Contiguity

Contiguity is a series of things in continuous connection, a grouping of parts in contiguous physical contact. The concept was first set out in the Law of Contiguity, one of Aristotle's Laws of Association, which states that things which occur in proximity to each other in time or space are readily associated.

Biology
A cluster of genes that are located close to one another at a chromosome locus. Contiguous gene disorders result from deletions or duplications of a chromosome segment, thus causing a contiguous gene imbalance.

Computer science
Elements of memory are contiguous if they are, or appear to be, adjacent or connected to one another.

Geography
Lands which are in physical contact with one another. In the United States, for example, the "48 contiguous states" exclude the states of Hawaii and Alaska, which do not share borders with other U.S. states.

Two or more contiguous municipalities can be consolidated into one, or one municipality can consist of many noncontiguous elements. For example, the Financially Distressed Municipalities Act allows the state of Pennsylvania to merge contiguous municipalities to reduce financial distress.

Geographic contiguity is important in biology, especially animal ranges. For a particular species, its habitat may be a 'contiguous range', or it might be broken, requiring periodic, typically seasonal migrations; (see: Disjunct distribution). The same concept of contiguous range is true for human transportation studies in an attempt to understand census geography. It also comes into play with electoral geography and politics.

Philosophy
Philosophers speak of contiguity when they assume two events or objects lying directly side by side in space and time without being connected by causality or any other principle.

Physics
Contiguity is a metallurgical property used to characterize microstructure of materials. It is computed by finding the ratio of solid-solid length to the sum of solid-solid and solid-liquid length of the microstructure.

Probability theory
Contiguity of sequences of probability measures is a property that may be used to derive asymptotic normality under the alternative of a statistical hypothesis. It is defined for a sequence of measurable spaces $$(\Omega_n, \mathcal F_n )_{n=1}^\infty$$ with two probability measure sequences, $$(P_n )_{n=1}^\infty$$ and $$(Q_n )_{n=1}^\infty$$. $$(Q_n )_{n=1}^\infty$$ is contiguous to $$(P_n )_{n=1}^\infty$$ if
 * $$\forall F_n \in \mathcal F_n : \big( P_n(F_n) \to 0 \big) \Rightarrow \big( Q_n(F_n) \to 0 \big) $$

as $$n \to \infty$$, and $$(Q_n )_{n=1}^\infty$$ is bi-contiguous to $$(P_n )_{n=1}^\infty$$ if
 * $$\forall F_n \in \mathcal F_n : \big( P_n(F_n) \to 0 \big) \Leftrightarrow \big( Q_n(F_n) \to 0 \big) $$

as $$n \to \infty$$.

The concept was originally introduced by Lucien Le Cam in the 1960s as part of his contribution to the development of abstract general asymptotic theory in mathematical statistics.

Psychology
Association by contiguity is the principle that ideas, memories, and experiences are linked when one is frequently experienced with the other. For example, if you constantly see a knife and a fork together they become linked (associated). The more these two items (stimuli) are perceived together the stronger the link between them. When one of the memories becomes activated later on, the linked (contiguously associated) memory becomes temporarily more activated and thus easier to be called into working memory. This process is known as priming, and the initial memory that primed the other is known as the retrieval cue.

Association by contiguity is the root of association by similarity. Association by similarity is the idea that one memory primes another through their common property or properties. Thus, an apple may prime a memory of a rose through the common property of red. These two become associated even though you may have never experienced an apple and a rose together (consistent with association by contiguity).

When one associated memory, a group of associated memories, or a whole line of associated memories becomes primed, this is known as spreading activation.

In conditioning, contiguity refers to how associated a reinforcer is with behaviour. The higher the contiguity between events the greater the strength of the behavioural relationship.

Edwin Ray Guthrie's contiguity theory deals with patterned movements.