Kantorovich-Rubinstein Distance and Barycenter for Finitely Supported Measures: Foundations and Algorithms

The purpose of this paper is to provide a systematic discussion of a generalized barycenter based on a variant of unbalanced optimal transport (UOT) that defines a distance between general non-negative, finitely supported measures by allowing for mass creation and destruction modeled by some cost parameter. They are denoted as Kantorovich–Rubinstein (KR) barycenter and distance. In particular, we detail the influence of the cost parameter to structural properties of the KR barycenter and the KR distance. For the latter we highlight a closed form solution on ultra-metric trees. The support of such KR barycenters of finitely supported measures turns out to be finite in general and its structure to be explicitly specified by the support of the input measures. Additionally, we prove the existence of sparse KR barycenters and discuss potential computational approaches. The performance of the KR barycenter is compared to the OT barycenter on a multitude of synthetic datasets. We also consider barycenters based on the recently introduced Gaussian Hellinger–Kantorovich and Wasserstein–Fisher–Rao distances

Characterization of fluids involved in the Gneiss-Charnockite transformation in Southern Kerala (India)

The characterization of fluids involved in the gneiss-charnockite transformation in southern Kerala are discussed. Using a variety of techniques, including microthermometry, Raman laser probe analysis, and mass spectrometry, it was concluded that the CO2-rich, N2-bearing metamorphic fluids in these rocks were internally-derived rather than having been introduced by CO2-streaming

Appearance of the Single Gyroid Network Phase in Nuclear Pasta Matter

Nuclear matter under the conditions of a supernova explosion unfolds into a rich variety of spatially structured phases, called nuclear pasta. We investigate the role of periodic network-like structures with negatively curved interfaces in nuclear pasta structures, by static and dynamic Hartree-Fock simulations in periodic lattices. As the most prominent result, we identify for the first time the {\it single gyroid} network structure of cubic chiral $I4_123$ symmetry, a well known configuration in nanostructured soft-matter systems, both as a dynamical state and as a cooled static solution. Single gyroid structures form spontaneously in the course of the dynamical simulations. Most of them are isomeric states. The very small energy differences to the ground state indicate its relevance for structures in nuclear pasta.Comment: 7 pages, 4 figure

Transcutaneous Vagus Nerve Stimulation May Enhance Only Specific Aspects of the Core Executive Functions. A Randomized Crossover Trial

Background: Individuals are able to perform goal-directed behaviors thanks to executive functions. According to the neurovisceral integration model, executive functions are upregulated by brain areas such as the prefrontal and cingulate cortices, which are also crucially involved in controlling cardiac vagal activity. An array of neuroimaging studies already showed that these same brain areas are activated by transcutaneous vagus nerve stimulation (tVNS). Despite evidence towards effects of tVNS on specific executive functions such as inhibitory control, there have been no studies investigating what type of inhibition is improved by tVNS by systematically addressing them within the same experiment. Furthermore, the effect of tVNS on another core executive function, cognitive flexibility, has not yet been investigated. Objective: We investigated the effects of tVNS on core executive functions such as inhibitory control and cognitive flexibility. Methods: Thirty-two participants (nine women, Mage = 23.17) took part in this study. Vagally-mediated heart rate variability parameters (root mean square of successive differences, RMSSD, and high frequency, HF) were measured while participants performed four different cognitive tasks that mainly rely on different aspects of both the aforementioned executive functions. Results: Despite clear conflict effects in the four tasks, only performance on the task used to measure set-shifting paradigm was improved by tVNS, with switch costs being lower during tVNS than during sham stimulation. Furthermore, HF increased during each of the cognitive flexibility tasks, although HF during tVNS did not differ from HF during sham stimulation. Conclusion: The results indicate for the first time a) that tVNS can increase cognitive flexibility in a set-shifting paradigm, and b) that tVNS may exert a stronger effect on cognitive flexibility than inhibition. The present study provides only partial evidence for the neurovisceral integration model. Future studies should address further paradigms that demand cognitive flexibility, thus investigating this new hypothesis on the specificity of the tVNS effects on cognitive flexibility

Transcutaneous vagus nerve stimulation via tragus or cymba conchae: Are its psychophysiological effects dependent on the stimulation area?

Efforts in optimizing transcutaneous vagus nerve stimulation (tVNS) are crucial to further develop its potential in improving cognitive and autonomic regulation. The present study focused on this topic. The aim was to compare for the first time the main stimulation areas of the ear currently used in studies with tVNS, taking cognitive as well as neurophysiological effects into account. The main areas to be compared with one another were tragus, cymba conchae, and earlobe (sham) stimulation. Post-error slowing, which has already been shown to be influenced by tVNS, was used to investigate the cognitive effects of tVNS when applied on the different auricular areas. On the neurophysiological level, we measured pupillary responses as an index of norepinephrine activity during post-error slowing, and cardiac vagal activity to investigate the activation of neural pathways involved in post-error slowing. Stimulation of different auricular areas led to no differences in post-error slowing and in pupillary responses. However, the neurological processes involved in post-error slowing could be observed, since norepinephrine activity increased after committing an error. Further, there was an increase in cardiac vagal activity over the test period that was independent of the stimulation areas. The results suggest that tVNS targeting the ear might have a non-specific effect on the processing of error commission, on pupillary responses, and on cardiac vagal activity. We conclude that it is necessary to consider alternatives for sham conditions other than electrical earlobe stimulation. [Abstract copyright: Copyright © 2021 Elsevier B.V. All rights reserved.

Superconducting Superstructure for the TESLA Collider

We discuss the new layout of a cavity chain (superstructure) allowing, we hope, significant cost reduction of the RF system of both linacs of the TESLA linear collider. The proposed scheme increases the fill factor and thus makes an effective gradient of an accelerator higher. We present mainly computations we have performed up to now and which encouraged us to order the copper model of the scheme, still keeping in mind that experiments with a beam will be necessary to prove if the proposed solution can be used for the acceleration.Comment: 11 page