Fiscal Sustainability in a New Keynesian Model

Recent work on optimal monetary and fiscal policy in New Keynesian models suggests that it is optimal to allow steady-state debt to follow a random walk. Leith and Wren-Lewis (2012) consider the nature of the timeinconsistency involved in such a policy and its implication for discretionary policy-making. We show that governments are tempted, given inflationary expectations, to utilize their monetary and fiscal instruments in the initial period to change the ultimate debt burden they need to service. We demonstrate that this temptation is only eliminated if following shocks, the new steady-state debt is equal to the original (efficient) debt level even though there is no explicit debt target in the government’s objective function. Analytically and in a series of numerical simulations we show which instrument is used to stabilize the debt depends crucially on the degree of nominal inertia and the size of the debt-stock. We also show that the welfare consequences of introducing debt are negligible for precommitment policies, but can be significant for discretionary policy. Finally, we assess the credibility of commitment policy by considering a quasi-commitment policy which allows for different probabilities of reneging on past promises. This on-line Appendix extends the results of this paper.

Fiscal Sustainability in a New Keynesian Model

Recent work on optimal monetary and fiscal policy in New Keynesian models suggests that it is optimal to allow steady-state debt to follow a random walk. Leith and Wren-Lewis (2012) consider the nature of the timeinconsistency involved in such a policy and its implication for discretionary policy-making. We show that governments are tempted, given inflationary expectations, to utilize their monetary and fiscal instruments in the initial period to change the ultimate debt burden they need to service. We demonstrate that this temptation is only eliminated if following shocks, the new steady-state debt is equal to the original (efficient) debt level even though there is no explicit debt target in the government’s objective function. Analytically and in a series of numerical simulations we show which instrument is used to stabilize the debt depends crucially on the degree of nominal inertia and the size of the debt-stock. We also show that the welfare consequences of introducing debt are negligible for precommitment policies, but can be significant for discretionary policy. Finally, we assess the credibility of commitment policy by considering a quasi-commitment policy which allows for different probabilities of reneging on past promises. This on-line Appendix extends the results of this paper.

Oscillations in a molecular structured cell population model

We consider a nonlinear cyclin content structured model of a cell population divided into proliferative and quiescent cells. We show, for particular values of the parameters, existence of solutions that do not depend on the cyclin content. We make numerical simulations for the general case obtaining, for some values of the parameters convergence to the steady state but also oscillations of the population for others.

Radiocarbon dating of modern groundwater: the role of the unsaturated zone

Biological and physical processes occurring in soils may lead to significant isotopic changes between the isotopic compositions of atmospheric CO2 and of soil CO2. Also, during water and gas transport from the soil surface to the water table, isotopic changes likely occur due to numerous physical processes such as gas production and diffusion, water advection, and gas-water-rock interactions. In most cases, these changes are not included in the correction models developed for groundwater dating, whereas they can significantly impact the calculation of the 14C age. We explore the role of these processes using: i) experimental data from two aquifer sites (Fontainebleau sands and Astian sands, France), ii) a distributed model to simulate the 14C activities of soil CO2, and iii) numerical simulations in order to highlight the role of the physical processes.¦The 13C content in soil CO2 showed seasonal variations and highlighted the competition between CO2 production and CO2 diffusion. Their respective contributions played a significant role in defining the isotopic composition of CO2 at the water table. On both study sites, variations of the 14C activity in soil CO2 reflect the competition between the fluxes of root derived-CO2 and organic matter derived-CO2. Since the nuclear weapon tests in the fifties and sixties, soil CO2 became significantly depleted in 14C compared to modern atmospheric CO2. Models that take into account this 14C depletion in soil CO2 for dating modern groundwater would lead to apparent younger 14C ages than models that only consider the 14C activity in atmospheric CO2. Moreover, since 2000-2005, the inverse effect is observed as soil CO2 is enriched in 14C compared to atmospheric CO2.¦Therefore, we conclude that the isotopic composition of CO2 at the water table have to be taken into account for the dating of modern groundwater. This requires a systematic sampling of soil CO2 and the measurement of its 13C and 14C contents. We used this information in a numerical simulation to calculate the evolution of isotopic composition of CO2 from the soil surface to the water table. This simulation integrated physical processes in the unsaturated zone (e.g. CO2 production and diffusion, water advection, etc.) and gas-water-rock interactions.

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on E. coli have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion.

Simulació numèrica de fenòmens de transferència de calor i dinàmics de fluids transitoris

The work carried out during the 4 year research activity can be barely classified in two main lines. On the one hand, a considerable effort is taken to address issues related with the verification of multi-dimensional and transient solutions that are obtained by numerical simulations. Within the studied cases, we can consider cases of piston-cylinder ows within geometries similar to those of hermetic reciprocating compressors.This issue is mentioned in Part I. On the other hand, numerical simulations of different phenomena have been performed. More emphasis has been given to the natural convection ow within enclosures. This is explained in Part II. The case extensively studied has been the natural convection ow. The natural convection ow within enclosures has attracted the attention of many researchers due to its potential to model numerous applications of engineering interest, such as cooling of electronic devices, air ow in buildings, heat transfer in solar collectors, among others. The natural convection studies corresponding to the parallelepipedic enclosures can be classified into two elementary classes: i) heating from a horizontal wall (heating from below); ii) heating from a vertical wall. The characteristic example of the former case is the Rayleigh-B_enard ow, however this research is on the cavities heated from the side. This configuration is referred commonly as the differentially heated cavity.

Effect of Knotting on the Shape of Polymers

Momentary configurations of long polymers at thermal equilibrium usually deviate from spherical symmetry and can be better described, on average, by a prolate ellipsoid. The asphericity and nature of asphericity (or prolateness) that describe these momentary ellipsoidal shapes of a polymer are determined by specific expressions involving the three principal moments of inertia calculated for configurations of the polymer. Earlier theoretical studies and numerical simulations have established that as the length of the polymer increases, the average shape for the statistical ensemble of random configurations asymptotically approaches a characteristic universal shape that depends on the solvent quality. It has been established, however, that these universal shapes differ for linear, circular, and branched chains. We investigate here the effect of knotting on the shape of cyclic polymers modeled as random isosegmental polygons. We observe that random polygons forming different knot types reach asymptotic shapes that are distinct from the ensemble average shape. For the same chain length, more complex knots are, on average, more spherical than less complex knots.

Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

Scaling behavior and equilibrium lengths of knotted polymers

We use numerical simulations to investigate how the chain length and topology of freely fluctuating knotted polymer rings affect their various spatial characteristics such as the radius of the smallest sphere enclosing momentary configurations of simulated polymer chains. We describe how the average value of a characteristic changes with the chain size and how this change depends on the topology of the modeled polymers. Although the scaling profiles of a spatial characteristic for distinct knot types do not intersect (at least, in the range of our data), the profiles for nontrivial knots intersect the corresponding profile obtained for phantom polymers, i.e., those that are free to explore all available topological states. For each knot type, this point of intersection defines its equilibrium length with respect to the spatial characteristic. At this chain length, a polymer forming a given knot type will not tend to increase or decrease. on average, the value of the spatial characteristic when the polymer is released from its topological constraint. We show interrelations between equilibrium lengths defined with respect to spatial characteristics of different character and observe that they are related to the lengths of ideal geometric configurations of the corresponding knot types.

Error estimate and control in the MSFV method for multiphase flow in porous media

n this paper the iterative MSFV method is extended to include the sequential implicit simulation of time dependent problems involving the solution of a system of pressure-saturation equations. To control numerical errors in simulation results, an error estimate, based on the residual of the MSFV approximate pressure field, is introduced. In the initial time steps in simulation iterations are employed until a specified accuracy in pressure is achieved. This initial solution is then used to improve the localization assumption at later time steps. Additional iterations in pressure solution are employed only when the pressure residual becomes larger than a specified threshold value. Efficiency of the strategy and the error control criteria are numerically investigated. This paper also shows that it is possible to derive an a-priori estimate and control based on the allowed pressure-equation residual to guarantee the desired accuracy in saturation calculation.

Symmetry-breaking in cumulative measures of shapes of polymer models.

Using numerical simulations we investigate shapes of random equilateral open and closed chains, one of the simplest models of freely fluctuating polymers in a solution. We are interested in the 3D density distribution of the modeled polymers where the polymers have been aligned with respect to their three principal axes of inertia. This type of approach was pioneered by Theodorou and Suter in 1985. While individual configurations of the modeled polymers are almost always nonsymmetric, the approach of Theodorou and Suter results in cumulative shapes that are highly symmetric. By taking advantage of asymmetries within the individual configurations, we modify the procedure of aligning independent configurations in a way that shows their asymmetry. This approach reveals, for example, that the 3D density distribution for linear polymers has a bean shape predicted theoretically by Kuhn. The symmetry-breaking approach reveals complementary information to the traditional, symmetrical, 3D density distributions originally introduced by Theodorou and Suter.

Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

Free-breathing 3 T magnetic resonance t(2)-mapping of the heart.

OBJECTIVES: This study sought to establish an accurate and reproducible T(2)-mapping cardiac magnetic resonance (CMR) methodology at 3 T and to evaluate it in healthy volunteers and patients with myocardial infarct. BACKGROUND: Myocardial edema affects the T(2) relaxation time on CMR. Therefore, T(2)-mapping has been established to characterize edema at 1.5 T. A 3 T implementation designed for longitudinal studies and aimed at guiding and monitoring therapy remains to be implemented, thoroughly characterized, and evaluated in vivo. METHODS: A free-breathing navigator-gated radial CMR pulse sequence with an adiabatic T(2) preparation module and an empirical fitting equation for T(2) quantification was optimized using numerical simulations and was validated at 3 T in a phantom study. Its reproducibility for myocardial T(2) quantification was then ascertained in healthy volunteers and improved using an external reference phantom with known T(2). In a small cohort of patients with established myocardial infarction, the local T(2) value and extent of the edematous region were determined and compared with conventional T(2)-weighted CMR and x-ray coronary angiography, where available. RESULTS: The numerical simulations and phantom study demonstrated that the empirical fitting equation is significantly more accurate for T(2) quantification than that for the more conventional exponential decay. The volunteer study consistently demonstrated a reproducibility error as low as 2 ± 1% using the external reference phantom and an average myocardial T(2) of 38.5 ± 4.5 ms. Intraobserver and interobserver variability in the volunteers were -0.04 ± 0.89 ms (p = 0.86) and -0.23 ± 0.91 ms (p = 0.87), respectively. In the infarction patients, the T(2) in edema was 62.4 ± 9.2 ms and was consistent with the x-ray angiographic findings. Simultaneously, the extent of the edematous region by T(2)-mapping correlated well with that from the T(2)-weighted images (r = 0.91). CONCLUSIONS: The new, well-characterized 3 T methodology enables robust and accurate cardiac T(2)-mapping at 3 T with high spatial resolution, while the addition of a reference phantom improves reproducibility. This technique may be well suited for longitudinal studies in patients with suspected or established heart disease.

Virus infection speeds: theory versus experiment

In order to explain the speed of Vesicular Stomatitis Virus VSV infections, we develop a simple model that improves previous approaches to the propagation of virus infections. For VSV infections, we find that the delay time elapsed between the adsorption of a viral particle into a cell and the release of its progeny has a veryimportant effect. Moreover, this delay time makes the adsorption rate essentially irrelevant in order to predict VSV infection speeds. Numerical simulations are in agreement with the analytical results. Our model satisfactorily explains the experimentally measured speeds of VSV infections

A continuous strain-space model of viral evolution within a host

Viruses rapidly evolve, and HIV in particular is known to be one of the fastest evolving human viruses. It is now commonly accepted that viral evolution is the cause of the intriguing dynamics exhibited during HIV infections and the ultimate success of the virus in its struggle with the immune system. To study viral evolution, we use a simple mathematical model of the within-host dynamics of HIV which incorporates random mutations. In this model, we assume a continuous distribution of viral strains in a one-dimensional phenotype space where random mutations are modelled by di ffusion. Numerical simulations show that random mutations combined with competition result in evolution towards higher Darwinian fitness: a stable traveling wave of evolution, moving towards higher levels of fi tness, is formed in the phenoty space.