173 research outputs found
Roman domination number of Generalized Petersen Graphs P(n,2)
A on a graph is a function
satisfying the condition that every vertex
with is adjacent to at least one vertex with . The
of a Roman domination function is the value . The minimum weight of a Roman dominating function on a graph is
called the of , denoted by . In
this paper, we study the {\it Roman domination number} of generalized Petersen
graphs P(n,2) and prove that .Comment: 9 page
The crossing number of locally twisted cubes
The {\it crossing number} of a graph is the minimum number of pairwise
intersections of edges in a drawing of . Motivated by the recent work
[Faria, L., Figueiredo, C.M.H. de, Sykora, O., Vrt'o, I.: An improved upper
bound on the crossing number of the hypercube. J. Graph Theory {\bf 59},
145--161 (2008)] which solves the upper bound conjecture on the crossing number
of -dimensional hypercube proposed by Erd\H{o}s and Guy, we give upper and
lower bounds of the crossing number of locally twisted cube, which is one of
variants of hypercube.Comment: 17 pages, 12 figure
SimpleNet: A Simple Network for Image Anomaly Detection and Localization
We propose a simple and application-friendly network (called SimpleNet) for
detecting and localizing anomalies. SimpleNet consists of four components: (1)
a pre-trained Feature Extractor that generates local features, (2) a shallow
Feature Adapter that transfers local features towards target domain, (3) a
simple Anomaly Feature Generator that counterfeits anomaly features by adding
Gaussian noise to normal features, and (4) a binary Anomaly Discriminator that
distinguishes anomaly features from normal features. During inference, the
Anomaly Feature Generator would be discarded. Our approach is based on three
intuitions. First, transforming pre-trained features to target-oriented
features helps avoid domain bias. Second, generating synthetic anomalies in
feature space is more effective, as defects may not have much commonality in
the image space. Third, a simple discriminator is much efficient and practical.
In spite of simplicity, SimpleNet outperforms previous methods quantitatively
and qualitatively. On the MVTec AD benchmark, SimpleNet achieves an anomaly
detection AUROC of 99.6%, reducing the error by 55.5% compared to the next best
performing model. Furthermore, SimpleNet is faster than existing methods, with
a high frame rate of 77 FPS on a 3080ti GPU. Additionally, SimpleNet
demonstrates significant improvements in performance on the One-Class Novelty
Detection task. Code: https://github.com/DonaldRR/SimpleNet.Comment: Accepted to CVPR 202
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