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.

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.