Cauchy distributionThe Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution is the distribution of the x-intercept of a ray issuing from with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero.
AcidAn acid is a molecule or ion capable of either donating a proton (i.e. hydrogen ion, H+), known as a Brønsted–Lowry acid, or forming a covalent bond with an electron pair, known as a Lewis acid. The first category of acids are the proton donors, or Brønsted–Lowry acids. In the special case of aqueous solutions, proton donors form the hydronium ion H3O+ and are known as Arrhenius acids. Brønsted and Lowry generalized the Arrhenius theory to include non-aqueous solvents.
Stable distributionIn probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).
EmergenceIn philosophy, systems theory, science, and art, emergence occurs when a complex entity has properties or behaviors that its parts do not have on their own, and emerge only when they interact in a wider whole. Emergence plays a central role in theories of integrative levels and of complex systems. For instance, the phenomenon of life as studied in biology is an emergent property of chemistry. In philosophy, theories that emphasize emergent properties have been called emergentism.
Marine prokaryotesMarine prokaryotes are marine bacteria and marine archaea. They are defined by their habitat as prokaryotes that live in marine environments, that is, in the saltwater of seas or oceans or the brackish water of coastal estuaries. All cellular life forms can be divided into prokaryotes and eukaryotes. Eukaryotes are organisms whose cells have a nucleus enclosed within membranes, whereas prokaryotes are the organisms that do not have a nucleus enclosed within a membrane.
Cross-correlationIn signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions.
Intraclass correlationIn statistics, the intraclass correlation, or the intraclass correlation coefficient (ICC), is a descriptive statistic that can be used when quantitative measurements are made on units that are organized into groups. It describes how strongly units in the same group resemble each other. While it is viewed as a type of correlation, unlike most other correlation measures, it operates on data structured as groups rather than data structured as paired observations.
EvolutionIn biology, evolution is the change in heritable characteristics of biological populations over successive generations. Evolution occurs when evolutionary processes such as natural selection (including sexual selection) and genetic drift act on genetic variation, resulting in certain characteristics becoming more or less common within a population over successive generations. The process of evolution has given rise to biodiversity at every level of biological organisation.
Correlation coefficientA correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution. Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where ±1 indicates the strongest possible agreement and 0 the strongest possible disagreement.
Pearson correlation coefficientIn statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations.
Three-domain systemThe three-domain system is a biological classification introduced by Carl Woese, Otto Kandler, and Mark Wheelis in 1990 that divides cellular life forms into three domains, namely Archaea, Bacteria, and Eukaryota. The key difference from earlier classifications such as the two-empire system and the five-kingdom classification is the splitting of Archaea from bacteria as completely different organisms. It has been challenged by the two-domain system that divides organisms into Bacteria and Archaea only, as Eukaryotes are considered as one group of Archaea.
Hydrothermal ventA hydrothermal vent is a fissure on the seabed from which geothermally heated water discharges. They are commonly found near volcanically active places, areas where tectonic plates are moving apart at mid-ocean ridges, ocean basins, and hotspots. Hydrothermal deposits are rocks and mineral ore deposits formed by the action of hydrothermal vents. Hydrothermal vents exist because the earth is both geologically active and has large amounts of water on its surface and within its crust.
