This work considers a special case of Lotka-Volterra equations, which means that in the system of two ordinary differential equations, we take the four parameters equal to one. The reason is that we want just to illus...This work considers a special case of Lotka-Volterra equations, which means that in the system of two ordinary differential equations, we take the four parameters equal to one. The reason is that we want just to illustrate the procedure to reduce that system to only one ordinary differential equation, such that we know its analytical solution. This idea will be applied to study the relations between a system of three ordinary differential equations, and a couple of partial differential equations. Lotka-Volterra equations are solved numerically by a fourth-order predictor-corrector method, which is initialized by an improved Euler method with a rather small time step because it is only a second-order algorithm. Then, it is proposed a model with three species, defined by ordinary differential equations.展开更多
AIM: To summarize the evidence available for the clinical effectiveness of insulin sensitizers in the treatment of nonalcoholic fatty liver disease (NAFLD) systematically. METHODS: Relevant articles were located using...AIM: To summarize the evidence available for the clinical effectiveness of insulin sensitizers in the treatment of nonalcoholic fatty liver disease (NAFLD) systematically. METHODS: Relevant articles were located using computer-assisted searches of Medline (1966-March 2006), EMBASE (1988-March 2006), CINAHL (1982-March 2003), Educational Resource Information Center (1966-March 2006), Library, Information Science & Technology Abstracts (1967-March 2006), Cochrane Database of Systematic Reviews, Database of Abstracts of Reviews of Effects (1994-2006), dissertations in ProQuest and FirstSearch databases. Manual searches were made in the abstracts from meetings of the American Gastroenterological Association (1999-2006), and the American Association for the Study of Liver Diseases (2003-2005). Studies were retrieved using the following selection criteria: (1) clinical trials using insulin sensitizers in subjects with NAFLD, (2) adult patients, (3) published as full manuscripts or abstracts, and (4) English, Spanish, German, and French languages only. Data were abstracted independently by two reviewers following standardized procedures. A face-to- face comparison of data was conducted to ensure the completeness and reliability of the abstraction process. RESULTS: Nine studies were included, six using metformin and three using thiazolidinediones. Only two studies were placebo-controlled trials. The mediansample size for all studies was 18 subjects. In the placebo-controlled trials, metformin improved insulin resistance markers and liver function tests, but not histological scores. In the single-arm trials, metformin and thiazolidinediones improved insulin resistance markers and liver function tests, and beneficial histological changes were reported. There is limited high-quality information available from which to draw categorical conclusions about the clinical use of insulin sensitizers in NAFLD.CONCLUSION: Current information indicates that the use of insulin sensitizers in NAFLD improves insulin resistance and liver function. Histological changes must be corroborated in randomized controlled trials.展开更多
文摘This work considers a special case of Lotka-Volterra equations, which means that in the system of two ordinary differential equations, we take the four parameters equal to one. The reason is that we want just to illustrate the procedure to reduce that system to only one ordinary differential equation, such that we know its analytical solution. This idea will be applied to study the relations between a system of three ordinary differential equations, and a couple of partial differential equations. Lotka-Volterra equations are solved numerically by a fourth-order predictor-corrector method, which is initialized by an improved Euler method with a rather small time step because it is only a second-order algorithm. Then, it is proposed a model with three species, defined by ordinary differential equations.
基金Supported by a Fogarty International Center Training Grant, No. 5 D43 TW00644
文摘AIM: To summarize the evidence available for the clinical effectiveness of insulin sensitizers in the treatment of nonalcoholic fatty liver disease (NAFLD) systematically. METHODS: Relevant articles were located using computer-assisted searches of Medline (1966-March 2006), EMBASE (1988-March 2006), CINAHL (1982-March 2003), Educational Resource Information Center (1966-March 2006), Library, Information Science & Technology Abstracts (1967-March 2006), Cochrane Database of Systematic Reviews, Database of Abstracts of Reviews of Effects (1994-2006), dissertations in ProQuest and FirstSearch databases. Manual searches were made in the abstracts from meetings of the American Gastroenterological Association (1999-2006), and the American Association for the Study of Liver Diseases (2003-2005). Studies were retrieved using the following selection criteria: (1) clinical trials using insulin sensitizers in subjects with NAFLD, (2) adult patients, (3) published as full manuscripts or abstracts, and (4) English, Spanish, German, and French languages only. Data were abstracted independently by two reviewers following standardized procedures. A face-to- face comparison of data was conducted to ensure the completeness and reliability of the abstraction process. RESULTS: Nine studies were included, six using metformin and three using thiazolidinediones. Only two studies were placebo-controlled trials. The mediansample size for all studies was 18 subjects. In the placebo-controlled trials, metformin improved insulin resistance markers and liver function tests, but not histological scores. In the single-arm trials, metformin and thiazolidinediones improved insulin resistance markers and liver function tests, and beneficial histological changes were reported. There is limited high-quality information available from which to draw categorical conclusions about the clinical use of insulin sensitizers in NAFLD.CONCLUSION: Current information indicates that the use of insulin sensitizers in NAFLD improves insulin resistance and liver function. Histological changes must be corroborated in randomized controlled trials.
