Prediction of Sunspot and Plage Coverage for Solar Cycle 25

Solar variability occurs over a broad range of spatial and temporal scales, from the Sun’s brightening over its lifetime to the fluctuations commonly associated with magnetic activity over minutes to years. The latter activity includes most prominently the 11 yr sunspot solar cycle and its modulations. Space weather events, in the form of solar flares, solar energetic particles, coronal mass ejections, and geomagnetic storms, have long been known to approximately follow the solar cycle occurring more frequently at solar maximum than solar minimum. These events can significantly impact our advanced technologies and critical infrastructures, making the prediction for the strength of future solar cycles particularly important. Several methods have been proposed to predict the strength of the next solar cycle, cycle 25, with results that are generally not always consistent. Most of these methods are based on the international sunspot number time series, or other indicators of solar activity. We present here a new approach that uses more than 100 yr of measured fractional areas of the visible solar disk covered by sunspots and plages and an empirical relationship for each of these two indices of solar activity in even–odd cycles. We anticipate that cycle 25 will peak in 2024 and will last for about 12 yr, slightly longer than cycle 24. We also found that, in terms of sunspot and plage areas coverage, the amplitude of cycle 25 will be substantially similar or slightly higher than cycle 24.

A Note on Stability for Maximal F-Free Graphs

Popielarz, Sahasrabuddhe and Snyder in 2018 proved that maximal $$K_{r+1}$$ K r + 1 -free graphs with $$(1-\frac{1}{r})\frac{n^2}{2}-o(n^{\frac{r+1}{r}})$$ ( 1 - 1 r ) n 2 2 - o ( n r + 1 r ) edges contain a complete r-partite subgraph on $$n-o(n)$$ n - o ( n ) vertices. This was very recently extended to odd cycles in place of $$K_3$$ K 3 by Wang, Wang, Yang and Yuan. We further extend it to some other 3-chromatic graphs, and obtain some other stability results along the way.

On Cycles, Attackers and Supporters --- A Contribution to The Investigation of Dynamics in Abstract Argumentation

argumentation as defined by Dung in his seminal 1995 paper is by now a major research area in knowledge representation and reasoning. Dynamics of abstract argumentation frameworks (AFs) as well as syntactical consequences of semantical facts of them are the central issues of this paper. The first main part is engaged with the systematical study of the influence of attackers and supporters regarding the acceptability status of whole sets and/or single arguments. In particular, we investigate the impact of addition or removal of arguments, a line of research that has been around for more than a decade. Apart from entirely new results, we revisit, generalize and sum up similar results from the literature. To gain a comprehensive formal and intuitive understanding of the behavior of AFs we put special effort in comparing different kind of semantics. We concentrate on classical admissibility-based semantics and also give pointers to semantics based on naivity and weak admissibility, a recently introduced mediating approach. In the second main part we show how to infer syntactical information from semantical one. For instance, it is well-known that if a finite AF possesses no stable extension, then it has to contain an odd-cycle. In this paper, we even present a characterization of this issue. Moreover, we show that the change of the number of extensions if adding or removing an argument allows to conclude the existence of certain even or odd cycles in the considered AF without having further information.