Complex geometryIn mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis.
Spatial databaseA spatial database is a general-purpose database (usually a relational database) that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools for querying and analyzing such data. Most spatial databases allow the representation of simple geometric objects such as points, lines and polygons. Some spatial databases handle more complex structures such as 3D objects, topological coverages, linear networks, and triangulated irregular networks (TINs).
Dimensionality reductionDimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with).
Almost complex manifoldIn mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. Every complex manifold is an almost complex manifold, but there are almost complex manifolds that are not complex manifolds. Almost complex structures have important applications in symplectic geometry. The concept is due to Charles Ehresmann and Heinz Hopf in the 1940s. Let M be a smooth manifold.
Natural selectionNatural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the heritable traits characteristic of a population over generations. Charles Darwin popularised the term "natural selection", contrasting it with artificial selection, which is intentional, whereas natural selection is not. Variation exists within all populations of organisms. This occurs partly because random mutations arise in the genome of an individual organism, and their offspring can inherit such mutations.
Prior probabilityA prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable.
SignalIn signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The IEEE Transactions on Signal Processing includes audio, video, speech, , sonar, and radar as examples of signals. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information.
Complex manifoldIn differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in , such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex manifold), and an almost complex manifold. Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds.
Hierarchical organizationA hierarchical organization or hierarchical organisation (see spelling differences) is an organizational structure where every entity in the organization, except one, is subordinate to a single other entity. This arrangement is a form of a hierarchy. In an organization, the hierarchy usually consists of a singular/group of power at the top with subsequent levels of power beneath them. This is the dominant mode of organization among large organizations; most corporations, governments, criminal enterprises, and organized religions are hierarchical organizations with different levels of management, power or authority.
VibrationVibration () is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The oscillations may be periodic, such as the motion of a pendulum, or random, such as the movement of a tire on a gravel road. Vibration can be desirable: for example, the motion of a tuning fork, the reed in a woodwind instrument or harmonica, a mobile phone, or the cone of a loudspeaker. In many cases, however, vibration is undesirable, wasting energy and creating unwanted sound.
Genetic variationGenetic variation is the difference in DNA among individuals or the differences between populations among the same species. The multiple sources of genetic variation include mutation and genetic recombination. Mutations are the ultimate sources of genetic variation, but other mechanisms, such as genetic drift, contribute to it, as well. Genetic variation can be identified at many levels. Identifying genetic variation is possible from observations of phenotypic variation in either quantitative traits (traits that vary continuously and are coded for by many genes (e.
Active learning (machine learning)Active learning is a special case of machine learning in which a learning algorithm can interactively query a user (or some other information source) to label new data points with the desired outputs. In statistics literature, it is sometimes also called optimal experimental design. The information source is also called teacher or oracle. There are situations in which unlabeled data is abundant but manual labeling is expensive. In such a scenario, learning algorithms can actively query the user/teacher for labels.
