Mössbauer rotor experiment as new proof of general relativity: Rigorous computation of the additional effect of clock synchronization

We received an Honorable Mention at the Gravity Research Foundation 2018 Awards for Essays on Gravitation by showing that a correct general relativistic interpretation of the Mössbauer rotor experiment represents a new, strong and independent proof of Einstein’s general theory of relativity (GTR). Here, we correct a mistake which was present in our previous computations on this important issue by deriving a rigorous computation of the additional effect of clock synchronization. Finally, we show that some recent criticisms on our general relativistic approach to the Mössbauer rotor experiment are incorrect, by ultimately confirming our important result.

Default mode contributions to automated information processing

Concurrent with mental processes that require rigorous computation and control, a series of automated decisions and actions govern our daily lives, providing efficient and adaptive responses to environmental demands. Using a cognitive flexibility task, we show that a set of brain regions collectively known as the default mode network plays a crucial role in such “autopilot” behavior, i.e., when rapidly selecting appropriate responses under predictable behavioral contexts. While applying learned rules, the default mode network shows both greater activity and connectivity. Furthermore, functional interactions between this network and hippocampal and parahippocampal areas as well as primary visual cortex correlate with the speed of accurate responses. These findings indicate a memory-based “autopilot role” for the default mode network, which may have important implications for our current understanding of healthy and adaptive brain processing.

Rigorous computation of invariant measures and fractal dimension for maps with contracting fibers: 2D Lorenz-like maps

We consider a class of maps from the unit square to itself preserving a contracting foliation and inducing a one-dimensional map having an absolutely continuous invariant measure. We show how the physical measure of those systems can be rigorously approximated with an explicitly given bound on the error with respect to the Wasserstein distance. We present a rigorous implementation of our algorithm using interval arithmetics, and the result of the computation on a non-trivial example of a Lorenz-like two-dimensional map and its attractor, obtaining a statement on its local dimension.

Bounds and algorithms for the -Bessel function of imaginary order

Using the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function${K}_{ir} (x)$of imaginary order and its first two derivatives with respect to the order. We also prove precise asymptotic bounds on more general (mixed) derivatives without working out numerical implied constants. Moreover, we present an absolutely and rapidly convergent series for the computation of${K}_{ir} (x)$and its derivatives, as well as a formula based on Fourier interpolation for computing with many values of$r$. Finally, we have implemented a subset of these features in a software library for fast and rigorous computation of${K}_{ir} (x)$.