A （p, q）-graph G is called super edge-magic if there exists a bijective function f ： V（G） U E（G） →{1, 2 p＋q} such that f（u）＋ f（v）＋f（uv） is a constant for each uv C E（G） and f（Y（G）） = {1,2,...,p}...A （p, q）-graph G is called super edge-magic if there exists a bijective function f ： V（G） U E（G） →{1, 2 p＋q} such that f（u）＋ f（v）＋f（uv） is a constant for each uv C E（G） and f（Y（G）） = {1,2,...,p}. In this paper, we introduce the concept of strong super edge-magic labeling as a particular class of super edge-magic labelings and we use such labelings in order to show that the number of super edge-magic labelings of an odd union of path-like trees （mT）, all of them of the same order, grows at least exponentially with m.展开更多
Natural killer(NK)cells,a subgroup of innate lymphoid cells,act as the first line of defense against cancer.Although some evidence shows that NK cells can develop in secondary lymphoid tissues,NK cells develop mainly ...Natural killer(NK)cells,a subgroup of innate lymphoid cells,act as the first line of defense against cancer.Although some evidence shows that NK cells can develop in secondary lymphoid tissues,NK cells develop mainly in the bone marrow(BM)and egress into the blood circulation when they mature.They then migrate to and settle down in peripheral tissues,though some special subsets home back into the BM or secondary lymphoid organs.Owing to its success in allogeneic adoptive transfer for cancer treatment and its“off-the-shelf”potential,NK cell-based immunotherapy is attracting increasing attention in the treatment of various cancers.However,insufficient infiltration of adoptively transferred NK cells limits clinical utility,especially for solid tumors.Expansion of NK cells or engineered chimeric antigen receptor(CAR)NK cells ex vivo prior to adoptive transfer by using various cytokines alters the profiles of chemokine receptors,which affects the infiltration of transferred NK cells into tumor tissue.Several factors control NK cell trafficking and homing,including cell-intrinsic factors(e.g.,transcriptional factors),cell-extrinsic factors(e.g.,integrins,selectins,chemokines and their corresponding receptors,signals induced by cytokines,sphingosine-1-phosphate(S1P),etc.),and the cellular microenvironment.Here,we summarize the profiles and mechanisms of NK cell homing and trafficking at steady state and during tumor development,aiming to improve NK cell-based cancer immunotherapy.展开更多
A （δ, g）-cage is a δ-regular graph with girth g and with the least possible number of vertices. In this paper, we show that all （δ, g）-cages with odd girth g ≥ 9 are r-connected, where （r - 1）2 ≤δ ＋ x/δ ...A （δ, g）-cage is a δ-regular graph with girth g and with the least possible number of vertices. In this paper, we show that all （δ, g）-cages with odd girth g ≥ 9 are r-connected, where （r - 1）2 ≤δ ＋ x/δ - 2 〈 r2 and all （δ, g）-cages with even girth g 〉 10 are r-connected, where r is the largest integer satisfying r（r-1）2/4 ＋ 1 ＋ 2r（r - 1） ≤δ. These results support a conjecture of Fkl, Huang and Rodger that all （δ, g）-cages are 6-connected.展开更多
基金Supported by the Slovak VEGA (Grant No.1/4005/07)Spanish Research Council (Grant No.BFM2002-00412)
文摘A （p, q）-graph G is called super edge-magic if there exists a bijective function f ： V（G） U E（G） →{1, 2 p＋q} such that f（u）＋ f（v）＋f（uv） is a constant for each uv C E（G） and f（Y（G）） = {1,2,...,p}. In this paper, we introduce the concept of strong super edge-magic labeling as a particular class of super edge-magic labelings and we use such labelings in order to show that the number of super edge-magic labelings of an odd union of path-like trees （mT）, all of them of the same order, grows at least exponentially with m.
基金supported by National Natural Science Foundation of China(Nos.81922068 and 81874313)Y.D.This study was also supported by funding from the National Key Research and Development Project(Nos.2020YFA0113500 and 2019YFA0111200) Y.D.This study was also supported by National undergraduate training program for innovation and entrepreneurship(No.2020XBK28)to Y.D.
文摘Natural killer(NK)cells,a subgroup of innate lymphoid cells,act as the first line of defense against cancer.Although some evidence shows that NK cells can develop in secondary lymphoid tissues,NK cells develop mainly in the bone marrow(BM)and egress into the blood circulation when they mature.They then migrate to and settle down in peripheral tissues,though some special subsets home back into the BM or secondary lymphoid organs.Owing to its success in allogeneic adoptive transfer for cancer treatment and its“off-the-shelf”potential,NK cell-based immunotherapy is attracting increasing attention in the treatment of various cancers.However,insufficient infiltration of adoptively transferred NK cells limits clinical utility,especially for solid tumors.Expansion of NK cells or engineered chimeric antigen receptor(CAR)NK cells ex vivo prior to adoptive transfer by using various cytokines alters the profiles of chemokine receptors,which affects the infiltration of transferred NK cells into tumor tissue.Several factors control NK cell trafficking and homing,including cell-intrinsic factors(e.g.,transcriptional factors),cell-extrinsic factors(e.g.,integrins,selectins,chemokines and their corresponding receptors,signals induced by cytokines,sphingosine-1-phosphate(S1P),etc.),and the cellular microenvironment.Here,we summarize the profiles and mechanisms of NK cell homing and trafficking at steady state and during tumor development,aiming to improve NK cell-based cancer immunotherapy.
文摘A （δ, g）-cage is a δ-regular graph with girth g and with the least possible number of vertices. In this paper, we show that all （δ, g）-cages with odd girth g ≥ 9 are r-connected, where （r - 1）2 ≤δ ＋ x/δ - 2 〈 r2 and all （δ, g）-cages with even girth g 〉 10 are r-connected, where r is the largest integer satisfying r（r-1）2/4 ＋ 1 ＋ 2r（r - 1） ≤δ. These results support a conjecture of Fkl, Huang and Rodger that all （δ, g）-cages are 6-connected.
