Two-sided learning in new keynesian models: dynamics, (lack of) convergence and the value of information

This paper investigates the role of learning by private agents and the central bank (two-sided learning) in a New Keynesian framework in which both sides of the economy have asymmetric and imperfect knowledge about the true data generating process. We assume that all agents employ the data that they observe (which may be distinct for different sets of agents) to form beliefs about unknown aspects of the true model of the economy, use their beliefs to decide on actions, and revise these beliefs through a statistical learning algorithm as new information becomes available. We study the short-run dynamics of our model and derive its policy recommendations, particularly with respect to central bank communications. We demonstrate that two-sided learning can generate substantial increases in volatility and persistence, and alter the behavior of the variables in the model in a signifficant way. Our simulations do not converge to a symmetric rational expectations equilibrium and we highlight one source that invalidates the convergence results of Marcet and Sargent (1989). Finally, we identify a novel aspect of central bank communication in models of learning: communication can be harmful if the central bank's model is substantially mis-specified

Analysis and Monte Carlo simulations of a model for the spread of infectious diseases in heterogeneous metapopulations

We present a study of the continuous-time equations governing the dynamics of a susceptible infected-susceptible model on heterogeneous metapopulations. These equations have been recently proposed as an alternative formulation for the spread of infectious diseases in metapopulations in a continuous-time framework. Individual-based Monte Carlo simulations of epidemic spread in uncorrelated networks are also performed revealing a good agreement with analytical predictions under the assumption of simultaneous transmission or recovery and migration processes

Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene photochemistry

A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments

Two-sided learning in New Keynesian models: Dynamics, (lack of) convergence and the value of information

This paper investigates the role of learning by private agents and the central bank(two-sided learning) in a New Keynesian framework in which both sides of the economyhave asymmetric and imperfect knowledge about the true data generating process. Weassume that all agents employ the data that they observe (which may be distinct fordifferent sets of agents) to form beliefs about unknown aspects of the true model ofthe economy, use their beliefs to decide on actions, and revise these beliefs througha statistical learning algorithm as new information becomes available. We study theshort-run dynamics of our model and derive its policy recommendations, particularlywith respect to central bank communications. We demonstrate that two-sided learningcan generate substantial increases in volatility and persistence, and alter the behaviorof the variables in the model in a significant way. Our simulations do not convergeto a symmetric rational expectations equilibrium and we highlight one source thatinvalidates the convergence results of Marcet and Sargent (1989). Finally, we identifya novel aspect of central bank communication in models of learning: communicationcan be harmful if the central bank's model is substantially mis-specified.

Testing demographic models of effective population size.

Due to practical difficulties in obtaining direct genetic estimates of effective sizes, conservation biologists have to rely on so-called 'demographic models' which combine life-history and mating-system parameters with F-statistics in order to produce indirect estimates of effective sizes. However, for the same practical reasons that prevent direct genetic estimates, the accuracy of demographic models is difficult to evaluate. Here we use individual-based, genetically explicit computer simulations in order to investigate the accuracy of two such demographic models aimed at investigating the hierarchical structure of populations. We show that, by and large, these models provide good estimates under a wide range of mating systems and dispersal patterns. However, one of the models should be avoided whenever the focal species' breeding system approaches monogamy with no sex bias in dispersal or when a substructure within social groups is suspected because effective sizes may then be strongly overestimated. The timing during the life cycle at which F-statistics are evaluated is also of crucial importance and attention should be paid to it when designing field sampling since different demographic models assume different timings. Our study shows that individual-based, genetically explicit models provide a promising way of evaluating the accuracy of demographic models of effective size and delineate their field of applicability.

Evolution in heterogeneous populations: from migration models to fixation probabilities.

Although dispersal is recognized as a key issue in several fields of population biology (such as behavioral ecology, population genetics, metapopulation dynamics or evolutionary modeling), these disciplines focus on different aspects of the concept and often make different implicit assumptions regarding migration models. Using simulations, we investigate how such assumptions translate into effective gene flow and fixation probability of selected alleles. Assumptions regarding migration type (e.g. source-sink, resident pre-emption, or balanced dispersal) and patterns (e.g. stepping-stone versus island dispersal) have large impacts when demes differ in sizes or selective pressures. The effects of fragmentation, as well as the spatial localization of newly arising mutations, also strongly depend on migration type and patterns. Migration rate also matters: depending on the migration type, fixation probabilities at an intermediate migration rate may lie outside the range defined by the low- and high-migration limits when demes differ in sizes. Given the extreme sensitivity of fixation probability to characteristics of dispersal, we underline the importance of making explicit (and documenting empirically) the crucial ecological/ behavioral assumptions underlying migration models.

Estimating learning models from experimental data

We study the statistical properties of three estimation methods for a model of learning that is often fitted to experimental data: quadratic deviation measures without unobserved heterogeneity, and maximum likelihood withand without unobserved heterogeneity. After discussing identification issues, we show that the estimators are consistent and provide their asymptotic distribution. Using Monte Carlo simulations, we show that ignoring unobserved heterogeneity can lead to seriously biased estimations in samples which have the typical length of actual experiments. Better small sample properties areobtained if unobserved heterogeneity is introduced. That is, rather than estimating the parameters for each individual, the individual parameters are considered random variables, and the distribution of those random variables is estimated.

On heuristic and linear models of judgment: Mapping the demand for knowledge

Research on judgment and decision making presents a confusing picture of human abilities. For example, much research has emphasized the dysfunctional aspects of judgmental heuristics, and yet, other findings suggest that these can be highly effective. A further line of research has modeled judgment as resulting from as if linear models. This paper illuminates the distinctions in these approaches by providing a common analytical framework based on the central theoretical premise that understanding human performance requires specifying how characteristics of the decision rules people use interact with the demands of the tasks they face. Our work synthesizes the analytical tools of lens model research with novel methodology developed to specify the effectiveness of heuristics in different environments and allows direct comparisons between the different approaches. We illustrate with both theoretical analyses and simulations. We further link our results to the empirical literature by a meta-analysis of lens model studies and estimate both human andheuristic performance in the same tasks. Our results highlight the trade-off betweenlinear models and heuristics. Whereas the former are cognitively demanding, the latterare simple to use. However, they require knowledge and thus maps of when andwhich heuristic to employ.

The effects of physiologically plausible connectivity structure on local and global dynamics in large scale brain models.

Functionally relevant large scale brain dynamics operates within the framework imposed by anatomical connectivity and time delays due to finite transmission speeds. To gain insight on the reliability and comparability of large scale brain network simulations, we investigate the effects of variations in the anatomical connectivity. Two different sets of detailed global connectivity structures are explored, the first extracted from the CoCoMac database and rescaled to the spatial extent of the human brain, the second derived from white-matter tractography applied to diffusion spectrum imaging (DSI) for a human subject. We use the combination of graph theoretical measures of the connection matrices and numerical simulations to explicate the importance of both connectivity strength and delays in shaping dynamic behaviour. Our results demonstrate that the brain dynamics derived from the CoCoMac database are more complex and biologically more realistic than the one based on the DSI database. We propose that the reason for this difference is the absence of directed weights in the DSI connectivity matrix.

Simulations of action of DNA topoisomerases to investigate boundaries and shapes of spaces of knots.

The configuration space available to randomly cyclized polymers is divided into subspaces accessible to individual knot types. A phantom chain utilized in numerical simulations of polymers can explore all subspaces, whereas a real closed chain forming a figure-of-eight knot, for example, is confined to a subspace corresponding to this knot type only. One can conceptually compare the assembly of configuration spaces of various knot types to a complex foam where individual cells delimit the configuration space available to a given knot type. Neighboring cells in the foam harbor knots that can be converted into each other by just one intersegmental passage. Such a segment-segment passage occurring at the level of knotted configurations corresponds to a passage through the interface between neighboring cells in the foamy knot space. Using a DNA topoisomerase-inspired simulation approach we characterize here the effective interface area between neighboring knot spaces as well as the surface-to-volume ratio of individual knot spaces. These results provide a reference system required for better understanding mechanisms of action of various DNA topoisomerases.

The role of energy correlations on Coulomb suppression in ballistic conductors contacted to degenerate reservoirs

Coulomb suppression of shot noise in a ballistic diode connected to degenerate ideal contacts is analyzed in terms of the correlations taking place between current fluctuations due to carriers injected with different energies. By using Monte Carlo simulations we show that at low frequencies the origin of Coulomb suppression can be traced back to the negative correlations existing between electrons injected with an energy close to that of the potential barrier present in the diode active region and all other carriers injected with higher energies. Correlations between electrons with energy above the potential barrier with the rest of electrons are found to influence significantly the spectra at high frequency in the cutoff region.

Simulations in evolution. II. Relative fitness and the propagation of mutants.

In Neo-Darwinism, variation and natural selection are the two evolutionary mechanisms which propel biological evolution. Our previous article presented a histogram model [1] consisting in populations of individuals whose number changed under the influence of variation and/or fitness, the total population remaining constant. Individuals are classified into bins, and the content of each bin is calculated generation after generation by an Excel spreadsheet. Here, we apply the histogram model to a stable population with fitness F(1)=1.00 in which one or two fitter mutants emerge. In a first scenario, a single mutant emerged in the population whose fitness was greater than 1.00. The simulations ended when the original population was reduced to a single individual. The histogram model was validated by excellent agreement between its predictions and those of a classical continuous function (Eqn. 1) which predicts the number of generations needed for a favorable mutation to spread throughout a population. But in contrast to Eqn. 1, our histogram model is adaptable to more complex scenarios, as demonstrated here. In the second and third scenarios, the original population was present at time zero together with two mutants which differed from the original population by two higher and distinct fitness values. In the fourth scenario, the large original population was present at time zero together with one fitter mutant. After a number of generations, when the mutant offspring had multiplied, a second mutant was introduced whose fitness was even greater. The histogram model also allows Shannon entropy (SE) to be monitored continuously as the information content of the total population decreases or increases. The results of these simulations illustrate, in a graphically didactic manner, the influence of natural selection, operating through relative fitness, in the emergence and dominance of a fitter mutant.

Systematic trends in self-consistent calculations of linear quantum wires

Systematic trends in the properties of a linear split-gate heterojunction are studied by solving iteratively the Poisson and Schrödinger equations for different gate potentials and temperatures. A two-dimensional approximation is presented that is much simpler in the numerical implementation and that accurately reproduces all significant trends. In deriving this approximation, we provide a rigorous and quantitative basis for the formulation of models that assumes a two-dimensional character for the electron gas at the junction.

Quantum cavitation in liquid helium

Using a functional-integral approach, we have determined the temperature below which cavitation in liquid helium is driven by thermally assisted quantum tunneling. For both helium isotopes, we have obtained the crossover temperature in the whole range of allowed negative pressures. Our results are compatible with recent experimental results on 4He.

Wave-vector dependence of spin and density multipole excitations in quantum dots

We have employed time-dependent local-spin density-functional theory to analyze the multipole spin and charge density excitations in GaAs-AlxGa1-xAs quantum dots. The on-plane transferred momentum degree of freedom has been taken into account, and the wave-vector dependence of the excitations is discussed. In agreement with previous experiments, we have found that the energies of these modes do not depend on the transferred wave vector, although their intensities do. Comparison with a recent resonant Raman scattering experiment [C. Schüller et al., Phys. Rev. Lett. 80, 2673 (1998)] is made. This allows us to identify the angular momentum of several of the observed modes as well as to reproduce their energies