Graphpad Prism Significance On Graphs

[Jennifer Leos]

Ingraph theory, a Halin graph is a type of planar graph, constructed by connecting the leaves of a tree into a cycle.The tree must have at least four vertices, none of which has exactly two neighbors; it should be drawn in the plane so none of its edges cross (this is called a planar embedding), and the cycleconnects the leaves in their clockwise ordering in this embedding. Thus, the cycle forms the outer face of the Halin graph, with the tree inside it.[1]

Every Halin graph has a Hamiltonian cycle through all its vertices, as well as cycles of almost all lengths up to the number of vertices of the graph. Halin graphs can be recognized in linear time. Because Halin graphs have low treewidth, many computational problems that are hard on other kinds of planar graphs, such as finding Hamiltonian cycles, can be solved quickly on Halin graphs.

A star is a tree with exactly one internal vertex. Applying the Halin graph construction to a star produces a wheel graph, the graph of the (edges of) a pyramid.[4] The graph of a triangular prism is also a Halin graph: it can be drawn so that one of its rectangular faces is the exterior cycle, and the remaining edges form a tree with four leaves, two interior vertices, and five edges.[5]

Every Halin graph is 3-connected, meaning that it is not possible to delete two vertices from it and disconnect the remaining vertices. It is edge-minimal 3-connected, meaning that if any one of its edges is removed, the remaining graph will no longer be 3-connected.[1] By Steinitz's theorem, as a 3-connected planar graph, it can be represented as the set of vertices and edges of a convex polyhedron; that is, it is a polyhedral graph. The polyhedron that realizes the graph can be chosen so that the face containing all of the tree leaves is horizontal, and all of the other faces lie above it, with equal slopes.[8] As with every polyhedral graph, Halin graphs have a unique planar embedding, up to the choice of which of its faces is to be the outer face.[1]

Every Halin graph is a Hamiltonian graph, and every edge of the graph belongs to a Hamiltonian cycle. Moreover, any Halin graph remains Hamiltonian after the deletion of any vertex.[9]Because every tree without vertices of degree 2 contains two leaves that share the same parent, every Halin graph contains a triangle. In particular, it is not possible for a Halin graph to be a triangle-free graph nor a bipartite graph.[10]

More strongly, every Halin graph is almost pancyclic, in the sense that it has cycles of all lengths from 3 to n with the possible exception of a single even length. Moreover, any Halin graph remains almost pancyclic if a single edge is contracted, and every Halin graph without interior vertices of degree three is pancyclic.[12]

Every Halin graph has treewidth = 3.[18] Therefore, many graph optimization problems that are NP-complete for arbitrary planar graphs, such as finding a maximum independent set, may be solved in linear time on Halin graphs using dynamic programming[19] or Courcelle's theorem, or in some cases (such as the construction of Hamiltonian cycles) by direct algorithms.[17]However, it is NP-complete to find the largest Halin subgraph of a given graph, to test whether there exists a Halin subgraph that includes all vertices of a given graph, or to test whether a given graph is a subgraph of a larger Halin graph.[20]

In 1971, Halin introduced the Halin graphs as a class of minimally 3-vertex-connected graphs: for every edge in the graph, the removal of that edge reduces the connectivity of the graph.[2] These graphs gained significance with the discovery that many algorithmic problems that were computationally infeasible for arbitrary planar graphs could be solved efficiently on them.[9][16] This fact was later explained to be a consequence of their low treewidth, and of algorithmic meta-theorems like Courcelle's theorem that provide efficient solutions to these problems on any graph of low treewidth.[18][19]

The Halin graphs are sometimes also called skirted trees[11] or roofless polyhedra.[9] However, these names are ambiguous. Some authors use the name "skirted trees" to refer to planar graphs formed from trees by connecting the leaves into a cycle, but without requiring that the internal vertices of the tree have degree three or more.[24] And like "based polyhedra", the "roofless polyhedra" name may also refer to the cubic Halin graphs.[22] The convex polyhedra whose graphs are Halin graphs have also been called domes.[25]

Your scientific data from experiments and observations are easy to organize, analyze and visualized with the help of the software GraphPad Prism. Even without previous knowledge, statistical tests can simply be executed and their results can easily be interpreted.

GraphPad Prism was originally developed for experimental biologists, medicine scientists and pharmacologists. Meanwhile Graphpad Prism is used throughout the life sciences sector. Many undergraduate and graduate students also use this statistical program.

The program guides you through the process of analysis, facilitates the choice of the statistical tests and interpret the results. No other program allows the curve fitting so easy to learn and to simplify. Especially the non-linear regression serves as an important tool.

GraphPad Prism provides T-tests, one-way- and two-way ANOVA, non-parametric comparisons, linear and non-linear regression, analysis of contingency tables and survival analysis. In addition, GraphPad Prism offers a large selection of presentable graphs. The graphics engine is extremely flexible and admits various designs. Color palettes allow coloring of the graph by one click only.

GraphPad PRSIM was originally developed for the life sciences. The functions were expanded over the years and thus it is nowadays widely used in all scientific fields. More than 200,000 scientists in more than 110 countries rely on PRISM.

It is also used in academia to teach and learn statistical methods. PRISM is not meant to act as a full replacement for one of the comprehensive and expensive software packages in the field of statistics (SAS, JMP, SPSS, SYSTAT, Minitab) , but it can be perfectly used by non statisticians to execute the basic hypothesis testing and model fitting, as usually done in laboratories and in clinical research.

Characteristic for GraphPad PRISM are the comprehensive library of statistical analysis functions for location tests including nonparametric procedures, linear and nonlinear regression, contingency tables and some special routines for clinical research. Some examples are: t-Test, One-Way- and Two-Way-ANOVA, Kruskal-Wallis- and Mann-Whitney-Test, Repeated-Measures-Analysis, Bland-Altman Plots and Receiver Operating Characteristic (ROC) Curves. No software can compete in terms of simplicity of model specification and robustness of the results in terms of nonlinear regression. PRISM has a built in library of 110 regression models, including meaningfully chose starting values for the fitting process. Examples are different dose-response-curves , Michaelis-Menten- and Enzyme-kinetic models.

On top of this GraphPad PRISM offers a wide variety of presentation quality graphics. The graphical engine is very flexible and easy to use, allowing a manifold of freedom to design your graph. E.g. color templates can be use to set all colors for a new graph with just a single click.

Routine analysis, which is very time consuming, can be automated . The “magic” function edits graphs, so they receive the same layout with just a few clicks. The “wand” function duplicates a complex set of analysis based on one dataset, onto a new dataset. The complete analysis outputs as well as all the graphs are duplicated with a single click. The "template" function is a special way to save a project. A template is an empty container for data, analysis, graphs and presentations. Whenever a template is opened you only need to import data and all subsequent steps of the analysis are already done. All that is left to do is save the project and print the results.

Graphpad PRISM is basically unsurpassed in its ease of use. The process of picking the correct statistical analysis procedure and the proper interpretation of the results are guided by the help system. The possibility to pick the wrong procedure or to misinterpret the data is minimized.

There are four different approaches to automation in PRISM. All of those four approaches can help you dealing more effectively, quickly and safely with routine tasks. For each section in the workflow you have an automation variant.

If you've already entered data onto an empty data table, it is too late to clone, too late to duplicate a family, and too late to open a template -- at least without copy and pasting data. Prism provides a great tool to solve this problem: the Wand (Wizard to ANalyze Data). Use it to analyze (and graph) the new table just like you already analyzed (and graphed) an existing table.

Prism Magic makes graphs consistent. Use the Prism Magic tool in the Change section of the Prism toolbar to make one graph look like another. You can choose any recently-used graph, any graph in an open project, or any graph saved as an example.

A template is a Prism file that you recycle. Choose a template, add new data, and all the analyses and graphs will be created automatically. Templates are an older feature, and we recommend you clone a graph, or use the Wand, instead.

If you've already entered data onto an empty data table, it is too late to using cloning or templates -- at least without copy and pasting. But it is not too late to apply a method to your data. Effectively, this means telling Prism to analyze (and graph) the new table just like you already analyzed (and graphed) an existing one. This is called using a Method. Method is comparable to Wand. The difference is: a Method is like a Template pre saved.

The welcome dialog functions as the central steering system for PRISM. It defines the different project types which trigger different types of graphs as well as different statistical analysis. The help systems offers a quick overview of the areas of application for each project type. A simple click on "Learn more"reveals a comprehensive and concise description for each project type.

3a8082e126