scholarly journals Twisted cubic and point-line incidence matrix in $$\mathrm {PG}(3,q)$$

2021 ◽  
Vol 89 (10) ◽  
pp. 2211-2233 ◽  
Author(s):  
Alexander A. Davydov ◽  
Stefano Marcugini ◽  
Fernanda Pambianco
Keyword(s):  
Incidence Matrix ◽  
Twisted Cubic ◽  
Point Line

Finite Projective Planes that Admit a Strongly Irreducible Collineation Group

1985 ◽  
Vol 37 (4) ◽  
pp. 579-611 ◽  
Author(s):  
Chat Yin Ho
Keyword(s):  
Group Theory ◽  
Coding Theory ◽  
Collineation Group ◽  
Incidence Matrix ◽  
Minimal Normal Subgroup ◽  
Finite Projective Plane ◽  
Projective Planes ◽  
Strongly Irreducible ◽  
Point Line ◽  
Strong Irreducibility

This paper studies how coding theory and group theory can be used to produce information about a finite projective plane π and a collineation group G of π.A new proof for Hering's bound on |G| is given in 2.5. Using the idea of coding theory developed in [9], a relation between two rows of the incidence matrix of π with respect to a tactical decomposition is obtained in 2.1. This result yields, among other things, some techniques in calculating |G|, and generalizes a result of Roth [16], [see 2.4 and 2.5].Hering [7] introduced the notion of strong irreducibility of G, that is, G does not leave invariant any point, line, triangle or proper subplane. He showed that if in addition G contains a non-trivial perspectivity, then there is a unique minimal normal subgroup of G. This subgroup is either non-abelian simple or isomorphic to the elementary abelian group Z3 × Z3 of order 9.

scholarly journals Identifying cell types from single-cell data based on similarities and dissimilarities between cells

2021 ◽  
Vol 22 (S3) ◽  
Author(s):  
Yuanyuan Li ◽  
Ping Luo ◽  
Yi Lu ◽  
Fang-Xiang Wu
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Spectral Clustering ◽  
Incidence Matrix ◽  
Expression Patterns ◽  
Cell Types ◽  
Clustering Method ◽  
Different Types ◽  
Cell Data ◽  
Spectral Clustering Method

Abstract Background With the development of the technology of single-cell sequence, revealing homogeneity and heterogeneity between cells has become a new area of computational systems biology research. However, the clustering of cell types becomes more complex with the mutual penetration between different types of cells and the instability of gene expression. One way of overcoming this problem is to group similar, related single cells together by the means of various clustering analysis methods. Although some methods such as spectral clustering can do well in the identification of cell types, they only consider the similarities between cells and ignore the influence of dissimilarities on clustering results. This methodology may limit the performance of most of the conventional clustering algorithms for the identification of clusters, it needs to develop special methods for high-dimensional sparse categorical data. Results Inspired by the phenomenon that same type cells have similar gene expression patterns, but different types of cells evoke dissimilar gene expression patterns, we improve the existing spectral clustering method for clustering single-cell data that is based on both similarities and dissimilarities between cells. The method first measures the similarity/dissimilarity among cells, then constructs the incidence matrix by fusing similarity matrix with dissimilarity matrix, and, finally, uses the eigenvalues of the incidence matrix to perform dimensionality reduction and employs the K-means algorithm in the low dimensional space to achieve clustering. The proposed improved spectral clustering method is compared with the conventional spectral clustering method in recognizing cell types on several real single-cell RNA-seq datasets. Conclusions In summary, we show that adding intercellular dissimilarity can effectively improve accuracy and achieve robustness and that improved spectral clustering method outperforms the traditional spectral clustering method in grouping cells.

Measure-wise disjoint Rauzy fractals with the same incidence matrix

2021 ◽  
Author(s):  
Klaus Scheicher ◽  
Víctor F. Sirvent ◽  
Paul Surer
Keyword(s):  
Incidence Matrix

scholarly journals A Multi-Feature Fusion Slam System Attaching Semantic Invariant to Points and Lines

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1196
Author(s):  
Gang Li ◽  
Yawen Zeng ◽  
Huilan Huang ◽  
Shaojian Song ◽  
Bin Liu ◽  
...  
Keyword(s):  
Feature Matching ◽  
Feature Fusion ◽  
Error Function ◽  
Line Segments ◽  
Cumulative Error ◽  
Localization And Mapping ◽  
Tracking Process ◽  
Line Features ◽  
Point Line ◽  
Segment Data

The traditional simultaneous localization and mapping (SLAM) system uses static points of the environment as features for real-time localization and mapping. When there are few available point features, the system is difficult to implement. A feasible solution is to introduce line features. In complex scenarios containing rich line segments, the description of line segments is not strongly differentiated, which can lead to incorrect association of line segment data, thus introducing errors into the system and aggravating the cumulative error of the system. To address this problem, a point-line stereo visual SLAM system incorporating semantic invariants is proposed in this paper. This system improves the accuracy of line feature matching by fusing line features with image semantic invariant information. When defining the error function, the semantic invariant is fused with the reprojection error function, and the semantic constraint is applied to reduce the cumulative error of the poses in the long-term tracking process. Experiments on the Office sequence of the TartanAir dataset and the KITTI dataset show that this system improves the matching accuracy of line features and suppresses the cumulative error of the SLAM system to some extent, and the mean relative pose error (RPE) is 1.38 and 0.0593 m, respectively.

scholarly journals On the rank of a network incidence matrix.

1992 ◽  
pp. 223-226
Author(s):  
Takashi AKAMATSU ◽  
Masao KUWAHARA
Keyword(s):  
Incidence Matrix
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