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.

Clinical and genetic investigation of a large Tunisian family with complete achromatopsia: identification of a new nonsense mutation in GNAT2 gene.

Complete achromatopsia is a rare autosomal recessive disease associated with CNGA3, CNGB3, GNAT2 and PDE6C mutations. This retinal disorder is characterized by complete loss of color discrimination due to the absence or alteration of the cones function. The purpose of the present study was the clinical and the genetic characterization of achromatopsia in a large consanguineous Tunisian family. Ophthalmic evaluation included a full clinical examination, color vision testing and electroretinography. Linkage analysis using microsatellite markers flanking CNGA3, CNGB3, GNAT2 and PDE6C genes was performed. Mutations were screened by direct sequencing. A total of 12 individuals were diagnosed with congenital complete achromatopsia. They are members of six nuclear consanguineous families belonging to the same large consanguineous family. Linkage analysis revealed linkage to GNAT2. Mutational screening of GNAT2 revealed three intronic variations c.119-69G>C, c.161+66A>T and c.875-31G>C that co-segregated with a novel mutation p.R313X. An identical GNAT2 haplotype segregating with this mutation was identified, indicating a founder mutation. All patients were homozygous for the p.R313X mutation. This is the first report of the clinical and genetic investigation of complete achromatopsia in North Africa and the largest family with recessive achromatopsia involving GNAT2; thus, providing a unique opportunity for genotype-phenotype correlation for this extremely rare condition.

Prise en charge des troubles oculomoteurs après effraction iatrogène de l'orbite au cours d'interventions sinusiennes endoscopiques [Management of motility disorders secondary to iatrogenic orbital fracture during endoscopic sinus surgery.]

PURPOSE: Orbital wall fracture may occur during endoscopic sinus surgery, resulting in oculomotor disorders. We report the management of four cases presenting with this surgical complication. METHODS: A non-comparative observational retrospective study was carried out on four patients presenting with diplopia after endoscopic ethmoidal sinus surgery. All patients underwent full ophthalmologic and orthoptic examination as well as orbital imaging. RESULTS: All four patients presented with diplopia secondary to a medial rectus lesion confirmed by orbital imaging. A large horizontal deviation as well as limitation of adduction was present in all cases. Surgical management consisted of conventional recession-resection procedures in three cases and muscle transposition in one patient. A useful field of binocular single vision was restored in two of the four patients. CONCLUSION: Orbital injury may occur during endoscopic sinus surgery and cause diplopia, usually secondary to medial rectus involvement due to the proximity of this muscle to the lamina papyracea of the ethmoid bone. Surgical management is based on orbital imaging, duration of the lesion, evaluation of anterior segment vasculature, results of forced duction testing and intraoperative findings. In most cases, treatment is aimed at the symptoms rather than the cause, and the functional prognosis remains guarded.

Shifts in species richness, herbivore specialization, and plant resistance along elevation gradients.

Environmental gradients have been postulated to generate patterns of diversity and diet specialization, in which more stable environments, such as tropical regions, should promote higher diversity and specialization. Using field sampling and phylogenetic analyses of butterfly fauna over an entire alpine region, we show that butterfly specialization (measured as the mean phylogenetic distance between utilized host plants) decreases at higher elevations, alongside a decreasing gradient of plant diversity. Consistent with current hypotheses on the relationship between biodiversity and the strength of species interactions, we experimentally show that a higher level of generalization at high elevations is associated with lower levels of plant resistance: across 16 pairs of plant species, low-elevation plants were more resistant vis-à-vis their congeneric alpine relatives. Thus, the links between diversity, herbivore diet specialization, and plant resistance along an elevation gradient suggest a causal relationship analogous to that hypothesized along latitudinal gradients.

Fractional hepatic de novo lipogenesis in healthy subjects during near-continuous oral nutrition and bed rest: a comparison with published data in artificially fed, critically ill patients.

BACKGROUND AND AIMS: In critically ill patients, fractional hepatic de novo lipogenesis increases in proportion to carbohydrate administration during isoenergetic nutrition. In this study, we sought to determine whether this increase may be the consequence of continuous enteral nutrition and bed rest. We, therefore, measured fractional hepatic de novo lipogenesis in a group of 12 healthy subjects during near-continuous oral feeding (hourly isoenergetic meals with a liquid formula containing 55% carbohydrate). In eight subjects, near-continuous enteral nutrition and bed rest were applied over a 10 h period. In the other four subjects, it was extended to 34 h. Fractional hepatic de novo lipogenesis was measured by infusing(13) C-labeled acetate and monitoring VLDL-(13)C palmitate enrichment with mass isotopomer distribution analysis. Fractional hepatic de novo lipogenesis was 3.2% (range 1.5-7.5%) in the eight subjects after 10 h of near continuous nutrition and 1.6% (range 1.3-2.0%) in the four subjects after 34 h of near-continuous nutrition and bed rest. This indicates that continuous nutrition and physical inactivity do not increase hepatic de novo lipogenesis. Fractional hepatic de novo lipogenesis previously reported in critically ill patients under similar nutritional conditions (9.3%) (range 5.3-15.8%) was markedly higher than in healthy subjects (P<0.001). These data from healthy subjects indicate that fractional hepatic de novo lipogenesis is increased in critically ill patients.

Eosinophilic esophagitis: Updated consensus recommendations for children and adults.

Eosinophilic esophagitis (EoE) is a clinicopathologic condition of increasing recognition and prevalence. In 2007, a consensus recommendation provided clinical and histopathologic guidance for the diagnosis and treatment of EoE; however, only a minority of physicians use the 2007 guidelines, which require fulfillment of both histologic and clinical features. Since 2007, the number of EoE publications has doubled, providing new disease insight. Accordingly, a panel of 33 physicians with expertise in pediatric and adult allergy/immunology, gastroenterology, and pathology conducted a systematic review of the EoE literature (since September 2006) using electronic databases. Based on the literature review and expertise of the panel, information and recommendations were provided in each of the following areas of EoE: diagnostics, genetics, allergy testing, therapeutics, and disease complications. Because accumulating animal and human data have provided evidence that EoE appears to be an antigen-driven immunologic process that involves multiple pathogenic pathways, a new conceptual definition is proposed highlighting that EoE represents a chronic, immune/antigen-mediated disease characterized clinically by symptoms related to esophageal dysfunction and histologically by eosinophil-predominant inflammation. The diagnostic guidelines continue to define EoE as an isolated chronic disorder of the esophagus diagnosed by the need of both clinical and pathologic features. Patients commonly have high rates of concurrent allergic diatheses, especially food sensitization, compared with the general population. Proved therapeutic options include chronic dietary elimination, topical corticosteroids, and esophageal dilation. Important additions since 2007 include genetic underpinnings that implicate EoE susceptibility caused by polymorphisms in the thymic stromal lymphopoietin protein gene and the description of a new potential disease phenotype, proton pump inhibitor-responsive esophageal eosinophila. Further advances and controversies regarding diagnostic methods, surrogate disease markers, allergy testing, and treatment approaches are discussed.

MMP-9 as predictive factor for response and progression free survival in breast cancer patients treated with bevacizumab and pegylated liposomal doxorubicin. A multicenter, single-arm phase II trial (SAKK24/06). On behalf of the Swiss Group for Clinical Cancer Research (SAKK).

The benefit of bevacizumab (Bv) has been shown in different tumors including colorectal cancer, renal cancer, pulmonary non-small cell cancer and also breast cancer. However to date, there is no established test evaluating the angiogenic status of a patient and monitoring the effects of anti-angiogenic treatments. Tumor angiogenesis is the result of a balance between multiple pro- and anti¬angiogenic molecules. There is very little published clinical data exploring the impact of the anti-angiogenic therapy on the different angiogenesis-related molecules and the potential role of these molecules as prognostic or predictive factors.

Effects of flecainide on exercise-induced ventricular arrhythmias and recurrences in genotype-negative patients with catecholaminergic polymorphic ventricular tachycardia.

BACKGROUND: Conventional therapy with beta-blockers is incompletely effective in preventing arrhythmic events in patients with catecholaminergic polymorphic ventricular tachycardia (CPVT). We have previously discovered that flecainide in addition to conventional drug therapy prevents ventricular arrhythmias in patients with genotype-positive CPVT. OBJECTIVE: To study the efficacy of flecainide in patients with genotype-negative CPVT. METHODS: We studied the efficacy of flecainide for reducing ventricular arrhythmias during exercise testing and preventing arrhythmia events during long-term follow-up. RESULTS: Twelve patients with genotype-negative CPVT were treated with flecainide. Conventional therapy failed to control ventricular arrhythmias in all patients. Flecainide was initiated because of significant ventricular arrhythmias (n = 8), syncope (n = 3), or cardiac arrest (n = 1). At the baseline exercise test before flecainide, 6 patients had ventricular tachycardia and 5 patients had bigeminal or frequent ventricular premature beats. Flecainide reduced ventricular arrhythmias at the exercise test in 8 patients compared to conventional therapy, similar to that in patients with genotype-positive CPVT in our previous report. Notably, flecainide completely prevented ventricular arrhythmias in 7 patients. Flecainide was continued in all patients except for one who had ventricular tachycardia at the exercise test on flecainide. During a follow-up of 48±94 months, arrhythmia events (sudden cardiac death and aborted cardiac arrest) associated with noncompliance occurred in 2 patients. Flecainide was not discontinued owing to side effects in any of the patients. CONCLUSIONS: Flecainide was effective in patients with genotype-negative CPVT, suggesting that spontaneous Ca(2+) release from ryanodine channels plays a role in arrhythmia susceptibility, similar to that in patients with genotype-positive CPVT.

Late Cretaceous and Paleogene Radiolaria from the Nicoya Peninsula, Costa Rica: a tectonostratigraphic application

Detailed field mapping and paleontological dating in the central and southeastern Nicoya Peninsula has revealed Late Cretaceous and Paleogene radiolarian-bearing siliceous mudstones. These rocks belong to two terranes (Matambfi and Manzanillo) that are partially contemporaneous with the Nicoya Complex, but are genetically different. While the Nicoya Complex is formed exclusively by intraplate igneous rocks with associated radiolarites, the studied sections include variable amounts of are-derived volcanic and terrigenous materials. These fore-arc terranes include mafic to intermediate volcaniclastics and associated pelagic and hemipelagic rocks rich in biogenic silica. Radiolarian preservation in these sediments is often enhanced by the presence of silica-saturated volcanic tuffs and debris. Seven out of 29 samples from different outcrops yielded relatively well-preserved radiolarian faunas. In total, 60 species belonging to 34 genera were present in these faunas, ranging in age from middle Turonian-Santonian to late Thanetian-Ypresian.

Improved blood pressure control by monitoring compliance with antihypertensive therapy.

Compliance with antihypertensive therapy was monitored for three months using an electronic medication dispenser in 35 patients remaining hypertensive despite the once-daily administration of a blood pressure lowering drug (either as monotherapy or as fixed-dose combination therapy). During the monitoring of compliance, the treatment was unchanged but blood pressure decreased significantly (p < 0.001) from 167.9/100.4 +/- 16.3/7.2 mmHg (mean +/- SD) to 152.5/90.9 +/- 20.9/11.5 mmHg. The percentage of days with one opening per day was 80.8 +/- 20.5. Thus, discussing with the patient about compliance with the prescribed drug regimen and monitoring compliance for a few months allows better control of blood pressure. This most likely reflects increased compliance with antihypertensive drug therapy.

Detection of EPO doping and blood doping: the haematological module of the Athlete Biological Passport.

The increase of the body's capacity to transport oxygen is a prime target for doping athletes in all endurance sports. For this pupose, blood transfusions or erythropoiesis stimulating agents (ESA), such as erythropoietin, NESP, and CERA are used. As direct detection of such manipulations is difficult, biomarkers that are connected to the haematopoietic system (haemoglobin concentration, reticulocytes) are monitored over time (Athlete Biological Passport (ABP)) and analyzed using mathematical models to identify patterns suspicious of doping. With this information, athletes can either be sanctioned directly based on their profile or targeted with conventional doping tests. Key issues for the appropriate use of the ABP are correct targeting and use of all available information (e.g. whereabouts, cross sectional population data) in a forensic manner. Future developments of the passport include the correction of all concentration-based variables for shifts in plasma volume, which might considerably increase sensitivity. New passport markers from the genomic, proteomic, and metabolomic level might add further information, but need to be validated before integration into the passport procedure. A first assessment of blood data of federations that have implemented the passport show encouraging signs of a decreased blood-doping prevalence in their athletes, which adds scientific credibility to this innovative concept in the fight against ESA- and blood doping. Copyright © 2012 John Wiley & Sons, Ltd.

Hypertonie oculaire dans l'orbitopathie dysthyroidienne: considerations physiopathologiques, diagnostiques et therapeutiques. A propos de trois cas significatifs. [Intraocular high pressure in thyroid-associated orbitopathy: physiopathological mechanisms, diagnosis, and management. Three case reports]

PURPOSE: To determine the mechanisms and treatment of ocular hypertension in patients with thyroid-associated orbitopathy and to differenciate it from glaucomatous damage. DESIGN: Three case reports. METHODS: Retrospective review of clinical findings, course, and treatment of the three patients. RESULTS: Elevated intraocular pressure in thyroid-associated orbitopathy observed in the three cases may involve different physiopathological abnormalities such as disturbances of venous circulation, compression by infiltrative muscles, and long corticosteroid use. In the first two cases, defects demonstrated in the perimetry are in consistent with glaucomatous damage. In the third case, visual field abnormalities may be compatible with a glaucomatous disease, but all defects resolved after therapy. Treatement was of the greatest difficulty for the three cases, associating antiglaucomatous medication, steroids, orbital radiotherapy, orbital decompression and extraocular muscle surgery. Intraocular pressure was controlled in all cases. CONCLUSIONS: Elevated intraocular pressure in thyroid-associated orbitopathy is distinguished from glaucomatous disease by its physiopathological mechanisms, clinical course, visual field defects, and treatment. The management of this hypertension is closely related to the treatment of dysthyroid orbitopathy.

Establishment of HEV RNA reverse transcriptase PCR assays for the diagnosis of acute and chronic hepatitis E

Background and aim: H epatitis E v irus (HEV) infection has emerged as a c ause o f travel-related a nd autochthonous a cute hepatitis as well as chronic hepatitis in immunosuppressed patients. While t ravel-related cases a re c aused primarily b y infections w ith HEV of g enotype 1 ( HEV-1), autochthonous c ases a nd chronic cases a re d ue t o genotype 3 (HEV-3), which is s hared between humans and diverse animal species. The aim of this study was to establish HEV RNA detection assays f or q uantitative v iral load testing and genotyping. Methods: V iral RNA was p urified from plasma or s erum a nd converted to cDNA prior to (1) multiplex real-time PCR for HEV RNA quantification and (2) multiplex PCR coupled to DNA sequencing for HEV genotype determination. Real-time PCR was d esigned to match a ll known HEV genotypes available i n Genbank while PCR was designed using conserved primers flanking a variable region of the HEV RNA. Results: In a validation panel, the newly developed assays allowed for the reliable detection and genotyping of HEV-1 or HEV-3. Cases of t ravel-related and a utochthonous a cute h epatitis E a s well a s chronic hepatitis E i n immunosuppressed patients have b een identified using t hese a ssays a nd will be p resented in detail. Anti- HEV antibodies were n egative i n three well-characterized patients with chronic hepatitis E after organ transplantation. Conclusions: We developed and validated a quantitative HEV RNA detection assay that c an now be o ffered on a r outine basis (www.chuv.ch/imul/imu-collaborations-viral_hepatitis). Genotyping can also be offered on selected cases. HEV RNA detection is key in diagnosing chronic hepatitis E i n immunosuppressed patients with unexplained transaminase elevations, as serology can be negative in these patients.

Coronary MR angiography: comparison of quantitative and qualitative data from four techniques.

OBJECTIVE: The optimal coronary MR angiography sequence has yet to be determined. We sought to quantitatively and qualitatively compare four coronary MR angiography sequences. SUBJECTS AND METHODS. Free-breathing coronary MR angiography was performed in 12 patients using four imaging sequences (turbo field-echo, fast spin-echo, balanced fast field-echo, and spiral turbo field-echo). Quantitative comparisons, including signal-to-noise ratio, contrast-to-noise ratio, vessel diameter, and vessel sharpness, were performed using a semiautomated analysis tool. Accuracy for detection of hemodynamically significant disease (> 50%) was assessed in comparison with radiographic coronary angiography. RESULTS: Signal-to-noise and contrast-to-noise ratios were markedly increased using the spiral (25.7 +/- 5.7 and 15.2 +/- 3.9) and balanced fast field-echo (23.5 +/- 11.7 and 14.4 +/- 8.1) sequences compared with the turbo field-echo (12.5 +/- 2.7 and 8.3 +/- 2.6) sequence (p < 0.05). Vessel diameter was smaller with the spiral sequence (2.6 +/- 0.5 mm) than with the other techniques (turbo field-echo, 3.0 +/- 0.5 mm, p = 0.6; balanced fast field-echo, 3.1 +/- 0.5 mm, p < 0.01; fast spin-echo, 3.1 +/- 0.5 mm, p < 0.01). Vessel sharpness was highest with the balanced fast field-echo sequence (61.6% +/- 8.5% compared with turbo field-echo, 44.0% +/- 6.6%; spiral, 44.7% +/- 6.5%; fast spin-echo, 18.4% +/- 6.7%; p < 0.001). The overall accuracies of the sequences were similar (range, 74% for turbo field-echo, 79% for spiral). Scanning time for the fast spin-echo sequences was longest (10.5 +/- 0.6 min), and for the spiral acquisitions was shortest (5.2 +/- 0.3 min). CONCLUSION: Advantages in signal-to-noise and contrast-to-noise ratios, vessel sharpness, and the qualitative results appear to favor spiral and balanced fast field-echo coronary MR angiography sequences, although subjective accuracy for the detection of coronary artery disease was similar to that of other sequences.

Advantages of digital holographic microscopy for real-time full field absolute phase imaging

Different interferometric techniques were developed last decade to obtain full field, quantitative, and absolute phase imaging, such as phase-shifting, Fourier phase microscopy, Hilbert phase microscopy or digital holographic microscopy (DHM). Although, these techniques are very similar, DHM combines several advantages. In contrast, to phase shifting, DHM is indeed capable of single-shot hologram recording allowing a real-time absolute phase imaging. On the other hand, unlike to Fourier phase or Hilbert phase microscopy, DHM does not require to record in focus images of the specimen on the digital detector (CCD or CMOS camera), because a numerical focalization adjustment can be performed by a numerical wavefront propagation. Consequently, the depth of view of high NA microscope objectives is numerically extended. For example, two different biological cells, floating at different depths in a liquid, can be focalized numerically from the same digital hologram. Moreover, the numerical propagation associated to digital optics and automatic fitting procedures, permits vibrations insensitive full- field phase imaging and the complete compensation for a priori any image distortion or/and phase aberrations introduced for example by imperfections of holders or perfusion chamber. Examples of real-time full-field phase images of biological cells have been demonstrated. ©2008 COPYRIGHT SPIE