124 research outputs found
Extremal trees, unicyclic and bicyclic graphs with respect to -Sombor spectral radii
For a graph and , denote by (or for
short) the degree of vertex . The -Sombor matrix
() of a graph is a square matrix,
where the -entry is equal to if the vertices and are
adjacent, and 0 otherwise. The -Sombor spectral radius of , denoted by
, is the largest eigenvalue of
the -Sombor matrix . In this paper, we consider
the extremal trees, unicyclic and bicyclic graphs with respect to the
-Sombor spectral radii. We characterize completely the extremal graphs with
the first three maximum Sombor spectral radii, which answers partially a
problem posed by Liu et al. in [MATCH Commun. Math. Comput. Chem. 87 (2022)
59-87]
Fractional strong matching preclusion for two variants of hypercubes
Let F be a subset of edges and vertices of a graph G. If G-F has no fractional perfect matching, then F is a fractional strong matching preclusion set of G. The fractional strong matching preclusion number is the cardinality of a minimum fractional strong matching preclusion set. In this paper, we mainly study the fractional strong matching preclusion problem for two variants of hypercubes, the multiply twisted cube and the locally twisted cube, which are two of the most popular interconnection networks. In addition, we classify all the optimal fractional strong matching preclusion set of each
MPR-Net:Multi-Scale Pattern Reproduction Guided Universality Time Series Interpretable Forecasting
Time series forecasting has received wide interest from existing research due
to its broad applications and inherent challenging. The research challenge lies
in identifying effective patterns in historical series and applying them to
future forecasting. Advanced models based on point-wise connected MLP and
Transformer architectures have strong fitting power, but their secondary
computational complexity limits practicality. Additionally, those structures
inherently disrupt the temporal order, reducing the information utilization and
making the forecasting process uninterpretable. To solve these problems, this
paper proposes a forecasting model, MPR-Net. It first adaptively decomposes
multi-scale historical series patterns using convolution operation, then
constructs a pattern extension forecasting method based on the prior knowledge
of pattern reproduction, and finally reconstructs future patterns into future
series using deconvolution operation. By leveraging the temporal dependencies
present in the time series, MPR-Net not only achieves linear time complexity,
but also makes the forecasting process interpretable. By carrying out
sufficient experiments on more than ten real data sets of both short and long
term forecasting tasks, MPR-Net achieves the state of the art forecasting
performance, as well as good generalization and robustness performance
Fractional matching preclusion for butterfly derived networks
The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu [18] recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of G, denoted by fmp(G), is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of G, denoted by fsmp(G), is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we study the fractional matching preclusion number and the fractional strong matching preclusion number for butterfly network, augmented butterfly network and enhanced butterfly network
Progressive Scene Text Erasing with Self-Supervision
Scene text erasing seeks to erase text contents from scene images and current
state-of-the-art text erasing models are trained on large-scale synthetic data.
Although data synthetic engines can provide vast amounts of annotated training
samples, there are differences between synthetic and real-world data. In this
paper, we employ self-supervision for feature representation on unlabeled
real-world scene text images. A novel pretext task is designed to keep
consistent among text stroke masks of image variants. We design the Progressive
Erasing Network in order to remove residual texts. The scene text is erased
progressively by leveraging the intermediate generated results which provide
the foundation for subsequent higher quality results. Experiments show that our
method significantly improves the generalization of the text erasing task and
achieves state-of-the-art performance on public benchmarks
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