Solving heterogeneous-agent models by projection and perturbation

The paper proposes a numerical solution method for general equilibrium models with a continuum of heterogeneous agents, which combines elements of projection and of perturbation methods. The basic idea is to solve first for the stationary solutionof the model, without aggregate shocks but with fully specified idiosyncratic shocks. Afterwards one computes a first-order perturbation of the solution in the aggregate shocks. This approach allows to include a high-dimensional representation of the cross-sectional distribution in the state vector. The method is applied to a model of household saving with uninsurable income risk and liquidity constraints. The model includes not only productivity shocks, but also shocks to redistributive taxation, which cause substantial short-run variation in the cross-sectional distribution of wealth. If those shocks are operative, it is shown that a solution method based on very few statistics of the distribution is not suitable, while the proposed method can solve the model with high accuracy, at least for the case of small aggregate shocks. Techniques are discussed to reduce the dimension of the state space such that higher order perturbations are feasible.Matlab programs to solve the model can be downloaded.

X-ray diffraction, thermal analysis, and Raman scattering study of K2BeF4 and comparation to other member of the (beta)-K2SO4 family with ferroelectric -paraelectric transition

Thermal analysis, powder diffraction, and Raman scattering as a function of the temperature were carried out on K2BeF4. Moreover, the crystal structure was determined at 293 K from powder diffraction. The compound shows a transition from Pna21 to Pnam space group at 921 K with a transition enthalpy of 5 kJ/mol. The transition is assumed to be first order because the compound shows metastability. Structurally and spectroscopically the transition is similar to those observed in (NH4)2SO4, which suggests that the low-temperature phase is ferroelectric. In order to confirm it, the spontaneous polarization has been computed using an ionic model.

Tax reforms and inequality: theoretical and empirical implications

In this paper we examine the effect of tax policy on the relationship between inequality and growth in a two-sector non-scale model. With non-scale models, the longrun equilibrium growth rate is determined by technological parameters and it is independent of macroeconomic policy instruments. However, this fact does not imply that fiscal policy is unimportant for long-run economic performance. It indeed has important effects on the different levels of key economic variables such as per capita stock of capital and output. Hence, although the economy grows at the same rate across steady states, the bases for economic growth may be different.The model has three essential features. First, we explicitly model skill accumulation, second, we introduce government finance into the production function, and we introduce an income tax to mirror the fiscal events of the 1980¿s and 1990¿s in the US. The fact that the non-scale model is associated with higher order dynamics enables it to replicate the distinctly non-linear nature of inequality in the US with relative ease. The results derived in this paper attract attention to the fact that the non-scale growth model does not only fit the US data well for the long-run (Jones, 1995b) but also that it possesses unique abilities in explaining short term fluctuations of the economy. It is shown that during transition the response of the relative simulated wage to changes in the tax code is rather non-monotonic, quite in accordance to the US inequality pattern in the 1980¿s and early 1990¿s.More specifically, we have analyzed in detail the dynamics following the simulation of an isolated tax decrease and an isolated tax increase. So, after a tax decrease the skill premium follows a lower trajectory than the one it would follow without a tax decrease. Hence we are able to reduce inequality for several periods after the fiscal shock. On the contrary, following a tax increase, the evolution of the skill premium remains above the trajectory carried on by the skill premium under a situation with no tax increase. Consequently, a tax increase would imply a higher level of inequality in the economy

Tax reforms and inequality: theoretical and empirical implications

In this paper we examine the effect of tax policy on the relationship between inequality and growth in a two-sector non-scale model. With non-scale models, the longrun equilibrium growth rate is determined by technological parameters and it is independent of macroeconomic policy instruments. However, this fact does not imply that fiscal policy is unimportant for long-run economic performance. It indeed has important effects on the different levels of key economic variables such as per capita stock of capital and output. Hence, although the economy grows at the same rate across steady states, the bases for economic growth may be different.The model has three essential features. First, we explicitly model skill accumulation, second, we introduce government finance into the production function, and we introduce an income tax to mirror the fiscal events of the 1980¿s and 1990¿s in the US. The fact that the non-scale model is associated with higher order dynamics enables it to replicate the distinctly non-linear nature of inequality in the US with relative ease. The results derived in this paper attract attention to the fact that the non-scale growth model does not only fit the US data well for the long-run (Jones, 1995b) but also that it possesses unique abilities in explaining short term fluctuations of the economy. It is shown that during transition the response of the relative simulated wage to changes in the tax code is rather non-monotonic, quite in accordance to the US inequality pattern in the 1980¿s and early 1990¿s.More specifically, we have analyzed in detail the dynamics following the simulation of an isolated tax decrease and an isolated tax increase. So, after a tax decrease the skill premium follows a lower trajectory than the one it would follow without a tax decrease. Hence we are able to reduce inequality for several periods after the fiscal shock. On the contrary, following a tax increase, the evolution of the skill premium remains above the trajectory carried on by the skill premium under a situation with no tax increase. Consequently, a tax increase would imply a higher level of inequality in the economy

Critical behavior of a system with orientational and positional degrees of freedom: A Monte Carlo simulation study

The critical behavior of a system constituted by molecules with a preferred symmetry axis is studied by means of a Monte Carlo simulation of a simplified two-dimensional model. The system exhibits two phase transitions, associated with the vanishing of the positional order of the center of mass of the molecules and with the orientational order of the symmetry axis. The evolution of the order parameters and the specific heat is also studied. The transition associated with the positional degrees of freedom is found to change from a second-order to a first-order behavior when the two phase transitions are close enough, due to the coupling with the orientational degrees of freedom. This fact is qualitatively compared with similar results found in pure liquid crystals and liquid-crystal mixtures.

Entropy change and magnetocaloric effect in Gd5(SixGe1-x)4

Isothermal magnetization curves up to 23 T have been measured in Gd5Si1.8Ge2.2. We show that the values of the entropy change at the first-order magnetostructural transition, obtained from the Clausius-Clapeyron equation and the Maxwell relation, are coincident, provided the Maxwell relation is evaluated only within the transition region and the maximum applied field is high enough to complete the transition. These values are also in agreement with the entropy change obtained from differential scanning calorimetry. We also show that a simple phenomenological model based on the temperature and field dependence of the magnetization accounts for these results.

Premartensitic transition driven by magnetoelastic interaction in bcc ferromagnetic Ni2MnGa

We show that the magnetoelastic coupling between the magnetization and the amplitude of a short wavelength phonon enables the existence of a first order premartensitic transition from a bcc to a micromodulated phase in Ni2MnGa. Such a magnetoelastic coupling has been experimentally evidenced by ac susceptibility and ultrasonic measurements under an applied magnetic field. A latent heat around 9 J/mol has been measured using a highly sensitive calorimeter. This value is in very good agreement with the value predicted by a proposed model.

Athermal character of structural phase transitions

The significance of thermal fluctuations in nucleation in structural first-order phase transitions has been examined. The prototypical case of martensitic transitions has been experimentally investigated by means of acoustic emission techniques. We propose a model based on the mean first-passage time to account for the experimental observations. Our study provides a unified framework to establish the conditions for isothermal and athermal transitions to be observed.

Coherent Stranski-Krastanov growth in 1+1 dimensions with anharmonic interactions: An equilibrium study

The formation of coherently strained three-dimensional (3D) islands on top of the wetting layer in the Stranski-Krastanov mode of growth is considered in a model in 1 + 1 dimensions accounting for the anharmonicity and nonconvexity of the real interatomic forces. It is shown that coherent 3D islands can be expected to form in compressed rather than expanded overlayers beyond a critical lattice misfit. In expanded overlayers the classical Stranski-Krastanov growth is expected to occur because the misfit dislocations can become energetically favored at smaller island sizes. The thermodynamic reason for coherent 3D islanding is incomplete wetting owing to the weaker adhesion of the edge atoms. Monolayer height islands with a critical size appear as necessary precursors of the 3D islands. This explains the experimentally observed narrow size distribution of the 3D islands. The 2D-3D transformation takes place by consecutive rearrangements of mono- to bilayer, bi- to trilayer islands, etc., after the corresponding critical sizes have been exceeded. The rearrangements are initiated by nucleation events, each one needing to overcome a lower energetic barrier than the one before. The model is in good qualitative agreement with available experimental observations.

Generalized adiabatic invariance

In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m - 1) time derivatives of the Hamiltonian at the initial and final time instants are equal to zero.] Here we look for a quantity that is an adiabatic invariant to mth order for any Hamiltonian that changes slowly in time, and that does not fulfill any special condition (its first time derivatives are not zero initially and finally).

Entropy change and magnetocaloric effect in Gd5(SixGe1-x)4

Isothermal magnetization curves up to 23 T have been measured in Gd5Si1.8Ge2.2. We show that the values of the entropy change at the first-order magnetostructural transition, obtained from the Clausius-Clapeyron equation and the Maxwell relation, are coincident, provided the Maxwell relation is evaluated only within the transition region and the maximum applied field is high enough to complete the transition. These values are also in agreement with the entropy change obtained from differential scanning calorimetry. We also show that a simple phenomenological model based on the temperature and field dependence of the magnetization accounts for these results.

X-ray diffraction, thermal analysis, and Raman scattering study of K2BeF4 and comparation to other member of the (beta)-K2SO4 family with ferroelectric -paraelectric transition

Thermal analysis, powder diffraction, and Raman scattering as a function of the temperature were carried out on K2BeF4. Moreover, the crystal structure was determined at 293 K from powder diffraction. The compound shows a transition from Pna21 to Pnam space group at 921 K with a transition enthalpy of 5 kJ/mol. The transition is assumed to be first order because the compound shows metastability. Structurally and spectroscopically the transition is similar to those observed in (NH4)2SO4, which suggests that the low-temperature phase is ferroelectric. In order to confirm it, the spontaneous polarization has been computed using an ionic model.

Susceptibilitat genètica al càncer gàstric: caracterització de les interaccions de segon ordre entre gens i variants identificades en l’estudi EPIC‐EURGAST

En aquest Treball de Final de Grau s’exposen els resultats de l’anàlisi de les dades genètiques del projecte EurGast2 "Genetic susceptibility, environmental exposure and gastric cancer risk in an European population”, estudi cas‐control niat a la cohort europea EPIC “European Prospective lnvestigation into Cancer and Nutrition”, que té per objectiu l’estudi dels factors genètics i ambientals associats amb el risc de desenvolupar càncer gàstric (CG). A partir de les dades resultants de l’estudi EurGast2, en el què es van analitzar 1.294 SNPs en 365 casos de càncer gàstric i 1.284 controls en l’anàlisi Single SNP previ, la hipòtesi de partida del present Treball de Final de Grau és que algunes variants amb un efecte marginal molt feble, però que conjuntament amb altres variants estarien associades al risc de CG, podrien no haver‐se detectat. Així doncs, l’objectiu principal del projecte és la identificació d’interaccions de segon ordre entre variants genètiques de gens candidats implicades en la carcinogènesi de càncer gàstric. L’anàlisi de les interaccions s’ha dut a terme aplicant el mètode estadístic Model‐based Multifactor Dimensionality Reduction Method (MB‐MDR), desenvolupat per Calle et al. l’any 2008 i s’han aplicat dues metodologies de filtratge per seleccionar les interaccions que s’exploraran: 1) filtratge d’interaccions amb un SNP significatiu en el Single SNP analysis i 2) filtratge d’interaccions segons la mesura Sinèrgia. Els resultats del projecte han identificat 5 interaccions de segon ordre entre SNPs associades significativament amb un major risc de desenvolupar càncer gàstric, amb p‐valor inferior a 10‐4. Les interaccions identificades corresponen a interaccions entre els gens MPO i CDH1, XRCC1 i GAS6, ADH1B i NR5A2 i IL4R i IL1RN (que s’ha validat en les dues metodologies de filtratge). Excepte CDH1, cap altre d’aquests gens s’havia associat significativament amb el CG o prioritzat en les anàlisis prèvies, el que confirma l’interès d’analitzar les interaccions genètiques de segon ordre. Aquestes poden ser un punt de partida per altres anàlisis destinades a confirmar gens putatius i a estudiar a nivell biològic i molecular els mecanismes de carcinogènesi, i orientades a la recerca de noves dianes terapèutiques i mètodes de diagnosi i pronòstic més eficients.

Approximate polytope ensemble for one-class classification

In this work, a new one-class classification ensemble strategy called approximate polytope ensemble is presented. The main contribution of the paper is threefold. First, the geometrical concept of convex hull is used to define the boundary of the target class defining the problem. Expansions and contractions of this geometrical structure are introduced in order to avoid over-fitting. Second, the decision whether a point belongs to the convex hull model in high dimensional spaces is approximated by means of random projections and an ensemble decision process. Finally, a tiling strategy is proposed in order to model non-convex structures. Experimental results show that the proposed strategy is significantly better than state of the art one-class classification methods on over 200 datasets.

Reaction-diffusion lattice gas: Theory and computer results

We report on the study of nonequilibrium ordering in the reaction-diffusion lattice gas. It is a kinetic model that relaxes towards steady states under the simultaneous competition of a thermally activated creation-annihilation $(reaction$) process at temperature T, and a diffusion process driven by a heat bath at temperature T?T. The phase diagram as one varies T and T, the system dimension d, the relative priori probabilities for the two processes, and their dynamical rates is investigated. We compare mean-field theory, new Monte Carlo data, and known exact results for some limiting cases. In particular, no evidence of Landau critical behavior is found numerically when d=2 for Metropolis rates but Onsager critical points and a variety of first-order phase transitions.