Curse of dimensionalityThe curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming. Dimensionally cursed phenomena occur in domains such as numerical analysis, sampling, combinatorics, machine learning, data mining and databases.
Mutual informationIn probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons (bits), nats or hartleys) obtained about one random variable by observing the other random variable. The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.
Serre spectral sequenceIn mathematics, the Serre spectral sequence (sometimes Leray–Serre spectral sequence to acknowledge earlier work of Jean Leray in the Leray spectral sequence) is an important tool in algebraic topology. It expresses, in the language of homological algebra, the singular (co)homology of the total space X of a (Serre) fibration in terms of the (co)homology of the base space B and the fiber F. The result is due to Jean-Pierre Serre in his doctoral dissertation. Let be a Serre fibration of topological spaces, and let F be the (path-connected) fiber.
Ecological classificationEcological classification or ecological typology is the classification of land or water into geographical units that represent variation in one or more ecological features. Traditional approaches focus on geology, topography, biogeography, soils, vegetation, climate conditions, living species, habitats, water resources, and sometimes also anthropic factors. Most approaches pursue the cartographical delineation or regionalisation of distinct areas for mapping and planning.
Leray spectral sequenceIn mathematics, the Leray spectral sequence was a pioneering example in homological algebra, introduced in 1946 by Jean Leray. It is usually seen nowadays as a special case of the Grothendieck spectral sequence. Let be a continuous map of topological spaces, which in particular gives a functor from sheaves of abelian groups on to sheaves of abelian groups on .
GeoreferencingGeoreferencing or georegistration is a type of coordinate transformation that binds a digital raster image or vector database that represents a geographic space (usually a scanned map or aerial photograph) to a spatial reference system, thus locating the digital data in the real world. It is thus the geographic form of . The term can refer to the mathematical formulas used to perform the transformation, the metadata stored or within the image file to specify the transformation, or the process of manually or automatically aligning the image to the real world to create such metadata.
Geophysical surveyGeophysical survey is the systematic collection of geophysical data for spatial studies. Detection and analysis of the geophysical signals forms the core of Geophysical signal processing. The magnetic and gravitational fields emanating from the Earth's interior hold essential information concerning seismic activities and the internal structure. Hence, detection and analysis of the electric and Magnetic fields is very crucial.
Light-secondThe light-second is a unit of length useful in astronomy, telecommunications and relativistic physics. It is defined as the distance that light travels in free space in one second, and is equal to exactly 299 792 458 metres (approximately 983 571 055 ft). Just as the second forms the basis for other units of time, the light-second can form the basis for other units of length, ranging from the light-nanosecond (299.8mm or just under one international foot) to the light-minute, light-hour and light-day, which are sometimes used in popular science publications.
