Boolean Algebra

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The Boolean Algebra Tool

Why Use the Boolean Algebra Tool

The Boolean Algebra Tools preforms a Union, Intersection, or Exception on at least two GeneSets. It then provides a listing of genes grouped by the number of GeneSets they have in common. This view may allow you to quickly determine new relationships between GeneSets and create a new GeneSet based on your findings.

Understanding The Boolean Algebra Tool

Union of two sets. - source
The Union of two or more GeneSets is defined as every gene which is in any of the sets. For example, if GeneSet A = {2,4,5,6} and GeneSet B = {1,2,3} then A U B = {1, 2, 3, 4, 5, 6}. The Boolean Algebra tool will return all the genes in the selected GeneSets and indicate the GeneSet(s) it is found in.

Intersection of two sets. -  source
The Intersection of two sets A and B is defined as the set that contains all elements of A that also belong to B (or all elements of B that also belong to A), but no other elements. The Boolean Algebra tool will return all combinations of intersections for the selected GeneSets. Section headings on the results indicate how many GeneSets the gene has in common. For example, say there are three GeneSets, and A = {1, 2}, B = {1, 3}, and C = {1, 3}. The Boolean Algebra Tool will not only return the results that A ∩ B ∩ C = {1}, it will also return the intersection of B and C which is equal to 3.

Intersection of three sets.
The red shaded areas in the figure to the right represent the results which would be returned from the Boolean Algebra tool for an Intersection operation on three GeneSets.

Intersection of two sets. -  [1]
The third set logic operation the Boolean Algebra tool provides is Except, sometimes also referred to as Minus or Complement. For example, if GeneSet A = {1,2} and GeneSet B = {2,3}, A minus B would be {1}. For the Boolean Algebra's tools purposes, the list of genes that is returned will be those which are only found uniquely in one GeneSet. For example, if A = {1}. B = {1, 2}, and C = { 2, 4, 5}, the tool will return the following genes: 4, and 5.

Exception of three sets.
The red shaded areas in the figure to the right represent the results which would be returned from the Boolean Algebra tool for an Exception operation on three GeneSets.

Using the Boolean Algebra Tool

Access the Boolean Algebra Tool through the Analyze Genesets tab under the Analyze Genesets option.
From the "Analyze Genesets" tab, select "Analyze Genesets". To generate Boolean Algebra results, you must first select at least two GeneSets from a project. Projects may be created and updated by uploading GeneSets, searching the GeneWeaver database, or through the use of other tools in the GeneWeaver System. Please see the documentation for uploading GeneSets, Search, or Manage GeneSets to learn more about these functions. On this page, all the GeneSets in a particular project can be selected by clicking the check box to the left of the project's name. Also, individual GeneSets in a project can be selected by expanding the project by clicking on the project's name and then clicking the check boxes for individual GeneSets within a project. Either option is valid, but at least two GeneSets need to be selected to run the Boolean Algebra tool. After that, select the "Boolean Algebra" from the Analysis Tools box. This tool box is located to the left of your projects. After this selection, three radio buttons will appear. Please select "Union", "Intersection", or "Except" depending on the results you wish to run. Then, press the run button.
Boolean 1.png
Figure 1: After the GeneSets have been selected, select "Boolean Algebra" from from the Analysis Tools box.

After the tool runs, you will be redirect to your results page. The results are separated out based on the number of GeneSets the gene was found in for the particular set operation in decreasing order. For example in Figure 2 below, a union on a three GeneSets was performed. There was not a gene found in common with all three GeneSets, but there was a gene found in common with two of the GeneSets. This result is displayed first, and the GeneSets it was found in is displayed in the "In Gene Sets" column in the results table.
Boolean 2.png
Figure 2: Example of Union Boolean Algebra results.

For each gene, links are provided to direct you to different websites to learn more information about the particular gene. These links can be found under the "Linkouts" column in the table. By using the toggle switch under the "Emphasis" column in the table, you can give emphasis to a particular gene. This will allow it to show up more prominently as you use other GeneWeaver features. Based on your findings, you can also select genes to form a new GeneSet. This can be accomplished by checking the check box located on the far right of each gene's row. Once all of your desired genes to add to your new GeneSet are selected, press the orange "Add to New GeneSet" button location on the top of this page. This will redirect you to the Upload GeneSet form page where a few fields will be auto-populated for you. Most notably, the Gene List under Gene Information on the bottom of the form will be filled out with each gene's identifier and value. Please read the this link [2] more information about uploading a new GeneSet into GeneWeaver.
Boolean 3.png
Figure 3: Gene List box from Upload GeneSet form.
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