Computational geometry.

We report the evolution of magnetic field and its energy in NOAA active region 11158 over 5 days based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Fast flux emergence and strong shearing motion led to a quadrupolar sunspot complex that produced several major eruptions, including the first X-class flare of Solar Cycle 24. Extrapolated non-linear force-free coronal fields show substantial electric current and free energy increase during early flux emergence near a low-lying sigmoidal filament with sheared kilogauss field in the filament channel. The computed magnetic free energy reaches a maximum of ∼2.6 × 10 32 erg, about 50% of which is stored below 6 Mm. It decreases by ∼0.3 × 10 32 erg within 1 hour of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, the photospheric field changed rapidly: horizontal field was enhanced by 28% in the core region, becoming more inclined and more parallel to the polarity inversion line. Such change is consistent with the conjectured coronal field “implosion”, and is supported by the coronal loop retraction observed by the Atmospheric Imaging Assembly (AIA). The extrapolated field becomes more “compact” after the flare, with shorter loops in the core region, probably because of reconnection. The coronal field becomes slightly more sheared in the lowest layer, relaxes faster with height, and is overall less energetic.

Evolution of Magnetic Field and Energy in A Major Eruptive Active Region Based on SDO/HMI Observation

Thiacalixarenes, a subclass of "third generation" calixarenes, exhibit many interesting features such as enlarged ring size, facile chemical modification, and metal complexation due to the presence of bridging sulfur atoms. The thiacalixarene scaffold is a unique host with vast possibilities for functionalization not only at the upper and lower rim but also at the bridging sulfide groups. Modified thiacalixarenes have been used for many applications such as the detection and separation of biologically important cations, anions, and bio-analytes, mimicking molecular logic gates and devices, and synthesis of self-assembled coordination cages, multinuclear complexes, magnetic materials and luminescent materials. This review article summarizes recent developments in the derivatization methods of thiacalixarenes and their utilization in various applications.

Recent developments of thiacalixarene based molecular motifs

Recently, cloud point extraction (CPE) has been an attractive subject as an alternative to liquid-liquid extraction. The technique is based on the property of most non-ionic surfactants in aqueous solutions to form micelles and become turbid when heated to the cloud point temperature. This review covers a selection of the literature published on applications of CPE in determination of metal ions over the period between 2004 and 2008.

Separation and preconcentration by a cloud point extraction procedure for determination of metals: an overview.

Applied Methods of the Theory of Random Functions. By A. A. Sveshnikov. Pp. ix, 321. 1966. (Pergamon.)

Magnetic ﬁelds are responsible for a multitude of Solar phenomena, including such destructive events as solar ﬂares and coronal mass ejections, with the number of such events rising as we approach the peak of the 11-year solar cycle, in approximately 2025. High-precision spectropolarimetric observations are necessary to understand the variability of the Sun. The ﬁeld of quantitative inference of magnetic ﬁeld vectors and related solar atmospheric parameters from such observations has long been investigated. In recent years, very sophisticated codes for spectropolarimetric observations have been developed. Over the past two decades, neural networks have been shown to be a fast and accurate alternative to classic inversion technique methods. However, most of these codes can be used to obtain point estimates of the parameters, so ambiguities, the degenera-cies, and the uncertainties of each parameter remain uncovered. In this paper, we provide end-to-end inversion codes based on the simple Milne-Eddington model of the stellar atmosphere and deep neural networks to both parameter estimation and their uncertainty intervals. The proposed framework is designed in such a way that it can be expanded and adapted to other atmospheric models or combinations of them. Additional information can also be incorporated di-rectly into the model. It is demonstrated that the proposed architecture provides high accuracy of results, including a reliable uncertainty estimation, even in the multidimensional case. The models are tested using simulation and real data samples.

Stokes inversion techniques with neural networks: analysis of uncertainty in parameter estimation

Abstract In the current paper, we investigate topological invariants, calculated by HMI LOS magnetograms as complexity descriptors of solar magnetic fields. We compared them with the physical parameters provided by the Space-weather HMI Active Region Patches (SHARP). We have repeated forecasting experiment of Stanford Solar Observatories Group with the same positive and negative active region patches database, but replace SHARP parameters with topological invariants of corresponding LOS magnetograms. The classification results turned out practically identical to those obtained by the Stanford Solar Observatory group. This means that using LOS magnetograms retains enough complexity for magnetic field description.

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Comparison of Predictive Efficiency of Topological Descriptors and SHARP in Solar Flares Forecasting

Detection of the deterministic component from noised time series is a common procedure in the solar–terrestrial coupling problem when climate is modeled, solar activity is analyzed, or a signal associated with helium is extracted. Such series are mostly generated by the superposition of different processes for which the concept of a noise component cannot be determined formally. A method based on the combination of time-series topological embedding in Euclidean space and the identification of a persistent cycle by homology theory methods is proposed. The method application is demonstrated based on actual data.

Topological diagnostics of the cyclic component of the time series associated with helium

The Maunder butterfly pattern is the most complete spatial-temporal representation of observed changes in solar activity in the 11-year cycle over a period of 12–24 cycle. The well-known empirical relation is used to transform Greenwich sunspot areas into magnetic flux, and the distances between the butterfly wings are then calculated with the Fisher–Rao metric. We found that the similarities or differences in the patterns of the individual butterfly wings in this metric are approximately the same for each hemisphere. The wings were the closest for a sequence of strong cycles, while there is a tendency for a series of weak cycles to form cycles in pairs with the implementation of an analog of the Gnevyshev–Olya rule.

I. S. Knyazeva

Papers

Stokes inversion techniques with neural networks: analysis of uncertainty in parameter estimation

Comparison of Predictive Efficiency of Topological Descriptors and SHARP in Solar Flares Forecasting

Topological diagnostics of the cyclic component of the time series associated with helium

Features of Spatiotemporal Clustering in a Maunder Butterfly Diagram

Modelling graph dynamics of flaring active regions using SDO/HMI data