Estimating a Signal In the Presence of an Unknown Background

We describe a method for fitting distributions to data which only requires knowledge of the parametric form of either the signal or the background but not both. The unknown distribution is fit using a non-parametric kernel density estimator. The method returns parameter estimates as well as errors on those estimates. Simulation studies show that these estimates are unbiased and that the errors are correct

Coupled forward-backward trajectory approach for non-equilibrium electron-ion dynamics

We introduce a simple ansatz for the wavefunction of a many-body system based on coupled forward and backward-propagating semiclassical trajectories. This method is primarily aimed at, but not limited to, treating nonequilibrium dynamics in electron-phonon systems. The time-evolution of the system is obtained from the Euler-Lagrange variational principle, and we show that this ansatz yields Ehrenfest mean field theory in the limit that the forward and backward trajectories are orthogonal, and in the limit that they coalesce. We investigate accuracy and performance of this method by simulating electronic relaxation in the spin-boson model and the Holstein model. Although this method involves only pairs of semiclassical trajectories, it shows a substantial improvement over mean field theory, capturing quantum coherence of nuclear dynamics as well as electron-nuclear correlations. This improvement is particularly evident in nonadiabatic systems, where the accuracy of this coupled trajectory method extends well beyond the perturbative electron-phonon coupling regime. This approach thus provides an attractive route forward to the ab-initio description of relaxation processes, such as thermalization, in condensed phase systems

Distributional impacts of carbon taxation and revenue recycling: a behavioural microsimulation. ESRI WP626, June 2019

Carbon taxation is a regressive policy which contributes to public opposition towards same. We employ the Exact Affine Stone Index demand system to examine the extent to which carbon taxation in Ireland reduces emissions, as well as its distributional impacts. The Engel curves for various commodity groupings are found to be non-linear, which renders the particular demand system we have chosen more suitable than other methods found in the extant literature. We find that a carbon tax increase can decrease emissions, but is indeed regressive. Recycling the revenues to households mitigates these regressive effects. A targeted allocation that directs the revenues towards less affluent households is found to reduce inequality more than flat allocation that divides the revenues equally amongst all households; however both methods are capable of mitigating the regressive effects of the tax increase

Altruistic behavior pays, or the importance of fluctuations in evolutionary game theory

Human behavior is one of the main problems for evolution, as it is often the case that human actions are disadvantageous for the self and advantageous for other people. Behind this puzzle are our beliefs about rational behavior, based on game theory. Here we show that by going beyond the standard game-theoretical conventions, apparently altruistic behavior can be understood as self-interested. We discuss in detail an example related to the so called Ultimatum game and illustrate the appearance of altruistic behavior induced by fluctuations. In addition, we claim that in general settings, fluctuations play a very relevant role, and we support this claim by considering a completely different example, namely the Stag-Hunt game.Comment: For the proceedings of the 8th Granada Seminar on Computational Physics (AIP Proceedeings Series

Time and energy-resolved two photon-photoemission of the Cu(100) and Cu(111) metal surfaces

We present calculations on energy- and time-resolved two-photon photoemission spectra of images states in Cu(100) and Cu(111) surfaces. The surface is modeled by a 1D effective potential and the states are propagated within a real-space, real-time method. To obtain the energy resolved spectra we employ a geometrical approach based on a subdivision of space into two regions. We treat electronic inelastic effects by taking into account the scattering rates calculated within a GW scheme. To get further insight into the decaying mechanism we have also studied the effect of the variation of the classical Hartree potential during the excitation. This effect turns out to be small.Comment: 11 pages, 7 figure

Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics

Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.Comment: Review, 48 pages, 26 figure