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Point location
Point location is a computational geometry method that preprocesses a subdivision of space so repeated queries quickly report the region containing a query point, with optimal structures achieving logarithmic query time in linear space.
Point pattern analysis
Point pattern analysis is the branch of statistics that tests whether the locations of events in space are clustered, dispersed, or random, fitting point process models.
Point process
A point process, sometimes studied as point process theory, is a stochastic model for randomly occurring events in time or space, such as customer arrivals or earthquakes.
Point spectrum
The point spectrum of a linear operator is the set of its eigenvalues, one of the three standard parts of the spectrum in functional analysis.
Point spread function
The point spread function (PSF) of an optical system is the image it forms of a point source, describing how diffraction and aberrations blur the point.
Pointclass
A pointclass is a collection of pointsets, subsets of Polish spaces, organizing definable sets of reals into hierarchies, chiefly the Borel and projective pointclasses of descriptive set theory.
Pointer states
Pointer states are quantum states that remain intact when a system interacts with its environment, while their superpositions decohere; the concept was introduced by Wojciech Zurek in 1982.
Pointless topology
Pointless topology, also called point-free topology or locale theory, is an approach to topology that studies lattices of open sets called locales instead of sets of points.
Pointwise convergence
Pointwise convergence is a mode of convergence for sequences of functions where each point's values converge, without requiring the same rate everywhere; it is weaker than uniform convergence.
Pointwise mutual information
Pointwise mutual information, introduced by Robert Fano in 1961, is a measure of how much more often two outcomes co-occur than independence would predict, with wide use in linguistics and NLP.
Poisson approximation
Poisson approximation, known as the law of rare events or law of small numbers, approximates the distribution of many rare random events by a Poisson distribution with the same mean.
Poisson bracket
The Poisson bracket is an operation on functions of a mechanical system's positions and momenta, defined as a sum of mixed partial derivatives that governs time evolution in Hamiltonian mechanics.
Poisson distribution
The Poisson distribution is a discrete probability distribution giving the probability that a number of events occurs in a fixed interval at a constant average rate, with mean and variance equal to the single parameter λ.
Poisson limit theorem
The Poisson limit theorem, or law of rare events, states that a binomial distribution with many trials and small success probability converges to a Poisson distribution.
Poisson point process
The Poisson point process, also known as the Poisson random point field, is a mathematical model for events scattered without interaction, with independent counts in disjoint regions.
Poisson regression
Poisson regression is a generalized linear model used to predict counts of events, such as hospital admissions, from explanatory variables, assuming the response follows a Poisson distribution.
Poisson sampling
Poisson sampling is a survey sampling design in which each population unit is selected independently with its own inclusion probability, giving a random sample size.
Poisson–Boltzmann equation
The Poisson–Boltzmann equation is a mean-field partial differential equation describing ion distributions and electrostatic potential around charged surfaces, the central continuum model of the electrical double layer.
Poisson's equation
Poisson's equation, also known as the Poisson problem, is a second-order elliptic partial differential equation relating a potential's curvature to source density like charge or mass.
Poisson's ratio
Poisson's ratio, symbol ν, measures how much a stretched material contracts sideways: about 0.5 for rubber, 0.27 to 0.33 for steel, and near zero for cork.
Pol Swings
Pol Swings was a Belgian astrophysicist at the University of Liège known for the Swings effect in cometary spectra and president of the International Astronomical Union.
Polar (star)
A polar, or AM Herculis star, is a magnetic cataclysmic variable binary whose strongly magnetized white dwarf accretes gas directly from its companion without an accretion disk.
Polar amplification
Polar amplification is the phenomenon in which the polar regions warm faster than the global average; Arctic amplification has warmed nearly four times the global rate.
Polar cell
The polar cell is the smallest and weakest of the three atmospheric circulation cells in each hemisphere, where air rises near 60–70° latitude and sinks over the pole.
Polar climate
A polar climate, Köppen group E, is a climate where no month's mean exceeds 10 °C, roughly the limit of tree growth, subdivided into tundra and ice-cap climates.
Polar coordinate system
The polar coordinate system, also known as polar coordinates, is a two-dimensional coordinate system describing each point by its distance and angle from a fixed pole.
Polar cusp
The polar cusp is a funnel-shaped region of the dayside, high-latitude magnetosphere where solar wind plasma has direct access to the ionosphere, first measured in situ in 1971.
Polar decomposition
The polar decomposition, or polar factorization, is a matrix factorization A = UH into a unitary or orthonormal-column factor U and a Hermitian positive semidefinite factor H.
Polar front
The polar front is the semi-permanent boundary between cold polar air and warmer low-latitude air in each hemisphere's midlatitudes, along which most extratropical cyclones form.
Polar low
A polar low is a small but intense maritime cyclone that forms over high-latitude oceans in winter, producing gale-force winds, heavy snowfall, high waves, and icing.