The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust fo...The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust for the model.However,the analytical expressions of MSED and MD are currently only available in the hypercube,but both types of deviations in other studies are just approximations.Although it can obtain good approximations in the low-dimensional case,the calculation will be more complicated for an experiment with more variables.Therefore,in this paper,an algorithm based on lattice point partitioning design is proposed to obtain the analytical expression of the MSED and MD in the region covered by the lattice points.Furthermore,the design’s optimality is considered and illustrated by examples under the same uniformity.展开更多
This paper discussed Bayesian variable selection methods for models from split-plot mixture designs using samples from Metropolis-Hastings within the Gibbs sampling algorithm. Bayesian variable selection is easy to im...This paper discussed Bayesian variable selection methods for models from split-plot mixture designs using samples from Metropolis-Hastings within the Gibbs sampling algorithm. Bayesian variable selection is easy to implement due to the improvement in computing via MCMC sampling. We described the Bayesian methodology by introducing the Bayesian framework, and explaining Markov Chain Monte Carlo (MCMC) sampling. The Metropolis-Hastings within Gibbs sampling was used to draw dependent samples from the full conditional distributions which were explained. In mixture experiments with process variables, the response depends not only on the proportions of the mixture components but also on the effects of the process variables. In many such mixture-process variable experiments, constraints such as time or cost prohibit the selection of treatments completely at random. In these situations, restrictions on the randomisation force the level combinations of one group of factors to be fixed and the combinations of the other group of factors are run. Then a new level of the first-factor group is set and combinations of the other factors are run. We discussed the computational algorithm for the Stochastic Search Variable Selection (SSVS) in linear mixed models. We extended the computational algorithm of SSVS to fit models from split-plot mixture design by introducing the algorithm of the Stochastic Search Variable Selection for Split-plot Design (SSVS-SPD). The motivation of this extension is that we have two different levels of the experimental units, one for the whole plots and the other for subplots in the split-plot mixture design.展开更多
The pathway and fate of heavy metals were studied in 10m3 enclosures at Xiamen Bay in 1985. The dissolved metals added are removed rather quickly during the first days, and their half-removal times ( t1/2) (d) are as ...The pathway and fate of heavy metals were studied in 10m3 enclosures at Xiamen Bay in 1985. The dissolved metals added are removed rather quickly during the first days, and their half-removal times ( t1/2) (d) are as follows: Pb 5. 4-5. 8, Hg 6. 7-14, Zn 11-22, Cu 16 - 29, and Cd 30-89. Zinc is transferred biologically to particles during phytoplankton bloom. The main Fate of added metals after 27 days is as follows; over 80% Cd and 60% Cu remain in dissolved phase, more than 60% Pb and 50% Hg transfer to settling settlement, while Zn is equally distributed in dissolved phase and settling settlement. The wall uptake is less than 2% of the total metals added. Organic materials play an essential role in the partition and the transfer of heavy metals in water column. Terrigenous and autochthonous particles show different affinities to different metals. Most heavy metals associate weakly with zooplankton. The Binding of Cd, Pb, Zn and Cu to the particles shows distinctive features related to the diagenetic alteration.展开更多
[Objectives]This study was conducted to develop a health-care product with smooth taste and high nutrition.[Methods]With natural wheat germ powder as the main raw material and maltodextrin,white sugar,compound stabili...[Objectives]This study was conducted to develop a health-care product with smooth taste and high nutrition.[Methods]With natural wheat germ powder as the main raw material and maltodextrin,white sugar,compound stabilizer and other materials as auxiliary materials,the formula of wheat germ solid beverage was optimized using sensory evaluation value as an index,through the mixture experiment method and fuzzy mathematical analysis.[Results]The optimal formula of wheat germ solid beverage was:sugar 11.51%,maltodextrin 37.89%,wheat germ powder 50%,compound stabilizer 0.6%(arabic gum 0.3%,xanthan gum 0.3%),soya bean lecithin 0.2%,ethyl maltol 0.002%,and vanillin 0.003%.[Conclusions]This study provides a theoretical basis for expanding the market-oriented production and application of wheat germ.展开更多
[Objectives]To study the effects of different material ratios on the dissolution of Tongmai pills.[Methods]Based on mixture uniform experiment design,the fiber,starch and grease-resin materials in Tongmai pills were p...[Objectives]To study the effects of different material ratios on the dissolution of Tongmai pills.[Methods]Based on mixture uniform experiment design,the fiber,starch and grease-resin materials in Tongmai pills were proportioned.The contents of strychnine,brucine,paeoniflorin,calycosin,ferulic acid,hesperidin and salvianolic acid B in the solution were determined by HPLC,and the content of total flavonoids was determined by ultraviolet spectrophotometry.The weight coefficient of index components was determined by analytic hierarchy process,and the SAS software was used to optimize the dissolution model and calculate the dissolution parameter T40.MATLAB was used to establish a mathematical model and realize the data visualization between material ratio and dissolution parameter T40.[Results]The mathematical model between material ratio and dissolution parameter was T40=8.93-5.31X1-5.83X2+17.67X1X3(X1,X2,X3 are fiber,starch and grease-resin materials respectively,r2=0.9706,P=0.01,RMSE=0.5696).[Conclusions]Fiber can effectively promote the dissolution(P<0.05).Starch can promote the dissolution,but the effect is not obvious(P=0.05).The interaction between fiber and grease-resin can inhibit the dissolution,but was not significant(P=0.07).展开更多
Lipid nanoparticles(LNPs)are critical for the delivery of drugs and nucleic acids.However,current mRNA-LNP formulations require stringent freezing for storage,which limits their global distribution.Our previous studie...Lipid nanoparticles(LNPs)are critical for the delivery of drugs and nucleic acids.However,current mRNA-LNP formulations require stringent freezing for storage,which limits their global distribution.Our previous studies demonstrated that optimizing the lipid type or molar ratio of Comirnaty-type mRNA-LNPs could enhance their lyophilization stability,thus improving their long-term storage stability under mild conditions.This study aims to enhance the storage stability of Spikevax-type mRNA-LNPs by optimizing lipid compositions and utilizing lyophilization for storage at 4�C.Fifteen mRNA-LNP formulations were evaluated for their physicochemical properties and transfection efficiency(TE)in human embryonic kidney(HEK)-293T cells using the I-optimal design of mixture experiments.Mathematical models were developed to predict the relationships among encapsulation efficiency,transfection performance and lipid ratios.The optimized mRNA-LNP formulation(N4),with a 1,2-distearoyl-sn-glycero-3-phosphocholine(DSPC)-to-cholesterol ratio of 0.36,exhibited superior stability and TE after lyophilization.N4 outperformed the original Spikevax formulation in several cell lines,including eye-derived ARPE-19 cells and lung-derived A549 cells.In vivo,N4 demonstrated high TE in the spleen of C57BL/6 mice both before and after lyophilization,with no signals observed in the kidneys,heart or eyes.These findings suggest that the optimized N4 formulation offers a robust,stable and efficient delivery system for gene therapy and vaccines,potentially overcoming the storage limitations of current Spikevax-type mRNA-LNPs and broadening their therapeutic applications.展开更多
基金Supported by Science and Technology Fund for Basic Research of Guizhou Province([2020]1Y010)National Nature Sciences Foundation of China(11901260,12071096,12501342)Specialized Fund for the Doctoral Development of Kaili University(BS202502028)。
文摘The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust for the model.However,the analytical expressions of MSED and MD are currently only available in the hypercube,but both types of deviations in other studies are just approximations.Although it can obtain good approximations in the low-dimensional case,the calculation will be more complicated for an experiment with more variables.Therefore,in this paper,an algorithm based on lattice point partitioning design is proposed to obtain the analytical expression of the MSED and MD in the region covered by the lattice points.Furthermore,the design’s optimality is considered and illustrated by examples under the same uniformity.
文摘This paper discussed Bayesian variable selection methods for models from split-plot mixture designs using samples from Metropolis-Hastings within the Gibbs sampling algorithm. Bayesian variable selection is easy to implement due to the improvement in computing via MCMC sampling. We described the Bayesian methodology by introducing the Bayesian framework, and explaining Markov Chain Monte Carlo (MCMC) sampling. The Metropolis-Hastings within Gibbs sampling was used to draw dependent samples from the full conditional distributions which were explained. In mixture experiments with process variables, the response depends not only on the proportions of the mixture components but also on the effects of the process variables. In many such mixture-process variable experiments, constraints such as time or cost prohibit the selection of treatments completely at random. In these situations, restrictions on the randomisation force the level combinations of one group of factors to be fixed and the combinations of the other group of factors are run. Then a new level of the first-factor group is set and combinations of the other factors are run. We discussed the computational algorithm for the Stochastic Search Variable Selection (SSVS) in linear mixed models. We extended the computational algorithm of SSVS to fit models from split-plot mixture design by introducing the algorithm of the Stochastic Search Variable Selection for Split-plot Design (SSVS-SPD). The motivation of this extension is that we have two different levels of the experimental units, one for the whole plots and the other for subplots in the split-plot mixture design.
文摘The pathway and fate of heavy metals were studied in 10m3 enclosures at Xiamen Bay in 1985. The dissolved metals added are removed rather quickly during the first days, and their half-removal times ( t1/2) (d) are as follows: Pb 5. 4-5. 8, Hg 6. 7-14, Zn 11-22, Cu 16 - 29, and Cd 30-89. Zinc is transferred biologically to particles during phytoplankton bloom. The main Fate of added metals after 27 days is as follows; over 80% Cd and 60% Cu remain in dissolved phase, more than 60% Pb and 50% Hg transfer to settling settlement, while Zn is equally distributed in dissolved phase and settling settlement. The wall uptake is less than 2% of the total metals added. Organic materials play an essential role in the partition and the transfer of heavy metals in water column. Terrigenous and autochthonous particles show different affinities to different metals. Most heavy metals associate weakly with zooplankton. The Binding of Cd, Pb, Zn and Cu to the particles shows distinctive features related to the diagenetic alteration.
文摘[Objectives]This study was conducted to develop a health-care product with smooth taste and high nutrition.[Methods]With natural wheat germ powder as the main raw material and maltodextrin,white sugar,compound stabilizer and other materials as auxiliary materials,the formula of wheat germ solid beverage was optimized using sensory evaluation value as an index,through the mixture experiment method and fuzzy mathematical analysis.[Results]The optimal formula of wheat germ solid beverage was:sugar 11.51%,maltodextrin 37.89%,wheat germ powder 50%,compound stabilizer 0.6%(arabic gum 0.3%,xanthan gum 0.3%),soya bean lecithin 0.2%,ethyl maltol 0.002%,and vanillin 0.003%.[Conclusions]This study provides a theoretical basis for expanding the market-oriented production and application of wheat germ.
基金Supported by Science and Technology Research and Development Plan Project of Chengde City(201706A043)Hospital Pharmaceutical Research Project for Young Scholars of Hebei Pharmaceutical Association(2020-Hbsyxhqn0029)+2 种基金Development Plan Project of Science and Technology Department of Henan Province(142102310278)Special Project for Traditional Chinese Medicine Scientific Research of Henan Province(2014ZY01018)Key scientific research project of Education Department of Henan Province(13A350597).
文摘[Objectives]To study the effects of different material ratios on the dissolution of Tongmai pills.[Methods]Based on mixture uniform experiment design,the fiber,starch and grease-resin materials in Tongmai pills were proportioned.The contents of strychnine,brucine,paeoniflorin,calycosin,ferulic acid,hesperidin and salvianolic acid B in the solution were determined by HPLC,and the content of total flavonoids was determined by ultraviolet spectrophotometry.The weight coefficient of index components was determined by analytic hierarchy process,and the SAS software was used to optimize the dissolution model and calculate the dissolution parameter T40.MATLAB was used to establish a mathematical model and realize the data visualization between material ratio and dissolution parameter T40.[Results]The mathematical model between material ratio and dissolution parameter was T40=8.93-5.31X1-5.83X2+17.67X1X3(X1,X2,X3 are fiber,starch and grease-resin materials respectively,r2=0.9706,P=0.01,RMSE=0.5696).[Conclusions]Fiber can effectively promote the dissolution(P<0.05).Starch can promote the dissolution,but the effect is not obvious(P=0.05).The interaction between fiber and grease-resin can inhibit the dissolution,but was not significant(P=0.07).
基金supported by the Zhejiang Provincial Natural Science Foundation of China(LQ24H120006)the Wenzhou Municipal Science and Technology Bureau(Y2023799)+3 种基金the Startup Foundation for Scientific Research,Eye Hospital,Wenzhou Medical University(KYQD20211204)the National Natural Science Foundation of China(52250710155)the National Key Research and Development Program of China(2021YFA1101200,2022YFA1105501)the Project of State Key Laboratory of Ophthalmology,Optometry and Visual Science,the Wenzhou Medical University(J02-20210201).
文摘Lipid nanoparticles(LNPs)are critical for the delivery of drugs and nucleic acids.However,current mRNA-LNP formulations require stringent freezing for storage,which limits their global distribution.Our previous studies demonstrated that optimizing the lipid type or molar ratio of Comirnaty-type mRNA-LNPs could enhance their lyophilization stability,thus improving their long-term storage stability under mild conditions.This study aims to enhance the storage stability of Spikevax-type mRNA-LNPs by optimizing lipid compositions and utilizing lyophilization for storage at 4�C.Fifteen mRNA-LNP formulations were evaluated for their physicochemical properties and transfection efficiency(TE)in human embryonic kidney(HEK)-293T cells using the I-optimal design of mixture experiments.Mathematical models were developed to predict the relationships among encapsulation efficiency,transfection performance and lipid ratios.The optimized mRNA-LNP formulation(N4),with a 1,2-distearoyl-sn-glycero-3-phosphocholine(DSPC)-to-cholesterol ratio of 0.36,exhibited superior stability and TE after lyophilization.N4 outperformed the original Spikevax formulation in several cell lines,including eye-derived ARPE-19 cells and lung-derived A549 cells.In vivo,N4 demonstrated high TE in the spleen of C57BL/6 mice both before and after lyophilization,with no signals observed in the kidneys,heart or eyes.These findings suggest that the optimized N4 formulation offers a robust,stable and efficient delivery system for gene therapy and vaccines,potentially overcoming the storage limitations of current Spikevax-type mRNA-LNPs and broadening their therapeutic applications.
