Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

The Spread of free-riding behavior in a social network

We study a model where agents, located in a social network, decide whether to exert effort or not in experimenting with a new technology (or acquiring a new skill, innovating, etc.). We assume that agents have strong incentives to free ride on their neighbors' effort decisions. In the static version of the model efforts are chosen simultaneously. In equilibrium, agents exerting effort are never connected with each other and all other agents are connected with at least one agent exerting effort. We propose a mean-field dynamics in which agents choose in each period the best response to the last period's decisions of their neighbors. We characterize the equilibrium of such a dynamics and show how the pattern of free riders in the network depends on properties of the connectivity distribution.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

New methods for detecting antibiotic resistant bacteria and preventing their spread

Methicillin resistant Staphylococcus aureus (MRSA) bacteria have emerged in the early 1980's in numerous health care institutions around the world. The main transmission mechanism within hospitals and healthcare facilities is through the hands of health care workers. Resistant to several antibiotics, the MRSA is one of the most feared pathogens in the hospital setting since it is very difficult to eradicate with the standard treatments. There are still a limited number of anti-MRSA antibiotics but the first cases of resistance to these compounds have already been reported and their frequency is likely to increase in the coming years. Every year, the MRSA infections result in major human and financial costs, due to the high associated mortality and expenses related to the required care. Measures towards a faster detection of resistant bacteria and establishment of appropriate antibiotic treatment parameters are fundamental. Also as part as infection prevention, diminution of bacteria present on the commonly touched surfaces could also limit the spread and selection of antibiotic resistant bacteria. During my thesis, projects were developed around MRSA and antibiotic resistance investigation using innovative technologies. The thesis was subdivided in three main parts with the use of atomic force microscopy AFM for antibiotic resistance detection in part 1, the importance of the bacterial inoculum size in the selection of antibiotic resistance in part 2 and the testing of antimicrobial surfaces creating by sputtering copper onto polyester in part 3. In part 1 the AFM was used two different ways, first for the measurement of stiffness (elasticity) of bacteria and second as a nanosensor for antibiotic susceptibility testing. The stiffness of MRSA with different susceptibility profiles to vancomycin was investigated using the stiffness tomography mode of the AFM and results have demonstrated and increased stiffness in the vancomycin resistant strains that also paralleled with increased thickness of the bacterial cell wall. Parts of the AFM were also used to build a new antibiotic susceptibility-testing device. This nano sensor was able to measure vibrations emitted from living bacteria that ceased definitively upon antibiotic exposure to which they were susceptible but restarted after antibiotic removal to which they were resistant, allowing in a matter of minute the assessment of antibiotic susceptibility determination. In part 2 the inoculum effect (IE) of vancomycin, daptomycin and linezolid and its importance in antibiotic resistance selection was investigated with MRSA during a 15 days of cycling experiment. Results indicated that a high bacterial inoculum and a prolonged antibiotic exposure were two key factors in the in vitro antibiotic resistance selection in MRSA and should be taken into consideration when choosing the drug treatment. Finally in part 3 bactericidal textile surfaces were investigated against MRSA. Polyesters coated after 160 seconds of copper sputtering have demonstrated a high bactericidal activity reducing the bacterial load of at least 3 logio after one hour of contact. -- Au cours des dernières décennies, des bactéries multirésistantes aux antibiotiques (BMR) ont émergé dans les hôpitaux du monde entier. Depuis lors, le nombre de BMR et la prévalence des infections liées aux soins (IAS) continuent de croître et sont associés à une augmentation des taux de morbidité et de mortalité ainsi qu'à des coûts élevés. De plus, le nombre de résistance à différentes classes d'antibiotiques a également augmenté parmi les BMR, limitant ainsi les options thérapeutiques disponibles lorsqu'elles ont liées a des infections. Des mesures visant une détection plus rapide des bactéries résistantes ainsi que l'établissement des paramètres de traitement antibiotiques adéquats sont primordiales lors d'infections déjà présentes. Dans une optique de prévention, la diminution des bactéries présentes sur les surfaces communément touchées pourrait aussi freiner la dissémination et l'évolution des bactéries résistantes. Durant ma thèse, différents projets incluant des nouvelles technologies et évoluant autour de la résistance antibiotique ont été traités. Des nouvelles technologies telles que le microscope à force atomique (AFM) et la pulvérisation cathodique de cuivre (PCC) ont été utilisées, et le Staphylococcus aureus résistant à la méticilline (SARM) a été la principale BMR étudiée. Deux grandes lignes de recherche ont été développées; la première visant à détecter la résistance antibiotique plus rapidement avec l'AFM et la seconde visant à prévenir la dissémination des BMR avec des surfaces crées grâce à la PCC. L'AFM a tout d'abord été utilisé en tant que microscope à sonde locale afin d'investiguer la résistance à la vancomycine chez les SARMs. Les résultats ont démontré que la rigidité de la paroi augmentait avec la résistance à la vancomycine et que celle-ci corrélait aussi avec une augmentation de l'épaisseur des parois, vérifiée grâce à la microscopie électronique. Des parties d'un AFM ont été ensuite utilisées afin de créer un nouveau dispositif de test de sensibilité aux antibiotiques, un nanocapteur. Ce nanocapteur mesure des vibrations produites par les bactéries vivantes. Après l'ajout d'antibiotique, les vibrations cessent définitivement chez les bactéries sensibles à l'antibiotique. En revanche pour les bactéries résistantes, les vibrations reprennent après le retrait de l'antibiotique dans le milieu permettant ainsi, en l'espace de minutes de détecter la sensibilité de la bactérie à un antibiotique. La PCC a été utilisée afin de créer des surfaces bactéricides pour la prévention de la viabilité des BMR sur des surfaces inertes. Des polyesters finement recouverts de cuivre (Cu), connu pour ses propriétés bactéricides, ont été produits et testés contre des SARMs. Une méthode de détection de viabilité des bactéries sur ces surfaces a été mise au point, et les polyesters obtenus après 160 secondes de pulvérisation au Cu ont démontré une excellente activité bactéricide, diminuant la charge bactérienne d'au moins 3 logio après une heure de contact. En conclusion, l'utilisation de nouvelles technologies nous a permis d'évoluer vers de méthodes de détection de la résistance antibiotique plus rapides ainsi que vers le développement d'un nouveau type de surface bactéricide, dans le but d'améliorer le diagnostic et la gestion des BMR.

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities (Draft 1)

We extend a reduced form model for pricing pass-through mortgage backed securities (MBS) and provide a novel hedging tool for investors in this market. To calculate the price of an MBS, traders use what is known as option-adjusted spread (OAS). The resulting OAS value represents the required basis points adjustment to reference curve discounting rates needed to match an observed market price. The OAS suffers from some drawbacks. For example, it remains constant until the maturity of the bond (thirty years in mortgage-backed securities), and does not incorporate interest rate volatility. We suggest instead what we call dynamic option adjusted spread (DOAS). The latter allows investors in the mortgage market to account for both prepayment risk and changes of the yield curve.

Hawtreyan “Credit Deadlock” or Keynesian “Liquidity Trap”? Lessons for Japan from the Great Depression

This paper outlines the ideas of Ralph Hawtrey and Lauchlin Currie on the need for monetised fiscal deficit spending in 1930s USA to combat the deep depression into which the economy had been allowed to sink. In such exceptional circumstances of “credit deadlock” in which banks were afraid to lend and households and business afraid to borrow, the deadlock could best be broken through the spending of new money into circulation via large fiscal deficits. This complementarity of fiscal and monetary policy was shown to be essential, and as such indicates the potential power of monetary policy – in contrast to the Keynesian “liquidity trap” view that it is powerless This lesson was not learned by the Japanese authorities in their response to the asset price collapse of 1991-92, resulting in a lost decade as ballooning fiscal deficits were neutralised throughout the 1990s by unhelpfully tight monetary policy with the Bank of Japan refusing to monetise the deficits.

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities (Draft 2)

We extend a reduced form model for pricing pass-through mortgage backed securities (MBS) and provide a novel hedging tool for investors in this market. To calculate the price of an MBS, traders use what is known as option-adjusted spread (OAS). The resulting OAS value represents the required basis points adjustment to reference curve discounting rates needed to match an observed market price. The OAS suffers from some drawbacks. For example, it remains constant until the maturity of the bond (thirty years in mortgage-backed securities), and does not incorporate interest rate volatility. We suggest instead what we call dynamic option adjusted spread (DOAS), which allows investors in the mortgage market to account for both prepayment risk and changes of the yield curve.

Interest Rate Co-movements, Global Factors and the Long End of the Term Spread

The disconnect between rising short and low long interest rates has been a distinctive feature of the 2000s. Both research and policy circles have argued that international forces, such as global monetary policy (e.g. Rogoff, 2006); international business cycles (e.g. Borio and Filardo, 2007); or a global savings glut (e.g Bernanke, 2005) may be responsible. In this paper, we employ recent advances in panel data econometrics to document the disconnect and link it explicitly to the existence of a global latent factor that dominates the long end of the term spread for the recent period; the saving glut story emerges as the most likely contender for the global factor.

Estimating Phillips Curves in Turbulent Times using the ECB’s Survey of Professional Forecasters

This paper uses forecasts from the European Central Bank's Survey of Professional Forecasters to investigate the relationship between inflation and inflation expectations in the euro area. We use theoretical structures based on the New Keynesian and Neoclassical Phillips curves to inform our empirical work. Given the relatively short data span of the Survey of Professional Forecasters and the need to control for many explanatory variables, we use dynamic model averaging in order to ensure a parsimonious econometric speci cation. We use both regression-based and VAR-based methods. We find no support for the backward looking behavior embedded in the Neo-classical Phillips curve. Much more support is found for the forward looking behavior of the New Keynesian Phillips curve, but most of this support is found after the beginning of the financial crisis.

Estimating United States Phillips Curves With Expectations Consistent With The Statistical Process Of Inflation

‘Modern’ Phillips curve theories predict inflation is an integrated, or near integrated, process. However, inflation appears bounded above and below in developed economies and so cannot be ‘truly’ integrated and more likely stationary around a shifting mean. If agents believe inflation is integrated as in the ‘modern’ theories then they are making systematic errors concerning the statistical process of inflation. An alternative theory of the Phillips curve is developed that is consistent with the ‘true’ statistical process of inflation. It is demonstrated that United States inflation data is consistent with the alternative theory but not with the existing ‘modern’ theories.

Environmental Kuznets Curves for Carbon Emissions: A Critical Survey

The empirical finding of an inverse U-shaped relationship between per capita income and pollution, the so-called Environmental Kuznets Curve (EKC), suggests that as countries experience economic growth, environmental deterioration decelerates and thus becomes less of an issue. Focusing on the prime example of carbon emissions, the present article provides a critical review of the new econometric techniques that have questioned the baseline polynomial specification in the EKC literature. We discuss issues related to the functional form, heterogeneity, “spurious” regressions and spatial dependence to address whether and to what extent the EKC can be observed. Despite these new approaches, there is still no clear-cut evidence supporting the existence of the EKC for carbon emissions. JEL classifications: C20; Q32; Q50; O13 Keywords: Environmental Kuznets Curve; Carbon emissions; Functional form; Heterogeneity; “Spurious” regressions; Spatial dependence.Residential satisfaction is often used as a barometer to assess the performance of public policy and programmes designed to raise individuals' well-being. However, the fact that responses elicited from residents might be biased by subjective, non-observable factors casts doubt on whether these responses can be taken as trustable indicators of the individuals' housing situation. Emotional factors such as aspirations or expectations might affect individuals' cognitions of their true residential situation. To disentangle this puzzle, we investigated whether identical residential attributes can be perceived differently depending on tenure status. Our results indicate that tenure status is crucial not only in determining the level of housing satisfaction, but also regarding how dwellers perceive their housing characteristics. Keywords: Housing satisfaction, subjective well-being, homeownership. JEL classification: D1, R2.

A computational and geometric approach to phase resetting curves and surfaces

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

Pecuniary Externality through Credit Constraints: Two Examples without Uncertainty

This paper is a contribution to the growing literature on constrained inefficiencies in economies with financial frictions. The purpose is to present two simple examples, inspired by the stochastic models in Gersbach-Rochet (2012) and Lorenzoni (2008), of deterministic environments in which such inefficiencies arise through credit constraints. Common to both examples is a pecuniary externality, which operates through an asset price. In the second example, a simple transfer between two groups of agents can bring about a Pareto improvement. In a first best economy, there are no pecuniary externalities because marginal productivities are equalised. But when agents face credit constraints, there is a wedge between their marginal productivities and those of the non-credit-constrained agents. The wedge is the source of the pecuniary externality: economies with these kinds of imperfections in credit markets are not second-best efficient. This is akin to the constrained inefficiency of an economy with incomplete markets, as in Geanakoplos and Polemarchakis (1986).

On hyperbolic once-punctured-torus bundles IV: automata for lightning curves

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

A Multiple Break Panel Approach to Estimating United States Phillips Curves

Phillips curves are often estimated without due attention being paid to the underlying time series properties of the data. In particular, the consequences of inflation having discrete breaks in mean have not been studied adequately. We show by means of simulations and a detailed empirical example based on United States data that not taking account of breaks may lead to biased, and therefore spurious, estimates of Phillips curves. We suggest a method to account for the breaks in mean inflation and obtain meaningful and unbiased estimates of the short- and long-run Phillips curves in the United States.