Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satis...Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satisfies ∥V<sub>1</sub>∣ - ∣V<sub>2</sub>∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V<sub>1</sub>, V<sub>2</sub>) such that ∀v ∈ V<sub>1</sub>, at least half minuses one of the neighbors of v are in the V<sub>2</sub>;∀v ∈ V<sub>2</sub>, at least half minuses one of the neighbors of v are in the V<sub>1</sub>. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.展开更多
The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the gr...The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001.The difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transformation is defined by means of combinatorial operations.They discuss its advantages over the graph homotopy transformation.As its applications,they investigate the mapping class group of a graph and the 1-order M P-homotopy group of a pointed simple graph.Moreover,they show that the 1-order M P-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.展开更多
电力系统多样化的运行方式对薄弱支路辨识的速度与拓扑泛化性提出更高要求。结合图深度学习及解释方法对薄弱支路进行辨识与溯因分析。采用基于初始残差和单位映射的图卷积神经网络(graph convolutional network via initial residual a...电力系统多样化的运行方式对薄弱支路辨识的速度与拓扑泛化性提出更高要求。结合图深度学习及解释方法对薄弱支路进行辨识与溯因分析。采用基于初始残差和单位映射的图卷积神经网络(graph convolutional network via initial residual and identity mapping,GCNII)搭建薄弱支路辨识模型,模型可基于拓扑关系聚合元件特征,结合邻近电网的安全态势评估支路的薄弱程度。采用基于互信息优化的解释方法分析辨识模型的决策依据,提取薄弱支路的主导因子。IEEE68节点系统、实际电网算例结果表明,辨识模型具有较好的辨识准确性和拓扑泛化性,溯因分析结果符合传统机理认知所得结论,可为连锁故障的实时预警和预防控制提供有效指导。展开更多
Anticipating future actions without observing any partial videos of future actions plays an important role in action prediction and is also a challenging task.To obtain abundant information for action anticipation,som...Anticipating future actions without observing any partial videos of future actions plays an important role in action prediction and is also a challenging task.To obtain abundant information for action anticipation,some methods integrate multimodal contexts,including scene object labels.However,extensively labelling each frame in video datasets requires considerable effort.In this paper,we develop a weakly supervised method that integrates global motion and local finegrained features from current action videos to predict next action label without the need for specific scene context labels.Specifically,we extract diverse types of local features with weakly supervised learning,including object appearance and human pose representations without ground truth.Moreover,we construct a graph convolutional network for exploiting the inherent relationships of humans and objects under present incidents.We evaluate the proposed model on two datasets,the MPII-Cooking dataset and the EPIC-Kitchens dataset,and we demonstrate the generalizability and effectiveness of our approach for action anticipation.展开更多
In this paper, we present a complete classification for locally-primitive arctransitive graphs which have square-free order and valency 10. The classification involves nine graphs and three infinite families of graphs.
In this paper, a characterization of all pentavalent arc-transitive graphs is given. It is shown that each pentavalent arc-transitive covering graph F is a regular simple or elementary abelian covering graph. In parti...In this paper, a characterization of all pentavalent arc-transitive graphs is given. It is shown that each pentavalent arc-transitive covering graph F is a regular simple or elementary abelian covering graph. In particular, the elementary abelian covering groups are Z3,Z5or a subgroup of Z2^5.展开更多
Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakl...Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakly closed graphs as a generalization of the closed graph,and we prove that the quotient ring S/JG of the polynomial ring S=K[x1,...,xn,y1,...,yn]with K a field and n=|V(G)|is F-pure if G is weakly closed.This fact is a generalization of Ohtani's theorem.展开更多
The relative xity of a permutation group is the maximum proportion of the points xed by a non-trivial element of the group,and the relative xity of a graph is the relative xity of its automorphism group,viewed as a pe...The relative xity of a permutation group is the maximum proportion of the points xed by a non-trivial element of the group,and the relative xity of a graph is the relative xity of its automorphism group,viewed as a permutation group on the vertex-set of the graph.We prove in this paper that the relative xity of connected 2-arc-transitive graphs of a xed valence tends to 0 as the number of vertices grows to in nity.We prove the same result for the class of arc-transitive graphs of a xed prime valence,and more generally,for any class of arc-transitive locally-L graphs,where L is a xed quasiprimitive graph-restrictive permutation group.展开更多
In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency 11.The list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and th...In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency 11.The list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and the graphs associated with the simple group J1 and PSL(2,p),where p is a prime.展开更多
We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form<h...We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form<h>×D,where h has infinite order and D is finite.展开更多
针对脑电检测的研究需要,研发了微弱EEG脑电信号采集专用芯片系统。该芯片使用斩波稳定去噪声技术,首先利用2 k Hz的斩波频率对100 Hz以下的EEG信号进行频域隔离,然后利用RRL纹波抑制环路反馈进行调制后位于chopper频率处的主要由失调...针对脑电检测的研究需要,研发了微弱EEG脑电信号采集专用芯片系统。该芯片使用斩波稳定去噪声技术,首先利用2 k Hz的斩波频率对100 Hz以下的EEG信号进行频域隔离,然后利用RRL纹波抑制环路反馈进行调制后位于chopper频率处的主要由失调与低频1/f闪烁噪声引起的纹波电压的抑制;单级斩波放大使用电流复用、亚阈值跨导增强技术对来自EEG传感器的低频（〈100 Hz）小信号（5~100μV）进行40 d B增益的稳定中频放大;级联S/H电路进行去累积毛刺滤波,配合前面斩波技术,达到整体低噪声性能;VGA/LPF通过改变输入、反馈/负载电容,分别进行增益/带宽的数字调整。EEG-DSP加速芯片实现对多通道采集的控制以及信号处理编码。设计使用SMICRF 180 nm混合工艺,使用Cadence的Spectre软件进行功能前/后仿真,使用Caliber工具进行DRC/LVS的版图验收。最后,对设计芯片进行实际测试,结果表明放大芯片关键性能为：8.1μW/通道、面积6.3 mm2/8通道、0.8μVrms（BW=100 Hz）等效输入噪声;该款自主研发的脑电斩波放大芯片性能达到国内外前列的水平,可进行正确的脑电EEG采集,可应用于可穿戴领域、对后续脑电数据分析具有重要的使用价值。展开更多
文摘Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satisfies ∥V<sub>1</sub>∣ - ∣V<sub>2</sub>∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V<sub>1</sub>, V<sub>2</sub>) such that ∀v ∈ V<sub>1</sub>, at least half minuses one of the neighbors of v are in the V<sub>2</sub>;∀v ∈ V<sub>2</sub>, at least half minuses one of the neighbors of v are in the V<sub>1</sub>. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.
基金supported by the National Natural Science Foundation of China(No.11771116)。
文摘The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001.The difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transformation is defined by means of combinatorial operations.They discuss its advantages over the graph homotopy transformation.As its applications,they investigate the mapping class group of a graph and the 1-order M P-homotopy group of a pointed simple graph.Moreover,they show that the 1-order M P-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.
文摘电力系统多样化的运行方式对薄弱支路辨识的速度与拓扑泛化性提出更高要求。结合图深度学习及解释方法对薄弱支路进行辨识与溯因分析。采用基于初始残差和单位映射的图卷积神经网络(graph convolutional network via initial residual and identity mapping,GCNII)搭建薄弱支路辨识模型,模型可基于拓扑关系聚合元件特征,结合邻近电网的安全态势评估支路的薄弱程度。采用基于互信息优化的解释方法分析辨识模型的决策依据,提取薄弱支路的主导因子。IEEE68节点系统、实际电网算例结果表明,辨识模型具有较好的辨识准确性和拓扑泛化性,溯因分析结果符合传统机理认知所得结论,可为连锁故障的实时预警和预防控制提供有效指导。
基金Project supported by the National Natural Science Foundation of China (No.19831050, No.10171086) the Shanxi Provincial Natural Science Foundation of China (No.20011004)+1 种基金 the Key Program of the Ministry of Education of China (No.02023) the Returned A
文摘In this paper, a complete classification of arc-transitive cubic graphs of order 4p is given.
基金supported partially by the National Natural Science Foundation of China(NSFC)(Grant Nos.U1911401 and U1811461)Guangdong NSF Project(2020B1515120085,2018B030312002)+2 种基金Guangzhou Research Project(201902010037)Research Projects of Zhejiang Lab(2019KD0AB03)the Key-Area Research and Development Program of Guangzhou(202007030004).
文摘Anticipating future actions without observing any partial videos of future actions plays an important role in action prediction and is also a challenging task.To obtain abundant information for action anticipation,some methods integrate multimodal contexts,including scene object labels.However,extensively labelling each frame in video datasets requires considerable effort.In this paper,we develop a weakly supervised method that integrates global motion and local finegrained features from current action videos to predict next action label without the need for specific scene context labels.Specifically,we extract diverse types of local features with weakly supervised learning,including object appearance and human pose representations without ground truth.Moreover,we construct a graph convolutional network for exploiting the inherent relationships of humans and objects under present incidents.We evaluate the proposed model on two datasets,the MPII-Cooking dataset and the EPIC-Kitchens dataset,and we demonstrate the generalizability and effectiveness of our approach for action anticipation.
基金This work was supported by the National Natural Science Foundation of China （grants 11371204, 11731002）.
文摘In this paper, we present a complete classification for locally-primitive arctransitive graphs which have square-free order and valency 10. The classification involves nine graphs and three infinite families of graphs.
文摘In this paper, a characterization of all pentavalent arc-transitive graphs is given. It is shown that each pentavalent arc-transitive covering graph F is a regular simple or elementary abelian covering graph. In particular, the elementary abelian covering groups are Z3,Z5or a subgroup of Z2^5.
文摘Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakly closed graphs as a generalization of the closed graph,and we prove that the quotient ring S/JG of the polynomial ring S=K[x1,...,xn,y1,...,yn]with K a field and n=|V(G)|is F-pure if G is weakly closed.This fact is a generalization of Ohtani's theorem.
基金supported by the Austrian Science Fund(FWF)Project W1230-N13.The second author was supported by the Research Programme P1-0294the Research Project J1-1691,both funded by the Slovenian Research Agency(ARRS).
文摘The relative xity of a permutation group is the maximum proportion of the points xed by a non-trivial element of the group,and the relative xity of a graph is the relative xity of its automorphism group,viewed as a permutation group on the vertex-set of the graph.We prove in this paper that the relative xity of connected 2-arc-transitive graphs of a xed valence tends to 0 as the number of vertices grows to in nity.We prove the same result for the class of arc-transitive graphs of a xed prime valence,and more generally,for any class of arc-transitive locally-L graphs,where L is a xed quasiprimitive graph-restrictive permutation group.
基金supported by the National Natural Science Foundation of China(11731002,11701503,11971248,12061089)and the Fundamental Research Funds for the Central Universities.
文摘In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency 11.The list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and the graphs associated with the simple group J1 and PSL(2,p),where p is a prime.
文摘We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form<h>×D,where h has infinite order and D is finite.
