteria. Of these conditions, 316 were associated with mutations in one or more of 226 different genes, ranging from common, recurrent mutations to "private" found in single families or individuals. Thus, the Nosology is a hybrid between a list of clinically defined disorders, waiting for molecular clarification, and an annotated database documenting the phenotypic spectrum produced by mutations in a given gene. The Nosology should be useful for the diagnosis of patients with genetic skeletal diseases, particularly in view of the information flood expected with the novel sequencing technologies; in the delineation of clinical entities and novel disorders, by providing an overview of established nosologic entities; and for scientists looking for the clinical correlates of genes, proteins and pathways involved in skeletal biology. © 2011 Wiley-Liss, Inc.

L'examen neuropsychologique en pratique quotidienne [Neuropsychological test in daily practice]

Neuropsychology is a scientific discipline, born in the XIX century, and bridges the fields of neurology and psychology. Neuropsychologists apply scientific knowledge about the relationship between brain function and mental performances. The major clinical role of a neuropsychological evaluation is to help to establish medical and functional diagnosis in patients (adults or infants) with different neurological pathologies such as stroke, traumatic brain injury, dementia, epilepsy.... Such analysis necessitates accurate observation of behaviour and administration of tests of mental abilities (e.g. language, memory...). Test results can also help to clarify the nature of cognitive difficulties and to support the formulation of plans for neuropsychological therapy and functional adjustment in every day life.

The combination of social and personal contexts affects dominance hierarchy development in shore crabs, Carcinus maenas

Many animals that live in groups maintain competitive relationships, yet avoid continual fighting, by forming dominance hierarchies. We compare predictions of stochastic, individual-based models with empirical experimental evidence using shore crabs to test competing hypotheses regarding hierarchy development. The models test (1) what information individuals use when deciding to fight or retreat, (2) how past experience affects current resource-holding potential, and (3) how individuals deal with changes to the social environment. First, we conclude that crabs assess only their own state and not their opponent's when deciding to fight or retreat. Second, willingness to enter, and performance in, aggressive contests are influenced by previous contest outcomes. Winning increases the likelihood of both fighting and winning future interactions, while losing has the opposite effect. Third, when groups with established dominance hierarchies dissolve and new groups form, individuals reassess their ranks, showing no memory of previous rank or group affiliation. With every change in group composition, individuals fight for their new ranks. This iterative process carries over as groups dissolve and form, which has important implications for the relationship between ability and hierarchy rank. We conclude that dominance hierarchies emerge through an interaction of individual and social factors, and discuss these findings in terms of an underlying mechanism. Overall, our results are consistent with crabs using a cumulative assessment strategy iterated across changes in group composition, in which aggression is constrained by an absolute threshold in energy spent and damage received while fighting.

Photoactive sawhorse-type diruthenium tetracarbonyl complexes

Sawhorse-type diruthenium tetracarbonyl complexes incorporating carboxyphenyl porphyrin bridges and pyridine axial ligands have been prepared, characterized and evaluated as potential photosensitizing and chemotherapeutic agents in several human cancer cells (A2780, A549, Me300, HeLa). The mono carboxyphenyl porphyrin derivatives, 5-(4-carboxyphenyl)-10,15,20-triphenyl-21,23H-porphyrin (HOOCR1-H2) and 5-(4-carboxyphenyl)-10,15,20-triphenylporphyrin-Zn (HOOCR1-Zn), after reaction with Ru-3(CO)(12) and pyridine, give the dinuclear complexes [Ru-2(CO)(4)(OOCR1-H2)(2)(NC5H5)(2)] (1) and [Ru-2(CO)(4)-(OOCR1-Zn)(2)(NC5H5)(2)] (2), respectively. Under the same reaction conditions, the di-carboxyphenyl porphyrin derivatives, 5,10-di(4-carboxyphenyl)-15,20-diphenyl-21,23H-porphyrin (HOOCR2-H2COOH) and 5,10-di(4-carboxyphenyl)-15,20-diphenylporphyrin-Zn (HOOCR2-ZnCOOH), give rise to the tetranuclear complexes, [{Ru-2(CO)(4)(NC5H5)(2)}(2)(OOCR2-H2COO)(2)] (3) and [{Ru-2(CO)(4)(NC5H5)(2! )}(2)(OOCR2-ZnCOO)(2)] (4), in which two sawhorse diruthenium tetracarbonyl units are linked by the di-carboxyphenyl porphyrin ligands. When tested in human cancer cell lines, both Zn(II) metallo-porphyrin derivatives 2 and 4 and the tetranuclear derivative 3 show some degree of cytotoxicity in the dark, but seem to present no phototoxicity upon irradiation at 652 nm. These results demonstrate the effect of the Zn(II) ion insertion into the porphyrin core, resulting in increased cytotoxicity and decreased phototoxicity. On the other hand, complex 1, the less cytotoxic derivative with IC50 > 170 mu M in HeLa cervix and A2780 ovarian cancer cell lines, shows an excellent phototoxicity toward these cancer cell lines with LD50 comprised between 4.5 and 7.5 J/cm(2) (irradiance 30 mW/cm(2)) at 5 mu M concentration (incubation time: 24 h). Overall, an excellent ratio between photo-and cytotoxicity has been found for the metal-free porphyrin derivative [Ru-2(CO)(4)(OOCR1-H2)(2)(! NC5H5)(2)] (1).

Guidelines for the use and interpretation of assays for monitoring autophagy.

In 2008 we published the first set of guidelines for standardizing research in autophagy. Since then, research on this topic has continued to accelerate, and many new scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Accordingly, it is important to update these guidelines for monitoring autophagy in different organisms. Various reviews have described the range of assays that have been used for this purpose. Nevertheless, there continues to be confusion regarding acceptable methods to measure autophagy, especially in multicellular eukaryotes. A key point that needs to be emphasized is that there is a difference between measurements that monitor the numbers or volume of autophagic elements (e.g., autophagosomes or autolysosomes) at any stage of the autophagic process vs. those that measure flux through the autophagy pathway (i.e., the complete process); thus, a block in macroautophagy that results in autophagosome accumulation needs to be differentiated from stimuli that result in increased autophagic activity, defined as increased autophagy induction coupled with increased delivery to, and degradation within, lysosomes (in most higher eukaryotes and some protists such as Dictyostelium) or the vacuole (in plants and fungi). In other words, it is especially important that investigators new to the field understand that the appearance of more autophagosomes does not necessarily equate with more autophagy. In fact, in many cases, autophagosomes accumulate because of a block in trafficking to lysosomes without a concomitant change in autophagosome biogenesis, whereas an increase in autolysosomes may reflect a reduction in degradative activity. Here, we present a set of guidelines for the selection and interpretation of methods for use by investigators who aim to examine macroautophagy and related processes, as well as for reviewers who need to provide realistic and reasonable critiques of papers that are focused on these processes. These guidelines are not meant to be a formulaic set of rules, because the appropriate assays depend in part on the question being asked and the system being used. In addition, we emphasize that no individual assay is guaranteed to be the most appropriate one in every situation, and we strongly recommend the use of multiple assays to monitor autophagy. In these guidelines, we consider these various methods of assessing autophagy and what information can, or cannot, be obtained from them. Finally, by discussing the merits and limits of particular autophagy assays, we hope to encourage technical innovation in the field.

Social rationality and scales of action: inter-ethnic relations in cockfighting and game-fishing, Raiatea, French Polynesia

This article challenges the notion of economic rationality as a criterion for explaining ethnic boundary maintenance. It offers an ethnographic analysis of inter-ethnic relations in the context of games (cockfights and game-fishing contests) in the island of Raiatea (French Polynesia). Although all players engage in the same basic gambling practices, money is differentially scaled and mobilized by the Tahitian and Chinese participants. Building on recent pragmatic approaches to rationality, it is shown that the players' rationalities differ not from the point of view of economic maximization, but only in so far as they participate in social relations at different scales.

Catalytic and anticancer activities of sawhorse-type diruthenium tetracarbonyl complexes derived from fluorinated fatty acids

The reaction of fluorinated fatty acids, perfluorobutyric acid (C3F7CO2H), and perfluorododecanoic acid (C11F23CO2H), with dodecacarbonyltriruthenium (Ru-3(CO)(12)) under reflux in tetrahydrofuran, followed by addition of two-electron donors (L) such as pyridine, 1,3,5-triaza-7-phosphatricyclo[3.3.1.1]decane, or triphenylphosphine, gives stable diruthenium complexes Ru-2(CO)(4)((2)-(2)-O2CC3F7)(2)(L)(2) (1a, L=C5H5N; 1b, L=PTA; 1c, L=PPh3) and Ru-2(CO)(4)((2)-(2)-O2CC11F23)(2)(L)(2) (2a, L=C5H5N; 2b, L=PTA; 2c, L=PPh3). The catalytic activity of the complexes for hydrogenation of styrene under supercritical carbon dioxide has been assessed and compared to the analogous triphenylphosphine complexes with non-fluorinated carboxylato groups Ru-2(CO)(4)((2)-(2)-O2CC3H7)(2)(PPh3)(2) (3) and Ru-2(CO)(4)((2)-(2)-O2CC11H23)(2)(PPh3)(2) (4). In addition, the cytotoxicities of the fluorinated complexes 1 were also evaluated on several human cancer cell lines (A2780, A549, Me300, HeLa). The complexes appear to be moderately cytotoxic, showing greater activity on the Me300 melanoma cells. Single-crystal X-ray structure analyses of 1a and 3 show the typical sawhorse-type arrangement of the diruthenium tetracarbonyl backbone with two bridging carboxylates and two terminal ligands occupying the axial positions.

Sibling rivalry and vocal negotiation in the barn owl Tyto alba

Chez les animaux, les jeunes dépendant des parents durant leur développement sont en compétition pour obtenir la nourriture, qu'ils quémandent par des cris et postures ostentatoires et se disputent physiquement. Les frères et soeurs n'ont pas la même compétitivité, en particulier s'ils diffèrent en âge, et leur niveau de faim fluctue dans le temps. Comme dans tout type de compétition, chacun doit ajuster son investissement aux rivaux, c'est à dire aux besoins et comportements de ses frères et soeurs. Dans le contexte de la famille, selon la théorie de sélection de parentèle, les jeunes bénéficient de leur survie mutuelle et donc de la propagation de la part de gènes qu'ils ont en commun. L'hypothèse de la « négociation frères-soeurs » prédit que, sous certaines conditions, les jeunes négocient entre eux la nourriture, ce qui réduit les coûts de compétition et permet de favoriser les frères et soeurs les plus affamés. La littérature actuelle se focalise sur les signaux de quémande entre enfants et parents et les interactions compétitives frères-soeurs sont étudiées principalement au sein de paires, alors que les nichées ou portées en comprennent souvent de nombreux. Cette thèse vise à mieux comprendre comment et jusqu'à quel point plusieurs jeunes ajustent mutuellement leurs signaux de besoin. C'est une question importante, étant donné que cela influence la répartition de nourriture entre eux, donc la résolution du conflit qui les oppose et à terme leur valeur évolutive. Le modèle d'étude est la chouette effraie (Tyto alba), chez laquelle jusqu'à neufs poussins émettent des milliers de cris chacun par nuit. Ils négocieraient entre eux la prochaine proie indivisible rapportée au nid avant que les parents ne reviennent : un poussin affamé crie plus qu'un autre moins affamé, ce qui dissuade ce dernier de crier en retour et par la suite de quémander la nourriture aux parents. L'investissement optimal correspondrait donc à écarter son frère en permanence vu que l'arrivée des parents est imprévisible, mais à moindre coût. Dans un premier axe, nous avons exploré au sein de dyades les mécanismes acoustiques permettant aux poussins de doser leur effort vocal durant les heures de compétition où ils sont laissés seuls au nid. Nous avons trouvé que les poussins évitent de crier simultanément, ce qui optimiserait la discrimination du nombre et de la durée de leurs cris, lesquels reflètent de façon honnête leur niveau de faim et donc leur motivation. L'alternance des cris paraît particulièrement adaptée au fait que les poussins se fient à des variations temporelles subtiles dans le rythme et la durée de leurs vocalisations pour prendre la parole. En particulier, allonger ses cris tout en criant moins dissuade efficacement le rival de répondre, ce qui permet de monopoliser la parole dans de longs « monologues ». Ces règles seraient universelles puisqu'elles ne dépendent pas de la séniorité, de la faim, ni de la parenté et les poussins répondent à un playback de façon similaire à un vrai frère. Tous ces résultats apportent la première preuve expérimentale que les juvéniles communiquent de façon honnête sur leurs besoins, ajustent activement le rythme de leurs cris et utilisent des composantes multiples de leurs vocalisations d'une façon qui réduit le coût de la compétition. De plus, il s'agit de la première démonstration que des règles de conversation régissent de longs échanges vocaux chez les animaux de façon comparable aux règles basiques observées chez l'Homme. Dans un second axe, nous avons exploré les stratégies comportementales que les poussins adoptent pour rivaliser avec plusieurs frères et soeurs, par le biais d'expériences de playback. Nous avons trouvé que les poussins mémorisent des asymétries de compétitivité entre deux individus qui dialoguent et répondent plus agressivement au moins compétitif une fois qu'ils sont confrontés à chacun isolément. Dans la même ligne, quand ils entendent un nombre variable d'individus criant à un taux variable, les poussins investissent le plus contre des rivaux moins nombreux et moins motivés. En accord avec les prédictions des modèles théoriques, les poussins de chouette effraie escaladent donc les conflits pour lesquels leur chance de gagner contrebalance le plus l'énergie dépensée. Nous révélons ainsi que 1) les jeunes frères et soeurs 'espionnent' les interactions de leurs rivaux pour évaluer leur compétitivité relative, ce qui est sans doute moins coûteux qu'une confrontation directe avec chacun, et 2) dosent leur investissement vocal en fonction du nombre de rivaux actuellement en compétition et de leur motivation de façon concomitante. Ces résultats montrent que les interactions entre frères et soeurs au nid reposent sur des mécanismes similaires à ceux observés, mais encore de façon anecdotique, chez les adultes non apparentés qui se disputent les territoires et partenaires sexuels. Cette thèse souligne donc combien il est crucial de considérer dorénavant la famille comme un réseau de communication à part entière pour mieux comprendre comment les jeunes résolvent les conflits autour du partage des ressources parentales. Plus généralement, elle révèle l'importance de la dynamique temporelle des vocalisations dans les conflits et la communication des animaux. A la lumière de nos résultats, la chouette effraie apparaît comme un modèle clé pour de futures recherches sur la résolution des conflits et la communication acoustique. - In species with parental care, offspring contest priority access to food by begging through conspicuous postures and vocalisations and by physically jockeying. Siblings differ in their competitiveness, especially in the case of age and size hierarchies, and their hunger level fluctuates in time. As in competition in general, each individual should adjust its investment to opponents that is to say to its siblings' needs and behaviours. In the particular context of family, according to kin selection theory, siblings derive extra fitness benefits from their mutual survival and hence the spreading of the genes they share. The "sibling negotiation" predicts that, under certain conditions, young would negotiate among them priority access to food, which reduces competition costs and enables promoting the most hungry siblings. To date, the literature focuses on signals of need between parents and offspring and competitive interactions (in particular among siblings) are mostly studied within pairwise interactions, yet they commonly involve more numerous rivals. This PhD aims at better understanding how and the extent to which several young siblings compete through signalling. This is important since this influences how food is allocated among them, thus the outcome of sibling rivalry and ultimately their fitness. I use the barn owl (Tyto alba) as a model, in which the one to nine nestlings emit a simple noisy call thousands of times per night. Thereby, they would negotiate among them priority access to the indivisible food next delivered prior to parents' feeding visits. A hungry nestling emits more calls than a less hungry sibling, which deters it to call in return and ultimately beg food at parents. The optimal investment thus corresponds to constantly deterring the rival to compete, given that parents' arrival is unpredictable, but at the lowest costs. In the first axis of my thesis, we explored within dyads the acoustic mechanisms by which owlets dose vocal effort when competing during the hours they are left alone. We found that owlets avoid overlapping each other's calls. This would enhance the discrimination of both call number and duration, which honestly reflect individuals' hunger level and hence motivation to compete. Such antiphony seems best adapted to the fact that siblings actually use subtle temporal variations in the rhythm and duration of their calls to take or give their turn. Owlets alternate monologs, in which lengthening calls efficiently deters the rival to respond while reducing call number. Such rules depend neither on seniority, hunger level nor kinship since nestlings responded similarly to a live sibling and an unrelated playback individual. Taken together, these findings provide the first experimental proof that dependent young honestly communicate about their need, actively adjust the timing of their calls and use multicomponent signals in a way that reduces vocal costs. Moreover, this is the first demonstration of conversational rules underlying animal long-lasting vocal exchanges comparable to the basic turn-taking signals observed in humans. In the second axis, we focused on the behavioural strategies owlets adopt to compete with more than one sibling, using playback experiments. We found that singleton bystanders memorised competitive asymmetries between two playback individuals dialoguing and responded more aggressively to the submissive one once they later faced each of both alone. Moreover, when hearing a varying number of nestlings calling at varying rates, owlets vocally invested the most towards fewer and less motivated rivals. In line with predictions from models on conflict settlement, barn owls thus escalate contests in which their chance of winning best counterbalances the energy spent. These results reveal that young socially eavesdrop on their siblings' interactions to assess their relative competitiveness at likely lower costs than direct confrontation, and dose vocal effort relative to both their number and motivation. This shows that young siblings' interactions imply mechanisms similar to those observed, yet still anecdotally, in unrelated adults that contest mates and territories. This PhD therefore highlights how crucial it is to further consider family as a communication network to better understand how siblings resolve conflicts over the share of parental resources. More generally, it provides important insights into the role of the temporal dynamics of signalling during animal contests and communication. In the light of our findings, the barn owl emerges as a key model for future research on conflict resolution and acoustic communication in animals.