Automatic topic detection seems unavoidable in social media analysis due to big text data which their users generate. Clustering-based methods are one of the most important and up-to-date categories in topic detection. The goal of this research is to have a wide study on this category. Therefore, this paper aims to study the main components of clustering-based-topic-detection, which are embedding methods, distance metrics, and clustering algorithms. Transfer learning and consequently pretrained language models and word embeddings have been considered in recent years. Regarding the importance of embedding methods, the efficiency of five new embedding methods, from earlier to recent ones, are compared in this paper. To conduct our study, two commonly used distance metrics, in addition to five important clustering algorithms in the field of topic detection, are implemented by the authors. As COVID-19 has turned into a hot trending topic on social networks in recent years, a dataset including one-month tweets collected with COVID-19-related hashtags is used for this study. More than 7500 experiments are performed to determine tunable parameters. Then all combinations of embedding methods, distance metrics and clustering algorithms (50 combinations) are evaluated using Silhouette metric. Results show that T5 strongly outperforms other embedding methods, cosine distance is weakly better than other distance metrics, and DBSCAN is superior to other clustering algorithms.

For a given measure space (X, B, m) we construct all measure spaces (Y, C, l) in which (X, B, m) is embeddable. The construction is modeled on the ultrafilter construction of the Stone-Cech compactification of a completely regular topological space.Under certain conditions the construction simplifies. Examples are given when this simplification occurs.

By a brief review on the applications of wavelets in solving optimal control problems, a multi resolution analysis for two dimensional Sobolev spaces and the square spline wavelets are considered. Regarding the density and approximation properties of these wavelets, for the first time, they are employed for solving optimal control problems by embedding method. Existence and the determination way for the solution are also discussed. Finally, the abilities of the new approach are explained by a numerical example and some comparisons.

Several approaches have been employed for grid adaptation. The most widely used ones utilize adaptive-grid redistribution and adaptive-grid embedding. However, the combination of these two main methods (r-h) is also possible. This work compares redistribution and embedding with a combination of these two methods for steady transonic airfoil flows. The Euler equations are integrated into a steady state by an explicit, finite volume, Ni’s Lax-Wendroff scheme. Comparison with other numerical solutions is employed in order to evaluate the accuracy and efficiency of the techniques. The combination of adaptive-grid redistribution and embedding is somewhat more complex than the adaptive embedding method, but the results indicate that for two-dimensional invisid flows, when high accuracy is required, their combination is more efficient.

One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph embedding problem. In this paper we compute the lower bound for dilation and congestion of embedding onto wheel-like networks. Further, we compute the exact dilation of embedding wheellike networks into hypertrees, proving that the lower bound obtained is sharp. Again, we compute the exact congestion of embedding windmill graphs into circulant graphs, proving that the lower bound obtained is sharp. Further, we compute the exact wirelength of embedding wheels and fans into 1, 2-fault hamiltonian graphs. Using this we estimate the exact wirelength of embedding wheels and fans into circulant graphs, generalized Petersen graphs, augmented cubes, crossed cubes, Möbius cubes, twisted cubes, twisted n-cubes, locally twisted cubes, generalized twisted cubes, odd-dimensional cube connected cycle, hierarchical cubic networks, alternating group graphs, arrangement graphs, 3-regular planer hamiltonian graphs, star graphs, generalised matching networks, fully connected cubic networks, tori and 1-fault traceable graphs.

In the image stegenography, the distortion of stego image will be increased by increasing the number of embedded bits and this makes the enemy be much more suspicious about the existence of secret information in the images. One can use the matrix embedding technique to alleviate this problem which can be done by dividing the cover image into some blocks and limiting the changes in each block. However, the embedding capacity will be limited by this technique. In this article, a solution to this problem (limited embedding capacity), a modified version of Fan’s method, is presented. In this technique, the maximum number of changes in each block is chosen to be 2 instead of 1 in Fan’s technique which leads to reducing the blocks length and increasing the embedding capacity. The results revealed that for a given capacity, the stego image distortion is decreased and the embedding capacity is increased in compared with the other existing methods in this field. Also, the stego images have high PSNR along with high vision quality which leads to more security.

Purpose: The aims of the paper are to obtain necessary and sufficient conditions of existence and smoothness for non-polynomial spline spaces of fifth order, to establish the uniqueness of the Bφ-spline spaces in the class C4 among mentioned spaces (under condition of fixed grid), and to prove the embedding of the Bφ-spline spaces corresponding to embedded grids.Methods: In the paper, the approximation relations with initial grid and with complete chain of vectors are applied to obtain the minimal spline spaces. Usage of locally orthogonal chain of vectors gives opportunity to construct special approximation relations from which the initial space of Bφ splines is constructed.Results: Deletion of a knot from initial grid gives a new grid, and as result, a new space of Bφ splines is embedded in the initial space mentioned above.Conclusions: Consequent deletion of the knots (one by one) generates the sequence of the embedded spaces of Bφ splines. Obtained results are successfully proved. They may be applied to spline-wavelet decompositions.

Letf ¹1; 3 be a positive integer. We prove that there exists a numerical semigroup S with embedding dimension three such that f is the Frobenius number of S. We also show that the same fact holds for affine semigroups in higher dimensional monoids.