A t-tone coloring of a graph assigns t distinct colors to each vertex with vertices at distance d having fewer than d colors in common.The t-tone chromatic number of a graph is the smallest number of colors used in al...A t-tone coloring of a graph assigns t distinct colors to each vertex with vertices at distance d having fewer than d colors in common.The t-tone chromatic number of a graph is the smallest number of colors used in all t-tone colorings of that graph.In this article,we study t-tone coloring of some finite planar lattices and obtain exact formulas for their t-tone chromatic number.展开更多
Fig(Ficus carica L.)with purple-red peel cultivars are popular among consumers and exhibit better storability.While DNA methylation influences fruit ripening and color development,its specific role in fig fruit remain...Fig(Ficus carica L.)with purple-red peel cultivars are popular among consumers and exhibit better storability.While DNA methylation influences fruit ripening and color development,its specific role in fig fruit remains unclear.This study explores the impact of DNA methylation on the fig peel coloration.Enzymatic colorimetric detection revealed that the level of‘Purple Peel’fig DNA methylation decreases with fig fruit ripening and coloring.Treatment of young fruit with the DNA-methylation inhibitor azacytidine induced peel coloration,suggesting that a decrease in DNA-methylation level promotes fig peel coloration.Seven members of DNA methyltransferases and three members of DNA demethylases were identified from a high-level fig genome,highlighting FcMET1 and FcDRM2 as stable proteins,ensuring functional expression.Reference to the Arabidopsis protein interaction network map predicted that FcMET1 is in a central position,suggesting a crucial regulatory role in multiple biological processes.Correlation analysis revealed a positive correlation between FcMET1 expression during peel development and the level of total DNA methylation.Weighted gene co-expression network analysis identified co-expression of FcMET1 with the color-related transcription factors MYB,bHLH and WD40,as well as with eight structural genes in the flavonoid-biosynthesis pathway.The expression of FcUFGT3 was negatively correlated with that of FcMET1.McrBC-PCR and Bisulfite Sequencing detection showed that a low methylation level of the FcUFGT3 promoter corresponds with its high expression in colored fig.This investigation of the mechanism of DNA methylation provides a theoretical basis for understanding the role of DNA-methylation modifications in fig ripening and coloring.展开更多
Image coloring is an inherently uncertain and multimodal problem.By inputting a grayscale image into a coloring network,visually plausible colored photos can be generated.Conventional methods primarily rely on semanti...Image coloring is an inherently uncertain and multimodal problem.By inputting a grayscale image into a coloring network,visually plausible colored photos can be generated.Conventional methods primarily rely on semantic information for image colorization.These methods still suffer from color contamination and semantic confusion.This is largely due to the limited capacity of convolutional neural networks to learn deep semantic information inherent in images effectively.In this paper,we propose a network structure that addresses these limitations by leveraging multi-level semantic information classification and fusion.Additionally,we introduce a global semantic fusion network to combat the issues of color contamination.The proposed coloring encoder accurately extracts object-level semantic information from images.To further enhance visual plausibility,we employ a self-supervised adversarial training method.We train the network structure on various datasets with varying amounts of data and evaluate its performance using the ImageNet validation set and COCO validation set.Experimental results demonstrate that our proposed algorithm can generate more realistic images compared to previous approaches,showcasing its high generalization ability.展开更多
A proper conflict-free k-coloring of a graph is a proper k-coloring in which each nonisolated vertex has a color that appears ex-actly once in its open neighborhood.A graph is PCF k-colorable if it admits a proper con...A proper conflict-free k-coloring of a graph is a proper k-coloring in which each nonisolated vertex has a color that appears ex-actly once in its open neighborhood.A graph is PCF k-colorable if it admits a proper conflict-free k-coloring.The PCF chromatic number of a graph G,denoted by χ_(pcf)(G),is the minimum k such that G is PCF k-colorable.Caro et al conjectured that for a connected graph G with maximum degreeΔ≥3,χ_(pcf)(G)≤Δ+1.One case in this conjecture,a connected graph with maximum degree 3 is PCF 4-colorable,can be derived from the result of Liu and Yu.Jiménez et al stated that the upper bound of PCF chromatic number of a graph G is max{5,x(G)}without a proof.In this paper,we give new proofs of the two results above and derive that for a connected graph G with maximum degreeΔ≥3,its complete subdivision is PCF(Δ+1)-colorable.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12271210)the Scientific Research Foundation of Jimei University(Grant No.Q202201).
文摘A t-tone coloring of a graph assigns t distinct colors to each vertex with vertices at distance d having fewer than d colors in common.The t-tone chromatic number of a graph is the smallest number of colors used in all t-tone colorings of that graph.In this article,we study t-tone coloring of some finite planar lattices and obtain exact formulas for their t-tone chromatic number.
基金supported by 111 Project(Grant No.B17043)China Postdoctoral Science Foundation(Grant No.2022M723425).
文摘Fig(Ficus carica L.)with purple-red peel cultivars are popular among consumers and exhibit better storability.While DNA methylation influences fruit ripening and color development,its specific role in fig fruit remains unclear.This study explores the impact of DNA methylation on the fig peel coloration.Enzymatic colorimetric detection revealed that the level of‘Purple Peel’fig DNA methylation decreases with fig fruit ripening and coloring.Treatment of young fruit with the DNA-methylation inhibitor azacytidine induced peel coloration,suggesting that a decrease in DNA-methylation level promotes fig peel coloration.Seven members of DNA methyltransferases and three members of DNA demethylases were identified from a high-level fig genome,highlighting FcMET1 and FcDRM2 as stable proteins,ensuring functional expression.Reference to the Arabidopsis protein interaction network map predicted that FcMET1 is in a central position,suggesting a crucial regulatory role in multiple biological processes.Correlation analysis revealed a positive correlation between FcMET1 expression during peel development and the level of total DNA methylation.Weighted gene co-expression network analysis identified co-expression of FcMET1 with the color-related transcription factors MYB,bHLH and WD40,as well as with eight structural genes in the flavonoid-biosynthesis pathway.The expression of FcUFGT3 was negatively correlated with that of FcMET1.McrBC-PCR and Bisulfite Sequencing detection showed that a low methylation level of the FcUFGT3 promoter corresponds with its high expression in colored fig.This investigation of the mechanism of DNA methylation provides a theoretical basis for understanding the role of DNA-methylation modifications in fig ripening and coloring.
基金supported by the Key Technologies R&D Program of Tianjin(Nos.24YFZCSN00030 and 24YFYSHZ00090)。
文摘Image coloring is an inherently uncertain and multimodal problem.By inputting a grayscale image into a coloring network,visually plausible colored photos can be generated.Conventional methods primarily rely on semantic information for image colorization.These methods still suffer from color contamination and semantic confusion.This is largely due to the limited capacity of convolutional neural networks to learn deep semantic information inherent in images effectively.In this paper,we propose a network structure that addresses these limitations by leveraging multi-level semantic information classification and fusion.Additionally,we introduce a global semantic fusion network to combat the issues of color contamination.The proposed coloring encoder accurately extracts object-level semantic information from images.To further enhance visual plausibility,we employ a self-supervised adversarial training method.We train the network structure on various datasets with varying amounts of data and evaluate its performance using the ImageNet validation set and COCO validation set.Experimental results demonstrate that our proposed algorithm can generate more realistic images compared to previous approaches,showcasing its high generalization ability.
基金Supported by the Youth Fund of Lanzhou Jiaotong University(1200061328)。
文摘A proper conflict-free k-coloring of a graph is a proper k-coloring in which each nonisolated vertex has a color that appears ex-actly once in its open neighborhood.A graph is PCF k-colorable if it admits a proper conflict-free k-coloring.The PCF chromatic number of a graph G,denoted by χ_(pcf)(G),is the minimum k such that G is PCF k-colorable.Caro et al conjectured that for a connected graph G with maximum degreeΔ≥3,χ_(pcf)(G)≤Δ+1.One case in this conjecture,a connected graph with maximum degree 3 is PCF 4-colorable,can be derived from the result of Liu and Yu.Jiménez et al stated that the upper bound of PCF chromatic number of a graph G is max{5,x(G)}without a proof.In this paper,we give new proofs of the two results above and derive that for a connected graph G with maximum degreeΔ≥3,its complete subdivision is PCF(Δ+1)-colorable.
