Promotion and growth diagrams for fans of Dyck paths and vacillating tableaux

We construct an injection from the set of $r$-fans of Dyck paths (resp. vacillation tableaux) of length $n$ into the set of chord diagrams on $[n]$ that intertwines promotion and rotation. This is done in two different ways, namely as fillings of promotion--evacuation diagrams and in terms of Fomin growth diagrams. Our analysis uses the fact that $r$-fans of Dyck paths and vacillating tableaux can be viewed as highest weight elements of weight zero in crystals of type $B_r$ and $C_r$, respectively, which in turn can be analyzed using virtual crystals. On the level of Fomin growth diagrams, the virtualization process corresponds to Krattenthaler's blow up construction. One of the motivations for finding rotation invariant diagrammatic bases such as chord diagrams is the cyclic sieving phenomenon. Indeed, we give a cyclic sieving phenomenon on $r$-fans of Dyck paths and vacillating tableaux using the promotion action.Comment: 40 pages, 13 figure

A single polyploidization event at the origin of the tetraploid genome of Coffea arabica is responsible for the extremely low genetic variation in wild and cultivated germplasm

The genome of the allotetraploid species Coffea arabica L. was sequenced to assemble independently the two component subgenomes (putatively deriving from C. canephora and C. eugenioides) and to perform a genome-wide analysis of the genetic diversity in cultivated coffee germplasm and in wild populations growing in the center of origin of the species. We assembled a total length of 1.536 Gbp, 444 Mb and 527 Mb of which were assigned to the canephora and eugenioides subgenomes, respectively, and predicted 46,562 gene models, 21,254 and 22,888 of which were assigned to the canephora and to the eugeniodes subgenome, respectively. Through a genome-wide SNP genotyping of 736 C. arabica accessions, we analyzed the genetic diversity in the species and its relationship with geographic distribution and historical records. We observed a weak population structure due to low-frequency derived alleles and highly negative values of Taijma's D, suggesting a recent and severe bottleneck, most likely resulting from a single event of polyploidization, not only for the cultivated germplasm but also for the entire species. This conclusion is strongly supported by forward simulations of mutation accumulation. However, PCA revealed a cline of genetic diversity reflecting a west-to-east geographical distribution from the center of origin in East Africa to the Arabian Peninsula. The extremely low levels of variation observed in the species, as a consequence of the polyploidization event, make the exploitation of diversity within the species for breeding purposes less interesting than in most crop species and stress the need for introgression of new variability from the diploid progenitors

ECCD-induced sawtooth crashes at W7-X

The optimised superconducting stellarator W7-X generates its rotational transform by means of external coils, therefore no toroidal current is necessary for plasma confinement. Electron cyclotron current drive experiments were conducted for strikeline control and safe divertor operation. During current drive experiments periodic and repetitive crashes of the central electron temperature, similar to sawtooth crashes in tokamaks, were detected. Measurements from soft x-ray tomography and electron cyclotron emission show that the crashes are preceded by weak oscillating precursors and a displacement of the plasma core, consistent with a (m, n)=(1, 1) mode. The displacement occurs within 100μs, followed by expulsion and redistribution of the core into the external part of the plasma. Two types of crashes, with different frequencies and amplitudes are detected in the experimental program. For these non-stationary parameters a strong dependence on the toroidal current is found. A 1-D heuristic model for current diffusion is proposed as a first step to explain the characteristic crash time. Initial results show that the modelled current diffusion timescale is consistent with the initial crash frequency and that the toroidal current rise shifts the position where the instability is triggered, resulting in larger crash amplitudes

Describing complex interactions of social-ecological systems for tipping point assessments: an analytical framework

Humans play an interconnecting role in social-ecological systems (SES), they are part of these systems and act as agents of their destruction and regulation. This study aims to provide an analytical framework, which combines the concept of SES with the concept of tipping dynamics. As a result, we propose an analytical framework describing relevant dynamics and feedbacks within SES based on two matrixes: the “tipping matrix” and the “cross-impact matrix.” We take the Southwestern Amazon as an example for tropical regions at large and apply the proposed analytical framework to identify key underlying sub-systems within the study region: the soil ecosystem, the household livelihood system, the regional social system, and the regional climate system, which are interconnected through a network of feedbacks. We consider these sub-systems as tipping elements (TE), which when put under stress, can cross a tipping point (TP), resulting in a qualitative and potentially irreversible change of the respective TE. By systematically assessing linkages and feedbacks within and between TEs, our proposed analytical framework can provide an entry point for empirically assessing tipping point dynamics such as “tipping cascades,” which means that the crossing of a TP in one TE may force the tipping of another TE. Policy implications: The proposed joint description of the structure and dynamics within and across SES in respect to characteristics of tipping point dynamics promotes a better understanding of human-nature interactions and critical linkages within regional SES that may be used for effectively informing and directing empirical tipping point assessments, monitoring or intervention purposes. Thereby, the framework can inform policy-making for enhancing the resilience of regional SES

Describing complex interactions of social-ecological systems for tipping point assessments: an analytical framework

Humans play an interconnecting role in social-ecological systems (SES), they are part of these systems and act as agents of their destruction and regulation. This study aims to provide an analytical framework, which combines the concept of SES with the concept of tipping dynamics. As a result, we propose an analytical framework describing relevant dynamics and feedbacks within SES based on two matrixes: the “tipping matrix” and the “cross-impact matrix.” We take the Southwestern Amazon as an example for tropical regions at large and apply the proposed analytical framework to identify key underlying sub-systems within the study region: the soil ecosystem, the household livelihood system, the regional social system, and the regional climate system, which are interconnected through a network of feedbacks. We consider these sub-systems as tipping elements (TE), which when put under stress, can cross a tipping point (TP), resulting in a qualitative and potentially irreversible change of the respective TE. By systematically assessing linkages and feedbacks within and between TEs, our proposed analytical framework can provide an entry point for empirically assessing tipping point dynamics such as “tipping cascades,” which means that the crossing of a TP in one TE may force the tipping of another TE. Policy implications: The proposed joint description of the structure and dynamics within and across SES in respect to characteristics of tipping point dynamics promotes a better understanding of human-nature interactions and critical linkages within regional SES that may be used for effectively informing and directing empirical tipping point assessments, monitoring or intervention purposes. Thereby, the framework can inform policy-making for enhancing the resilience of regional SES