Metropolized Randomized Maximum Likelihood for sampling from multimodal distributions

This article describes a method for using optimization to derive efficient independent transition functions for Markov chain Monte Carlo simulations. Our interest is in sampling from a posterior density $\pi(x)$ for problems in which the dimension of the model space is large, $\pi(x)$ is multimodal with regions of low probability separating the modes, and evaluation of the likelihood is expensive. We restrict our attention to the special case for which the target density is the product of a multivariate Gaussian prior and a likelihood function for which the errors in observations are additive and Gaussian

Abundance of Rice Root Aphid Among Selected Plant Species and on Plants Grown With Different Soil-Surface Media

The rice root aphid, Rhopalosiphum rufiabdominalis (Sasaki), is distributed worldwide and colonizes a wide range of plants. However, relatively little is known about the suitability of different host plants, optimal rearing techniques, and the aphid’s impact on plant fitness. To improve understanding of these factors, laboratory experiments were conducted to compare the abundance of rice root aphid on plants grown using three different soil-surface media and among selected monocotyledonous and dicotyledonous plants. Rice root aphid was more abundant on plants grown with a sandy soil surface than a surface with fine wood chips or only bare non-sandy soil. Rice root aphid was more abundant on ‘Elbon’ rye than on ‘Bart 38,’ ‘Dart,’ ‘Fletcher’ and ‘Ramona 50’ wheat. More winged rice root aphids were produced on Elbon rye than on Dart wheat, but the number of winged aphids on Elbon rye did not differ from that on other wheat lines. Rice root aphid was more abundant on Elbon rye and ‘TAM 110’ wheat than on ‘Marmin,’ ‘Marshall’ and ‘Sharp’ wheat. Additional observations with monocotyledonous plants showed that abundance of rice root aphid on ‘Kivu 85’ triticale was comparable to that on Elbon rye. Rice root aphid did not reproduce on potato or soybean, although winged adults persisted up to 24 days on caged potato plants. The implications of differential abundance of rice root aphid on plants are discussed in regard to colony rearing, future experiments and possible pest management considerations

Using Experimental Economics to Measure Social Capital And Predict Financial Decisions

Questions remain as to whether results from experimental economics games are generalizable to real decisions in non-laboratory settings. Furthermore, important questions persist about whether social capital can help solve seemingly missing credit markets. I conduct two experiments, a Trust game and a Public Goods game, and a survey to measure social capital. I then examine whether behavior in the games predicts repayment of loans to a Peruvian group lending microfinance program. Since the structure of these loans relies heavily on social capital to enforce repayment, this is a relevant and important test of the games, as well as of other measures of social capital. I find that individuals identified as "trustworthy" by the Trust game are in fact less likely to default on their loans. I do not find similar support for the Trust game as a measure of trust.trust game, experimental economics, microfinance

Self Similar Renormalization Group Applied to Diffusion in non-Gaussian Potentials

We study the problem of the computation of the effective diffusion constant of a Brownian particle diffusing in a random potential which is given by a function $V(\phi)$ of a Gaussian field $\phi$. A self similar renormalization group analysis is applied to a mathematically related problem of the effective permeability of a random porous medium from which the diffusion constant of the random potential problem can be extracted. This renormalization group approach reproduces practically all known exact results in one and two dimensions. The results are confronted with numerical simulations and we find that their accuracy is good up to points well beyond the expected perturbative regime. The results obtained are also tentatively applied to interacting particle systems without disorder and we obtain expressions for the self-diffusion constant in terms of the excess thermodynamic entropy. This result is of a form that has commonly been used to fit the self diffusion constant in molecular dynamics simulations.Comment: 14 pages, 3 .eps figures, IOP style fil

Effective diffusion constant in a two dimensional medium of charged point scatterers

We obtain exact results for the effective diffusion constant of a two dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure

Weak non-linear surface charging effects in electrolytic films

A simple model of soap films with nonionic surfactants stabilized by added electrolyte is studied. The model exhibits charge regularization due to the incorporation of a physical mechanism responsible for the formation of a surface charge. We use a Gaussian field theory in the film but the full non-linear surface terms which are then treated at a one-loop level by calculating the mean-field Poisson-Boltzmann solution and then the fluctuations about this solution. We carefully analyze the renormalization of the theory and apply it to a triple layer model for a thin film with Stern layer of thickness $h$. For this model we give expressions for the surface charge $\sigma(L)$ and the disjoining pressure $P_d(L)$ and show their dependence on the parameters. The influence of image charges naturally arise in the formalism and we show that predictions depend strongly on $h$ because of their effects. In particular, we show that the surface charge vanishes as the film thickness $L \to 0$. The fluctuation terms about this class of theories exhibit a Casimir-like attraction across the film and although this attraction is well known to be negligible compared with the mean-field component for thick films in the presence of electrolyte, in the model studied here these fluctuations also affect the surface charge regulation leading to a fluctuation component in the disjoining pressure which has the same behavior as the mean-field component even for large film thickness.Comment: 17 pages, 12 figures, latex sourc

Aging on Parisi's tree

We present a detailed study of simple `tree' models for off equilibrium dynamics and aging in glassy systems. The simplest tree describes the landscape of a random energy model, whereas multifurcating trees occur in the solution of the Sherrington-Kirkpatrick model. An important ingredient taken from these models is the exponential distribution of deep free-energies, which translate into a power-law distribution of the residence time within metastable `valleys'. These power law distributions have infinite mean in the spin-glass phase and this leads to the aging phenomenon. To each level of the tree are associated an overlap and the exponent of the time distribution. We solve these models for a finite (but arbitrary) number of levels and show that a two level tree accounts very well for many experimental observations (thermoremanent magnetisation, a.c susceptibility, second noise spectrum....). We introduce the idea that the deepest levels of the tree correspond to equilibrium dynamics whereas the upper levels correspond to aging. Temperature cycling experiments suggest that the borderline between the two is temperature dependent. The spin-glass transition corresponds to the temperature at which the uppermost level is put out of equilibrium but is subsequently followed by a sequence of (dynamical) phase transitions corresponding to non equilibrium dynamics within deeper and deeper levels. We tentatively try to relate this `tree' picture to the real space `droplet' model, and speculate on how the final description of spin-glasses might look like.Comment: 30 pages, RevTeX, 9 figures, available on request, report # 077 / SPEC / 199

Renormalization of Drift and Diffusivity in Random Gradient Flows

We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends linearly on the gradient of a gaussian random field with homogeneous statistics. The theoretical analysis is confirmed by numerical simulation. For the purely isotropic case the simulation, which measures the effective drift directly in a constant gradient background field, confirms the result previously obtained theoretically, that the effective diffusivity and effective drift are renormalized by the same factor from their local values. For this isotropic case we provide an intuitive explanation, based on a {\it spatial} average of local drift, for the renormalization of the effective drift parameter relative to its local value. We also investigate situations in which the isotropy is broken by the tensorial relationship of the local drift to the gradient of the random field. We find that the numerical simulation confirms a relatively simple renormalization group calculation for the effective diffusivity and drift tensors.Comment: Latex 16 pages, 5 figures ep