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Longer titles found: Complexification (Lie group) (view)

searching for Complexification 71 found (196 total)

Neuroevolution (1,943 words) [view diff] exact match in snippet view article find links to article

mutation. Complexification: the ability of the system (including evolutionary algorithm and genotype to phenotype mapping) to allow complexification of the

Witt algebra (348 words) [view diff] exact match in snippet view article find links to article

sphere that are holomorphic except at two fixed points. It is also the complexification of the Lie algebra of polynomial vector fields on a circle, and the

Cayley plane (412 words) [view diff] exact match in snippet view article find links to article

and 16. The complex Cayley plane is a homogeneous space under the complexification of the group E6 by a parabolic subgroup P1. It is the closed orbit

Hermitian manifold (1,507 words) [view diff] exact match in snippet view article find links to article

complexified tangent bundle. Since g is equal to its conjugate it is the complexification of a real form on TM. The symmetry and positive-definiteness of g on

Constructive neutral evolution (3,294 words) [view diff] exact match in snippet view article find links to article

one-directional or "ratchet-like" process. CNE models of systematic complexification may rely crucially on some systematic bias in the generation of variation

Viable system theory (1,684 words) [view diff] exact match in snippet view article find links to article

produce regression, chaos, or destruction. 6. Information drift and complexification The above steps can be iterated increasing the complexity of the system

West Uvean language (315 words) [view diff] exact match in snippet view article find links to article

vowels being added to the phonemic system of West Uvean; and to a complexification of the syllable structure, allowing for final consonants.: 534 /ɾ/

Euler class (2,004 words) [view diff] exact match in snippet view article find links to article

class of the complexification of E: p r ( E ) = c 2 r ( C ⊗ E ) {\displaystyle p_{r}(E)=c_{2r}(\mathbf {C} \otimes E)} . The complexification C ⊗ E {\displaystyle

ADE classification (2,595 words) [view diff] exact match in snippet view article find links to article

umbrella of root systems. He tried to introduce informal concepts of Complexification and Symplectization based on analogies between Picard–Lefschetz theory

Algebraic analysis (374 words) [view diff] exact match in snippet view article find links to article

Let M be a real-analytic manifold of dimension n, and let X be its complexification. The sheaf of microlocal functions on M is given as H n ( μ M ( O X

Representation theory of SL2(R) (1,827 words) [view diff] exact match in snippet view article

(1947), and Harish-Chandra (1952). We choose a basis H, X, Y for the complexification of the Lie algebra of SL(2, R) so that iH generates the Lie algebra

Jordan operator algebra (2,686 words) [view diff] exact match in snippet view article find links to article

on that operator. If a unital JB algebra is associative, then its complexification with its natural involution is a commutative C* algebra. It is therefore

C-symmetry (5,729 words) [view diff] exact match in snippet view article find links to article

which sorts these spinors into left and right-handed subspaces. The complexification is a key ingredient, and it provides "electromagnetism" in this generalized

Hodge structure (4,881 words) [view diff] exact match in snippet view article find links to article

group H Z {\displaystyle H_{\mathbb {Z} }} and a decomposition of its complexification H {\displaystyle H} into a direct sum of complex subspaces H p , q

Surprise (emotion) (1,786 words) [view diff] exact match in snippet view article

surprise cannot occur. Affective neuroscience Nihil admirari John Casti; Complexification: Explaining a Paradoxical World through the Science of Surprise . New

Theorem of the highest weight (1,103 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\mathfrak {g}}:={\mathfrak {k}}+i{\mathfrak {k}}} be the complexification of g {\displaystyle {\mathfrak {g}}} . Let T {\displaystyle T} be a

Lasse Rempe (370 words) [view diff] exact match in snippet view article find links to article

mathematical research to broader audiences". The dynamical plane of (the complexification of) the circle map, the simplest mathematical model of phase-locking

George David Birkhoff Prize (260 words) [view diff] exact match in snippet view article find links to article

of problems of transonic flow and airfoil design by the method of complexification, and to the development and application of scientific computing to

John Casti (1,661 words) [view diff] exact match in snippet view article find links to article

weather, stock market price movements and the outbreak of warfare; and Complexification, a study of complex systems and the manner in which they give rise

Carl H. Brans (685 words) [view diff] exact match in snippet view article find links to article

for symbolic manipulations. He summarized this work in terms of the complexification of the two-form fiber over space-time. He also worked on certain questions

Paenibacillus dendritiformis (1,849 words) [view diff] exact match in snippet view article find links to article

95:1143-1151. Ben-Jacob E. Bacterial self-organization: co-enhancement of complexification and adaptability in a dynamic environment. Phil. Trans. R. Soc. Lond

Kenneth Stanley (1,128 words) [view diff] exact match in snippet view article find links to article

Kenneth O. (2004). "Efficient Evolution of Neural Networks Through Complexification". Department of Computer Sciences, the University of Texas at Austin

Eisenstein integral (470 words) [view diff] exact match in snippet view article find links to article

= MAN is a cuspidal parabolic subgroup of G ν is an element of the complexification of a a is the Lie algebra of A in the Langlands decomposition P = MAN

Ravindra Shripad Kulkarni (722 words) [view diff] exact match in snippet view article find links to article

1073/pnas.69.9.2675. PMC 427014. PMID 16592016. Kulkarni RS (1975). "On complexification of real manifolds". Proceedings of the National Academy of Sciences

Earle–Hamilton fixed-point theorem (799 words) [view diff] exact match in snippet view article find links to article

complete metric space for the Bergman metric. The open semigroup of the complexification Gc taking the closure of D into D acts by contraction mappings, so

Maximal torus (1,734 words) [view diff] exact match in snippet view article find links to article

{g}}_{\mathbb {C} }:={\mathfrak {g}}\oplus i{\mathfrak {g}}} denote the complexification of g {\displaystyle {\mathfrak {g}}} . Then we say that an element

Neuroevolution of augmenting topologies (1,540 words) [view diff] exact match in snippet view article find links to article

Colin Green (2004). "Phased Searching with NEAT: Alternating Between Complexification And Simplification". {{cite journal}}: Cite journal requires |journal=

Segal–Bargmann space (2,026 words) [view diff] exact match in snippet view article find links to article

phase space C n {\displaystyle \mathbb {C} ^{n}} is then played by the complexification of the compact Lie group, such as SL ⁡ ( N , C ) {\displaystyle \operatorname

Angela McRobbie (3,305 words) [view diff] exact match in snippet view article find links to article

arguments. In the mid-1990s, McRobbie describes the occurrence of a "complexification of backlash" towards feminism, marking a decisive shift where the forces

Bitangents of a quartic (1,048 words) [view diff] exact match in snippet view article find links to article

Arnold, Vladimir, 1997, Toronto Lectures, Lecture 2: Symplectization, Complexification and Mathematical Trinities, June 1997 (last updated August, 1998).

Volume conjecture (1,038 words) [view diff] exact match in snippet view article find links to article

{\displaystyle T(p,q)} with q = 2 {\displaystyle q=2} (Hao Zheng). Using complexification, Murakami et al. (2002) proved that for a hyperbolic knot K {\displaystyle

Emergence (6,147 words) [view diff] exact match in snippet view article find links to article

2009.01367.x. hdl:2164/3035. S2CID 144579790. Casti, J. L. (1994). Complexification: Explaining a paradoxical world through the science of surprise. New

Australian Kriol (2,896 words) [view diff] exact match in snippet view article find links to article

creolization entailed a massive increase in the lexicon as well as a complexification of the grammar of the language. This creolization began in the early

Semi-simplicity (1,867 words) [view diff] exact match in snippet view article find links to article

unitarian trick: Every such g {\displaystyle {\mathfrak {g}}} is the complexification of the Lie algebra of a simply connected compact Lie group K {\displaystyle

Schizoanalysis (3,555 words) [view diff] exact match in snippet view article find links to article

which simplify the complex", schizoanalysis "will work towards its complexification, its processual enrichment, towards the consistency of its virtual

Lorentz invariance in loop quantum gravity (1,300 words) [view diff] exact match in snippet view article find links to article

Immirzi parameter is necessary to resolve an ambiguity in the process of complexification. These are some of the many ways in which different quantizations of

Compact group (4,472 words) [view diff] exact match in snippet view article find links to article

algebras. Indeed, if K is a simply connected compact Lie group, then the complexification of the Lie algebra of K is semisimple. Conversely, every complex semisimple

Paenibacillus vortex (1,774 words) [view diff] exact match in snippet view article find links to article

8:36. Ben-Jacob E: Bacterial self-organization: co-enhancement of complexification and adaptability in a dynamic environment. Phil Trans R Soc Lond A

Quantum group (4,983 words) [view diff] exact match in snippet view article find links to article

starting with any compact real form of a semisimple Lie algebra g its complexification as a real Lie algebra of twice the dimension splits into g and a certain

The Bathers (Gleizes) (3,734 words) [view diff] exact match in snippet view article

restricted to the imitative description of nature, and despite the complexification of visual stimuli (many views instead of one), the technique of painting

Edge-of-the-wedge theorem (1,930 words) [view diff] exact match in snippet view article find links to article

Wightman functions W(z1, ..., zn) depending on variables zi in the complexification of Minkowski spacetime. They are defined and holomorphic in the wedge

Slavic paganism (9,086 words) [view diff] exact match in snippet view article find links to article

the "Damp Mother Earth". Rybakov said the continuity and gradual complexification of Slavic religion started from devotion to life-giving forces (bereginy)

Epic of evolution (3,754 words) [view diff] exact match in snippet view article find links to article

that it is a notion that can interpret the enormous expansion and complexification of the physical universe (from the Big Bang outward), as well as the

Kostant polynomial (2,075 words) [view diff] exact match in snippet view article find links to article

generalized flag manifold K/T, also isomorphic to G/B where G is the complexification of K and B is the corresponding Borel subgroup. Armand Borel showed

Prehomogeneous vector space (1,712 words) [view diff] exact match in snippet view article find links to article

representation). In each case a generic point in V identifies it with the complexification of a Jordan algebra of 3 × 3 hermitian matrices (over the division

Weyl's theorem on complete reducibility (2,465 words) [view diff] exact match in snippet view article find links to article

complex semisimple Lie algebra g {\displaystyle {\mathfrak {g}}} is the complexification of the Lie algebra of a simply connected compact Lie group K {\displaystyle

Paenibacillus (2,904 words) [view diff] exact match in snippet view article find links to article

Ben-Jacob E (June 2003). "Bacterial self-organization: co-enhancement of complexification and adaptability in a dynamic environment". Philosophical Transactions

Peak complexity (699 words) [view diff] exact match in snippet view article find links to article

correct the errors caused by organisations' systems. For Tainter, complexification flows from the need for societies to solve problems. The first problems

Chern–Weil homomorphism (2,782 words) [view diff] exact match in snippet view article find links to article

where we wrote E ⊗ C {\displaystyle E\otimes \mathbb {C} } for the complexification of E. Equivalently, it is the image under the Chern–Weil homomorphism

Clebsch–Gordan coefficients for SU(3) (7,686 words) [view diff] exact match in snippet view article

factors of i in these formulas, this is technically a basis for the complexification of the su(3) Lie algebra, namely sl(3,C). The preceding basis is then

Butcher group (4,050 words) [view diff] exact match in snippet view article find links to article

Butcher group. Φ can be regarded as a map γ of the unit circle into the complexification GC of G (maps into C instead of R). As such it has a Birkhoff factorization

Simon Raab (873 words) [view diff] exact match in snippet view article find links to article

Parleau Sculpture "Complexification" (2011) by Simon Raab

Pierre Clastres (5,263 words) [view diff] exact match in snippet view article find links to article

in all societies. For him, the State does not emerge because of the complexification of productive or political forces but it rises when a community reaches

Pierre Teilhard de Chardin (13,537 words) [view diff] exact match in snippet view article find links to article

becomes spirit and humanity moves towards a super-humanity thanks to complexification (physico-chemical, then biological, then human), socialization, scientific

Big History (10,062 words) [view diff] exact match in snippet view article find links to article

Chardin examined links between cosmic evolution and a tendency towards complexification (including human consciousness), while envisaging compatibility between

Cro-Magnon (19,521 words) [view diff] exact match in snippet view article find links to article

Magdalenian culture about 14,000 years ago. There is a notable technological complexification coinciding with the replacement of Neanderthals with Cro-Magnons in

Uniformly bounded representation (3,535 words) [view diff] exact match in snippet view article find links to article

bounded representation on H 'σ. The action of the standard basis of the complexification Lie algebra on this basis can be computed: π s ( L 0 ) f m = m f m

Freudenthal magic square (2,914 words) [view diff] exact match in snippet view article find links to article

here if K is not algebraically closed. In the case K = C, this is the complexification of the Freudenthal magic squares for R discussed so far. The squares

Elena Sergeevna Bulgakova (801 words) [view diff] exact match in snippet view article find links to article

disorder of contemporary fiction: narrative self-organization through complexification (Thesis). OCLC 53089862. Archived from the original on 2024-06-24.

Jacob Klapwijk (3,264 words) [view diff] exact match in snippet view article find links to article

beings are conditioned by but not simply identifiable as parts of the complexification process that characterizes the physical world. This "levelism" (John

Schwarzian derivative (7,155 words) [view diff] exact match in snippet view article find links to article

+ n . {\displaystyle [d_{m},d_{n}]=(m-n)d_{m+n}.} A basis for the complexification of Fλ(S1) is given by v n = e i n θ ( d θ ) λ , {\displaystyle v_{n}=e^{in\theta

Eshel Ben-Jacob (3,846 words) [view diff] exact match in snippet view article find links to article

247–282 (2000). ^ 1"Bacterial Self-Organization: Co-Enhancement of Complexification and Adaptability in a Dynamic Environment". Ben-Jacob, E., Philosophical

Majorana equation (8,807 words) [view diff] exact match in snippet view article find links to article

only the Lorentz transformations acting on the Majorana spinor; the complexification plays no role. A detailed treatment of these topics can be found in

Philip Loring (1,319 words) [view diff] exact match in snippet view article find links to article

Routledge. 2019. With Palash Sanyal. "Indicators of Complexity and Over-Complexification in Global Food Systems." Frontiers in Sustainable Food Systems. 2021

Jiro Takamatsu (6,890 words) [view diff] exact match in snippet view article find links to article

(“A Plan for World Ex-pansion”), Takamatsu portrays an ever-evolving complexification of social ties. Yoshida Kenchi describes Takamatsu's rose as reminiscent

Slavic Native Faith and politics (6,857 words) [view diff] exact match in snippet view article find links to article

the Kurgan hypothesis. Boris Rybakov emphasised the continuity and complexification of Slavic religion through the centuries. According to the scholar

Finite subgroups of SU(2) (3,956 words) [view diff] exact match in snippet view article

that of SO(3), can be developed in many different ways: using the complexification Gc = SL(2,C) and the double coset decomposition Gc = B ⋅ w ⋅ B ∐ B

Neolithic in the Near East (26,111 words) [view diff] exact match in snippet view article find links to article

from the Levantine area to the Mesopotamian plain, where a process of complexification began, leading a few millennia later to the emergence of the "urban

Research transparency (8,509 words) [view diff] exact match in snippet view article find links to article

transparency has also been motivated by the diversification and the complexification of the open science publishing landscape: "Triggered by a wide variety

Animals in the Ancient Near East (14,141 words) [view diff] exact match in snippet view article find links to article

complex societies from the 4th millennium onwards (social and political complexification with urbanization, the emergence of the State, and the development

Slavic Native Faith (30,197 words) [view diff] exact match in snippet view article find links to article

"trifunctional hypothesis". Boris Rybakov emphasised the continuity and complexification of Slavic religion through the centuries. Laruelle observed that Rodnovery