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.

Mortality from cardiovascular and cerebrovascular diseases in Europe and other areas of the world: an update.

OBJECTIVE: To update trends in mortality from coronary heart diseases (CHD) and cerebrovascular diseases (CVD) over the period 1981-2004 in Europe, the USA, Latin America, Japan and other selected areas of the world. METHODS: Age-standardized mortality rates were derived from the World Health Organization database. Joinpoint analysis was used to identify significant changes in trends. RESULTS: In the European Union (27 countries), CHD mortality in men declined from 139/100,000 in 1985-1989 to 93/100,000 in 2000-2004 (-33%). In women, the fall was from 61/100,000 to 44/100,000 (-27%). In this area, a decline by over 30% was also registered in CVD mortality for both sexes. In the Russian Federation and other countries of the former Soviet Union, CHD rates in 2000-2004 were exceedingly high, around 380/100,000 men and 170/100,000 women in Russia, 430 for men and 240 for women in Ukraine, 420 and 200 in Belarus. For CVD, a similar situation was registered, with mortality rates of 226/100,000 for men and 159/100,000 for women in 2004 in the Russian Federation, and more than 24% increase since the late 1980s for men and 15% for women. CHD and CVD mortality continued to decline in most Latin American countries, Australia and other areas considered, including Asia (even if with marked differences). CONCLUSION: Although mortality from CHD and CVD continues to decline in several areas of the world including most countries of Europe and of the America providing data and Australia, unfavourable trends were still observed in the Russian Federation and other countries of the former Soviet Union, whose recent rates remain exceedingly high.

Skeletal Muscle Mitochondrial and Lipid Droplet Volume Density: Validity of Electron Microscopy Point-counting Measurements

Mitochondrial (M) and lipid droplet (L) volume density (vd) are often used in exercise research. Vd is the volume of muscle occupied by M and L. The means of calculating these percents are accomplished by applying a grid to a 2D image taken with transmission electron microscopy; however, it is not known which grid best predicts these values. PURPOSE: To determine the grid with the least variability of Mvd and Lvd in human skeletal muscle. METHODS: Muscle biopsies were taken from vastus lateralis of 10 healthy adults, trained (N=6) and untrained (N=4). Samples of 5-10mg were fixed in 2.5% glutaraldehyde and embedded in EPON. Longitudinal sections of 60 nm were cut and 20 images were taken at random at 33,000x magnification. Vd was calculated as the number of times M or L touched two intersecting grid lines (called a point) divided by the total number of points using 3 different sizes of grids with squares of 1000x1000nm sides (corresponding to 1µm2), 500x500nm (0.25µm2) and 250x250nm (0.0625µm2). Statistics included coefficient of variation (CV), 1 way-BS ANOVA and spearman correlations. RESULTS: Mean age was 67 ± 4 yo, mean VO2peak 2.29 ± 0.70 L/min and mean BMI 25.1 ± 3.7 kg/m2. Mean Mvd was 6.39% ± 0.71 for the 1000nm squares, 6.01% ± 0.70 for the 500nm and 6.37% ± 0.80 for the 250nm. Lvd was 1.28% ± 0.03 for the 1000nm, 1.41% ± 0.02 for the 500nm and 1.38% ± 0.02 for the 250nm. The mean CV of the three grids was 6.65% ±1.15 for Mvd with no significant differences between grids (P>0.05). Mean CV for Lvd was 13.83% ± 3.51, with a significant difference between the 1000nm squares and the two other grids (P<0.05). The 500nm squares grid showed the least variability between subjects. Mvd showed a positive correlation with VO2peak (r = 0.89, p < 0.05) but not with weight, height, or age. No correlations were found with Lvd. CONCLUSION: Different size grids have different variability in assessing skeletal muscle Mvd and Lvd. The grid size of 500x500nm (240 points) was more reliable than 1000x1000nm (56 points). 250x250nm (1023 points) did not show better reliability compared with the 500x500nm, but was more time consuming. Thus, choosing a grid with square size of 500x500nm seems the best option. This is particularly relevant as most grids used in the literature are either 100 points or 400 points without clear information on their square size.

Antidoping programme and biological monitoring before and during the 2014 FIFA World Cup Brazil.

BACKGROUND: The FIFA has implemented an important antidoping programme for the 2014 FIFA World Cup. AIM: To perform the analyses before and during the World Cup with biological monitoring of blood and urine samples. METHODS: All qualified players from the 32 teams participating in the World Cup were tested out-of-competition. During the World Cup, 2-8 players per match were tested. Over 1000 samples were collected in total and analysed in the WADA accredited Laboratory of Lausanne. RESULTS: The quality of the analyses was at the required level as described in the WADA technical documents. The urinary steroid profiles of the players were stable and consistent with previously published papers on football players. During the competition, amphetamine was detected in a sample collected on a player who had a therapeutic use exemption for attention deficit hyperactivity disorder. The blood passport data showed no significant difference in haemoglobin values between out-of-competition and postmatch samples. CONCLUSIONS: Logistical issues linked to biological samples collection, and the overseas shipment during the World Cup did not impair the quality of the analyses, especially when used as the biological passport of football players.

Biogeographic origin and radiation of the Old World crocidurine shrews (Mammalia: Soricidae) inferred from mitochondrial and nuclear genes.

The crocidurine shrews include the most speciose genus of mammals, Crocidura. The origin and evolution of their radiation is, however, poorly understood because of very scant fossil records and a rather conservative external morphology between species. Here, we use an alignment of 3560 base pairs of mitochondrial and nuclear DNA to generate a phylogenetic hypothesis for the evolution of Old World shrews of the subfamily Crocidurinae. These molecular data confirm the monophyly of the speciose African and Eurasian Crocidura, which also includes the fossorial, monotypic genus Diplomesodon. The phylogenetic reconstructions give further credit to a paraphyletic position of Suncus shrews, which are placed into at least two independent clades (one in Africa and sister to Sylvisorex and one in Eurasia), at the base of the Crocidura radiation. Therefore, we recommend restricting the genus Suncus to the Palaearctic and Oriental taxa, and to consider all the African Suncus as Sylvisorex. Using molecular dating and biogeographic reconstruction analyses, we suggest a Palaearctic-Oriental origin for Crocidura dating back to the Upper Miocene (6.8 million years ago) and several subsequent colonisations of the Afrotropical region by independent lineages of Crocidura.

Public particiation and the legitimacy of intergovernmental decision-making : a focus on the World Trade Organization

The legitimacy of the WTO's decision-making process has always been questioned, and many have advocated public participation mechanisms as a remedy. The present study considers the limits and potential of these mechanisms by advancing a conceptual framework, which distinguishes the four 'implementation parameters' of public participation: the goal, the object, the modalities, and the actors. It addresses the issue of legitimacy by considering to what extent, and by virtue of which legal developments, one can see implementing the democratic principle as a goal for public participation in the context of the WTO. By analyzing the institutional structure of the WTO and its different types of decisions, it then outlines how this goal should influence the object and modalities of public participation, which decision-making procedures should be opened to public participation, and how the mechanisms should be implemented in practice. Finally, it suggests speciflrc amendments to existing WTO affangements on public participation

Religion is good, belief is better: religion, religiosity, and substance use among young swiss men.

We examined the influence of religious denomination (RD) and religiosity/spirituality on licit and illicit substance use beyond the potential impact of parental variables. Data from a representative sample of Swiss men (n = 5,387) approximately 20 years old were collected between August 2010 and November 2011. We asked single item questions about RD and religious self-description (RSD) (including aspects of spirituality). Alcohol use, smoking, and illicit drug use was measured as outcome variables. Logistic regressions (adjusting for parenting and socioeconomic background) revealed that religiosity/spirituality was inversely associated with substance use and that it was more strongly associated than denomination. RD, particularly having no denomination, was independently associated with the use of most substances. The study's limitations, and the implications for future work are noted.