Irregular Riemann-Hilbert Correspondence and Enhanced Subanalytic Sheaves

In [arXiv:2109.13991], the author explained a relation between enhanced ind-sheaves and enhanced subanalytic sheaves. In this paper, we shall define C-constructability for enhanced subanalytic sheaves which was announced in [arXiv:2109.13991], and show that there exists an equivalence of categories between the triangulated category of C-constructible enhanced subanalytic sheaves and the one of holonomic D-modules.Comment: 28 pages. arXiv admin note: text overlap with arXiv:2301.01138, arXiv:2109.13991, arXiv:2004.1351

Finiteness properties of Ind-Sheaves with Ring Actions

In this paper, we shall consider some finiteness of ind-sheaves with ring actions. As the main result of this paper, there exists an equivalence of categories between the abelian category of coherent ind-$\beta\mathcal{A}$-modules and the one of coherent $\mathcal{A}$-modules, where $\mathcal{A}$ is a sheaf of k-algebras and $\Bbbk$ is a field.Comment: 16pages, to appear in Indian Journal of Pure and Applied Mathematic

Novel Approximate Statistical Algorithm for Large Complex Datasets

In the field of pattern recognition, principal component analysis (PCA) is one of the most well-known feature extraction methods for reducing the dimensionality of high-dimensional datasets. Simple-PCA (SPCA), which is a faster version of PCA, performs effectively with iterative operated learning. However, SPCA might not be efficient when input data are distributed in a complex manner because it learns without using the class information in the dataset. Thus, SPCA cannot be said to be optimal from the perspective of feature extraction for classification. In this study, we propose a new learning algorithm that uses the class information in the dataset. Eigenvectors spanning the eigenspace of the dataset are produced by calculating the data variations within each class. We present our proposed algorithm and discuss the results of our experiments that used UCI datasets to compare SPCA and our proposed algorithm