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).
Finite-difference time-domain method'Finite-difference time-domain' (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational electrodynamics (finding approximate solutions to the associated system of differential equations). Since it is a time-domain method, FDTD solutions can cover a wide frequency range with a single simulation run, and treat nonlinear material properties in a natural way.
Porro prismIn optics, a Porro prism, named for its inventor Ignazio Porro, is a type of reflection prism used in optical instruments to alter the orientation of an . It consists of a block of material shaped like a right geometric prism with right-angled triangular end faces. In operation, light enters the large rectangular face of the prism, undergoes total internal reflection twice from the sloped faces, and exits again through the large rectangular face. When the light enters and therefore exits the glass at normal incidence, the prism is not dispersive.
Vibrations of a circular membraneA two-dimensional elastic membrane under tension can support transverse vibrations. The properties of an idealized drumhead can be modeled by the vibrations of a circular membrane of uniform thickness, attached to a rigid frame. Due to the phenomenon of resonance, at certain vibration frequencies, its resonant frequencies, the membrane can store vibrational energy, the surface moving in a characteristic pattern of standing waves. This is called a normal mode.
DuoprismIn geometry of 4 dimensions or higher, a double prism or duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher. The Cartesian product of an n-polytope and an m-polytope is an (n+m)-polytope, where n and m are dimensions of 2 (polygon) or higher. The lowest-dimensional duoprisms exist in 4-dimensional space as 4-polytopes being the Cartesian product of two polygons in 2-dimensional Euclidean space.
Top-down parsingTop-down parsing in computer science is a parsing strategy where one first looks at the highest level of the parse tree and works down the parse tree by using the rewriting rules of a formal grammar. LL parsers are a type of parser that uses a top-down parsing strategy. Top-down parsing is a strategy of analyzing unknown data relationships by hypothesizing general parse tree structures and then considering whether the known fundamental structures are compatible with the hypothesis.
Bottom-up parsingIn computer science, parsing reveals the grammatical structure of linear input text, as a first step in working out its meaning. Bottom-up parsing recognizes the text's lowest-level small details first, before its mid-level structures, and leaving the highest-level overall structure to last. The bottom-up name comes from the concept of a parse tree, in which the most detailed parts are at the bottom of the upside-down tree, and larger structures composed from them are in successively higher layers, until at the top or "root" of the tree a single unit describes the entire input stream.
