Chapter 6 Glossary

R

A programming language and environment for statistical computing, data analysis, and graphical representation. R is widely used in scientific research due to its extensive ecosystem of custom packages with emphasis on reproducibility.

R package

A bundled collection of R functions, data, documentation, and metadata that extends the base functionality of R. Packages can be installed from CRAN, Bioconductor, or GitHub, and are essential for tasks like data modeling, visualization, and scientific analysis workflows in bioinformatics.

Venn diagram

A graphical representation of all possible logical relationships between a collection of sets. Each set is shown as a circle, and all possible intersections are depicted—even if some are empty. Venn diagrams are especially useful for illustrating complete overlap structures but can become cluttered with more than 3–4 sets.

Euler diagram

A simplified set diagram that shows only the actual (non-empty) relationships between sets. Unlike Venn diagrams, Euler diagrams omit intersections that don’t exist, making them more concise and readable when dealing with sparse or realistic data overlap.

intersection

In set theory, the intersection of two or more sets refers to the elements shared by each set. In Venndir visualizations, the intersection contains the overlapping region shared between two or more sets.

union

In set theory, the union of two or more sets contains the unique set of elements present in any of the sets. In Venndir visualization, the union represents the combined geometric region covering any sets involved.

subtraction

In set theory, subtraction is also known as set difference, which yields the elements present in one set and not in another. For example, A - B includes elements in set A that are absent from B.

In venndir visualization, the subtraction is used to represent a geometric region from one set that does not overlap any region of another set.

buffer region

In geometry, a buffer region is zone created by expanding or shrinking a geometric shape by a fixed distance.

For expansion, it defines a region with fixed distance from any solid point in the geometric shape. It is used in Venndir to create "outer border", and to place text labels outside the Venn or Euler diagrems.

For shrinking, it defines a region with fixed distanct inside the border of the geometric shape. It is used in Venndir to create "inner border", and to array multiple text labels inside specific regions.

agreement

Property of two or more elements that all agree in direction or sign.

concordance

Property of two or more elements that agree in direction or sign.

concordant

Description for two or more elements that agree in direction or sign.

disagreement

Property of two or more elements that do not all agree in direction or sign.

discordance

Property of two or more elements that do not agree in direction or sign, equivalent to the term discordance.

discordant

Description for two or more elements that do not agree in direction or sign.

vector

In R, a one-dimensional sequence of elements of the same base type (e.g., character or numeric). In Venndir, a vector is used to represent elements of a set, sometimes also with directional sign.

set

A collection of unique elements. In Venndir, a set represents a group of items where the items are typically genes, features, or observations that share a common label or condition. For example, the items may be differentially expressed genes (DEGs) from a statistical contrast.

In Venndir, a set is stored as a vector in one of two ways: 1. a character vector of items without vector names (set), 2. a numeric vector of signs, often but not strictly -1 and 1, where item names are stored as vector names (signed set).

signed data

A dataset in which each element carries a direction label (e.g., "up" or "down", "positive" or "negative", "gain" or "loss"). This signature guides Venndir in assigning directional sign-aware overlaps and patterns.

Signed data may be used to create a signed set in Venndir.

signed set

A specialized type of set used in Venndir to store elements with directional sign. Signs are stored as vector values, and items are stored as vector names.

Signed sets are required components in a signed setlist.

list

In R, a list is an ordered collection of objects that may contain elements of different types and structures. A list is commonly used to store a collection of different objects, and may even contain other lists.

In Venndir, a setlist is a named list with multiple sets. The list names store the name of each set.

setlist

In Venndir, a named list of sets, where set names are stored as list names. where each set is stored as a vector. The set names are stored in list names.

signed setlist

A specialized form of setlist in which each element is a signed set. Each set therefore represents items as vector names, where values contain the directional sign, and names store the items.

Venn overlap

A Venn overlap refers to a specific set theory comparison such as intersection and/or subtraction. Venn overlaps are defined when two or more sets are compared.

A property of a Venn overlap is that each item may be assigned to only one such Venn overlap.

For example, consider Venn overlaps which involve three sets 'A', 'B', 'C'. An item may be only present or absent in each of the three sets. Therefore, if an item exists in 'A&B' it is present in 'A' and 'B' and not in 'C'.

In Venn overlap terminology 'A' refers to the set of item present in 'A' that are not present in 'B' nor in 'C'.

main counts

In Venndir, main counts refers to the number of items in a Venn overlap, without regard to directional sign. The items in a Venn overlap may separately be tabulated by sign to produce signed counts.

signed counts

In Venndir, signed counts refers to the number of items in a Venn overlap tabulated by additional directional criteria. For example, overlap type 'each' will tabulate items based upon each combination of signs observed in the Venn overlap. For a Venn overlap of the intersection of 'A' and 'B', with sign values -1 and 1, there may be four tabulated values:

• '1 1'
• '1 -1'
• '-1 1'
• '1 1'

matrix

A type of data object in R called a matrix that is used to store two-dimensional data by row and column. A matrix in R can only store one data type in each cell.

incidence matrix

A matrix encoding set membership. Rows represent elements, columns represent sets. The matrix values are 1 if the element is present, and either 0 or NA otherwise.

In Venndir, any non-empty value indicates the element (row) is present in the set (column), where "" empty string is considered an empty value.

signed incidence matrix

An enhanced incidence matrix that represents set membership and directional sign. A signed incidence matrix encodes sign as the matrix value, usually values such as:

• 1 for positive or "up" direction,
• -1 for negative or "down" direction, and
• 0 or NA for absence of the element.

That said, Venndir will recognize any non-empty value as a sign, empty values include 0, NA, and ''.

data visualization

Graphical representation of data intended to provide insight, pattern recognition, and communication. In Venndir, data visualization helps to summarize set relationships such as overlaps, directionality, and concordance of direction.

markdown

A plain text style of writing that encodes special formatting by following a lightweight markup language.

Venndir supports the CommonMark specification, which is summarized by the CommonMark.org Summary. The main features used by Venndir:

• Font changes: bold, italics
• inline images
• lists (like this one)