Learning why things change: The Difference-Based Causality Learner

In this paper, we present the Difference-Based Causality Learner (DBCL), an algorithm for learning a class of discrete-time dynamic models that represents all causation across time by means of difference equations driving change in a system. We motivate this representation with real-world mechanical systems and prove DBCL's correctness for learning structure from time series data, an endeavour that is complicated by the existence of latent derivatives that have to be detected. We also prove that, under common assumptions for causal discovery, DBCL will identify the presence or absence of feedback loops, making the model more useful for predicting the effects of manipulating variables when the system is in equilibrium. We argue analytically and show empirically the advantages of DBCL over vector autoregression (VAR) and Granger causality models as well as modified forms of Bayesian and constraintbased structure discovery algorithms. Finally, we show that our algorithm can discover causal directions of alpha rhythms in human brains from EEG data

A new efficient hyperelastic finite element model for graphene and its application to carbon nanotubes and nanocones

A new hyperelastic material model is proposed for graphene-based structures, such as graphene, carbon nanotubes (CNTs) and carbon nanocones (CNC). The proposed model is based on a set of invariants obtained from the right surface Cauchy-Green strain tensor and a structural tensor. The model is fully nonlinear and can simulate buckling and postbuckling behavior. It is calibrated from existing quantum data. It is implemented within a rotation-free isogeometric shell formulation. The speedup of the model is 1.5 relative to the finite element model of Ghaffari et al. [1], which is based on the logarithmic strain formulation of Kumar and Parks [2]. The material behavior is verified by testing uniaxial tension and pure shear. The performance of the material model is illustrated by several numerical examples. The examples include bending, twisting, and wall contact of CNTs and CNCs. The wall contact is modeled with a coarse grained contact model based on the Lennard-Jones potential. The buckling and post-buckling behavior is captured in the examples. The results are compared with reference results from the literature and there is good agreement

Effects of transcranial direct current stimulation over left dorsolateral pFC on the attentional blink depend on individual baseline performance

Selection mechanisms that dynamically gate only relevant perceptual information for further processing and sustained representation in working memory are critical for goal-directed behavior. We examined whether this gating process can be modulated by anodal transcranial direct current stimulation (tDCS) over left dorsolateral pFC (DLPFC)a region known to play a key role in working memory and conscious access. Specifically, we examined the effects of tDCS on the magnitude of the so-called attentional blink (AB), a deficit in identifying the second of two targets presented in rapid succession. Thirty-four participants performed a standard AB task before (baseline), during, and after 20 min of 1-mA anodal and cathodal tDCS in two separate sessions. On the basis of previous reports linking individual differences in AB magnitude to individual differences in DLPFC activity and on suggestions that effects of tDCS depend on baseline brain activity levels, we hypothesized that anodal tDCS over left DLPFC would modulate the magnitude of the AB as a function of individual baseline AB magnitude. Indeed, individual differences analyses revealed that anodal tDCS decreased the AB in participants with a large baseline AB but increased the AB in participants with a small baseline AB. This effect was only observed during (but not after) stimulation, was not found for cathodal tDCS, and could not be explained by regression to the mean. Notably, the effects of tDCS were not apparent at the group level, highlighting the importance of taking individual variability in performance into account when evaluating the effectiveness of tDCS. These findings support the idea that left DLPFC plays a critical role in the AB and in conscious access more generally. They are also in line with the notion that there is an optimal level of prefrontal activity for cognitive function, with both too little and too much activity hurting performance

Approximate computations with modular curves

This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations with modular curves and their Jacobians. These approximations are done in polynomial time in the dimension and the required number of significant digits. We explain the main ideas of how the approximations are done, illustrating them with examples, and we sketch some applications in number theory