Where does theta collide?

A special function built from an infinite sum whose terms carry a squared exponent, giving it a strong repeating structure that makes it a basic building block for elliptic functions and related objects. Jacobi named and organised these functions in his 1829 Fundamenta Nova Theoriae Functionum Ellipticarum, writing them with the Greek letter theta and using them to construct the doubly repeating functions at the centre of that theory; Whittaker and Watson's 1927 A Course of Modern Analysis later gave the standard reference account of their properties. Here theta names a function on the plane of complex numbers, an object of pure analysis, and it has nothing to do with a brain rhythm, a price sensitivity, or a grammatical rule.[1][2]

Unit

A function value at a point, given a lattice or period parameter

Recovery means

Not applicable

Measured by

Defined and studied analytically through its series, its transformation rules, and its zeros, not measured empirically

A slow, regular electrical rhythm of roughly four to eight cycles per second recorded from the brain, strongest in the hippocampus and linked to movement, memory, and states of arousal. Jung and Kornmüller first described this regular hippocampal rhythm in their 1938 recordings of deep brain activity, and Green and Arduini's 1954 study established its tie to arousal and its place in hippocampal function; the letter name theta comes from the convention that labels bands of brain-wave frequency with Greek letters. Here theta names a measured oscillation in living neural tissue, distinct from a function in mathematics, a change in an option's value, or a role assigned to a noun.[3][4]

Unit

An oscillation near four to eight cycles per second in a brain-activity recording

Recovery means

Not applicable

Measured by

Recorded by electrodes as voltage over time and quantified by the power in the four to eight cycles per second band

The rate at which the value of an option falls as time passes and its expiry draws nearer, holding everything else fixed. It follows from the option-pricing model set out by Black and Scholes in their 1973 paper, in which an option's value is a function of time and theta is that value's sensitivity to the passage of time; in later trading practice theta became one of the named sensitivities, the Greeks, used to describe and hedge an option position. Here theta names a number attached to a financial contract, one of a family of price sensitivities, unrelated to a mathematical function, a brain rhythm, or a rule of grammar.[5]

Unit

The change in an option's price per day, or per year, of time passing

Recovery means

Not applicable

Measured by

Computed as the partial derivative of a pricing model with respect to time, or estimated from observed price changes

A label for the part a noun phrase plays in the situation a verb describes, such as the one doing an action or the one an action is done to, assigned to it by the verb it depends on. Chomsky introduced theta roles and the surrounding theta theory in his 1981 Lectures on Government and Binding, where theta stands for thematic and the theory states that each such role is given out exactly once; the idea drew on earlier accounts of thematic relations in grammar. Here theta names a relation between a verb and a noun phrase in the structure of a sentence, distinct from a mathematical function, a brain rhythm, or a price sensitivity.[6]

Unit

One thematic role assigned by a predicate to an argument

Recovery means

Not applicable

Measured by

Identified by grammatical analysis of which arguments a predicate requires and what part each one plays