Intrinsic optical bistability of thin films of linear molecular aggregates: The one-exciton approximation

We perform a theoretical study of the nonlinear optical response of an ultrathin film consisting of oriented linear aggregates. A single aggregate is described by a Frenkel exciton Hamiltonian with uncorrelated on-site disorder. The exciton wave functions and energies are found exactly by numerically diagonalizing the Hamiltonian. The principal restriction we impose is that only the optical transitions between the ground state and optically dominant states of the one-exciton manifold are considered, whereas transitions to other states, including those of higher exciton manifolds, are neglected. The optical dynamics of the system is treated within the framework of truncated optical Maxwell-Bloch equations in which the electric polarization is calculated by using a joint distribution of the transition frequency and the transition dipole moment of the optically dominant states. This function contains all the statistical information about these two quantities that govern the optical response, and is obtained numerically by sampling many disorder realizations. We derive a steady-state equation that establishes a relationship between the output and input intensities of the electric field and show that within a certain range of the parameter space this equation exhibits a three-valued solution for the output field. A time-domain analysis is employed to investigate the stability of different branches of the three-valued solutions and to get insight into switching times. We discuss the possibility to experimentally verify the bistable behavior.Comment: 13 two-column pages, 8 figures, accepted to the Journal of Chemical Physic

A review of applications of the Bayes factor in psychological research

The last 25 years have shown a steady increase in attention for the Bayes factor as a tool for hypothesis evaluation and model selection. The present review highlights the potential of the Bayes factor in psychological research. We discuss six types of applications: Bayesian evaluation of point null, interval, and informative hypotheses, Bayesian evidence synthesis, Bayesian variable selection and model averaging, and Bayesian evaluation of cognitive models. We elaborate what each application entails, give illustrative examples, and provide an overview of key references and software with links to other applications. The paper is concluded with a discussion of the opportunities and pitfalls of Bayes factor applications and a sketch of corresponding future research lines

The weight of representing the body: addressing the potentially indefinite number of body representations in healthy individuals

There is little consensus about the characteristics and number of body representations in the brain. In the present paper, we examine the main problems that are encountered when trying to dissociate multiple body representations in healthy individuals with the use of bodily illusions. Traditionally, task-dependent bodily illusion effects have been taken as evidence for dissociable underlying body representations. Although this reasoning holds well when the dissociation is made between different types of tasks that are closely linked to different body representations, it becomes problematic when found within the same response task (i.e., within the same type of representation). Hence, this experimental approach to investigating body representations runs the risk of identifying as many different body representations as there are significantly different experimental outputs. Here, we discuss and illustrate a different approach to this pluralism by shifting the focus towards investigating task-dependency of illusion outputs in combination with the type of multisensory input. Finally, we present two examples of behavioural bodily illusion experiments and apply Bayesian model selection to illustrate how this different approach of dissociating and classifying multiple body representations can be applied

Mixtures of peaked power Batschelet distributions for circular data with application to saccade directions

Circular data are encountered throughout a variety of scientific disciplines, such as in eye movement research as the direction of saccades. Motivated by such applications, mixtures of peaked circular distributions are developed. The peaked distributions are a novel family of Batschelet-type distributions, where the shape of the distribution is warped by means of a transformation function. Because the Inverse Batschelet distribution features an implicit inverse that is not computationally feasible for large or complex data, an alternative called the Power Batschelet distribution is introduced. This distribution is easy to compute and mimics the behavior of the Inverse Batschelet distribution. Inference is performed in both the frequentist framework, through Expectation–Maximization (EM) and the bootstrap, and the Bayesian framework, through MCMC. All parameters can be fixed, which may be done by assumption to reduce the number of parameters. Model comparison can be performed through information criteria or through bridge sampling in the Bayesian framework, which allows performing a wealth of hypothesis tests through the Bayes factor. An R package, flexcircmix, is available to perform these analyses