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.

Importance of sequences adjacent to the terminal tripeptide in the import of a peroxisomal Candida tropicalis protein in plant peroxisomes.

The peroxisome targeting signal (PTS) required for import of the rat acyl-CoA oxidase (AOX; EC 1.3.3.6) and the Candida tropicalis multifunctional protein (MFP) in plant peroxisomes was assessed in transgenic Arabidopsis thaliana (L.) Heynh. The native rat AOX accumulated in peroxisomes in A. thaliana cotyledons and targeting was dependent on the presence of the C-terminal tripeptide S-K-L. In contrast, the native C. tropicalis MFP, containing the consensus PTS sequence A-K-I was not targeted to plant peroxisomes. Modification of the carboxy terminus to the S-K-L tripeptide also failed to deliver the MFP to peroxisomes while addition of the last 34 amino acids of the Brassica napus isocitrate lyase, containing the terminal tripeptide S-R-M, enabled import of the fusion protein into peroxisomes. These results underline the influence of the amino acids adjacent to the terminal tripeptide of the C. tropicalis MFP on peroxisomal targeting, even in the context of a protein having a consensus PTS sequence S-K-L.

Periodic Sequences of Arbitrage: A Tale of Four Currencies

This paper investigates arbitrage chains involving four currencies and four foreign exchange trader-arbitrageurs. In contrast with the three-currency case, we fi nd that arbitrage operations when four currencies are present may appear periodic in nature, and not involve smooth convergence to a \balanced" ensemble of exchange rates in which the law of one price holds. The goal of this article is to understand some interesting features of sequences of arbitrage operations, features which might well be relevant in other contexts in finance and economics.

Strong exceptional sequences of vector bundles on certain Fano varieties

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

A public key encryption based on third order linear sequences

Based on third order linear sequences, an improvement version of the Diffie-Hellman distribution key scheme and the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Deletion, insertion and translocation of DNA sequences contribute to chromosome size polimorphism in Plasmodium berghei

Extensive chromosome size polymorphism in Plasmodium berghei in vivo mitotic multiplication. Size differences between homologous chromosomes mainly involve rearrangements in the subtelomeric regions while internal chromosomal regions are more conserved. Size differences are almost exclusively due to differences in the copy number of a 2.3 kb subtelomeric repeat unit. Not only deletion of 2.3 kb repeats occurs, but addition of new copies of this repeat sometimes results in the formation of enlarged chromosomes. Even chromosomes which originally lack 2.3 kb repeats, can acquire these during mitotic multiplication. In one karyotype mutant, 2.3 kb repeats were inserted within one of the original telomeres of chromosome 4, creating an internal stretch oftelomeric repeats. Chromosome translocation can contribute to chromosome size polymorphism as well We found a karyotype mutant in which chromosome 7 with a size of about 1.4 Mb is translocated to chromosome 13/14 with a size of about 3 Mb, resulting in a rearranged chromosome, which was shown to contain a junction between internal DNA sequences of chromosome 13/14 and subtelomeric 2.3 kb repeats of chromosome 7. In this mutant a new chromosome of 1.4 Mb is present which consists of part of chromosome 13/14.

Identification of schistosome-infected snails by detecting schistosomal antigens and DNA sequences

Cercarial shedding tests do not provide species identification of the shistosomes concerned and cannot detect prepatent schistosomal infections. We have demonstrated that both immunodetection by ELISA of schistosomal antigens in snail hemophlymph, and dot hybridization of snail extracts by DNA probe representing highly repeated sequences, proved suitable for detecting infected snails during prepatnecy as well as patency. A group-specific monoclonal antibody was found to be suitable for detecting Schistosoma mansoni infection in Biomphalaria sp., but not for positive identification of S. haematobium in Blulinus sp. Comparative evaluation of the diagnostic qualities, and technical aspects and cost of these tests, point to the superiority of the immunodetection approach for large scale detection of snails prepatently infected with S. mansoni. This approach is potentially useful for providing extended information on schistosome-snail epidemiology that may facilitate rapid evaluation of the danger of post-control reinfection, and help make decisions on the time and place of supplementary control measures. In this context the potential usefulness of the immunodetection or DNA probing approach for facilitating catalytic model representation of schistosome-snail epidemiology warrants further evaluation. Specific identification of S. haematobium in Bulinus by either of these approaches may be possible depending on the development of suitable antibodies or DNA probes.

CD8+ T-cell response to NY-ESO-1: relative antigenicity and in vitro immunogenicity of natural and analogue sequences.

We have shown previously that HLA-A*0201 melanoma patients can frequently develop a CTL response to the cancer testis antigen NY-ESO-1. In the present study, we have analyzed in detail the relative antigenicity and in vitro immunogenicity of natural and modified NY-ESO-1 peptide sequences. The results of this analysis revealed that, although suboptimal for binding to the HLA-A*0201 molecule, peptide NY-ESO-1 157-165 is, among natural sequences, very efficiently recognized by specific CTL clones derived from three melanoma patients. In contrast, peptides NY-ESO-1 157-167 and NY-ESO-1 155-163, which bind very strongly to HLA-A*0201, are recognized less efficiently. In agreement with previous data, substitution of peptide NY-ESO-1 157-165 COOH-terminal C with various other amino acids resulted in a significantly increased binding to HLA-A*0201 molecules as well as in an increased CTL recognition, although variable at the clonal level. Among natural peptides, NY-ESO-1 157-165 and NY-ESO-1 157-167 exhibited good in vitro immunogenicity, whereas peptide NY-ESO-1 155-163 was poorly immunogenic. The fine specificity of interaction between peptide NY-ESO-1 C165A, HLA-A*0201, and T-cell receptor was analyzed at the molecular level using a series of variant peptides containing single alanine substitutions. The findings reported here have significant implications for the formulation of NY-ESO-1-based vaccines as well as for the monitoring of either natural or vaccine-induced NY-ESO-1-specific CTL responses in cancer patients.

N-terminal amino acid sequences of the major outer membrane proteins from a Neisseria meningitidis group B strain isolated in Brazil

The four dominant outer membrane proteins (46, 38, 33 and 28 kDa) were detected by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) in a semi-purified preparation of vesicle membranes of a Neisseria meningitidis (N44/89, B:4:P1.15:P5.5,7) strain isolated in Brazil. The N-terminal amino acid sequence for the 46 kDa and 28 kDa proteins matched that reported by others for class 1 and 5 proteins respectively, whereas the sequence (25 amino acids) for the 38 kDa (class 3) protein was similar to class 1 meningococcal proteins. The sequence for the 33 kDa (class 4) was unique and not homologous to any known protein.

Les TIC a l'ensenyament de la modelització matemàtica en Ciències Econòmiques i en Ciències Experimentals

Aquest projecte proposa materials didàctics per a un nou plantejament de les assignatures de Matemàtiques dels primers cursos de Ciències Empresarials i d'Enginyeria Tècnica, més acord amb el procés de convergència europea, basat en la realització de projectes que anomenem “Tallers de Modelització Matemàtica” (TMM) en els quals: (1) Els alumnes parteixen de situacions i problemes reals per als quals han de construir per sí mateixos els models matemàtics més adients i, a partir de la manipulació adequada d’aquests models, poden obtenir la informació necessària per donar-los resposta. (2) El treball de construcció, experimentació i avaluació dels models es realitza amb el suport de la calculadora simbòlica Wiris i del full de càlcul Excel com a instruments “normalitzats” del treball matemàtic d’estudiants i professors. (3) S’adapten els programes de les assignatures de matemàtiques de primer curs per tal de poder-les associar a un petit nombre de Tallers que parteixen de situacions adaptades a cada titulació. L’assignatura de Matemàtiques per a les Ciències Empresarials s’articula entorn de dos tallers independents: “Matrius de transició” pel que fa a l’àlgebra lineal i “Previsió de vendes” per a la modelització funcional en una variable. L’assignatura de Matemàtiques per a l’Enginyeria s’articula entorn d’un únic taller, “Models de poblacions”, que abasta la majoria de continguts del curs: successions i models funcionals en una variable, àlgebra lineal i equacions diferencials. Un conjunt d’exercicis interactius basats en la calculadora simbòlica WIRIS (Wiris-player) serveix de suport per al treball tècnic imprescindible per al desenvolupament de les dues assignatures. L’experimentació d’aquests tallers durant 2 cursos consecutius (2006/07 i 2007/08) en dues universitats catalanes (URL i UAB) ha posat en evidència tant els innegables avantatges del nou dispositiu docent per a l’aprenentatge dels estudiants, així com les restriccions institucionals que actualment dificulten la seva gestió i difusió.

trEST, trGEN and Hits: access to databases of predicted protein sequences.

High throughput genome (HTG) and expressed sequence tag (EST) sequences are currently the most abundant nucleotide sequence classes in the public database. The large volume, high degree of fragmentation and lack of gene structure annotations prevent efficient and effective searches of HTG and EST data for protein sequence homologies by standard search methods. Here, we briefly describe three newly developed resources that should make discovery of interesting genes in these sequence classes easier in the future, especially to biologists not having access to a powerful local bioinformatics environment. trEST and trGEN are regularly regenerated databases of hypothetical protein sequences predicted from EST and HTG sequences, respectively. Hits is a web-based data retrieval and analysis system providing access to precomputed matches between protein sequences (including sequences from trEST and trGEN) and patterns and profiles from Prosite and Pfam. The three resources can be accessed via the Hits home page (http://hits. isb-sib.ch).

Ribonucleotide reductase genes of Bacillus prophages: a refuge to introns and intein coding sequences.

The ribonucleotide reductase gene tandem bnrdE/bnrdF in SPbeta-related prophages of different Bacillus spp. isolates presents different configurations of intervening sequences, comprising one to three of six non-homologous splicing elements. Insertion sites of group I introns and intein DNA are clustered in three relatively short segments encoding functionally important domains of the ribonucleotide reductase. Comparison of the bnrdE homologs reveals mutual exclusion of a group I intron and an intein coding sequence flanking the codon that specifies a conserved cysteine. In vivo splicing was demonstrated for all introns. However, for two of them a part of the mRNA precursor molecules remains unspliced. Intergenic bnrdE-bnrdF regions are unexpectedly long, comprising between 238 and 541 nt. The longest encodes a putative polypeptide related to HNH homing endonucleases.

Development and testing of novel chloroplast microsatellite markers for Lolium perenne and other grasses (Poaceae) from de novo sequencing and in silico sequences

Twelve primers to amplify microsatellite markers from the chloroplast genome of Lolium perenne were designed and optimized using de novo sequencing and in silico sequences. With one exception, each locus was polymorphic with a range from two to nine alleles in L. perenne. The newly developed primer pairs cross-amplified in different species of Lolium and in 50 other grass species representing nine grass subfamilies.

Identification of Transcribed Sequences (ESTs) in the Trypanosoma cruzi Genome Project

Random single pass sequencing of cDNA fragments, also known as generation of Expressed Sequence Tags (ESTs), has been highly successful in the study of the gene content of higher organisms, and forms an integral part of most genome projects, with the objective to identify new genes and targets for disease control and prevention and to generate mapping probes. In the Trypanosoma cruzi genome project, EST sequencing has also been a starting point, and here we report data on the first 797 sequences obtained, partly from a CL Brener epimastigote non-normalized library, partly on a normalized library. Only around 30% of the sequences obtained showed similarity with Genbank and dbEST databases, half of which with sequences already reported for T. cruzi.