Set inversion

In mathematics, set inversion is the problem of characterizing the preimage X of a set Y by a function f, i.e., X = f⁻¹(Y) = {x ∈ Rⁿ | f(x) ∈ Y}. It can also be viewed as the problem of describing the solution set of the quantified constraint "∃ y . [f(x)=y ∧ Y(y)]", where Y(y) is a constraint, for example, an inequality, describing the set Y.

In most applications, f is a function from Rⁿ to R^p and the set Y is a box of R^p (i.e. a Cartesian product of p intervals of R).

When f is nonlinear the set inversion problem can be solved using interval analysis combined with a branch-and-bound algorithm.

The main idea consists in building a paving of R^p made with non-overlapping boxes. For each box [x], we perform the following tests:

To check the two first tests, we need an interval extension (or an inclusion function) [f] for f. Classified boxes are stored into subpavings, i.e., union of non overlapping boxes. The algorithm can be made more efficient by replacing the inclusion tests by contractors.

Inversion (artwork)

Inversion was a 2005 artwork by sculptors Dan Havel and Dean Ruck of Houston Alternative Art.

Havel and Ruck altered two buildings owned by the Art League of Houston on the corner of Montrose Boulevard and Willard Street. The exterior skins of the houses were peeled off and used to create a large vortex that funneled into the small central hallway connecting the two buildings and eventually exited through a small hole into an adjacent courtyard.Inversion has become one of Houston’s most well-known, albeit vanished, sculptures. The structure was later demolished to make way for a new Art League building.

Art League Houston owned the two houses and had used them for art classes and exhibitions for over 30 years. The organisation commissioned Havel and Ruck to transform them into an artwork in demolition. The sculpture was opened on May 21, 2005, and was visible from Montrose Boulevard until its demolition the next month.

Years later, the artwork continues to be cited on design blogs.

Inversion (evolutionary biology)

In evolutionary developmental biology, inversion refers to the hypothesis that during the course of animal evolution, the structures along the dorsoventral (DV) axis have taken on an orientation opposite that of the ancestral form. As early as 1822, the French naturalist Étienne Geoffroy Saint-Hilaire noted that the organization of dorsal and ventral structures in arthropods is opposite that of mammals. Five decades later, in light of Darwin's theory of "descent with modification", German zoologist Anton Dohrn proposed that these groups arose from a common ancestor which possessed a body plan similar to that of modern annelids with a ventral nerve cord and dorsal heart. Whereas this arrangement is retained in arthropods and other protostomes, in chordate deuterostomes, the nerve cord is located dorsally and the heart ventrally. The inversion hypothesis was met with criticism each time it was proposed, and has periodically resurfaced and been rejected. However, some modern molecular embryologists suggest that recent findings support the idea of inversion.

Inversion (video game)

Inversion is a third-person shooter video game developed by Saber Interactive and published by Namco Bandai Games for Microsoft Windows,PlayStation 3 and Xbox 360. It was released on June 5, 2012 in North America, July 12, 2012 in Australia and on July 13, 2012 in Europe for PlayStation 3 and Xbox 360. It was later released for Microsoft Windows on June 8, 2012 in Europe, July 12, 2012 in Australia and July 26, 2012 in North America. It features gravity manipulation and destructible environments.

Plot

In Vanguard City, policeman Davis Russell and his partner Leo Delgado are on duty when the city comes under attack by an army of strange barbaric soldiers called Lutadores armed with gravity-defying technology. As panic spreads in the wake of the attack, Davis and Leo hurry to Davis' apartment to check on his wife Cara and his daughter Leila. Upon arrival, the duo find Cara wounded and Leila missing. Cara dies of her injuries and Davis and Leo are soon captured by the Lutadores, who have taken control of the city.

Set (music)

A set (pitch set, pitch-class set, set class, set form, set genus, pitch collection) in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.

A set by itself does not necessarily possess any additional structure, such as an ordering. Nevertheless, it is often musically important to consider sets that are equipped with an order relation (called segments); in such contexts, bare sets are often referred to as "unordered", for the sake of emphasis.

Two-element sets are called dyads, three-element sets trichords (occasionally "triads", though this is easily confused with the traditional meaning of the word triad). Sets of higher cardinalities are called tetrachords (or tetrads), pentachords (or pentads), hexachords (or hexads), heptachords (heptads or, sometimes, mixing Latin and Greek roots, "septachords"—e.g.,), octachords (octads), nonachords (nonads), decachords (decads), undecachords, and, finally, the dodecachord.

Set construction

Set construction is the process by which a construction manager undertakes to build full scale scenery suitable for viewing by camera, as specified by a production designer or art director working in collaboration with the director of a production to create a set for a theatrical, film or television production. The set designer produces a scale model, scale drawings, paint elevations (a scale painting supplied to the scenic painter of each element that requires painting), and research about props, textures, and so on. Scale drawings typically include a groundplan, elevation, and section of the complete set, as well as more detailed drawings of individual scenic elements which, in theatrical productions, may be static, flown, or built onto scenery wagons. Models and paint elevations are frequently hand-produced, though in recent years, many Production Designers and most commercial theatres have begun producing scale drawings with the aid of computer drafting programs such as AutoCAD or Vectorworks.

Associative containers

In computing, associative containers refer to a group of class templates in the standard library of the C++ programming language that implement ordered associative arrays. Being templates, they can be used to store arbitrary elements, such as integers or custom classes. The following containers are defined in the current revision of the C++ standard: set, map, multiset, multimap. Each of these containers differ only on constraints placed on their elements.

The associative containers are similar to the unordered associative containers in C++ standard library, the only difference is that the unordered associative containers, as their name implies, do not order their elements.

Design

Characteristics