arthur schopenhauer, in four aspects root of the principle of sufficient reason, criticized kant’s interpretation of causality, which is written in the second analogy contained in the section of principles of pure understanding. these criticisms express themselves along three main axes. by considering these criticisms, this article seeks to defend kant’s account and to show that schopenhauer di...

To gain insight into complex systems it is a key challenge to infer nonlinear causal directional relations from observational time-series data. Specifically, estimating relationships between interacting components in large with only short recordings over few temporal observations remains an important, yet unresolved problem. Here, we introduce large-scale Nonlinear Granger Causality (lsNGC) app...

Introduction: Ensuring an adequate Depth of Anesthesia (DOA) during surgery is essential for anesthesiologists. Since the effect of anesthetic drugs is on the central nervous system, brain signals such as Electroencephalogram (EEG) can be used for DOA estimation. Anesthesia can interfere among brain regions, so the relationship among different areas can be a key factor in the anesthetic process...

In this paper we discuss one dimensional scattering and inverse scattering for the Helmholtz equation on the half line from the point of view of the layer stripping. By full or nonlinear scattering, we mean the transformation between the index of refraction (actually half of its logarithmic derivative) and the reflection coefficient. We refer to this mapping as nonlinear scattering, because the...

BACKGROUND Quantifying associations in neuroscience (and many other scientific disciplines) is often challenged by high-dimensionality, nonlinearity and noisy observations. Many classic methods have either poor power or poor scalability on data sets of the same or different scales such as genetical, physiological and image data. NEW METHOD Based on the framework of reproducing kernel Hilbert ...

Linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear effects can be of comparable magnitude to the linear ones and still be highly suppressed at low energies. This can offer alternative approaches to quantum gravity and to the...