Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is propo...Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.展开更多
The title compound, {(H3O)4(NH4)4[Mo8O28]?2H2O}n 1, has been synthesized from the reaction of Zn(OAc)2 and (NH4)6Mo7O24?4H2O in aqueous solution at ambient tempe- rature, and its crystal structure was determined by ...The title compound, {(H3O)4(NH4)4[Mo8O28]?2H2O}n 1, has been synthesized from the reaction of Zn(OAc)2 and (NH4)6Mo7O24?4H2O in aqueous solution at ambient tempe- rature, and its crystal structure was determined by X-ray single-crystal analysis with the following crystallographic data: monoclinic system, space group P21/n, a = 9.5234(6), b = 11.3235(8), c = 14.8812(10) ?, β = 107.467(2)o, V = 1530.77(18) ?3, Z = 4, F(000) = 1336, μ = 3.293 mm-1 and Dc = 3.037 g/cm3. The final R = 0.0619 for 2691 observed reflections (I > 2σ(I)). X-ray crys- tal structure analysis showed that the novel one-dimensional chain compound is built up by basic {Mo8O28} units via single μ2-O, and such chains are further linked into a three-dimensional net- work by hydrogen bonds.展开更多
This research aim to evaluate hydro-meteorological data from the Yamuna River Basin,Uttarakhand,India,utilizing Extreme Value Distribution of Frequency Analysis and the Markov Chain Approach.This method assesses persi...This research aim to evaluate hydro-meteorological data from the Yamuna River Basin,Uttarakhand,India,utilizing Extreme Value Distribution of Frequency Analysis and the Markov Chain Approach.This method assesses persistence and allows for combinatorial probability estimations such as initial and transitional probabilities.The hydrologic data was generated(in-situ)and received from Uttarakhand Jal Vidut Nigam Limited(UJVNL),and meteorological data was acquired from NASA’s archives MERRA-2 product.A total of sixteen years(2005-2020)of data was used to foresee daily Precipitation from 2020 to 2022.MERRA-2 products are utilized as observed and forecast values for daily Precipitation throughout the monsoon season,which runs from July to September.Markov Chain and Long Short-Term Memory(LSTM)findings for 2020,2021,and 2022 were observed,and anticipated values for daily rainfall during the monsoon season between July and September.According to test findings,the artificial intelligence technique cannot anticipate future regional meteorological formations;the correlation coefficient R^(2) is around 0.12.According to the randomly verified precipitation data findings,the Markov Chain model has a success rate of 79.17 percent.The results suggest that extended return periods should be a warning sign for drought and flood risk in the Himalayan region.This study gives a better knowledge of the water budget,climate change variability,and impact of global warming,ultimately leading to improved water resource management and better emergency planning to the establishment of the Early Warning System(EWS)for extreme occurrences such as cloudbursts,flash floods,landslides hazards in the complex Himalayan region.展开更多
A new compound with one-dimensional spin chains, Ba9Co3Se(15), was synthesized under high pressure and high temperature conditions and systematically characterized via structural, transport and magnetic measurements. ...A new compound with one-dimensional spin chains, Ba9Co3Se(15), was synthesized under high pressure and high temperature conditions and systematically characterized via structural, transport and magnetic measurements. Ba9Co3Se(15) crystallizes in a hexagonal structure with the space group P-6c2(No. 188) and lattice constants of a = b = 9.6765 ? and c = 18.9562 ?. The structure consists of trimeric face-sharing octahedral CoSe6 chains, which are arranged in a triangular lattice in the ab-plane and separated by Ba atoms. The distance of the nearest neighbor of CoSe6 chains is very large, given by the lattice constant a = 9.6765 ?. The Weiss temperature Tθ associated with the intra-chain coupling strength is about -346 K. However, no long-range magnetic order but a spin glass transition at ~ 3 K has been observed. Our results indicate that the spin glass behavior in Ba9Co3Se(15) mainly arises from the magnetic frustration due to the geometrically frustrated triangular lattice.展开更多
We further calculate the dependence of xT on T in high magnetic fields,where X denotes susceptibility and T is temperature,using our previous research work - Green function's decoupling approximate approach,for th...We further calculate the dependence of xT on T in high magnetic fields,where X denotes susceptibility and T is temperature,using our previous research work - Green function's decoupling approximate approach,for the one-dimensional ferrimagnetic chain with alternating spins 1 and 1/2.We find a linear correlation in certain range of magnetic field between the temperature of xT maximum and the magnetic field.Moreover,we simply analyze its physical meaning by our approach.展开更多
A vanadyl phosphate containing a new member of tancoite-like single chain, (DAPH2)[VIVO(HPO4)2]·xH20 (x ≈ 0.2, DAP = 1,3-diaminopropane, C3H10N2), has been synthesized under hydro(solvo)thermal condition...A vanadyl phosphate containing a new member of tancoite-like single chain, (DAPH2)[VIVO(HPO4)2]·xH20 (x ≈ 0.2, DAP = 1,3-diaminopropane, C3H10N2), has been synthesized under hydro(solvo)thermal conditions. It crystallizes in orthorhombic space group P21212 (No. 18) with a = 7.1730(14), b = 19.252(4), c = 8.6557(17) A, Z= 4, V= 1195.3(4)A3, C3H14.38N2P2VO9.19, Mr = 338.47, Dc = 1.881 g/cm3,μ(MoKa) = 1.138 mm-1 and F(000) = 692. The final full-matrix least-squares refinement converged to R = 0.0408, wR = 0.1046 for 2498 observed reflections with I 〉 2σ(I) and R = 0.0456 and wR = 0.1080 for all data (2750) and S = 1.001. Its one-dimensional 1 structure consists of tancoite-like ∞1 {vIVO(HPO4)2}2- single chains surrounded by DAPH22+ ions and water molecules. The single chain is built from trans-corner-sharing octahedral {VIV= O…VIV} backbone loop-branched by HPO4 groups like staple forming a new member of tancoite single chain. Due to the special coordination of VIVO6, the ∞1 {VO(HPO4)2-} chain adopts a larger M-O-M angle (V-O-V = 135°) than those of tancoite chains reported before. The corner-sharing linear {VIV = O…VIV} chain structure also leads to a one-dimensional weak antiferromagnetic interaction at low temperature. The magnetic measurements confirm the 4+ valence state of vanadium. IR and TG results of the title compound are also discussed.展开更多
We study the ground-state information of one-dimensional Heisenberg chain with alternating D-term. Given the ground-state phase diagram, the ground-state energy and the entanglement entropy are obtained by tensor-net ...We study the ground-state information of one-dimensional Heisenberg chain with alternating D-term. Given the ground-state phase diagram, the ground-state energy and the entanglement entropy are obtained by tensor-net work algorithm. The phase transition points are shown in the entanglement entropy figure. The results are agreed with the phase diagram.展开更多
The complexe{[K(DB18-crown-6)]_(2)(CH_(3)CN)}[Pt(SCN)_(4)]was synthesized and characterized by elemental analysis,IR spectrum and X-ray diffraction analysis.The complexe belongs to monoclinic,space group c2/c with cel...The complexe{[K(DB18-crown-6)]_(2)(CH_(3)CN)}[Pt(SCN)_(4)]was synthesized and characterized by elemental analysis,IR spectrum and X-ray diffraction analysis.The complexe belongs to monoclinic,space group c2/c with cell dimensions,a=2.5904(8),6=1.3653(4),c-1.84706(6)nm,β=123.811(4)°,V=5-339(3)nm^(3),Z=4,.Dcalcd=l.577 g/cm^(3),F(000)=2552,R_(1)=0.051 l,wR_(2)=0.1411.The complexe shows one-dimensional chain of{[K(DB18-crown-6)]+complex cation and[Pt(SCN),i]2-complex anion bridged by N atom of CHaCN moleculer between two[K(DB18-crown-6)]_(2)[Pt(SCN)_(4)]groups respectively.展开更多
目的 针对妇幼卫生纵向数据的任意缺失模式,采用多重填补方法进行填补,探求最佳填补结果,以便对数据作进一步分析与研究。方法 运用SAS9.0 ,采用多重填补方法Markov China Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。...目的 针对妇幼卫生纵向数据的任意缺失模式,采用多重填补方法进行填补,探求最佳填补结果,以便对数据作进一步分析与研究。方法 运用SAS9.0 ,采用多重填补方法Markov China Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。结果 填补5次所得结果最优。结论 多重填补方法可以处理有缺失数据资料中的许多普遍问题,可提高统计效率,尤其是MCMC模型在处理复杂的缺失数据上,优势明显。展开更多
Modeling non coding background sequences appropriately is important for the detection of regulatory elements from DNA sequences. Based on the chi square statistic test, some explanations about why to choose higher ...Modeling non coding background sequences appropriately is important for the detection of regulatory elements from DNA sequences. Based on the chi square statistic test, some explanations about why to choose higher order Markov chain model and how to automatically select the proper order are given in this paper. The chi square test is first run on synthetic data sets to show that it can efficiently find the proper order of Markov chain. Using chi square test, distinct higher order context dependences inherent in ten sets of sequences of yeast S.cerevisiae from other literature have been found. So the Markov chain with higher order would be more suitable for modeling the non coding background sequences than an independent model.展开更多
A Markov chain-based stochastic model (MCM) is developed to simulate the movement of particles in a 2D bubbling fluidized bed (BFB). The state spaces are determined by the discretized physical cells of the bed, an...A Markov chain-based stochastic model (MCM) is developed to simulate the movement of particles in a 2D bubbling fluidized bed (BFB). The state spaces are determined by the discretized physical cells of the bed, and the transition probability matrix is directly calculated by the results of a discrete element method (DEM) simulation. The Markov property of the BFB is discussed by the comparison results calculated from both static and dynamic transition probability matrices. The static matrix is calculated based on the Markov chain while the dynamic matrix is calculated based on the memory property of the particle movement. Results show that the difference in the trends of particle movement between the static and dynamic matrix calculation is very small. Besides, the particle mixing curves of the MCM and DEM have the same trend and similar numerical values, and the details show the time averaged characteristic of the MCM and also expose its shortcoming in describing the instantaneous particle dynamics in the BFB.展开更多
目的探讨基于Markov Chain Monte Carlo(MCMC)模型的多重估算法在处理医院调查资料缺失数据中的应用。方法运用SAS9.2编写程序,在分析数据的分布类型和缺失机制的基础上,采用MCMC法对缺失数据进行多次填补和联合统计推断,分析多重估算...目的探讨基于Markov Chain Monte Carlo(MCMC)模型的多重估算法在处理医院调查资料缺失数据中的应用。方法运用SAS9.2编写程序,在分析数据的分布类型和缺失机制的基础上,采用MCMC法对缺失数据进行多次填补和联合统计推断,分析多重估算法的优势。结果数据服从多元正态分布与随机缺失,采用MCMC法填补10次所得的结果最佳。结论多重估算既可反映缺失数据的不确定性,又可充分利用现有资料的信息、提高统计效率、对模型的估计结果更加可信,是处理缺失数据的有效方法。展开更多
The Mesoproterozoic Wumishan Formation in the Jixian section of Tianjin is a succession of 3300-m-thick carbonate strata formed in a period of about 100 Ma (1310±20 Ma-1207±10 Ma). In this succession of stra...The Mesoproterozoic Wumishan Formation in the Jixian section of Tianjin is a succession of 3300-m-thick carbonate strata formed in a period of about 100 Ma (1310±20 Ma-1207±10 Ma). In this succession of strata, the carbonate metre-scale cyclic sequences belonging to peritidal type with an approximately symmetrical lithofacies-succession are best developed. The wide development of 1:4 stacking patterns shows that these metre-scale cyclic sequences are genetically related to the short-eccentricity cycles, which are called the Wumishan cyclothems that could truly represent sedimentary cycles. Generally, massive and thick-bedded calcareous dolomites and dolomitic limestones of stromatolite biostromes and thrombolite bioherms constitute the central part of the Wumishan cyclothems. The lower and upper parts consist of tidal flat dolostones, sandy-muddy dolostone and the top part is composed of lagoonal facies dolomitic shales with a paleosol cap. Therefore, an approximately symmetrical lithofacies-succession is formed. Many features such as the clear deepening and shoaling vectors of cyclothems, and all kinds of marks of fresh-water diagenesis indicate that the Wumishan cyclothems are the product of autocyclic sedimentation governed by allocyclic high-frequency sea-level changes. The results of a Markov chain analysis reaffirm the existence of the lithofacies-succession model of the Wumishan cyclothems. The boundaries of the Wumishan cyclothems are marked by the instantaneous exposed punctuated surface, which leads to the discrepancy between the cyclothems and the parasequences of the sequence stratigraphy terminology system. It is difficult to form a judgment that the time span of the Milankovitch cycles in the Precambrian is certainly equal to that of the Phanerozoic, but the regularly vertical stacking patterns of the seventh-order rhythms, sixth-order cyclothems and fifth-order parasequence sets still indicate their consistency with the duration of the Milankovitch cycles in the Phanerozoic.展开更多
文摘Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.
基金This project was supported by the 973 program of the MOST (001CB108906) the National Natural Science Foundation of China (90206040+4 种基金20073048) the NSF of Fujian Province (2002F015 2002J006) the State Key Lab of Chemistry (030065) the Chinese Academy of Sciences
文摘The title compound, {(H3O)4(NH4)4[Mo8O28]?2H2O}n 1, has been synthesized from the reaction of Zn(OAc)2 and (NH4)6Mo7O24?4H2O in aqueous solution at ambient tempe- rature, and its crystal structure was determined by X-ray single-crystal analysis with the following crystallographic data: monoclinic system, space group P21/n, a = 9.5234(6), b = 11.3235(8), c = 14.8812(10) ?, β = 107.467(2)o, V = 1530.77(18) ?3, Z = 4, F(000) = 1336, μ = 3.293 mm-1 and Dc = 3.037 g/cm3. The final R = 0.0619 for 2691 observed reflections (I > 2σ(I)). X-ray crys- tal structure analysis showed that the novel one-dimensional chain compound is built up by basic {Mo8O28} units via single μ2-O, and such chains are further linked into a three-dimensional net- work by hydrogen bonds.
基金This research work was carried out during the SERB,SIRE fellowship (File No.SIR/2022/000972)tenure at Keio University,Japan.
文摘This research aim to evaluate hydro-meteorological data from the Yamuna River Basin,Uttarakhand,India,utilizing Extreme Value Distribution of Frequency Analysis and the Markov Chain Approach.This method assesses persistence and allows for combinatorial probability estimations such as initial and transitional probabilities.The hydrologic data was generated(in-situ)and received from Uttarakhand Jal Vidut Nigam Limited(UJVNL),and meteorological data was acquired from NASA’s archives MERRA-2 product.A total of sixteen years(2005-2020)of data was used to foresee daily Precipitation from 2020 to 2022.MERRA-2 products are utilized as observed and forecast values for daily Precipitation throughout the monsoon season,which runs from July to September.Markov Chain and Long Short-Term Memory(LSTM)findings for 2020,2021,and 2022 were observed,and anticipated values for daily rainfall during the monsoon season between July and September.According to test findings,the artificial intelligence technique cannot anticipate future regional meteorological formations;the correlation coefficient R^(2) is around 0.12.According to the randomly verified precipitation data findings,the Markov Chain model has a success rate of 79.17 percent.The results suggest that extended return periods should be a warning sign for drought and flood risk in the Himalayan region.This study gives a better knowledge of the water budget,climate change variability,and impact of global warming,ultimately leading to improved water resource management and better emergency planning to the establishment of the Early Warning System(EWS)for extreme occurrences such as cloudbursts,flash floods,landslides hazards in the complex Himalayan region.
基金Project supported by the National Key R&D Program of China and the National Natural Science Foundation of China(Grant Nos.2018YFA0305700,2017YFA0302900,11974410,and 11534016)。
文摘A new compound with one-dimensional spin chains, Ba9Co3Se(15), was synthesized under high pressure and high temperature conditions and systematically characterized via structural, transport and magnetic measurements. Ba9Co3Se(15) crystallizes in a hexagonal structure with the space group P-6c2(No. 188) and lattice constants of a = b = 9.6765 ? and c = 18.9562 ?. The structure consists of trimeric face-sharing octahedral CoSe6 chains, which are arranged in a triangular lattice in the ab-plane and separated by Ba atoms. The distance of the nearest neighbor of CoSe6 chains is very large, given by the lattice constant a = 9.6765 ?. The Weiss temperature Tθ associated with the intra-chain coupling strength is about -346 K. However, no long-range magnetic order but a spin glass transition at ~ 3 K has been observed. Our results indicate that the spin glass behavior in Ba9Co3Se(15) mainly arises from the magnetic frustration due to the geometrically frustrated triangular lattice.
文摘We further calculate the dependence of xT on T in high magnetic fields,where X denotes susceptibility and T is temperature,using our previous research work - Green function's decoupling approximate approach,for the one-dimensional ferrimagnetic chain with alternating spins 1 and 1/2.We find a linear correlation in certain range of magnetic field between the temperature of xT maximum and the magnetic field.Moreover,we simply analyze its physical meaning by our approach.
基金Supported by the National Natural Science Foundation of China(No.21201144,21233004,and 40972035)Fundamental Research Funds for the Central Universities(No.2013121020)+1 种基金Natural Science Foundation of Fujian Province(No.2010J01308)Technological Innovation Platform of Fujian Province(2006L2003)
文摘A vanadyl phosphate containing a new member of tancoite-like single chain, (DAPH2)[VIVO(HPO4)2]·xH20 (x ≈ 0.2, DAP = 1,3-diaminopropane, C3H10N2), has been synthesized under hydro(solvo)thermal conditions. It crystallizes in orthorhombic space group P21212 (No. 18) with a = 7.1730(14), b = 19.252(4), c = 8.6557(17) A, Z= 4, V= 1195.3(4)A3, C3H14.38N2P2VO9.19, Mr = 338.47, Dc = 1.881 g/cm3,μ(MoKa) = 1.138 mm-1 and F(000) = 692. The final full-matrix least-squares refinement converged to R = 0.0408, wR = 0.1046 for 2498 observed reflections with I 〉 2σ(I) and R = 0.0456 and wR = 0.1080 for all data (2750) and S = 1.001. Its one-dimensional 1 structure consists of tancoite-like ∞1 {vIVO(HPO4)2}2- single chains surrounded by DAPH22+ ions and water molecules. The single chain is built from trans-corner-sharing octahedral {VIV= O…VIV} backbone loop-branched by HPO4 groups like staple forming a new member of tancoite single chain. Due to the special coordination of VIVO6, the ∞1 {VO(HPO4)2-} chain adopts a larger M-O-M angle (V-O-V = 135°) than those of tancoite chains reported before. The corner-sharing linear {VIV = O…VIV} chain structure also leads to a one-dimensional weak antiferromagnetic interaction at low temperature. The magnetic measurements confirm the 4+ valence state of vanadium. IR and TG results of the title compound are also discussed.
文摘We study the ground-state information of one-dimensional Heisenberg chain with alternating D-term. Given the ground-state phase diagram, the ground-state energy and the entanglement entropy are obtained by tensor-net work algorithm. The phase transition points are shown in the entanglement entropy figure. The results are agreed with the phase diagram.
文摘The complexe{[K(DB18-crown-6)]_(2)(CH_(3)CN)}[Pt(SCN)_(4)]was synthesized and characterized by elemental analysis,IR spectrum and X-ray diffraction analysis.The complexe belongs to monoclinic,space group c2/c with cell dimensions,a=2.5904(8),6=1.3653(4),c-1.84706(6)nm,β=123.811(4)°,V=5-339(3)nm^(3),Z=4,.Dcalcd=l.577 g/cm^(3),F(000)=2552,R_(1)=0.051 l,wR_(2)=0.1411.The complexe shows one-dimensional chain of{[K(DB18-crown-6)]+complex cation and[Pt(SCN),i]2-complex anion bridged by N atom of CHaCN moleculer between two[K(DB18-crown-6)]_(2)[Pt(SCN)_(4)]groups respectively.
文摘目的 针对妇幼卫生纵向数据的任意缺失模式,采用多重填补方法进行填补,探求最佳填补结果,以便对数据作进一步分析与研究。方法 运用SAS9.0 ,采用多重填补方法Markov China Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。结果 填补5次所得结果最优。结论 多重填补方法可以处理有缺失数据资料中的许多普遍问题,可提高统计效率,尤其是MCMC模型在处理复杂的缺失数据上,优势明显。
文摘Modeling non coding background sequences appropriately is important for the detection of regulatory elements from DNA sequences. Based on the chi square statistic test, some explanations about why to choose higher order Markov chain model and how to automatically select the proper order are given in this paper. The chi square test is first run on synthetic data sets to show that it can efficiently find the proper order of Markov chain. Using chi square test, distinct higher order context dependences inherent in ten sets of sequences of yeast S.cerevisiae from other literature have been found. So the Markov chain with higher order would be more suitable for modeling the non coding background sequences than an independent model.
基金The National Science Foundation of China(No.51276036,51306035)the Fundamental Research Funds for the Central Universities(No.KYLX_0114)
文摘A Markov chain-based stochastic model (MCM) is developed to simulate the movement of particles in a 2D bubbling fluidized bed (BFB). The state spaces are determined by the discretized physical cells of the bed, and the transition probability matrix is directly calculated by the results of a discrete element method (DEM) simulation. The Markov property of the BFB is discussed by the comparison results calculated from both static and dynamic transition probability matrices. The static matrix is calculated based on the Markov chain while the dynamic matrix is calculated based on the memory property of the particle movement. Results show that the difference in the trends of particle movement between the static and dynamic matrix calculation is very small. Besides, the particle mixing curves of the MCM and DEM have the same trend and similar numerical values, and the details show the time averaged characteristic of the MCM and also expose its shortcoming in describing the instantaneous particle dynamics in the BFB.
文摘目的探讨基于Markov Chain Monte Carlo(MCMC)模型的多重估算法在处理医院调查资料缺失数据中的应用。方法运用SAS9.2编写程序,在分析数据的分布类型和缺失机制的基础上,采用MCMC法对缺失数据进行多次填补和联合统计推断,分析多重估算法的优势。结果数据服从多元正态分布与随机缺失,采用MCMC法填补10次所得的结果最佳。结论多重估算既可反映缺失数据的不确定性,又可充分利用现有资料的信息、提高统计效率、对模型的估计结果更加可信,是处理缺失数据的有效方法。
文摘The Mesoproterozoic Wumishan Formation in the Jixian section of Tianjin is a succession of 3300-m-thick carbonate strata formed in a period of about 100 Ma (1310±20 Ma-1207±10 Ma). In this succession of strata, the carbonate metre-scale cyclic sequences belonging to peritidal type with an approximately symmetrical lithofacies-succession are best developed. The wide development of 1:4 stacking patterns shows that these metre-scale cyclic sequences are genetically related to the short-eccentricity cycles, which are called the Wumishan cyclothems that could truly represent sedimentary cycles. Generally, massive and thick-bedded calcareous dolomites and dolomitic limestones of stromatolite biostromes and thrombolite bioherms constitute the central part of the Wumishan cyclothems. The lower and upper parts consist of tidal flat dolostones, sandy-muddy dolostone and the top part is composed of lagoonal facies dolomitic shales with a paleosol cap. Therefore, an approximately symmetrical lithofacies-succession is formed. Many features such as the clear deepening and shoaling vectors of cyclothems, and all kinds of marks of fresh-water diagenesis indicate that the Wumishan cyclothems are the product of autocyclic sedimentation governed by allocyclic high-frequency sea-level changes. The results of a Markov chain analysis reaffirm the existence of the lithofacies-succession model of the Wumishan cyclothems. The boundaries of the Wumishan cyclothems are marked by the instantaneous exposed punctuated surface, which leads to the discrepancy between the cyclothems and the parasequences of the sequence stratigraphy terminology system. It is difficult to form a judgment that the time span of the Milankovitch cycles in the Precambrian is certainly equal to that of the Phanerozoic, but the regularly vertical stacking patterns of the seventh-order rhythms, sixth-order cyclothems and fifth-order parasequence sets still indicate their consistency with the duration of the Milankovitch cycles in the Phanerozoic.