A loopless graph on n vertices in which vertices are connected at least by a and at most by b edges is called a(a,b,n)-graph. A(b,b,n)-graph is called(b,n)-graph and is denoted by K_n^b(it is a complete graph), its co...A loopless graph on n vertices in which vertices are connected at least by a and at most by b edges is called a(a,b,n)-graph. A(b,b,n)-graph is called(b,n)-graph and is denoted by K_n^b(it is a complete graph), its complement by K_n^b. A non increasing sequence π =(d_1,…,d_n) of nonnegative integers is said to be(a,b,n) graphic if it is realizable by an(a,b,n)-graph. We say a simple graphic sequence π=(d_1,…,d_n) is potentially K_4-K_2∪K_2-graphic if it has a a realization containing an K_4-K_2∪K_2 as a subgraph where K_4 is a complete graph on four vertices and K_2∪K_2 is a set of independent edges. In this paper, we find the smallest degree sum such that every n-term graphical sequence contains K_4-K_2∪K_2 as subgraph.展开更多
For a given graph H, a graphic sequence π =(d1, d2, ···, dn) is said to be potentially H-graphic if π has a realization containing H as a subgraph. In this paper, we characterize the potentially C6+ P...For a given graph H, a graphic sequence π =(d1, d2, ···, dn) is said to be potentially H-graphic if π has a realization containing H as a subgraph. In this paper, we characterize the potentially C6+ P2-graphic sequences where C6+ P2 denotes the graph obtained from C6 by adding two adjacent edges to the three pairwise nonadjacent vertices of C6. Moreover, we use the characterization to determine the value of σ(C6+ P2, n).展开更多
Cancer progression involves the sonic hedgehog(SHH)pathway,in which the receptor PTCH1 actives the downstream pathways.Dysfunction of PTCH1 can lead to nevoid basal cell carcinoma Syndrome(NBCCs)including neoplastic d...Cancer progression involves the sonic hedgehog(SHH)pathway,in which the receptor PTCH1 actives the downstream pathways.Dysfunction of PTCH1 can lead to nevoid basal cell carcinoma Syndrome(NBCCs)including neoplastic disease and congenital disorder.To evaluate the relationship between PTCH1 and cancer,we applied the CRISPR/Cas9 system to knock out PTCH1 in oral nontumorous epithelial cells(GMSM-K).Then we screened six PTCH1 variants associated with cleft lip/palate(CL/P),one of the congenital disorders in NBCCs,and generated PTCH1 variant and wild-type recombinant PTCH1^(−/−)GMSM-K cell lines.Transcriptome sequencing was conducted in these cell lines.The results revealed that differentially expressed genes(DEGs)in PTCH1^(−/−)GMSM-K were enriched in extracellular compartments,contributing epithelial diseases by pathway enrichment analysis.RT-PCR confirmed that KRT34,KRT81,KRT86,PDGFB,and WNT10B genes,associated with extracellular compartments were highly expressed in PTCH1^(−/−).The Kyoto Encyclopedia of Genes and Genomes analysis also suggested that DEGs are closely related to focal adhesion,transcriptional misregulation,and proteoglycans in breast and gastric cancers.Comparative analysis of samples revealed that the CL/P-associated PTCH1 variants A443G and V908G are potentially carcinogenic.These findings provide new insights into the carcinogenic potential of PTCH1 dysfunction.展开更多
A variation in the classical Turn extremal problem is studied. A simple graph G of order n is said to have property P k if it contains a clique of size k+1 as its subgraph. An n term nonincreasing nonnegative integer ...A variation in the classical Turn extremal problem is studied. A simple graph G of order n is said to have property P k if it contains a clique of size k+1 as its subgraph. An n term nonincreasing nonnegative integer sequence π=(d 1,d 2,...,d n) is said to be graphic if it is the degree sequence of a simple graph G of order n and such a graph G is referred to as a realization of π . A graphic sequence π is said to be potentially P k graphic if it has a realization G having property P k . The problem: determine the smallest positive even number σ(k,n) such that every n term graphic sequence π=(d 1,d 2,...,d n) without zero terms and with degree sum σ(π)=d 1+d 2+...+d n at least σ(k,n) is potentially P k graphic has been proved positive.展开更多
We consider a variation of a classical Turán-type extremal problem as follows: Determine the smallest even integer σ(Kr,r,n) such that every n-term graphic sequence π = (d1,d2,...,dn) with term sum σ(π) = d1 ...We consider a variation of a classical Turán-type extremal problem as follows: Determine the smallest even integer σ(Kr,r,n) such that every n-term graphic sequence π = (d1,d2,...,dn) with term sum σ(π) = d1 + d2 + ... + dn ≥ σ(Kr,r,n) is potentially Kr,r-graphic, where Kr,r is an r × r complete bipartite graph, i.e. π has a realization G containing Kr,r as its subgraph. In this paper, the values σ(Kr,r,n) for even r and n ≥ 4r2 - r - 6 and for odd r and n ≥ 4r2 + 3r - 8 are determined.展开更多
Let a(Kr,+1 - K3,n) be the smallest even integer such that each n-term graphic sequence п= (d1,d2,…dn) with term sum σ(п) = d1 + d2 +…+ dn 〉 σ(Kr+1 -K3,n) has a realization containing Kr+1 - K3 as...Let a(Kr,+1 - K3,n) be the smallest even integer such that each n-term graphic sequence п= (d1,d2,…dn) with term sum σ(п) = d1 + d2 +…+ dn 〉 σ(Kr+1 -K3,n) has a realization containing Kr+1 - K3 as a subgraph, where Kr+1 -K3 is a graph obtained from a complete graph Kr+1 by deleting three edges which form a triangle. In this paper, we determine the value σ(Kr+1 - K3,n) for r ≥ 3 and n ≥ 3r+ 5.展开更多
For efficient energy consumption and control of effluent quality, the cycle duration for a sequencing batch reactor (SBR) needs to be adjusted by real-time control according to the characteristics and loading of waste...For efficient energy consumption and control of effluent quality, the cycle duration for a sequencing batch reactor (SBR) needs to be adjusted by real-time control according to the characteristics and loading of waste-water. In this study, an on-line information system for phosphorus removal processes was established. Based on the analysis for four systems with different ecological community structures and two operation modes, anaerobic-aerobic process and anaerobic-anaerobic process, the characteristic patterns of oxidation-reduction potential (ORP) and pH were related to phosphorous dynamics in the anaerobic, anoxic and aerobic phases, for determination of the end of phosphorous removal. In the operation mode of anaerobic-aerobic process, the pH profile in the anaerobic phase was used to estimate the relative amount of phosphorous accumulating organisms (PAOs) and glycogen accumulat-ing organisms (GAOs), which is beneficial to early detection of ecology community shifts. The on-line sensor val-ues of pH and ORP may be used as the parameters to adjust the duration for phosphorous removal and community shifts to cope with influent variations and maintain appropriate operation conditions.展开更多
Biological raw data are growing exponentially, providing a large amount of information on what life is. It is believed that potential functions and the rules governing protein behaviors can be revealed from analysis o...Biological raw data are growing exponentially, providing a large amount of information on what life is. It is believed that potential functions and the rules governing protein behaviors can be revealed from analysis on known native structures of proteins. Many knowledge-based potentials for proteins have been proposed. Contrary to most existing review articles which mainly describe technical details and applications of various potential models, the main foci for the discussion here are ideas and concepts involving the construction of potentials, including the relation between free energy and energy, the additivity of potentials of mean force and some key issues in potential construction. Sequence analysis is briefly viewed from an energetic viewpoint.展开更多
A non-increasing sequenceπ=(d_1,d_2,···,d_n)of nonnegative integers is said to be potentially hamiltonian-graphic(resp.potentially pancyclic-graphic)if it is realizable by a simple graph on n vertices ...A non-increasing sequenceπ=(d_1,d_2,···,d_n)of nonnegative integers is said to be potentially hamiltonian-graphic(resp.potentially pancyclic-graphic)if it is realizable by a simple graph on n vertices containing a hamiltonian cycle(resp.containing cycles of every length from 3 to n).A.R.Rao and S.B.Rao(J.Combin.Theory Ser.B,13(1972),185–191)and Kundu(Discrete Math.,6(1973),367–376)presented a characterization ofπ=(d_1,d_2,···,d_n)that is potentially hamiltonian-graphic.S.B.Rao(Lecture Notes in Math.,No.855,Springer Verlag,1981,417–440,Unsolved Problem 2)further posed the following problem:present a characterization ofπ=(d_1,d_2,···,d_n)that is potentially pancyclic-graphic.In this paper,we first give solution to this problem for the case of 4≤n≤11.Moreover,we also show that a near regular graphic sequenceπ=(d_1,d_2,···,d_n)with dn≥3 is potentially pancyclic-graphic.展开更多
Let n 〉 r, let lr --- (dl,d2,-,dn) be a non-increasing sequence of nonnegative integers and let Kr+l - e be the graph obtained from Kr+l by deleting one edge. If zr has a realization G containing Kr+l - e as a s...Let n 〉 r, let lr --- (dl,d2,-,dn) be a non-increasing sequence of nonnegative integers and let Kr+l - e be the graph obtained from Kr+l by deleting one edge. If zr has a realization G containing Kr+l - e as a subgraph, then r is said to be potentially Kr+l - e-graphic. In this paper, we give a characterization for a sequence π to be potentially Kr+l - e-graphic.展开更多
The topology of diode neutral-point-clamped(NPC)three-level inverter is prone to neutral-point potential offset.When the sum of three-phase current is zero,the virtual space vector pulse width modulation(VSVPWM)scheme...The topology of diode neutral-point-clamped(NPC)three-level inverter is prone to neutral-point potential offset.When the sum of three-phase current is zero,the virtual space vector pulse width modulation(VSVPWM)scheme does not cause the neutral-point voltage offset,but it lacks the ability to balance the deviation.For this reason,a neutral-point potential control strategy combining virtual space vector modulation and loop width control is proposed.The neutral-point potential is balanced by introducing the distribution factor for the regions with redundant vectors.For other regions,the potential is controlled by selecting a suitable switching sequence.Meanwhile,the effect on the virtual vector modulation is reduced within the loop width by setting an appropriate loop width,thereby improving the balance effect.The simulation results show that the proposed method has a strong ability to control the offset and has excellent potential balance performance under the conditions of balanced load,unbalanced load and asymmetric capacitance parameters.展开更多
文摘A loopless graph on n vertices in which vertices are connected at least by a and at most by b edges is called a(a,b,n)-graph. A(b,b,n)-graph is called(b,n)-graph and is denoted by K_n^b(it is a complete graph), its complement by K_n^b. A non increasing sequence π =(d_1,…,d_n) of nonnegative integers is said to be(a,b,n) graphic if it is realizable by an(a,b,n)-graph. We say a simple graphic sequence π=(d_1,…,d_n) is potentially K_4-K_2∪K_2-graphic if it has a a realization containing an K_4-K_2∪K_2 as a subgraph where K_4 is a complete graph on four vertices and K_2∪K_2 is a set of independent edges. In this paper, we find the smallest degree sum such that every n-term graphical sequence contains K_4-K_2∪K_2 as subgraph.
基金Foundation item: Supported by the National Natural Science Foundation of China(11101358) Supported by the Project of Fujian Education Department(JA11165)+1 种基金 Supported by the Project of Education Department of Fujian Province(JA12209) Supported by the Project of Zhangzhou Teacher's College(S11104)
文摘For a given graph H, a graphic sequence π =(d1, d2, ···, dn) is said to be potentially H-graphic if π has a realization containing H as a subgraph. In this paper, we characterize the potentially C6+ P2-graphic sequences where C6+ P2 denotes the graph obtained from C6 by adding two adjacent edges to the three pairwise nonadjacent vertices of C6. Moreover, we use the characterization to determine the value of σ(C6+ P2, n).
基金This work was supported by the Natural Science Foundation of China(Nos.81870747,82170916)Clinical Medicine Plus X–Young Scholars Project(PKU2021LCXQ003)the Fundamental Research Funds for the Central Universities(BMU2021YJ001).
文摘Cancer progression involves the sonic hedgehog(SHH)pathway,in which the receptor PTCH1 actives the downstream pathways.Dysfunction of PTCH1 can lead to nevoid basal cell carcinoma Syndrome(NBCCs)including neoplastic disease and congenital disorder.To evaluate the relationship between PTCH1 and cancer,we applied the CRISPR/Cas9 system to knock out PTCH1 in oral nontumorous epithelial cells(GMSM-K).Then we screened six PTCH1 variants associated with cleft lip/palate(CL/P),one of the congenital disorders in NBCCs,and generated PTCH1 variant and wild-type recombinant PTCH1^(−/−)GMSM-K cell lines.Transcriptome sequencing was conducted in these cell lines.The results revealed that differentially expressed genes(DEGs)in PTCH1^(−/−)GMSM-K were enriched in extracellular compartments,contributing epithelial diseases by pathway enrichment analysis.RT-PCR confirmed that KRT34,KRT81,KRT86,PDGFB,and WNT10B genes,associated with extracellular compartments were highly expressed in PTCH1^(−/−).The Kyoto Encyclopedia of Genes and Genomes analysis also suggested that DEGs are closely related to focal adhesion,transcriptional misregulation,and proteoglycans in breast and gastric cancers.Comparative analysis of samples revealed that the CL/P-associated PTCH1 variants A443G and V908G are potentially carcinogenic.These findings provide new insights into the carcinogenic potential of PTCH1 dysfunction.
文摘A variation in the classical Turn extremal problem is studied. A simple graph G of order n is said to have property P k if it contains a clique of size k+1 as its subgraph. An n term nonincreasing nonnegative integer sequence π=(d 1,d 2,...,d n) is said to be graphic if it is the degree sequence of a simple graph G of order n and such a graph G is referred to as a realization of π . A graphic sequence π is said to be potentially P k graphic if it has a realization G having property P k . The problem: determine the smallest positive even number σ(k,n) such that every n term graphic sequence π=(d 1,d 2,...,d n) without zero terms and with degree sum σ(π)=d 1+d 2+...+d n at least σ(k,n) is potentially P k graphic has been proved positive.
基金This work was supported by the National Natural Science Foundation of China (Grant No.19971086).
文摘We consider a variation of a classical Turán-type extremal problem as follows: Determine the smallest even integer σ(Kr,r,n) such that every n-term graphic sequence π = (d1,d2,...,dn) with term sum σ(π) = d1 + d2 + ... + dn ≥ σ(Kr,r,n) is potentially Kr,r-graphic, where Kr,r is an r × r complete bipartite graph, i.e. π has a realization G containing Kr,r as its subgraph. In this paper, the values σ(Kr,r,n) for even r and n ≥ 4r2 - r - 6 and for odd r and n ≥ 4r2 + 3r - 8 are determined.
基金Supported by the National Natural Science Foundation of China (No.10401010).
文摘Let a(Kr,+1 - K3,n) be the smallest even integer such that each n-term graphic sequence п= (d1,d2,…dn) with term sum σ(п) = d1 + d2 +…+ dn 〉 σ(Kr+1 -K3,n) has a realization containing Kr+1 - K3 as a subgraph, where Kr+1 -K3 is a graph obtained from a complete graph Kr+1 by deleting three edges which form a triangle. In this paper, we determine the value σ(Kr+1 - K3,n) for r ≥ 3 and n ≥ 3r+ 5.
基金Supported by the Project of Scientific Research Base and Scientific Innovation Platform of Beijing Municipal Education Com-mission (PXM2008_014204_050843)the National Natural Science Foundation of China (50808004)the DoctoralStartup Research Program of Beijing University of Technology
文摘For efficient energy consumption and control of effluent quality, the cycle duration for a sequencing batch reactor (SBR) needs to be adjusted by real-time control according to the characteristics and loading of waste-water. In this study, an on-line information system for phosphorus removal processes was established. Based on the analysis for four systems with different ecological community structures and two operation modes, anaerobic-aerobic process and anaerobic-anaerobic process, the characteristic patterns of oxidation-reduction potential (ORP) and pH were related to phosphorous dynamics in the anaerobic, anoxic and aerobic phases, for determination of the end of phosphorous removal. In the operation mode of anaerobic-aerobic process, the pH profile in the anaerobic phase was used to estimate the relative amount of phosphorous accumulating organisms (PAOs) and glycogen accumulat-ing organisms (GAOs), which is beneficial to early detection of ecology community shifts. The on-line sensor val-ues of pH and ORP may be used as the parameters to adjust the duration for phosphorous removal and community shifts to cope with influent variations and maintain appropriate operation conditions.
基金Project supported in part by the National Natural Science Foundation of China(Grant Nos.11175224 and 11121403)
文摘Biological raw data are growing exponentially, providing a large amount of information on what life is. It is believed that potential functions and the rules governing protein behaviors can be revealed from analysis on known native structures of proteins. Many knowledge-based potentials for proteins have been proposed. Contrary to most existing review articles which mainly describe technical details and applications of various potential models, the main foci for the discussion here are ideas and concepts involving the construction of potentials, including the relation between free energy and energy, the additivity of potentials of mean force and some key issues in potential construction. Sequence analysis is briefly viewed from an energetic viewpoint.
基金Supported by National Natural Science Foundation of China(Grant No.11561017)Natural Science Foundation of Hainan Province(Grant No.2016CXTD004)
文摘A non-increasing sequenceπ=(d_1,d_2,···,d_n)of nonnegative integers is said to be potentially hamiltonian-graphic(resp.potentially pancyclic-graphic)if it is realizable by a simple graph on n vertices containing a hamiltonian cycle(resp.containing cycles of every length from 3 to n).A.R.Rao and S.B.Rao(J.Combin.Theory Ser.B,13(1972),185–191)and Kundu(Discrete Math.,6(1973),367–376)presented a characterization ofπ=(d_1,d_2,···,d_n)that is potentially hamiltonian-graphic.S.B.Rao(Lecture Notes in Math.,No.855,Springer Verlag,1981,417–440,Unsolved Problem 2)further posed the following problem:present a characterization ofπ=(d_1,d_2,···,d_n)that is potentially pancyclic-graphic.In this paper,we first give solution to this problem for the case of 4≤n≤11.Moreover,we also show that a near regular graphic sequenceπ=(d_1,d_2,···,d_n)with dn≥3 is potentially pancyclic-graphic.
基金Supported by National Natural Science Foundation of China(Nos.11161016 and 10861006)
文摘Let n 〉 r, let lr --- (dl,d2,-,dn) be a non-increasing sequence of nonnegative integers and let Kr+l - e be the graph obtained from Kr+l by deleting one edge. If zr has a realization G containing Kr+l - e as a subgraph, then r is said to be potentially Kr+l - e-graphic. In this paper, we give a characterization for a sequence π to be potentially Kr+l - e-graphic.
基金National Natural Science Foundation of China(No.61761027)Postgraduate Education Reform Project of Lanzhou Jiaotong University(No.1600120101)
文摘The topology of diode neutral-point-clamped(NPC)three-level inverter is prone to neutral-point potential offset.When the sum of three-phase current is zero,the virtual space vector pulse width modulation(VSVPWM)scheme does not cause the neutral-point voltage offset,but it lacks the ability to balance the deviation.For this reason,a neutral-point potential control strategy combining virtual space vector modulation and loop width control is proposed.The neutral-point potential is balanced by introducing the distribution factor for the regions with redundant vectors.For other regions,the potential is controlled by selecting a suitable switching sequence.Meanwhile,the effect on the virtual vector modulation is reduced within the loop width by setting an appropriate loop width,thereby improving the balance effect.The simulation results show that the proposed method has a strong ability to control the offset and has excellent potential balance performance under the conditions of balanced load,unbalanced load and asymmetric capacitance parameters.