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.

Characterization of a Trypanosoma cruzi genomic fragment complementary to several species-specific mRNAs but different from the spliced leader sequence

We have isolated a clone of Trypanosoma cruzi genimic DNA, lambda 3b2-5, which contains sequences that are reiterated in the genome. Northtern blot analysis showed that clone 3b2-5 hybridizes to 1,200-5,000 bases different mRNA species. The number of mRNAs species hybridized to clone 3b2-5 exceeds its coding capacity showing that this clone carries sequences that are common to several mRNAs species and conserved in the poly A(+) RNA. These sequences are not homologous to the T. cruzi spliced leader sequence, since clone 3b2-5 hybridize to a synthetic 20 nucleotice complementary to the spliced leader sequence. Clone 3b2-5 does not hybridize to DNA and RNA from several genera of Trypanosomatidae and other Trypanosoma species indicating that it carries T. cruzi species-specific sequences.

Revealed cardinal preference

I prove that as long as we allow the marginal utility for money (lambda) to vary between purchases (similarly to the budget) then the quasi-linear and the ordinal budget-constrained models rationalize the same data. However, we know that lambda is approximately constant. I provide a simple constructive proof for the necessary and sufficient condition for the constant lambda rationalization, which I argue should replace the Generalized Axiom of Revealed Preference in empirical studies of consumer behavior. 'Go Cardinals!' It is the minimal requirement of any scientifi c theory that it is consistent with the data it is trying to explain. In the case of (Hicksian) consumer theory it was revealed preference -introduced by Samuelson (1938,1948) - that provided an empirical test to satisfy this need. At that time most of economic reasoning was done in terms of a competitive general equilibrium, a concept abstract enough so that it can be built on the ordinal preferences over baskets of goods - even if the extremely specialized ones of Arrow and Debreu. However, starting in the sixties, economics has moved beyond the 'invisible hand' explanation of how -even competitive- markets operate. A seemingly unavoidable step of this 'revolution' was that ever since, most economic research has been carried out in a partial equilibrium context. Now, the partial equilibrium approach does not mean that the rest of the markets are ignored, rather that they are held constant. In other words, there is a special commodity -call it money - that reflects the trade-offs of moving purchasing power across markets. As a result, the basic building block of consumer behavior in partial equilibrium is no longer the consumer's preferences over goods, rather her valuation of them, in terms of money. This new paradigm necessitates a new theory of revealed preference.

The marginal utility of money: A modern Marshallian approach to consumer choice

We reformulate neoclassical consumer choice by focusing on lambda, the marginal utility of money. As the opportunity cost of current expenditure, lambda is approximated by the slope of the indirect utility function of the continuation. We argue that lambda can largely supplant the role of an arbitrary budget constraint in partial equilibrium analysis. The result is a better grounded, more flexible and more intuitive approach to consumer choice.

Tractable Consumer Choice

We derive a rational model of separable consumer choice which can also serve as a behavioral model. The central construct is [lambda] , the marginal utility of money, derived from the consumer's rest-of-life problem. We present a robust approximation of [lambda], and show how to incorporate liquidity constraints, indivisibilities and adaptation to a changing environment. We fi nd connections with numerous historical and recent constructs, both behavioral and neoclassical, and draw contrasts with standard partial equilibrium analysis. The result is a better grounded, more flexible and more intuitive description of consumer choice.

Consumer Behaviour in a Social Context: Implications for Environmental Policy

In this paper we summarise some of our recent work on consumer behaviour, drawing on recent developments in behavioural economics, in which consumers are embedded in a social context, so their behaviour is shaped by their interactions with other consumers. For the purpose of this paper we also allow consumption to cause environmental damage. Analysing the social context of consumption naturally lends itself to the use of game theoretic tools, and indicates that we seek to develop links between economics and sociology rather than economics and psychology, which has been the more predominant field for work in behavioural economics. We shall be concerned with three sets of issues: conspicuous consumption, consumption norms and altruistic behaviour. Our aim is to show that building links between sociological and economic approaches to the study of consumer behaviour can lead to significant and surprising implications for conventional economic policy prescriptions, especially with respect to environmental policy.

Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer.

Red blood cell (RBC) parameters such as morphology, volume, refractive index, and hemoglobin content are of great importance for diagnostic purposes. Existing approaches require complicated calibration procedures and robust cell perturbation. As a result, reference values for normal RBC differ depending on the method used. We present a way for measuring parameters of intact individual RBCs by using digital holographic microscopy (DHM), a new interferometric and label-free technique with nanometric axial sensitivity. The results are compared with values achieved by conventional techniques for RBC of the same donor and previously published figures. A DHM equipped with a laser diode (lambda = 663 nm) was used to record holograms in an off-axis geometry. Measurements of both RBC refractive indices and volumes were achieved via monitoring the quantitative phase map of RBC by means of a sequential perfusion of two isotonic solutions with different refractive indices obtained by the use of Nycodenz (decoupling procedure). Volume of RBCs labeled by membrane dye Dil was analyzed by confocal microscopy. The mean cell volume (MCV), red blood cell distribution width (RDW), and mean cell hemoglobin concentration (MCHC) were also measured with an impedance volume analyzer. DHM yielded RBC refractive index n = 1.418 +/- 0.012, volume 83 +/- 14 fl, MCH = 29.9 pg, and MCHC 362 +/- 40 g/l. Erythrocyte MCV, MCH, and MCHC achieved by an impedance volume analyzer were 82 fl, 28.6 pg, and 349 g/l, respectively. Confocal microscopy yielded 91 +/- 17 fl for RBC volume. In conclusion, DHM in combination with a decoupling procedure allows measuring noninvasively volume, refractive index, and hemoglobin content of single-living RBCs with a high accuracy.

The p53 gene expression and its developmental regulation in schistosomes

We have studied the gene expression, especially of the oncoproteins, and its regulation in schistosomes. Schistosomes have a complex life cycle with defined dimorphic lifestyle. The parasite are so far unique in biology in expressing oncogene products in their adult stage. In order to characterize the expression and developmental regulation, a lambda gt 11 cDNA library and lambda EMBL4 genomic DNA library of each growth stage of Schistosoma mansoni and S. japonicum was constructed, and was screened with various monoclonal antibodies against ongogene products. One positive plaque reacted to anti-p53 antibody (Ab-2, Oncogene Science, Inc.) was further analyzed. This fusion protein was about 120 KDa in molecular weights, and expressed as 1.4 Kb RNA in the adult stage. P53 gene is well-known as the negative regulator of the cell cicle, and the mutations in the gene are turning out to be the most common genetic alterations in human cancers. The comparison of the gene structure among species and stages were being conducted. Chromosome structures, C-band formation, and the results of in situ hybridization using the phage probe would be discussed.

Respuesta no lineal y criterios de diseño de puentes arco espaciales

El desarrollo más reciente de los puentes arco ha llevado a una nueva tipología: los “puentes arco espaciales”. Se entiende por puente arco espacial todo puente arco en el que, por su configuración geométrica y estructural, las cargas gravitatorias generan esfuerzos no contenidos en el plano del arco. Por un lado, aparecen para satisfacer las necesidades funcionales cuando estructuras en arco resultan las más adecuadas para sostener tableros curvos y evitar así apoyos intermedios. Desde un punto de vista estético, surgen como demanda de los nuevos puentes en entornos urbanos, buscando, no sólo una forma cuidada, sino persiguiendo convertirse en emblemas de la ciudad a partir de la originalidad y la innovación. Su proyecto y construcción es posible gracias a las grandes posibilidades que ofrecen los nuevos métodos de cálculo y dibujo por ordenador, en los que, a través del incremento de memoria y rapidez, cada vez se emplean programas más completos y nuevas modelizaciones, más cercanas a la realidad. No menos importante es el desarrollo de los medios auxiliares de construcción y de las herramientas de CAD/CAM, que convierte en construibles por control numérico formas de manufactura impensables. Ello trasciende en infinitas posibilidades de diseño y estructura. Sin embargo, el diseño y construcción de estas nuevas tipologías no ha estado acompañado por el avance en el estado del conocimiento fundamentado en la investigación, ya que se han desarrollado pocos estudios que explican parcialmente la respuesta estructural de estos puentes. Existe, por lo tanto, la necesidad de profundizar en el estado del conocimiento y clarificar su respuesta estructural, así como de plantear, finalmente, criterios de diseño que sirvan de apoyo en las fases de concepción y de proyecto a estas nuevas tipologías.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Cloning, Expression and Toxicity of a Mosquitocidal Toxin Gene of Bacillus thuringiensis subsp. medellin

Bacillus thuringiensis (Bt) subsp. medellin (Btmed) produces parasporal crystalline inclusions which are toxic to mosquito larvae. It has been shown that the inclusions of this bacterium contain mainly proteins of 94, 68 and 28-30 kDa. EcoRI partially digested total DNA of Btmed was cloned by using the Lambda Zap II cloning kit. Recombinant plaques were screened with a mouse policlonal antibody raised against the 94 kDa crystal protein of Btmed. One of the positive plaques was selected, and by in vivo excision, a recombinant pBluescript SK(-) was obtained. The gene encoding the 94 kDa toxin of Btmed DNA was cloned in a 4.4 kb DNA fragment. Btmed DNA was then subcloned as a EcoRI/EcoRI fragment into the shuttle vector pBU4 producing the recombinant plasmid pBTM3 and used to transform by electroporation Bt subsp. israelensis (Bti) crystal negative strain 4Q2-81. Toxicity to mosquito larvae was estimated by using first instar laboratory reared Aedes aegypti, and Culex quinquefasciatus larvae challenged with whole crystals. Toxicity results indicate that the purified inclusions from the recombinant Bti strain were toxic to all mosquito species tested, although the toxicity was not as high as the one produced by the crystal of the Btmed wild type strain. Poliacrylamide gel electrophoresis indicate that the inclusions produced by the recombinant strain Bti (pBTM3) were mainly composed of the 94 kDa protein of Btmed, as it was determined by Western blot

Life cycle and reproductive parameters of Clerada apicicornis signoret (Hemiptera: Lygaeidae) under laboratory conditions

The life cycle of Clerada apicicornis was determined under laboratory conditions. Mean development times in days were: egg 27.2, nymph I 12.5, nymph II 12, nymph III 13.4, nymph IV 16.4, nymph V 26. The life expectancy of adults ranged from 117 to 317 days (mean 196 days). Based on a cohort of 29 females of C. apicicornis, a horizontal life table was constructed. The following predictive parameters were obtained: net rate of reproduction (Ro = 48.31), intrinsic rate of population increase (r m = 0.153), generation time (Tc = 28.20 weeks), and finite rate of population increment (lambda = 1.16). The reproductive value (Vx) for each age class of the cohort females was calculated. The following observed parameters were calculated after mortality in each stage: net rate of reproduction (R'o=13.4), intrinsic rate of population increase (r c' =0.09 ), and finite rate of population increment (lambda' =1.1). The generation time (Tc' =27.4) was estimated using the methods of Laughlin and Bengstron. A vertical life table was elaborated and mortality was described for one generation of the cohort.

Adaptive Privacy Management System Design For Context-Aware Mobile Devices

While mobile technologies can provide great personalized services for mobile users, they also threaten their privacy. Such personalization-privacy paradox are particularly salient for context aware technology based mobile applications where user's behaviors, movement and habits can be associated with a consumer's personal identity. In this thesis, I studied the privacy issues in the mobile context, particularly focus on an adaptive privacy management system design for context-aware mobile devices, and explore the role of personalization and control over user's personal data. This allowed me to make multiple contributions, both theoretical and practical. In the theoretical world, I propose and prototype an adaptive Single-Sign On solution that use user's context information to protect user's private information for smartphone. To validate this solution, I first proved that user's context is a unique user identifier and context awareness technology can increase user's perceived ease of use of the system and service provider's authentication security. I then followed a design science research paradigm and implemented this solution into a mobile application called "Privacy Manager". I evaluated the utility by several focus group interviews, and overall the proposed solution fulfilled the expected function and users expressed their intentions to use this application. To better understand the personalization-privacy paradox, I built on the theoretical foundations of privacy calculus and technology acceptance model to conceptualize the theory of users' mobile privacy management. I also examined the role of personalization and control ability on my model and how these two elements interact with privacy calculus and mobile technology model. In the practical realm, this thesis contributes to the understanding of the tradeoff between the benefit of personalized services and user's privacy concerns it may cause. By pointing out new opportunities to rethink how user's context information can protect private data, it also suggests new elements for privacy related business models.

Comparative evaluation of pyrethroid insecticide formulations against Triatoma infestans (Klug): residual efficacy on four substrates

We investigated the residual efficacy of four insecticide formulations used in Chagas disease vector control campaigns: cyfluthrin 12.5% suspension concentrace (SC), lambda-cyhalothrin 10% wettable powder (WP), deltamethrin 2.5% SC, and 2.5% WP on four types of circular blocks of wood, straw with mud, straw with mud painted with lime, and mud containing 5% of cement. Three concentrations of these insecticides were tested: the LC90 (previously determined on filter paper), the double of the LC90, and the recommended operational dose. For each bioassay test, 15 third-stage nymphs of Triatoma infestans (Klug) (Hemiptera: Reduviidae) were exposed for 120 h to each treatment at 24 h, 30, 60, 90, and 180 days post-spraying. Mortality rates, moulting history and behaviour were recorded at 24, 48, 72, and 120 h of exposure. Mortality rates were highest during the first 30 days post-spraying. Highest mortality rates (above 50%) were observed for deltamethrin 2.5% SC and lambda-cyhalothrin 10% WP on wood blocks up to three months post-spraying. Mud was the substrate on which treatments showed lowest persistence, with the other two substrates showing intermediate residual efficacy of all treatments. During the first 30 days WP formulations were not as effective as SC flowable formulations but, overall in the longer term, WP gave grater mortality rates of T. infestans nymphs exposed at up to six months post-spraying. Porous surfaces, especially mud, showed most variability presumably due to absorption of the insecticide. In contrast the less porous surfaces (i.e. wood and lime-coated mud) kept mortality rates high for longer post-treatment, irrespective of the insecticide concentration used.

Xifratge d'arxius

Actualment l'ús de la criptografia ha arribat a ser del tot generalitzat, tant en els processos de transmissió i intercanvi segur d'informació, com en l'emmagatzematge secret de dades. Es tracta d'una disciplina els fonaments teòrics de la qual són en l'Àlgebra i en el Càlcul de Probabilitats. La programació d'interfícies gràfiques s'ha realitzat en Java i amb la manipulació, tot i que molt elemental, de documents XML.