First steps in synthetic guarded domain theory: step-indexing in the topos of trees

We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive definitions of terms, predicates, and types. In particular, we show how to solve recursive type equations involving dependent types. We propose that the internal logic of S provides the right setting for the synthetic construction of abstract versions of step-indexed models of programming languages and program logics. As an example, we show how to construct a model of a programming language with higher-order store and recursive types entirely inside the internal logic of S. Moreover, we give an axiomatic categorical treatment of models of synthetic guarded domain theory and prove that, for any complete Heyting algebra A with a well-founded basis, the topos of sheaves over A forms a model of synthetic guarded domain theory, generalizing the results for S

Fluid-dynamical and microscopic description of traffic flow: a data-driven comparison

A lot of work has been done to compare traffic flow models with reality; so far, this has been done separately for microscopic as well as for fluid-dynamical models of traffic flow. This paper compares directly the performance of both types of models to real data. The results indicate, that microscopic models on average seem to have a tiny advantage over fluid-dynamical models, however one may admit that for most applications the differences between the two are small. Furthermore, the relaxation time of the fluid-dynamical models turns out to be fairly small, of the order of two seconds, and are comparable with the results for the microscopic models. This indicates that the second order terms are weak, however, the calibration results indicate that the speed equation is in fact important and improves the calibration results of the models

Other-regarding behaviour: Testing guilt- and reciprocity-based models

We analyse two types of belief-dependant models of social preferences: guilt aversion and reciprocity. In particular, we test the relevance of their input variables (second-order beliefs and general dispositions for guilt/reciprocity). The data confirm the predictions of belief-dependant models. Both second-order beliefs and a participant's sensitivity to guilt/reciprocity are relevant for the decisions taken. Second-order beliefs appear to have an inverse U-shaped effect on the extent of kind behaviour.social preferences, other-regarding behaviour, belief-dependent models, experiments, trust game, guilt aversion, beliefs, psychological game theory, emotions, reciprocity

mgm: Estimating Time-Varying Mixed Graphical Models in High-Dimensional Data

We present the R-package mgm for the estimation of k-order Mixed Graphical Models (MGMs) and mixed Vector Autoregressive (mVAR) models in high-dimensional data. These are a useful extensions of graphical models for only one variable type, since data sets consisting of mixed types of variables (continuous, count, categorical) are ubiquitous. In addition, we allow to relax the stationarity assumption of both models by introducing time-varying versions MGMs and mVAR models based on a kernel weighting approach. Time-varying models offer a rich description of temporally evolving systems and allow to identify external influences on the model structure such as the impact of interventions. We provide the background of all implemented methods and provide fully reproducible examples that illustrate how to use the package