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.

The generic Hanna Neumann conjecture and post correspondence problem

"Vegeu el resum a l'inici del document del fitxer adjunt."

Serum Leptin Concentration, Body Mass Index and Incident Heart Failure: The Health, Aging, and Body Composition Study

Background: Leptin is produced primarily by adipocytes. Although originally associated with the central regulation of satiety and energy metabolism, increasing evidence indicates that leptin may be an important factor for congestive heart faire (CHF). In the study, we aimed to test the hypothesis that leptin may influence CHF pathophysiology via a pathway of increasing body mass index (BMI). Methods: We studied 2,389 elderly participants aged 70 and older (M; 1161, F: 1228) without CHF and with serum leptin measures at the Health Aging, and Body Composition study. We analyzed the association between serum leptin level and risk of incident CHF using Cox hazard proportional regression models. Elevated leptin level was defined as more than the highest quartile (Q4) of leptin distribution in the total sample for each gender. Adjusted-covariates included demographic, behavior, lipid and inflammation variables (partially-adjusted models), and further included BMI (fully-adjusted models). Results: In a mean 9-year follow-up, 316 participants (13.2%) developed CHF. The partially-adjusted models indicated that men and women with elevated serum leptin levels (>=9.89 ng/ml in men and >=25 ng/ml in women) had significantly higher risks of developing CHF than those with leptin level of less than Q4. The adjusted hazard ratios (95%CI) for incident CHF was 1.49 (1.04 -2.13) in men and 1.71 (1.12 -2.58) in women. However, these associations became non-significant after adjustment for including BMI for each gender. The fully-adjusted hazard ratios (95%CI) were 1.43 (0.94 -2.18) in men and 1.24 (0.77-1.99) in women. Conclusion: Subjects with elevated leptin levels have a higher risk of CHF. The study supports the hypothesis that the influence of leptin level on risk of CHF may be through a pathway related to increasing BMI.

Rapid high-performance liquid chromatographic determination with fluorescence detection of furosemide in human body fluids and its confirmation by gas chromatography-mass spectrometry.

Furosemide (FD: Lasix) is a loop diuretic which strongly increases both urine flow and electrolyte urinary excretion. Healthy volunteers were administered 40 mg orally (dissolved in water) and concentrations of FD were determined in serum and urine for up to 6 h for eight subjects, who absorbed water at a rate of 400 ml/h. Quantification was performed by HPLC with fluorescence detection (excitation at 233 nm, emission at 389 nm) with a limit of detection of 5 ng/ml for a 300-microliters sample. The elution of FD was completed within 4 min using a gradient of acetonitrile concentration rising from 30 to 50% in 0.08 M phosphoric acid. The delay to the peak serum concentration ranged from 60 to 120 min. FD was still easily measurable in the sera from all subjects 6 h after administration. In urine, the excretion rates reached their maximum between 1 and 3 h. The total amount of FD excreted in the urine averaged 11.2 mg (range 7.6-14.0 mg), with a mean urine volume of 3024 ml (range 2620-3596 ml). Moreover, the urine density was lower than 1.010 (recommended as an upper limit in doping analysis to screen diuretics) only for 2 h. An additional volunteer was administered 40 mg of FD and his urine was collected over a longer period. FD was still detectable 48 h after intake. Gas chromatography-mass spectrometry with different types of ionization was used to confirm the occurrence of FD after permethylation of the extract. Negative-ion chemical ionization, with ammonia as reactant gas, was found to be the most sensitive method of detection.

Effect of carbohydrate overfeeding on whole body macronutrient metabolism and expression of lipogenic enzymes in adipose tissue of lean and overweight humans

OBJECTIVE: Lipids stored in adipose tissue can originate from dietary lipids or from de novo lipogenesis (DNL) from carbohydrates. Whether DNL is abnormal in adipose tissue of overweight individuals remains unknown. The present study was undertaken to assess the effect of carbohydrate overfeeding on glucose-induced whole body DNL and adipose tissue lipogenic gene expression in lean and overweight humans. DESIGN: Prospective, cross-over study. SUBJECTS AND METHODS: A total of 11 lean (five male, six female, mean BMI 21.0+/-0.5 kg/m(2)) and eight overweight (four males, four females, mean BMI 30.1+/-0.6 kg/m(2)) volunteers were studied on two occasions. On one occasion, they received an isoenergetic diet containing 50% carbohydrate for 4 days prior to testing; on the other, they received a hyperenergetic diet (175% energy requirements) containing 71% carbohydrates. After each period of 4 days of controlled diet, they were studied over 6 h after having received 3.25 g glucose/kg fat free mass. Whole body glucose oxidation and net DNL were monitored by means of indirect calorimetry. An adipose tissue biopsy was obtained at the end of this 6-h period and the levels of SREBP-1c, acetyl CoA carboxylase, and fatty acid synthase mRNA were measured by real-time PCR. RESULTS: After isocaloric feeding, whole body net DNL amounted to 35+/-9 mg/kg fat free mass/5 h in lean subjects and to 49+/-3 mg/kg fat free mass/5 h in overweight subjects over the 5 h following glucose ingestion. These figures increased (P<0.001) to 156+/-21 mg/kg fat free mass/5 h in lean and 64+/-11 mg/kg fat free mass/5 h (P<0.05 vs lean) in overweight subjects after carbohydrate overfeeding. Whole body DNL after overfeeding was lower (P<0.001) and glycogen synthesis was higher (P<0.001) in overweight than in normal subjects. Adipose tissue SREBP-1c mRNA increased by 25% in overweight and by 43% in lean subjects (P<0.05) after carbohydrate overfeeding, whereas fatty acid synthase mRNA increased by 66 and 84% (P<0.05). CONCLUSION: Whole body net DNL is not increased during carbohydrate overfeeding in overweight individuals. Stimulation of adipose lipogenic enzymes is also not higher in overweight subjects. Carbohydrate overfeeding does not stimulate whole body net DNL nor expression of lipogenic enzymes in adipose tissue to a larger extent in overweight than lean subjects.

Body mass index, cigarette smoking, and alcohol consumption and cancers of the oral cavity, pharynx, and larynx: modeling odds ratios in pooled case-control data.

Odds ratios for head and neck cancer increase with greater cigarette and alcohol use and lower body mass index (BMI; weight (kg)/height(2) (m(2))). Using data from the International Head and Neck Cancer Epidemiology Consortium, the authors conducted a formal analysis of BMI as a modifier of smoking- and alcohol-related effects. Analysis of never and current smokers included 6,333 cases, while analysis of never drinkers and consumers of < or =10 drinks/day included 8,452 cases. There were 8,000 or more controls, depending on the analysis. Odds ratios for all sites increased with lower BMI, greater smoking, and greater drinking. In polytomous regression, odds ratios for BMI (P = 0.65), smoking (P = 0.52), and drinking (P = 0.73) were homogeneous for oral cavity and pharyngeal cancers. Odds ratios for BMI and drinking were greater for oral cavity/pharyngeal cancer (P < 0.01), while smoking odds ratios were greater for laryngeal cancer (P < 0.01). Lower BMI enhanced smoking- and drinking-related odds ratios for oral cavity/pharyngeal cancer (P < 0.01), while BMI did not modify smoking and drinking odds ratios for laryngeal cancer. The increased odds ratios for all sites with low BMI may suggest related carcinogenic mechanisms; however, BMI modification of smoking and drinking odds ratios for cancer of the oral cavity/pharynx but not larynx cancer suggests additional factors specific to oral cavity/pharynx cancer.

ADOS: an educational primary prevention programme for preventing excess body weight in adolescents.

OBJECTIVE: The prevalence of adolescent obesity has increased considerably over the past decade in Switzerland and has become a serious public health problem in Europe. Prevention of obesity using various comprehensive programmes appears to be very promising, although we must admit that several interventions had generally disappointing results compared with the objectives and target initially fixed. Holistic programmes including nutritional education combined with promotion of physical activity and behaviour modification constitute the key factors in the prevention of childhood and adolescent obesity. The purpose of this programme was to incorporate nutrition/physical education as well as psychological aspects in selected secondary schools (9th grade, 14-17 years). METHODS: The educational strategy was based on the development of a series of 13 practical workshops covering wide areas such as physical inactivity, body composition, sugar, energy density, invisible lipids, how to read food labels, is meal duration important? Do you eat with pleasure or not? Do you eat because you are hungry? Emotional eating. For teachers continuing education, a basic highly illustrated guide was developed as a companion booklet to the workshops. These materials were first validated by biology, physical education, dietician and psychologist teachers as well as school medical officers. RESULTS: Teachers considered the practical educational materials innovative and useful, motivational and easy to understand. Up to now (early 2008), the programme has been implemented in 50 classes or more from schools originating from three areas in the French part of Switzerland. Based on the 1-week pedometer value assessed before and after the 1 school-year programme, an initial evaluation indicated that overall physical placidity was significantly decreased as evidenced by a significant rise in the number of steps per day. CONCLUSION: Future evaluation will provide more information on the effectiveness of the ADOS programme.

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.

Sparse regularization for fiber ODF reconstruction: from the suboptimality of ℓ2 and ℓ1 priors to ℓ0.

Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a large variety of methods have been recently proposed to shorten the acquisition times. Among them, spherical deconvolution approaches have gained a lot of interest for their ability to reliably recover the intra-voxel fiber configuration with a relatively small number of data samples. To overcome the intrinsic instabilities of deconvolution, these methods use regularization schemes generally based on the assumption that the fiber orientation distribution (FOD) to be recovered in each voxel is sparse. The well known Constrained Spherical Deconvolution (CSD) approach resorts to Tikhonov regularization, based on an ℓ(2)-norm prior, which promotes a weak version of sparsity. Also, in the last few years compressed sensing has been advocated to further accelerate the acquisitions and ℓ(1)-norm minimization is generally employed as a means to promote sparsity in the recovered FODs. In this paper, we provide evidence that the use of an ℓ(1)-norm prior to regularize this class of problems is somewhat inconsistent with the fact that the fiber compartments all sum up to unity. To overcome this ℓ(1) inconsistency while simultaneously exploiting sparsity more optimally than through an ℓ(2) prior, we reformulate the reconstruction problem as a constrained formulation between a data term and a sparsity prior consisting in an explicit bound on the ℓ(0)norm of the FOD, i.e. on the number of fibers. The method has been tested both on synthetic and real data. Experimental results show that the proposed ℓ(0) formulation significantly reduces modeling errors compared to the state-of-the-art ℓ(2) and ℓ(1) regularization approaches.

The anabolic androgenic steroid fluoxymesterone inhibits 11β-hydroxysteroid dehydrogenase 2-dependent glucocorticoid inactivation.

Anabolic androgenic steroids (AAS) are testosterone derivatives used either clinically, in elite sports, or for body shaping with the goal to increase muscle size and strength. Clinically developed compounds and nonclinically tested designer steroids often marketed as food supplements are widely used. Despite the considerable evidence for various adverse effects of AAS use, the underlying molecular mechanisms are insufficiently understood. Here, we investigated whether some AAS, as a result of a lack of target selectivity, might inhibit 11β-hydroxysteroid dehydrogenase 2 (11β-HSD2)-dependent inactivation of glucocorticoids. Using recombinant human 11β-HSD2, we observed inhibitory effects for several AAS. Whereas oxymetholone, oxymesterone, danazol, and testosterone showed medium inhibitory potential, fluoxymesterone was a potent inhibitor of human 11β-HSD2 (half-maximal inhibitory concentration [IC(50)] of 60-100nM in cell lysates; IC(50) of 160nM in intact SW-620, and 530nM in MCF-7 cells). Measurements with rat kidney microsomes and lysates of cells expressing recombinant mouse 11β-HSD2 revealed much weaker inhibition by the AAS tested, indicating that the adverse effects of AAS-dependent 11β-HSD2 inhibition cannot be investigated in rats and mice. Furthermore, we provide evidence that fluoxymesterone is metabolized to 11-oxofluoxymesterone by human 11β-HSD2. Structural modeling revealed similar binding modes for fluoxymesterone and cortisol, supporting a competitive mode of inhibition of 11β-HSD2-dependent cortisol oxidation by this AAS. No direct modulation of mineralocorticoid receptor (MR) function was observed. Thus, 11β-HSD2 inhibition by fluoxymesterone may cause cortisol-induced MR activation, thereby leading to electrolyte disturbances and contributing to the development of hypertension and cardiovascular disease.

Symmetry for a Dirichlet-Neumann problem arising in water waves

"Vegeu el resum a l'inici del document del fitxer adjunt."

Introduced freshwater blenny influences the diet and body condition of the invasive dice snake in Lake Geneva

Non-indigenous species can have strong impacts on biodiversity by affecting trophic relationships in their new environments. The piscivorous dice snake (Natrix tessellata) has been introduced to Geneva Lake, western Switzerland, where the endangered viperine snake (Natrix maura) is native. Local, dramatic declines in the viperine snake population might be associated with the appearance of the dice snake through dietary overlap between these 2 species, which mainly feed on bullhead (Cottus gobio). In response to this decline, a control program for dice snake was implemented in 2007 to reduce numbers of this introduced snake. In 2010, a new species of fish, the freshwater blenny (Salaria fluviatilis), which shares the same habitat as the bullhead, was introduced into Lake Geneva and has since reached high densities. We determined the impact of freshwater blenny on diet composition and body condition of dice snakes. In addition, we tested for effects of the control program on the body condition of dice snakes and viperine snakes. We collected 294 dice snakes between 2007 and 2013. Based on morphology and a genetic marker (cytochrome b gene), we determined the ®sh species contained in these snakes' stomachs. We found a drastic switch in dice snake diet following the arrival of freshwater blenny, as consumption of bullhead declined by 68% and was replaced by the blenny. In addition, the body condition of dice snakes increased significantly after the arrival of freshwater blenny. The body condition of both snake species was positively correlated with the number of dice snakes removed from the study area. This finding has important implications concerning the conservation of the endangered viperine snake, and suggests that the control program of dice snakes should be continued.

Validity of impedance-based equations for the prediction of total body water as measured by deuterium dilution in African women.

BACKGROUND: Little information is available on the validity of simple and indirect body-composition methods in non-Western populations. Equations for predicting body composition are population-specific, and body composition differs between blacks and whites. OBJECTIVE: We tested the hypothesis that the validity of equations for predicting total body water (TBW) from bioelectrical impedance analysis measurements is likely to depend on the racial background of the group from which the equations were derived. DESIGN: The hypothesis was tested by comparing, in 36 African women, TBW values measured by deuterium dilution with those predicted by 23 equations developed in white, African American, or African subjects. These cross-validations in our African sample were also compared, whenever possible, with results from other studies in black subjects. RESULTS: Errors in predicting TBW showed acceptable values (1.3-1.9 kg) in all cases, whereas a large range of bias (0.2-6.1 kg) was observed independently of the ethnic origin of the sample from which the equations were derived. Three equations (2 from whites and 1 from blacks) showed nonsignificant bias and could be used in Africans. In all other cases, we observed either an overestimation or underestimation of TBW with variable bias values, regardless of racial background, yielding no clear trend for validity as a function of ethnic origin. CONCLUSIONS: The findings of this cross-validation study emphasize the need for further fundamental research to explore the causes of the poor validity of TBW prediction equations across populations rather than the need to develop new prediction equations for use in Africa.

Is the coiled body involved in nucleolar functions?

Coiled bodies (CBs) are structural constituents observed in nuclei of most eukaryotic cells. They usually occur in the nucleoplasm as well as in contact with the nucleolar surface. In this work we studied the hepatocyte nuclei of hibernating dormice in order to investigate possible modifications of CBs along the seasonal cycle. CBs were abundant during hibernation and rapidly disappeared upon arousal from hibernation. Moreover, CBs were frequently found to be integrated into the nucleolar body. Immunocytochemical analyses showed that CBs contain nucleoplasmic as well as nucleolar RNA-processing factors, suggesting an "ambiguous" role for this organelle in the nuclear functions.

Maximal Physiological Parameters during Partial Body-Weight Support Treadmill Testing.

PURPOSE: This study investigated maximal cardiometabolic response while running in a lower body positive pressure treadmill (antigravity treadmill (AG)), which reduces body weight (BW) and impact. The AG is used in rehabilitation of injuries but could have potential for high-speed running, if workload is maximally elevated. METHODS: Fourteen trained (nine male) runners (age 27 ± 5 yr; 10-km personal best, 38.1 ± 1.1 min) completed a treadmill incremental test (CON) to measure aerobic capacity and heart rate (V˙O2max and HRmax). They completed four identical tests (48 h apart, randomized order) on the AG at BW of 100%, 95%, 90%, and 85% (AG100 to AG85). Stride length and rate were measured at peak velocities (Vpeak). RESULTS: V˙O2max (mL·kg·min) was similar across all conditions (men: CON = 66.6 (3.0), AG100 = 65.6 (3.8), AG95 = 65.0 (5.4), AG90 = 65.6 (4.5), and AG85 = 65.0 (4.8); women: CON = 63.0 (4.6), AG100 = 61.4 (4.3), AG95 = 60.7 (4.8), AG90 = 61.4 (3.3), and AG85 = 62.8 (3.9)). Similar results were found for HRmax, except for AG85 in men and AG100 and AG90 in women, which were lower than CON. Vpeak (km·h) in men was 19.7 (0.9) in CON, which was lower than every other condition: AG100 = 21.0 (1.9) (P < 0.05), AG95 = 21.4 (1.8) (P < 0.01), AG90 = 22.3 (2.1) (P < 0.01), and AG85 = 22.6 (1.6) (P < 0.001). In women, Vpeak (km·h) was similar between CON (17.8 (1.1) ) and AG100 (19.3 (1.0)) but higher at AG95 = 19.5 (0.4) (P < 0.05), AG90 = 19.5 (0.8) (P < 0.05), and AG85 = 21.2 (0.9) (P < 0.01). CONCLUSIONS: The AG can be used at maximal exercise intensities at BW of 85% to 95%, reaching faster running speeds than normally feasible. The AG could be used for overspeed running programs at the highest metabolic response levels.