Repeated random subsampling validation
Repeated random subsampling validation, also known as Monte Carlo cross-validation or repeated holdout, is a model-validation method that averages test errors over many random train/test splits.
Repeated syndrome measurement
Repeated syndrome measurement is the practice of measuring a quantum code's error syndrome many times in succession, so errors can be tracked and corrected while the logical qubit stays encoded, a key to fault-tolerant quantum computing.
Repeating decimal
A repeating decimal, or recurring decimal, is a decimal in which a digit or block of digits repeats endlessly; it is exactly equivalent to the number being rational.
Repeating fast radio burst
A repeating fast radio burst is a fast radio burst source observed to emit multiple bursts from the same position; FRB 121102 was the first, identified in 2016, and about 60 are known.
Replica symmetry breaking
Replica symmetry breaking (RSB) is the loss of permutation symmetry among replicas in the replica method, introduced by Giorgio Parisi in 1978 to solve mean-field spin glasses.
Replica wormhole
A replica wormhole is a connected Euclidean spacetime geometry joining several replicas of a gravitational system in the path-integral computation of entanglement entropy. It underlies the island formula and Page curve.
Replication (scientific method)
Replication is the repetition of a scientific study, with new data, to test whether the original result holds; it is central to how science checks its findings.
Replication crisis
The replication crisis, also called the replicability or reproducibility crisis, is an ongoing methodological problem in science in which many published study results are difficult to reproduce.
Reporting guidelines for medical research
Reporting guidelines for medical research are checklists and flow diagrams, including CONSORT, STROBE, and PRISMA, that specify the minimum items a study report should contain.
Reprecipitation
Reprecipitation, also known as antisolvent precipitation or solvent displacement, is a solution-based method that makes organic microcrystals and nanoparticles by injecting a dilute solution into stirred water.
Representation ring
The representation ring R(G) of a group is the Grothendieck ring of its finite-dimensional representations, with addition from direct sums and multiplication from tensor products.
Representation theory
Representation theory, also called mathematical representation theory, is the branch of mathematics that studies abstract algebraic structures, chiefly groups, by representing their elements as linear transformations of vector spaces.
Representation theory of finite groups
The representation theory of finite groups studies how finite groups act on vector spaces, pioneered in the late 1800s by Frobenius, Schur, and Burnside, with Maschke's theorem its central structure.
Representation theory of Kac–Moody and affine algebras
The representation theory of Kac–Moody and affine algebras studies how infinite-dimensional Lie algebras act on vector spaces; for affine algebras, integrable representations carry a level, and the Weyl–Kac character formula yields number-theoretic identities.
Representation theory of semisimple Lie algebras
The representation theory of semisimple Lie algebras, or Cartan–Weyl theory, classifies how semisimple Lie algebras act linearly on vector spaces, with every irreducible determined by its highest weight.
Representation theory of SL2(R)
The representation theory of SL2(R), the non-compact simple Lie group of 2 × 2 real matrices with determinant 1, studies its unitary representations, classified by Bargmann in 1947 into principal, complementary, and discrete series.
Representation theory of SU(2)
The representation theory of SU(2) classifies how the special unitary group SU(2) acts on vector spaces, with irreducibles labeled by spin and dimension 2s + 1.
Representation theory of the Galilean group
The classification of how the Galilei group, the nonrelativistic space-time symmetry group, acts on quantum systems; its ray representations, classified by Bargmann in 1954, carry mass as a central charge.
Representation theory of the Lorentz group
The representation theory of the Lorentz group studies how Lorentz transformations act linearly on vector spaces, dividing into non-unitary finite-dimensional representations for classical fields and unitary representations for particles.
Representation theory of the symmetric group
The representation theory of the symmetric group (S_n) studies how permutations act on vector spaces; its irreducible representations, the Specht modules, are indexed by integer partitions of n.
Representations
Representations is a quarterly peer-reviewed academic journal published by the University of California Press since 1983, publishing interdisciplinary humanities essays on culture and described as a leading journal in interpretive social sciences.
Representative Concentration Pathway
A Representative Concentration Pathway (RCP) is one of four greenhouse gas and land use scenarios used in climate modeling, named for its radiative forcing by 2100.
Reproducibility
Reproducibility is the ability to obtain consistent results from scientific work, using the same data, code, and analysis; it differs from replicability, which uses new data.
Reproducibility Project: Psychology
The Reproducibility Project: Psychology was a 2015 Open Science Collaboration effort that replicated 100 psychology studies, finding only 36% produced significant results, a landmark of the open-science movement.
Reproducing kernel Hilbert space
A reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which evaluation at any point is continuous, a condition equivalent to a reproducing kernel existing.
Reproducing kernel method
The reproducing kernel method (RKM) is a numerical technique that solves differential and integral equations by representing the solution as a series in a reproducing kernel Hilbert space.
Reproduction & fertility
Reproduction & Fertility (ISSN 2633-8386) is a quarterly open-access peer-reviewed journal launched in 2020 by Bioscientifica for the Society for Reproduction and Fertility, sister journal to Reproduction, covering basic, translational, and clinical reproductive science.
Reptation
Reptation is the snake-like movement of a polymer chain through a hypothetical tube formed by neighboring chains in a melt, the central model of entangled polymer dynamics since de Gennes's 1971 theory.
Reptile search algorithm
The reptile search algorithm (RSA), also called reptile search, is a gradient-free metaheuristic mimicking crocodile encircling and hunting, introduced by Laith Abualigah and colleagues in 2021.
Repunit
A repunit is a whole number whose decimal digits are all 1, such as 11 or 111, with the name coined by Albert H. Beiler in 1966.