Subgraph isomorphism problemIn theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a subgraph that is isomorphic to H. Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. However certain other cases of subgraph isomorphism may be solved in polynomial time.
Source-code compatibilitySource-code compatibility (source-compatible) means that a program can run on computers (or operating systems), independently of binary-code compatibility and that the source code is needed for portability. The source code must be compiled before running, unless the computer used has an interpreter for the language at hand. The term is also used for assembly language compatibility, where the source is a human-readable form of machine code that must be converted into numerical (i.e. executable) machine code by an assembler.
Yoneda lemmaIn mathematics, the Yoneda lemma is arguably the most important result in . It is an abstract result on functors of the type morphisms into a fixed object. It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a miniature category with just one object and only isomorphisms). It allows the of any into a (contravariant set-valued functors) defined on that category. It also clarifies how the embedded category, of representable functors and their natural transformations, relates to the other objects in the larger functor category.
Principal bundleIn mathematics, a principal bundle is a mathematical object that formalizes some of the essential features of the Cartesian product of a space with a group . In the same way as with the Cartesian product, a principal bundle is equipped with An action of on , analogous to for a product space. A projection onto . For a product space, this is just the projection onto the first factor, . Unlike a product space, principal bundles lack a preferred choice of identity cross-section; they have no preferred analog of .
Frame bundleIn mathematics, a frame bundle is a principal fiber bundle F(E) associated to any vector bundle E. The fiber of F(E) over a point x is the set of all ordered bases, or frames, for Ex. The general linear group acts naturally on F(E) via a change of basis, giving the frame bundle the structure of a principal GL(k, R)-bundle (where k is the rank of E). The frame bundle of a smooth manifold is the one associated to its tangent bundle. For this reason it is sometimes called the tangent frame bundle.
Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
Sabina (region)Sabina (Latin: Sabinum), also called the Sabine Hills, is a region in central Italy. It is named after Sabina, the territory of the ancient Sabines, which was once bordered by Latium to the south, Picenum to the east, ancient Umbria to the north and Etruria to the west. It was separated from Umbria by the River Nar, today's Nera, and from Etruria by the River Tiber. Today, Sabina is mainly northeast of Rome in the regions Lazio, Umbria and Abruzzo.
SabinesThe Sabines (ˈseɪbaɪnz, , ˈsæbaɪnz, ; Sabini; Sabini, all exonyms) were an Italic people who lived in the central Apennine Mountains of the ancient Italian Peninsula, also inhabiting Latium north of the Anio before the founding of Rome. The Sabines divided into two populations just after the founding of Rome, which is described by Roman legend. The division, however it came about, is not legendary. The population closer to Rome transplanted itself to the new city and united with the preexisting citizenry, beginning a new heritage that descended from the Sabines but was also Latinized.
Marcus Terentius VarroMarcus Terentius Varro (116–27 BC) was a Roman polymath and a prolific author. He is regarded as ancient Rome's greatest scholar, and was described by Petrarch as "the third great light of Rome" (after Virgil and Cicero). He is sometimes called Varro Reatinus ("Varro of Rieti") to distinguish him from his younger contemporary Varro Atacinus. Varro was born in or near Reate (now Rieti) to a family thought to be of equestrian rank, and always remained close to his roots in the area, owning a large farm in the Reatine plain, reported as near Lago di Ripasottile, until his old age.
ReasonReason is the capacity of applying logic consciously by drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, language, mathematics, and art, and is normally considered to be a distinguishing ability possessed by humans. Reason is sometimes referred to as rationality. Reasoning is associated with the acts of thinking and cognition, and involves the use of one's intellect.
BijectionIn mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set; there are no unpaired elements between the two sets. In mathematical terms, a bijective function f: X → Y is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y.
