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Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity
(Springer Nature, 2024-08-31) Stodola, Marek; Hrdina, Jaroslav
Using the classification of Clifford algebras and Bott periodicity, we show how higher geometric algebras can be realized as matrices over classical low dimensional geometric algebras. This matrix representation allows us to use standard geometric algebra software packages more easily. As an example, we express the geometric algebra for conics (GAC) as a matrix over the Compass ruler algebra (CRA).
A Novel Technique for the Extraction of Dynamic Events in Extreme Ultraviolet Solar Images
(The American Astronomical Society, 2024-11-07) Kalenská, Petra; Rajmic, Pavel; Gebrtová, Karolína; Druckmüller, Miloslav
High-spatial-resolution images of the solar corona acquired in the extreme ultraviolet (EUV), most notably with the Atmospheric Imaging Assembly (AIA) instrument on the Solar Dynamics Observatory (SDO) reveal the abundance of dynamic events which range from flaring bright points and jets to erupting prominences and coronal mass ejections (CMEs). In this work we present novel techniques to extract such dynamic events from the more steady background corona using 17.1 nm SDO-AIA images. The techniques presented here treat any time series of coronal images as a matrix that can be decomposed into two matrices representing the background and the dynamic component, respectively. The latter has the properties of a so-called sparse matrix, and the proposed methods are classified as methods based on sparse representations. The proposed methods are the median-filter method, the principal component pursuit, and the dynamic-mode decomposition, all of which include data pre-processing using the noise-adaptive fuzzy equalization method. The study reveals that the median-filter method and the dynamic-mode decomposition enhance all motions in the time series and produce similar results. On the other hand, the principal component pursuit enables the clear differentiation of CMEs from the background corona, thus providing a valuable tool for the characterization of their acceleration profiles in the low corona as seen in the EUV.
Probing the Density Fine Structuring of the Solar Corona with Comet Lovejoy
(IOP Publishing, 2022-10-01) Nistic, Giuseppe; Zimbardo, Gaetano; Perri, Silvia; Nakariakov, Valery M.; Duckenfield, Timothy j.; Druckmüller, Miloslav
The passage of sungrazing comets in the solar corona can be a powerful tool to probe the local plasma properties. Here, we carry out a study of the striae pattern appearing in the tail of sungrazing Comet Lovejoy, as observed by the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory (SDO) during the inbound and outbound phases of the comet's orbit. We consider the images in EUV in the 171 angstrom bandpass, where emission from oxygen ions O4+ and O5+ is found. The striae are described as due to a beam of ions injected along the local magnetic field, with the initial beam velocity decaying because of collisions. Also, ion collisional diffusion contributes to ion propagation. Both the collision time for velocity decay and the diffusion coefficient for spatial spreading depend on the ambient plasma density. A probabilistic description of the ion beam density along the magnetic field is developed, where the beam position is given by the velocity decay and the spreading of diffusing ions is described by a Gaussian probability distribution. Profiles of emission intensity along the magnetic field are computed and compared with the profiles along the striae observed by AIA, showing a good agreement for most considered striae. The inferred coronal densities are then compared with a hydrostatic model of the solar corona. The results confirm that the coronal density is strongly spatially structured.
Identification of pollen taxa by different microscopy techniques
(PLOS, 2021-09-01) Pospiech, Matej; Javůrková, Zdeňka; Hrabec, Pavel; Štarha, Pavel; Ljasovská, Simona; Bednář, Josef; Tremlová, Bohuslava
Melissopalynology is an important analytical method to identify botanical origin of honey. Pollen grain recognition is commonly performed by visual inspection by a trained person. An alternative method for visual inspection is automated pollen analysis based on the image analysis technique. Image analysis transfers visual information to mathematical descriptions. In this work, the suitability of three microscopic techniques for automatic analysis of pollen grains was studied. 2D and 3D morphological characteristics, textural and colour features, and extended depth of focus characteristics were used for the pollen discrimination. In this study, 7 botanical taxa and a total of 2482 pollen grains were evaluated. The highest correct classification rate of 93.05% was achieved using the phase contrast microscopy, followed by the dark field microscopy reaching 91.02%, and finally by the light field microscopy reaching 88.88%. The most significant discriminant characteristics were morphological (2D and 3D) and colour characteristics. Our results confirm the potential of using automatic pollen analysis to discriminate pollen taxa in honey. This work provides the basis for further research where the taxa dataset will be increased, and new descriptors will be studied.
Half-linear differential equations: Regular variation, principal solutions, and asymptotic classes
(Bolyai Institute, University of Szeged, 2023-01-03) Řehák, Pavel
We are interested in the structure of the solution space of second-order half-linear differential equations taking into account various classifications regarding asymptotics of solutions. We focus on an exhaustive analysis of the relations among several types of classes which include the classes constructed with respect to the values of the limits of solutions and their quasiderivatives, the classes of regularly varying solutions, the classes of principal and nonprincipal solutions, and the classes of the so-lutions that obey certain asymptotic formulae. Many of our observations are new even in the case of linear differential equations, and we provide also the revision of existing results.

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