text:
Generalized additive model for location, scale and shape
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The Generalized Additive Model for Location, Scale and Shape (GAMLSS) is about statistical modelling and learning. GAMLSS is a modern distribution based approach to (semiparametric) regression analysis. A parametric distribution is assumed for the response (target) variable but the parameters of this distribution can vary according to explanatory variables using linear, nonlinear or smooth functions. In data science language GAMLSS is about supervised machine learning.
A guiding principle of GAMLSS is how to learn from data generated in many fields. In particular, the GAMLSS statistical framework enables flexible regression and smoothing models to be fitted to the data. The GAMLSS model assumes that the distribution of response variable has any parametric distribution which might be heavy or light-tailed, and positively or negatively skewed. In addition, all the parameters of the distribution [location (e.g., mean), scale (e.g., variance) and shape (skewness and kurtosis)] can be modelled as linear, nonlinear or smooth functions of explanatory variables.
Contents
[hide]
1 Overview of the model
2 What distributions can be used
3 References
4 Further reading
5 External links
Overview of the model[edit]
The generalized additive model for location, scale and shape (GAMLSS) is a statistical model developed by Rigby and Stasinopoulos and later expanded to overcome some of the limitations associated with the popular generalized linear models (GLMs) and generalized additive models (GAMs). For an overview of these limitations see Nelder and Wedderburn (1972)[1] and Hastie and Tibshirani's book.[2]
In GAMLSS the exponential family distribution assumption for the response variable, ( y {\displaystyle y} ), (essential in GLMs and GAMs), is relaxed and replaced by a general distribution family, including highly skew and/or kurtotic continuous and discrete distributions.
The systematic part of the model is expanded to allow modeling not only of the mean (or location) but other parameters of the distribution of y as linear and/or nonlinear, parametric and/or additive non-parametric functions of explanatory variables and/or random effects.
GAMLSS is especially suited for modelling a leptokurtic or platykurtic and/or positively or negatively skewed response variable. For count type response variable data it deals with over-dispersion by using proper over-dispersed discrete distributions. Heterogeneity also is dealt with by modelling the scale or shape parameters using explanatory variables. There are several packages written in R related to GAMLSS models.[3]
A GAMLSS model assumes independent observations y i {\displaystyle y_{i}} for i = 1 , 2 , … , n {\displaystyle i=1,2,\dots ,n} with probability (density) function f ( y i | μ i , σ i , ν i , τ i ) {\displaystyle f(y_{i}|\mu _{i},\sigma _{i},\nu _{i},\tau _{i})} conditional on ( μ i , σ i , ν i , τ i ) {\displaystyle (\mu _{i},\sigma _{i},\nu _{i},\tau _{i})} a vector of four distribution parameters, each of which can be a function to the explanatory variables. The first two population distribution parameters μ i {\displaystyle \mu _{i}} and σ i {\displaystyle \sigma _{i}} are usually characterized as location and scale parameters, while the remaining parameter(s), if any, are characterized as shape parameters, e.g. skewness and kurtosis parameters, although the model may be applied more generally to the parameters of any population distribution with up to four distribution parameters, and can be generalized to more than four distribution parameters.
g 1 ( μ ) = η 1 = X 1 β 1 + ∑ j = 1 J 1 h j 1 ( x j 1 ) g 2 ( σ ) = η 2 = X 2 β 2 + ∑ j = 1 J 2 h j 2 ( x j 2 ) g 3 ( ν ) = η 3 = X 3 β 3 + ∑ j = 1 J 3 h j 3 ( x j 3 ) g 4 ( τ ) = η 4 = X 4 β 4 + ∑ j = 1 J 4 h j 4 ( x j 4 ) {\displaystyle {\begin{aligned}g_{1}(\mu )=\eta _{1}=X_{1}\beta _{1}+\sum _{j=1}^{J_{1}}{h}_{j1}(x_{j1})\\g_{2}(\sigma )=\eta _{2}=X_{2}\beta _{2}+\sum _{j=1}^{J_{2}}{h}_{j2}(x_{j2})\\g_{3}(\nu )=\eta _{3}=X_{3}\beta _{3}+\sum _{j=1}^{J_{3}}{h}_{j3}(x_{j3})\\g_{4}(\tau )=\eta _{4}=X_{4}\beta _{4}+\sum _{j=1}^{J_{4}}{h}_{j4}(x_{j4})\end{aligned}}}
where μ, σ, ν, τ and η k {\displaystyle \eta _{k}} are vectors of length n {\displaystyle n} , β k T = ( β 1 k , β 2 k , … , β J k ′ k ) {\displaystyle \beta _{k}^{T}=(\beta _{1k},\beta _{2k},\ldots ,\beta _{J'_{k}k})} is a parameter vector of length J k ′ {\displaystyle J'_{k}} , X k {\displaystyle X_{k}} is a fixed known design matrix of order n × J k ′ {\displaystyle n\times J'_{k}} and h j k {\displaystyle h_{jk}} is a smooth non-parametric function of explanatory variable x j k {\displaystyle x_{jk}} , j = 1 , 2 , … , J k {\displaystyle j=1,2,\ldots ,J_{k}} and k = 1 , 2 , 3 , 4 {\displaystyle k=1,2,3,4} .
For centile estimation the WHO Multicentre Growth Reference Study Group have recommended GAMLSS and the Box-Cox power exponential (BCPE) distributions[4] for the construction of the WHO Child Growth Standards.[5][6]
What distributions can be used[edit]
The form of the distribution assumed for the response variable y, is very general. For example an implementation of GAMLSS in R[7] has around 50 different distributions available. Such implementations also allow use of truncated distributions and censored (or interval) response variables.[7]
References[edit]
Jump up ^ Nelder, J.A.; Wedderburn, R.W.M (1972). "Generalized linear models". J. R. Statist. Soc. A. 135: 370–384.
Jump up ^ Hastie, TJ; Tibshirani, RJ (1990). Generalized additive models. London: Chapman and Hall.
Jump up ^ Stasinopoulos, D. Mikis; Rigby, Robert A (December 2007). "Generalized additive models for location scale and shape (GAMLSS) in R". Journal of Statistical Software. 23 (7). doi:10.18637/jss.v023.i07.
Jump up ^ Rigby, Robert; Stasinopoulos, D. Mikis (February 2004). "Smooth Centile Curves for Skew and Kurtotic data Modelled Using the Box-Cox Power Exponential Distribution". Statistics in Medicine. 23 (19): 3053–3076. doi:10.1002/sim.1861.
Jump up ^ Borghi, E.; De Onis, M.; Garza, C.; Van Den Broeck, J.; Frongillo, E. A.; Grummer-Strawn, L.; Van Buuren, S.; Pan, H.; Molinari, L.; Martorell, R.; Onyango, A. W.; Martines, J. C.; WHO Multicentre Growth Reference Study Group (2006). "Construction of the World Health Organization child growth standards: Selection of methods for attained growth curves". Statistics in Medicine. 25 (2): 247–265. doi:10.1002/sim.2227. PMID 16143968.
Jump up ^ WHO Multicentre Growth Reference Study Group (2006) WHO Child Growth Standards: Length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age: Methods and development. Geneva: World Health Organization.
^ Jump up to: a b R packages for GAMLSS can be downloaded from here
Further reading[edit]
Beyerlein, A., Fahrmeir, L., Mansmann, U., Toschke., A. M. (2001) "Alternative regression models to assess increase in childhood BM". IBMC Medical Research Methodology, 2008, 8(59) doi:10.1186/1471-2288-8-59
Cole, T. J., Stanojevic, S., Stocks, J., Coates, A. L., Hankinson, J. L., Wade, A. M. (2009), "Age- and size-related reference ranges: A case study of spirometry through childhood and adulthood", Statistics in Medicine, 28(5), 880-898.Link
Fenske, N., Fahrmeir, L., Rzehak, P., Hohle, M. (25 September 2008), "Detection of risk factors for obesity in early childhood with quantile regression methods for longitudinal data", Department of Statistics: Technical Reports, No.38 Link
Hudson, I. L., Kim, S. W., Keatley, M. R. (2010), "Climatic Influences on the Flowering Phenology of Four Eucalypts: A GAMLSS Approach Phenological Research". In Phenological Research, Irene L. Hudson and Marie R. Keatley (eds), Springer Netherlands Link
Hudson, I. L., Rea, A., Dalrymple, M. L., Eilers, P. H. C. (2008), "Climate impacts on sudden infant death syndrome: a GAMLSS approach", Proceedings of the 23rd international workshop on statistical modelling pp. 277–280. Link
Nott, D (2006). "Semiparametric estimation of mean and variance functions for non-Gaussian data". Computational Statistics. 21 (3-4): 603–620. doi:10.1007/s00180-006-0017-9.
Serinaldi, F (2011). "Distributional modeling and short-term forecasting of electricity prices by Generalized Additive Models for Location, Scale and Shape". Energy Economics. 33 (6): 1216–1226. doi:10.1016/j.eneco.2011.05.001.
Serinaldi, F.; Cuomo, G. (2011). "Characterizing impulsive wave-in-deck loads on coastal bridges by probabilistic models of impact maxima and rise times". Coastal Engineering. 58 (9): 908–926. doi:10.1016/j.coastaleng.2011.05.010.
Serinaldi, F., Villarini, G., Smith, J. A., Krajewski, W. F. (2008), "Change-Point and Trend Analysis on Annual Maximum Discharge in Continental United States", American Geophysical Union Fall Meeting 2008, abstract #H21A-0803*
van Ogtrop, F. F.; Vervoort, R. W.; Heller, G. Z.; Stasinopoulos, D. M.; Rigby, R. A. (2011). "Long-range forecasting of intermittent streamflow". Hydrology and Earth System Sciences Discussions. 8 (1): 681–713. doi:10.5194/hessd-8-681-2011.
Villarini, G.; Serinaldi, F. (2011). "Development of statistical models for at-site probabilistic seasonal rainfall forecast". International Journal of Climatology. doi:10.1002/joc.3393.
Villarini, G.; Serinaldi, F.; Smith, J. A.; Krajewski, W. F. (2009). "On the stationarity of annual flood peaks in the continental United States during the 20th century". Water Resources Research. 45 (8). doi:10.1029/2008wr007645.
Villarini, G.; Smith, J. A.; Napolitano, F. (2010). "Nonstationary modeling of a long record of rainfall and temperature over Rome". Advances in Water Resources. 33: 1256–1267. doi:10.1016/j.advwatres.2010.03.013.
External links[edit]
GAMLSS official website gamlss.org
GAMLSS manual (downloadable)
Distribution tables in GAMLSS
The GAMLSS packages reference card (downloadable)
The booklet for the Utrecht short course on GAMLSS (downloadable)
R packages for GAMLSS on CRAN
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Seafloor spreading
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Age of oceanic lithosphere; youngest (red) is along spreading centers.
Seafloor spreading is a process that occurs at mid-ocean ridges, where new oceanic crust is formed through volcanic activity and then gradually moves away from the ridge. Seafloor spreading helps explain continental drift in the theory of plate tectonics. When oceanic plates diverge, tensional stress causes fractures to occur in the lithosphere.The motivating force for seafloor spreading ridges is tectonic plate pull rather than magma pressure, although there is typically significant magma activity at spreading ridges.[1] At a spreading center basaltic magma rises up the fractures and cools on the ocean floor to form new seabed. Hydrothermal vents are common at spreading centers. Older rocks will be found farther away from the spreading zone while younger rocks will be found nearer to the spreading zone. Additionally spreading rates determine if the ridge is a fast, intermediate, or slow. As a general rule, fast ridges see spreading rate of more than 9 cm/year. Intermediate ridges have a spreading rate of 4–9 cm/year while slow spreading ridges have a rate less than 4 cm/year.[2]
Earlier theories (e.g. by Alfred Wegener and Alexander du Toit) of continental drift postulated that continents "ploughed" through the sea. The idea that the seafloor itself moves (and also carries the continents with it) as it expands from a central axis was proposed by Harry Hess from Princeton University in the 1960s.[3] The theory is well accepted now, and the phenomenon is known to be caused by convection currents in the asthenosphere, which is ductile, or plastic, and the brittle lithosphere.[4][clarification needed]
Contents
[hide]
1 Incipient spreading
2 Continued spreading and subduction
3 Debate and search for mechanism
4 Sea floor global topography: half-space model
5 See also
6 References
7 External links
Incipient spreading[edit]
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Plates in the crust of the earth, according to the plate tectonics theory
In the general case, sea floor spreading starts as a rift in a continental land mass, similar to the Red Sea-East Africa Rift System today.[5] The process starts with heating at the base of the continental crust which causes it to become more plastic and less dense. Because less dense objects rise in relation to denser objects, the area being heated becomes a broad dome (see isostasy). As the crust bows upward, fractures occur that gradually grow into rifts. The typical rift system consists of three rift arms at approximately 120 degree angles. These areas are named triple junctions and can be found in several places across the world today. The separated margins of the continents evolve to form passive margins. Hess' theory was that new seafloor is formed when magma is forced upward toward the surface at a mid-ocean ridge.
If spreading continues past the incipient stage described above, two of the rift arms will open while the third arm stops opening and becomes a 'failed rift'. As the two active rifts continue to open, eventually the continental crust is attenuated as far as it will stretch. At this point basaltic oceanic crust begins to form between the separating continental fragments. When one of the rifts opens into the existing ocean, the rift system is flooded with seawater and becomes a new sea. The Red Sea is an example of a new arm of the sea. The East African rift was thought to be a "failed" arm that was opening somewhat more slowly than the other two arms, but in 2005 the Ethiopian Afar Geophysical Lithospheric Experiment[6] reported that in the Afar region last September,[when?] a 60 km fissure opened as wide as eight meters. During this period of initial flooding the new sea is sensitive to changes in climate and eustasy. As a result, the new sea will evaporate (partially or completely) several times before the elevation of the rift valley has been lowered to the point that the sea becomes stable. During this period of evaporation large evaporite deposits will be made in the rift valley. Later these deposits have the potential to become hydrocarbon seals and are of particular interest to petroleum geologists.
Sea floor spreading can stop during the process, but if it continues to the point that the continent is completely severed, then a new ocean basin is created. The Red Sea has not yet completely split Arabia from Africa, but a similar feature can be found on the other side of Africa that has broken completely free. South America once fit into the area of the Niger Delta. The Niger River has formed in the failed rift arm of the triple junction.
Continued spreading and subduction[edit]
Spreading at a mid-ocean ridge
As new seafloor forms and spreads apart from the mid-ocean ridge it slowly cools over time. Older seafloor is therefore colder than new seafloor, and older oceanic basins deeper than new oceanic basins due to isostasy. If the diameter of the earth remains relatively constant despite the production of new crust, a mechanism must exist by which crust is also destroyed. The destruction of oceanic crust occurs at subduction zones where oceanic crust is forced under either continental crust or oceanic crust. Today, the Atlantic basin is actively spreading at the Mid-Atlantic Ridge. Only a small portion of the oceanic crust produced in the Atlantic is subducted. However, the plates making up the Pacific Ocean are experiencing subduction along many of their boundaries which causes the volcanic activity in what has been termed the Ring of Fire of the Pacific Ocean. The Pacific is also home to one of the world's most active spreading centres (the East Pacific Rise) with spreading rates of up to 13 cm/yr. The Mid-Atlantic Ridge is a "textbook" slow-spreading centre, while the East Pacific Rise is used as an example of fast spreading. The differences in spreading rates affect not only the geometries of the ridges but also the geochemistry of the basalts that are produced.[7]
Since the new oceanic basins are shallower than the old oceanic basins, the total capacity of the world's ocean basins decreases during times of active sea floor spreading. During the opening of the Atlantic Ocean, sea level was so high that a Western Interior Seaway formed across North America from the Gulf of Mexico to the Arctic Ocean.
Debate and search for mechanism[edit]
At the Mid-Atlantic Ridge (and in other areas), material from the upper mantle rises through the faults between oceanic plates to form new crust as the plates move away from each other, a phenomenon first observed as continental drift. When Alfred Wegener first presented a hypothesis of continental drift in 1912, he suggested that continents ploughed through the ocean crust. This was impossible: oceanic crust is both more dense and more rigid than continental crust. Accordingly, Wegener's theory wasn't taken very seriously, especially in the United States.
Since then, it has been shown that the motion of the continents is linked to seafloor spreading. In the 1960s, the past record of geomagnetic reversals was noticed by observing the magnetic stripe "anomalies" on the ocean floor.[8] This results in broadly evident "stripes" from which the past magnetic field polarity can be inferred by looking at the data gathered from simply towing a magnetometer on the sea surface or from an aircraft. The stripes on one side of the mid-ocean ridge were the mirror image of those on the other side. The seafloor must have originated on the Earth's great fiery welts, like the Mid-Atlantic Ridge and the East Pacific Rise.
The driver for seafloor spreading in plates with active margins is the weight of the cool, dense, subducting slabs that pull them along. The magmatism at the ridge is considered to be "passive upswelling", which is caused by the plates being pulled apart under the weight of their own slabs.[9] This can be thought of as analogous to a rug on a table with little friction: when part of the rug is off of the table, its weight pulls the rest of the rug down with it.
Sea floor global topography: half-space model[edit]
To first approximation, sea floor global topography in areas without significant subduction can be estimated by the half-space model.[10] In this model, the seabed height is determined by the oceanic lithosphere temperature, due to thermal expansion. Oceanic lithosphere is continuously formed at a constant rate at the mid-ocean ridges. The source of the lithosphere has a half-plane shape (x = 0, z < 0) and a constant temperature T1. Due to its continuous creation, the lithosphere at x > 0 is moving away from the ridge at a constant velocity v, which is assumed large compared to other typical scales in the problem. The temperature at the upper boundary of the lithosphere (z=0) is a constant T0 = 0. Thus at x = 0 the temperature is the Heaviside step function T 1 ⋅ Θ ( − z ) {\displaystyle T_{1}\cdot \Theta (-z)} . Finally, we assume the system is at a quasi-steady state, so that the temperature distribution is constant in time, i.e. T=T(x,z).
By calculating in the frame of reference of the moving lithosphere (velocity v), which have spatial coordinate x' = x-vt, we may write T = T(x',z,t) and use the heat equation: ∂ T ∂ t = κ ∇ 2 T = κ ∂ 2 T ∂ 2 z + κ ∂ 2 T ∂ 2 x ′ {\displaystyle {\frac {\partial T}{\partial t}}=\kappa \nabla ^{2}T=\kappa {\frac {\partial ^{2}T}{\partial ^{2}z}}+\kappa {\frac {\partial ^{2}T}{\partial ^{2}x'}}} where κ {\displaystyle \kappa } is the thermal diffusivity of the mantle lithosphere.
Since T depends on x' and t only through the combination x = x ′ + v t {\displaystyle x=x'+vt} , we have: ∂ T ∂ x ′ = 1 v ⋅ ∂ T ∂ t {\displaystyle {\frac {\partial T}{\partial x'}}={\frac {1}{v}}\cdot {\frac {\partial T}{\partial t}}}
Thus: ∂ T ∂ t = κ ∇ 2 T = κ ∂ 2 T ∂ 2 z + κ v 2 ∂ 2 T ∂ 2 t {\displaystyle {\frac {\partial T}{\partial t}}=\kappa \nabla ^{2}T=\kappa {\frac {\partial ^{2}T}{\partial ^{2}z}}+{\frac {\kappa }{v^{2}}}{\frac {\partial ^{2}T}{\partial ^{2}t}}}
We now use the assumption that v {\displaystyle v} is large compared to other scales in the problem; we therefore neglect the last term in the equation, and get a 1-dimensional diffusion equation: ∂ T ∂ t = κ ∂ 2 T ∂ 2 z {\displaystyle {\frac {\partial T}{\partial t}}=\kappa {\frac {\partial ^{2}T}{\partial ^{2}z}}} with the initial conditions T ( t = 0 ) = T 1 ⋅ Θ ( − z ) {\displaystyle T(t=0)=T_{1}\cdot \Theta (-z)} .
The solution for z ≤ 0 {\displaystyle z\leq 0} is given by the error function erf {\displaystyle \operatorname {erf} } :
T ( x ′ , z , t ) = T 1 ⋅ erf  ( z 2 κ t ) {\displaystyle T(x',z,t)=T_{1}\cdot \operatorname {erf} \left({\frac {z}{2{\sqrt {\kappa t}}}}\right)} .
Due to the large velocity, the temperature dependence on the horizontal direction is negligible, and the height at time t (i.e. of sea floor of age t) can be calculated by integrating the thermal expansion over z:
h ( t ) = h 0 + α e f f ∫ 0 ∞ [ T ( z ) − T 1 ] d z = h 0 − 2 π α e f f T 1 κ t {\displaystyle h(t)=h_{0}+\alpha _{\mathrm {eff} }\int _{0}^{\infty }[T(z)-T_{1}]dz=h_{0}-{\frac {2}{\sqrt {\pi }}}\alpha _{\mathrm {eff} }T_{1}{\sqrt {\kappa t}}}
where α e f f {\displaystyle \alpha _{\mathrm {eff} }} is the effective volumetric thermal expansion coefficient, and h0 is the mid-ocean ridge height (compared to some reference).
Note that the assumption the v is relatively large is equivalently to the assumption that the thermal diffusivity κ {\displaystyle \kappa } is small compared to L 2 / T {\displaystyle L^{2}/T} , where L is the acean width (from mid-ocean ridges to continental shelf) and T is its age.
The effective thermal expansion coefficient α e f f {\displaystyle \alpha _{\mathrm {eff} }} is different from the usual thermal expansion coefficient α {\displaystyle \alpha } due to isostasic effect of the change in water column height above the lithosphere as it expands or retracts. Both coefficients are related by:
α e f f = α ⋅ ρ ρ − ρ w {\displaystyle \alpha _{\mathrm {eff} }=\alpha \cdot {\frac {\rho }{\rho -\rho _{w}}}}
where ρ ∼ 3.3 g / c m 3 {\displaystyle \rho \sim 3.3g/cm^{3}} is the rock density and ρ 0 = 1 g / c m 3 {\displaystyle \rho _{0}=1g/cm^{3}} is the density of water.
By substituting the parameters by their rough estimates: κ ∼ 8 ⋅ 10 − 7 {\displaystyle \kappa \sim 8\cdot 10^{-7}} m2/s, α ∼ 4 ⋅ 10 − 5 {\displaystyle \alpha \sim 4\cdot 10^{-5}} °C−1 and T1 ~1220 °C (for the Atlantic and Indian oceans) or ~1120 °C (for the eastern Pacific), we have:
h ( t ) ∼ h 0 − 350 t {\displaystyle h(t)\sim h_{0}-350{\sqrt {t}}}
for the eastern Pacific Ocean, and:
h ( t ) ∼ h 0 − 390 t {\displaystyle h(t)\sim h_{0}-390{\sqrt {t}}}
for the Atlantic and the Indian Ocean, where the height is in meters and time is in millions of years. To get the dependence on x, one must substitute t = x/v ~ Tx/L, where L is the distance between the ridge to the continental shelf (roughly half the ocean width), and T is the ocean age.
See also[edit]
Wikimedia Commons has media related to Seafloor spreading.
Divergent boundary
Mid-ocean ridge
Morley-Vine-Matthews hypothesis
References[edit]
Jump up ^ Tan, Yen Joe; Tolstoy, Maya; Waldhauser, Felix; Wilcock, William S. D. "Dynamics of a seafloor-spreading episode at the East Pacific Rise". Nature. 540 (7632): 261–265. doi:10.1038/nature20116.
Jump up ^ Tan, Yen Joe; Tolstoy, Maya; Waldhauser, Felix; Wilcock, William S. D. "Dynamics of a seafloor-spreading episode at the East Pacific Rise". Nature. 540 (7632): 261–265. doi:10.1038/nature20116.
Jump up ^ Hess, H. H. (November 1962). "History of Ocean Basins" (PDF). In A. E. J. Engel; Harold L. James; B. F. Leonard. Petrologic studies: a volume to honor A. F. Buddington. Boulder, CO: Geological Society of America. pp. 599–620. Retrieved 8 September 2010.
Jump up ^ Elsasser, Walter M. (1971). "Sea-Floor Spreading as Thermal Convection". Journal of Geophysical Research. 76: 1101. Bibcode:1971JGR....76.1101E. doi:10.1029/JB076i005p01101.
Jump up ^ Makris, J.; Ginzburg, A. (1987-09-15). "Sedimentary basins within the Dead Sea and other rift zones The Afar Depression: transition between continental rifting and sea-floor spreading". Tectonophysics. 141 (1): 199–214. doi:10.1016/0040-1951(87)90186-7.
Jump up ^ Bastow, Ian D.; Keir, Derek; Daly, Eve (2011-06-01). "The Ethiopia Afar Geoscientific Lithospheric Experiment (EAGLE): Probing the transition from continental rifting to incipient seafloor spreading". Geological Society of America Special Papers. 478: 51–76. ISSN 0072-1077. doi:10.1130/2011.2478(04).
Jump up ^ Bhagwat, S.B. (2009). Foundation of Geology Vol 1. Global Vision Publishing House. p. 83. ISBN 9788182202764.
Jump up ^ Vine, F. J.; Matthews, D. H. (1963). "Magnetic Anomalies Over Oceanic Ridges". Nature. 199: 947–949. doi:10.1038/199947a0.
Jump up ^ Patriat, Philippe; Achache, José (1984). "India–Eurasia collision chronology has implications for crustal shortening and driving mechanism of plates". Nature. 311 (5987): 615. Bibcode:1984Natur.311..615P. doi:10.1038/311615a0.
Jump up ^ Davis, E.E; Lister, C. R. B. (1974). "Fundamentals of Ridge Crest Topography". Earth and Planetary Science Letters. North-Holland Publishing Company. 21: 405–413. Bibcode:1974E&PSL..21..405D. doi:10.1016/0012-821X(74)90180-0.
External links[edit]
The Wikibook Historical Geology has a page on the topic of: Seafloor spreading
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History of programming languages
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This article's lead section does not adequately summarize key points of its contents. Please consider expanding the lead to provide an accessible overview of all important aspects of the article. Please discuss this issue on the article's talk page. (February 2018)
For a detailed timeline of events, see Timeline of programming languages.
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The first high-level programming language was Plankalkül, created by Konrad Zuse between 1942 and 1945[1]. The first high-level language to have an associated compiler, was created by Corrado Böhm in 1951, for his PhD thesis. The first commercially available language was FORTRAN (FORmula TRANslation); developed in 1956 (first manual appeared in 1956, but first developed in 1954) by John Backus, a worker at IBM.
When FORTRAN was first introduced it was treated with suspicion because of the belief that programs compiled from high-level language would be less efficient than those written directly in machine code. FORTRAN became popular because it provided a means of porting existing code to new computers, in a hardware market that was rapidly evolving. FORTRAN eventually became known for its efficiency. Over the years, FORTRAN had been updated, with standards released for FORTRAN-66, FORTRAN-77 and FORTRAN-92.
Contents
[hide]
1 Early history
2 First programming languages
3 Establishing fundamental paradigms
4 1980s: consolidation, modules, performance
5 1990s: the Internet age
6 Current trends
7 Prominent people
8 See also
9 References
10 Further reading
11 External links
Early history[edit]
During a nine-month period in 1842–1843, Ada Lovelace translated the memoir of Italian mathematician Luigi Menabrea about Charles Babbage's newest proposed machine, the analytical engine. With the article she appended a set of notes which specified in complete detail a method for calculating Bernoulli numbers with the engine, recognized by some historians as the world's first computer program.[2]
The first computer codes were specialized for their applications. In the first decades of the 20th century, numerical calculations were based on decimal numbers. Eventually it was realized that logic could be represented with numbers, not only with words. For example, Alonzo Church was able to express the lambda calculus in a formulatic way. The Turing machine was an abstraction of the operation of a tape-marking machine, for example, in use at the telephone companies. Turing machines set the basis for storage of programs as data in the von Neumann architecture of computers by representing a machine through a finite number. However, unlike the lambda calculus, Turing's code does not serve well as a basis for higher-level languages—its principal use is in rigorous analyses of algorithmic complexity.
To some people, what was the first modern programming language depends on how much power and human-readability is required before the status of "programming language" is granted. Jacquard Looms and Charles Babbage's Difference Engine both had simple, extremely limited languages for describing the actions that these machines should perform.
First programming languages[edit]
In the 1940s, the first recognizably modern electrically powered computers were created. The limited speed and memory capacity forced programmers to write hand tuned assembly language programs. It was eventually realized that programming in assembly language required a great deal of intellectual effort.
The first programming languages designed to communicate instructions to a computer were written in the 1950s. An early high-level programming language to be designed for a computer was Plankalkül, developed by the Germans for Z1 by Konrad Zuse between 1943 and 1945. However, it was not implemented until 1998 and 2000.[3]
John Mauchly's Short Code, proposed in 1949, was one of the first high-level languages ever developed for an electronic computer.[4] Unlike machine code, Short Code statements represented mathematical expressions in understandable form. However, the program had to be translated into machine code every time it ran, making the process much slower than running the equivalent machine code.
At the University of Manchester, Alick Glennie developed Autocode in the early 1950s, with the second iteration developed for the Mark 1 by R. A. Brooker in 1954, known as the "Mark 1 Autocode". Brooker also developed an autocode for the Ferranti Mercury in the 1950s in conjunction with the University of Manchester. The version for the EDSAC 2 was devised by D. F. Hartley of University of Cambridge Mathematical Laboratory in 1961. Known as EDSAC 2 Autocode, it was a straight development from Mercury Autocode adapted for local circumstances, and was noted for its object code optimisation and source-language diagnostics which were advanced for the time. A contemporary but separate thread of development, Atlas Autocode was developed for the University of Manchester Atlas 1 machine.
In 1954, language FORTRAN was invented at IBM by a team led by John Backus; it was the first widely used high level general purpose programming language to have a functional implementation, as opposed to just a design on paper.[5][6] It is still a popular language for high-performance computing[7] and is used for programs that benchmark and rank the world's fastest supercomputers.[8]
Another early programming language was devised by Grace Hopper in the US, called FLOW-MATIC. It was developed for the UNIVAC I at Remington Rand during the period from 1955 until 1959. Hopper found that business data processing customers were uncomfortable with mathematical notation, and in early 1955, she and her team wrote a specification for an English programming language and implemented a prototype.[9] The FLOW-MATIC compiler became publicly available in early 1958 and was substantially complete in 1959.[10] Flow-Matic was a major influence in the design of COBOL, since only it and its direct descendent AIMACO were in actual use at the time.[11]
Other languages still in use today include LISP (1958), invented by John McCarthy and COBOL (1959), created by the Short Range Committee. Another milestone in the late 1950s was the publication, by a committee of American and European computer scientists, of "a new language for algorithms"; the ALGOL 60 Report (the "ALGOrithmic Language"). This report consolidated many ideas circulating at the time and featured three key language innovations:
nested block structure: code sequences and associated declarations could be grouped into blocks without having to be turned into separate, explicitly named procedures;
lexical scoping: a block could have its own private variables, procedures and functions, invisible to code outside that block, that is, information hiding.
Another innovation, related to this, was in how the language was described:
a mathematically exact notation, Backus–Naur form (BNF), was used to describe the language's syntax. Nearly all subsequent programming languages have used a variant of BNF to describe the context-free portion of their syntax.
Algol 60 was particularly influential in the design of later languages, some of which soon became more popular. The Burroughs large systems were designed to be programmed in an extended subset of Algol.
Algol's key ideas were continued, producing ALGOL 68:
syntax and semantics became even more orthogonal, with anonymous routines, a recursive typing system with higher-order functions, etc.;
not only the context-free part, but the full language syntax and semantics were defined formally, in terms of Van Wijngaarden grammar, a formalism designed specifically for this purpose.
Algol 68's many little-used language features (for example, concurrent and parallel blocks) and its complex system of syntactic shortcuts and automatic type coercions made it unpopular with implementers and gained it a reputation of being difficult. Niklaus Wirth actually walked out of the design committee to create the simpler Pascal language.
Fortran
Some notable languages that were developed in this period include:
1951 – Regional Assembly Language
1952 – Autocode
1954 – IPL (forerunner to LISP)
1955 – FLOW-MATIC (led to COBOL)
1957 – FORTRAN (First compiler)
1957 – COMTRAN (precursor to COBOL)
1958 – LISP
1958 – ALGOL 58
1959 – FACT (forerunner to COBOL)
1959 – COBOL
1959 – RPG
1962 – APL
1962 – Simula
1962 – SNOBOL
1963 – CPL (forerunner to C)
1964 – Speakeasy (computational environment)
1964 – BASIC
1964 – PL/I
1966 – JOSS
1967 – BCPL (forerunner to C)
Establishing fundamental paradigms[edit]
Smalltalk
Scheme
The period from the late 1960s to the late 1970s brought a major flowering of programming languages. Most of the major language paradigms now in use were invented in this period:
Speakeasy (computational environment), developed in 1964 at Argonne National Laboratory (ANL) by Stanley Cohen, is an OOPS (object-oriented programming, much like the later MATLAB, IDL (programming language) and Mathematica) numerical package. Speakeasy has a clear Fortran foundation syntax. It first addressed efficient physics computation internally at ANL, was modified for research use (as "Modeleasy") for the Federal Reserve Board in the early 1970s and then was made available commercially; Speakeasy and Modeleasy are still in use currently.
Simula, invented in the late 1960s by Nygaard and Dahl as a superset of Algol 60, was the first language designed to support object-oriented programming.
C, an early systems programming language, was developed by Dennis Ritchie and Ken Thompson at Bell Labs between 1969 and 1973.
Smalltalk (mid-1970s) provided a complete ground-up design of an object-oriented language.
Prolog, designed in 1972 by Colmerauer, Roussel, and Kowalski, was the first logic programming language.
ML built a polymorphic type system (invented by Robin Milner in 1973) on top of Lisp,[12] pioneering statically typed functional programming languages.
Each of these languages spawned an entire family of descendants, and most modern languages count at least one of them in their ancestry.
The 1960s and 1970s also saw considerable debate over the merits of "structured programming", which essentially meant programming without the use of "goto". A significant fraction of programmers believed that, even in languages that provide "goto", it is bad programming style to use it except in rare circumstances. This debate was closely related to language design: some languages did not include a "goto" at all, which forced structured programming on the programmer.
To provide even faster compile times, some languages were structured for "one-pass compilers" which expect subordinate routines to be defined first, as with Pascal, where the main routine, or driver function, is the final section of the program listing.
Some notable languages that were developed in this period include:
1968 – Logo
1969 – B (forerunner to C)
1970 – Pascal
1970 – Forth
1972 – C
1972 – Smalltalk
1972 – Prolog
1973 – ML
1975 – Scheme
1978 – SQL (a query language, later extended)
1980s: consolidation, modules, performance[edit]
MATLAB
Erlang
Tcl
The 1980s were years of relative consolidation in imperative languages. Rather than inventing new paradigms, all of these movements elaborated upon the ideas invented in the previous decade. C++ combined object-oriented and systems programming. The United States government standardized Ada, a systems programming language intended for use by defense contractors. In Japan and elsewhere, vast sums were spent investigating so-called fifth-generation programming languages that incorporated logic programming constructs. The functional languages community moved to standardize ML and Lisp. Research in Miranda, a functional language with lazy evaluation, began to take hold in this decade.
One important new trend in language design was an increased focus on programming for large-scale systems through the use of modules, or large-scale organizational units of code. Modula, Ada, and ML all developed notable module systems in the 1980s. Module systems were often wedded to generic programming constructs---generics being, in essence, parametrized modules[citation needed] (see also polymorphism in object-oriented programming).
Although major new paradigms for imperative programming languages did not appear, many researchers expanded on the ideas of prior languages and adapted them to new contexts. For example, the languages of the Argus and Emerald systems adapted object-oriented programming to distributed systems.
The 1980s also brought advances in programming language implementation. The RISC movement in computer architecture postulated that hardware should be designed for compilers rather than for human assembly programmers. Aided by processor speed improvements that enabled increasingly aggressive compilation techniques, the RISC movement sparked greater interest in compilation technology for high-level languages.
Language technology continued along these lines well into the 1990s.
Some notable languages that were developed in this period include:
1980 – C++ (as C with classes, renamed in 1983)
1983 – Ada
1984 – Common Lisp
1984 – MATLAB
1984 - dBase III, dBase III Plus (Clipper and FoxPro as FoxBASE, later developing into Visual FoxPro
1985 – Eiffel
1986 – Objective-C
1986 – LabVIEW (Visual Programming Language)
1986 – Erlang
1987 – Perl
1988 – Tcl
1988 – Wolfram Language (as part of Mathematica, only got a separate name in June 2013)
1989 – FL (Backus)
1990s: the Internet age[edit]
Haskell
Lua
PHP
Rebol
The rapid growth of the Internet in the mid-1990s was the next major historic event in programming languages. By opening up a radically new platform for computer systems, the Internet created an opportunity for new languages to be adopted. In particular, the JavaScript programming language rose to popularity because of its early integration with the Netscape Navigator web browser. Various other scripting languages achieved widespread use in developing customized applications for web servers such as PHP. The 1990s saw no fundamental novelty in imperative languages, but much recombination and maturation of old ideas. This era began the spread of functional languages. A big driving philosophy was programmer productivity. Many "rapid application development" (RAD) languages emerged, which usually came with an IDE, garbage collection, and were descendants of older languages. All such languages were object-oriented. These included Object Pascal, Visual Basic, and Java. Java in particular received much attention.
More radical and innovative than the RAD languages were the new scripting languages. These did not directly descend from other languages and featured new syntaxes and more liberal incorporation of features. Many consider these scripting languages to be more productive than even the RAD languages, but often because of choices that make small programs simpler but large programs more difficult to write and maintain.[citation needed] Nevertheless, scripting languages came to be the most prominent ones used in connection with the Web.
Some notable languages that were developed in this period include:
1990 – Haskell
1991 – Python
1991 – Visual Basic
1993 – Lua
1993 – R
1994 – CLOS (part of ANSI Common Lisp)
1995 – Ruby
1995 – Ada 95
1995 – Java
1995 – Delphi (Object Pascal)
1995 – JavaScript
1995 – PHP
1997 – Rebol
Current trends[edit]
Programming language evolution continues, in both industry and research. Some of the recent trends have included:
D Programming Language
Groovy
Rust
Scratch
Swift
Increasing support for functional programming in mainstream languages used commercially, including pure functional programming for making code easier to reason about and easier to parallelise (at both micro- and macro- levels)
Constructs to support concurrent and distributed programming.
Mechanisms for adding security and reliability verification to the language: extended static checking, dependent typing, information flow control, static thread safety.
Alternative mechanisms for composability and modularity: mixins, traits, delegates, aspects.
Component-oriented software development.
Metaprogramming, reflection or access to the abstract syntax tree
AOP or Aspect Oriented Programming allowing developers to insert code in another module or class at "join points"
Domain specific languages and code generation
XML for graphical interface (XUL, XAML)
Increased interest in distribution and mobility.
Integration with databases, including XML and relational databases.
Open source as a developmental philosophy for languages, including the GNU Compiler Collection and languages such as Python, Ruby, and Scala.
Massively parallel languages for coding 2000 processor GPU graphics processing units and supercomputer arrays including OpenCL
Early research into (as-yet-unimplementable) quantum computing programming languages
More interest in visual programming languages like Scratch
Some notable languages developed during this period include:
2000 – ActionScript
2001 – C#
2001 – D
2002 – Scratch
2003 – Groovy
2003 – Scala
2005 – F#
2006 – PowerShell
2007 – Clojure
2009 – Go
2010 – Rust
2011 – Dart
2011 – Kotlin
2011 – Red
2011 - Elixir
2012 – Julia
2014 – Swift
2016 – Ring [13][14]
Prominent people[edit]
Anders Hejlsberg
Yukihiro Matsumoto
Grace M. Hopper
Bjarne Stroustrup
Niklaus Wirth
Some key people who helped develop programming languages:
Alan Cooper, developer of Visual Basic.
Alan Kay, pioneering work on object-oriented programming, and originator of Smalltalk.
Anders Hejlsberg, developer of Turbo Pascal, Delphi, C#, and TypeScript.
Bertrand Meyer, inventor of Eiffel.
Bjarne Stroustrup, developer of C++.
Brian Kernighan, co-author of the first book on the C programming language with Dennis Ritchie, coauthor of the AWK and AMPL programming languages.
Chris Lattner, creator of Swift and LLVM.
Dennis Ritchie, inventor of C. Unix Operating System, Plan 9 Operating System.
Grace Hopper, first to use the term compiler and developer of Flow-Matic, influenced development of COBOL. Popularized machine-independent programming languages and the term "debugging".
Guido van Rossum, creator of Python.
James Gosling, lead developer of Java and its precursor, Oak.
Jean Ichbiah, chief designer of Ada, Ada 83.
Jean-Yves Girard, co-inventor of the polymorphic lambda calculus (System F).
Jeff Bezanson, main designer, and one of the core developers of Julia.
Joe Armstrong, creator of Erlang.
John Backus, inventor of Fortran and cooperated in the design of ALGOL 58 and ALGOL 60.
John C. Reynolds, co-inventor of the polymorphic lambda calculus (System F).
John McCarthy, inventor of LISP.
John von Neumann, originator of the operating system concept.
Graydon Hoare, inventor of Rust.
Ken Thompson, inventor of B, Go Programming Language, Inferno Programming Language, and Unix Operating System co-author.
Kenneth E. Iverson, developer of APL, and co-developer of J along with Roger Hui.
Konrad Zuse, designed the first high-level programming language, Plankalkül (which influenced ALGOL 58[15]).
Kristen Nygaard, pioneered object-oriented programming, co-invented Simula.
Larry Wall, creator of the Perl programming language (see Perl and Perl 6).
Martin Odersky, creator of Scala, and previously a contributor to the design of Java.
Nathaniel Rochester, inventor of first assembler (IBM 701).
Niklaus Wirth, inventor of Pascal, Modula and Oberon.
Ole-Johan Dahl, pioneered object-oriented programming, co-invented Simula.
Rasmus Lerdorf, creator of PHP
Rich Hickey, creator of Clojure.
Robin Milner, inventor of ML, and sharing credit for Hindley–Milner polymorphic type inference.
Stephen Wolfram, creator of Mathematica.
Tom Love and Brad Cox, creator of Objective-C.
Walter Bright, creator of D.
Yukihiro Matsumoto, creator of Ruby.
See also[edit]
ACM
SIGPLAN
History of Programming Languages Conference
History of compiler writing
History of computing hardware
Programming language
Timeline of computing
Timeline of programming languages
List of programming languages
List of programmers
References[edit]
Jump up ^ Knuth, Donald E.; Pardo, Luis Trabb. "Early development of programming languages". Encyclopedia of Computer Science and Technology. Marcel Dekker. 7: 419–493.
Jump up ^ J. Fuegi and J. Francis (October–December 2003), "Lovelace & Babbage and the creation of the 1843 'notes'", Annals of the History of Computing, 25 (4): 16, 19, 25, doi:10.1109/MAHC.2003.1253887
Jump up ^ Rojas, Raúl, et al. (2000). "Plankalkül: The First High-Level Programming Language and its Implementation". Institut frame Informatik, Freie Universität Berlin, Technical Report B-3/2000. (full text)
Jump up ^ Sebesta, W.S. (2006). Concepts of Programming Languages. p. 44. ISBN 0-321-33025-0.
Jump up ^ "Fortran creator John Backus dies - Tech and gadgets- msnbc.com". MSNBC. 2007-03-20. Retrieved 2010-04-25.
Jump up ^ "CSC-302 99S : Class 02: A Brief History of Programming Languages". Math.grin.edu. Retrieved 2010-04-25.
Jump up ^ Eugene Loh (18 June 2010). "The Ideal HPC Programming Language". Queue. Association of Computing Machines. 8 (6).
Jump up ^ "HPL - A Portable Implementation of the High-Performance Linpack Benchmark for Distributed-Memory Computers". Retrieved 2015-02-21.
Jump up ^ Hopper (1978) p. 16.
Jump up ^ Sammet (1969) p. 316
Jump up ^ Sammet (1978) p. 204.
Jump up ^ Gordon, Michael J. C. (1996). "From LCF to HOL: a short history" (PDF). p. 3. Retrieved 2015-05-04. Edinburgh LCF, including the ML interpreter, was implemented in Lisp.
Jump up ^ Rubin Liu (28 February 2018). "The evolution of the Ring programming language, Ring in Top 50 programming languages according to TIOBE Index". codeproject.com. Code_Project.
Jump up ^ TIOBE (2 March 2018). "TIOBE Index, Ring in Top 50 programming languages according to TIOBE Index". www.tiobe.com. TIOBE_index.
Jump up ^ Rojas, Raúl; Hashagen, Ulf (2002). The First Computers: History and Architectures. MIT Press. p. 292. ISBN 978-0262681377. Retrieved October 25, 2013.
Further reading[edit]
Rosen, Saul, (editor), Programming Systems and Languages, McGraw-Hill, 1967.
Sammet, Jean E., Programming Languages: History and Fundamentals, Prentice-Hall, 1969.
Sammet, Jean E. (July 1972). "Programming Languages: History and Future". Communications of the ACM. 15 (7): 601–610. doi:10.1145/361454.361485.
Richard L. Wexelblat (ed.): History of Programming Languages, Academic Press 1981.
Thomas J. Bergin and Richard G. Gibson (eds.): History of Programming Languages, Addison Wesley, 1996.
External links[edit]
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