Question: Irish Measure was one of three systems which were used in different areas, but who were the ancestors of the third measure most made up of?

Context articles: Kullback–Leibler divergence
Irish measure
Areas of mathematics
Triple modular redundancy
Conditioned place preference
Ulster Scots people
Qafiz
LIBOR market model
Propagule pressure
Old Irish units of measurement

In mathematical statistics, the Kullback–Leibler divergence also called relative entropy is a measure of how one probability distribution diverges from a second expected probability distribution.
 Applications include characterizing the relative (Shannon) entropy in information systems, randomness in continuous time-series, and information gain when comparing statistical models of inference.
 In contrast to variation of information, it is a distribution-wise "asymmetric" measure and thus does not qualify as a statistical "metric" of spread.
 In the simple case, a Kullback–Leibler divergence of 0 indicates that we can expect similar, if not the same, behavior of two different distributions, while a Kullback–Leibler divergence of 1 indicates that the two distributions behave in such a different manner that the expectation given the first distribution approaches zero.
 In somewhat simplified terms, it is a measure of surprise, with diverse applications such as applied statistics, fluid mechanics, neuroscience, and machine learning.
Irish measure or plantation measure was a system of units of land measurement used in Ireland from the 16th century plantations until the 19th century, with residual use into the 20th century.
 The units were based on "English measure" but used a linear perch measuring 7 yard as opposed to the English rod of 5.5 yard .
 Thus, linear units such as the furlong and mile, which were defined in terms of perches, were longer by a factor of 14:11 (~27% more) in Irish measure, while areas such as the rood or acre were larger by 196:121 (~62% more).
 After the Act of Union 1800, Ireland was part of the United Kingdom of Great Britain and Ireland, whose Parliament passed the Weights and Measures Act 1824, which established English measure in Ireland as "Imperial measure" or "statute measure".
 Imperial measure soon replaced Irish measure in the use of the Dublin Castle administration, but Irish measure persisted in local government, and longer still in private use.
 A third system, "Scotch measure" or "Cunningham measure", was also used in Ulster Scots areas.
Mathematics encompasses a growing variety and depth of subjects over history, and comprehension requires a system to categorize and organize the many subjects into more general areas of mathematics.
 A number of different classification schemes have arisen, and though they share some similarities, there are differences due in part to the different purposes they serve.
 In addition, as mathematics continues to be developed, these classification schemes must change as well to account for newly created areas or newly discovered links between different areas.
 Classification is made more difficult by some subjects, often the most active, which straddle the boundary between different areas.
In computing, triple modular redundancy, sometimes called triple-mode redundancy, (TMR) is a fault-tolerant form of N-modular redundancy, in which three systems perform a process and that result is processed by a majority-voting system to produce a single output.
 If any one of the three systems fails, the other two systems can correct and mask the fault.
Conditioned place preference (CPP) is a form of Pavlovian conditioning used to measure the motivational effects of objects or experiences.
 This paradigm can also be used to measure conditioned place aversion with an identical procedure involving aversive stimuli instead.
 Both procedures usually involve mice or rats as subjects.
 This procedure can be used to measure extinction and of the conditioned stimulus.
 Certain drugs are used in this paradigm to measure their reinforcing properties.
 Two different methods are used to choose the compartments to be conditioned, and these are biased vs. unbiased.
 The biased method allows the animal to explore the apparatus, and the compartment they least prefer is the one that the drug is administered in and the one they most prefer is the one where the vehicle is injected.
 This method allows the animal to choose the compartment they get the drug and vehicle in.
 In comparison, the unbiased method does not allow the animal to choose what compartment they get the drug and vehicle in and instead the researcher chooses the compartments.
The Ulster Scots (Ulster-Scots: "Ulstèr-Scotch"), also called Ulster-Scots people (Ulster-Scots: "Ulstèr-Scotch fowk") or, outside the British Isles, Scots-Irish (Ulster-Scots: "Scotch-Airisch"), are an ethnic group in Ireland, found mostly in the Ulster region and to a lesser extent in the rest of Ireland.
 Their ancestors were mostly Protestant Lowland Scottish migrants, the largest numbers coming from Galloway, Lanarkshire, Renfrewshire, Ayrshire and the Scottish Borders, with others coming from further north in the Scottish Lowlands and, to a much lesser extent, from the Highlands.
Qafiz (Arabic: قفيز‎ ‎ from Aramaic qpīzā from Ancient Greek καπίθη from Persian kabīz) is a traditional Arabian unit of measure for several quantities including volume, weight and area which took several different values depending on the time and region.
 The oldest accurate information about it is that of the qafiz of Hajjaj which equaled one Sa' of the Prophet's (4.2125 Litter).
 It is still used in at least one country— Libya— to measure quantities of olive oil.
 In Libya it measures about 7 liters (almost 2 gallons).
 A measurement derived from it is cafisu (aka.
 cafiso or caffiso) and is still in use in Malta, Calabria and Sicily and is also used to measure olive oil.
 It generally measures 16-17 litres.
 Formerly a same name unit of measurement (aka cafesse) was used to measure the grain.
 Traditionally, qafiz, also denoted a unit for measuring land, equaling 360 square dhira' (sq.
 cubits).
The LIBOR market model, also known as the BGM Model (Brace Gatarek Musiela Model, in reference to the names of some of the inventors) is a financial model of interest rates.
 It is used for pricing interest rate derivatives, especially exotic derivatives like Bermudan swaptions, ratchet caps and floors, target redemption notes, autocaps, zero coupon swaptions, constant maturity swaps and spread options, among many others.
 The quantities that are modeled, rather than the short rate or instantaneous forward rates (like in the Heath-Jarrow-Morton framework) are a set of forward rates (also called forward LIBORs), which have the advantage of being directly observable in the market, and whose volatilities are naturally linked to traded contracts.
 Each forward rate is modeled by a lognormal process under its forward measure, i.e. a Black model leading to a Black formula for interest rate caps.
 This formula is the market standard to quote cap prices in terms of implied volatilities, hence the term "market model".
 The LIBOR market model may be interpreted as a collection of forward LIBOR dynamics for different forward rates with spanning tenors and maturities, each forward rate being consistent with a Black interest rate caplet formula for its canonical maturity.
 One can write the different rates dynamics under a common pricing measure, for example the forward measure for a preferred single maturity, and in this case forward rates will not be lognormal under the unique measure in general, leading to the need for numerical methods such as monte carlo simulation or approximations like the frozen drift assumption.
Propagule pressure (also termed introduction effort) is a composite measure of the number of individuals of a species released into a region to which they are not native.
 It incorporates estimates of the absolute number of individuals involved in any one release event (propagule size) and the number of discrete release events (propagule number).
 As the number of releases or the number of individuals released increases, propagule pressure also increases.
 Propagule pressure can be defined as the quality, quantity, and frequency of invading organisms (Groom, 2006).
 Propagule pressure is a key element to why some introduced species persist while others do not (Lockwood, 2005).
 Species introduced in large quantities and consistent quantities prove more likely to survive, whereas species introduced in small numbers with only a few release events are more likely to go extinct (Lockwood, 2005).
 Propagule pressure is a composite measure to the number of individuals released into a non-native region (Lockwood, 2005).
 Three approaches are used to study and measure propagule pressure.
 One approach introduces a specific amount of propagules into controlled plots.
 A second approach allows introduced species to mature and colonize naturally while observing native and non-native species during the colonization.
 The final approach used to study and measure propagule pressure utilizes past records of the numbers of individuals introduced, including natural introductions and intentional introductions (Colautti et al., 2003).
Early Irish law texts record a wide variety of units of measurement, organised into various systems.
 These were used from Early Christian Ireland (Middle Ages) or perhaps earlier, before being displaced by Irish measure from the 16th century onward.