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A k-structure generalization of the theory of 2-structures

1994
*
Theoretical Computer Science
*

*A*. and R. McConnell,

*A*

*k*-

*structure*

*generalization*

*of*

*the*

*theory*

*of*

*2*-

*structures*, Theoretical Computer Science 132 ( ... Acknowledgment

*The*authors would like to thank Hal Gabow for pointing out

*the*relationship between

*the*prime tree decomposition

*of*

*2*-

*structures*and

*the*previous work on

*the*modular decomposition

*of*graphs ... Although

*2*-

*structures*and

*k*-ary relations are both

*generalizations*

*of*

*the*notion

*of*

*a*graph, neither is

*a*

*generalization*

*of*

*the*other. ...

##
###
A generalization of categorification, and higher "theory" of algebras
[article]

2016
*
arXiv
*
pre-print

Higher

arXiv:1509.01582v3
fatcat:2z6gpzpekvbg5o6h47ni5temxa
*theories*are obtained by iterating*a*certain process, which we call "theorization",*generalizing*categorification in*the*sense*of*Louis Crane. ... Indeed, our "*theories*" are 'higher order'*generalizations**of*coloured operad or multicategory, where we see an operad as analogous to Lawvere's*theory*. ...*structure**2*-maps (see above) are invertible, •*K*-*structure*is said to be*a*virtualization*of**K*-*structure*if T is fully faithful on*the*underlying*2*-groupoids, and*K*-*structures*are characterized among*K*-*structures*...##
###
Depicting qudit quantum mechanics and mutually unbiased qudit theories

2014
*
Electronic Proceedings in Theoretical Computer Science
*

*The*calculus allows us to analyze

*the*

*structure*

*of*qudit stabilizer quantum mechanics and provides

*a*geometrical picture

*of*qudit stabilizer

*theory*using D-toruses, which

*generalizes*

*the*Bloch sphere picture ... We define

*the*notion

*of*

*a*mutually unbiased qudit

*theory*and study two particular instances

*of*these

*theories*in detail: qudit stabilizer quantum mechanics and Spekkens-Schreiber toy

*theory*for dits. ... Acknowledgments I would like to thank both

*of*my supervisors Bob Coecke and Terry Rudolph for insightful discussions. ...

##
###
The Origin of Structures in Generalized Gravity

1998
*
General Relativity and Gravitation
*

In

doi:10.1023/a:1018861906676
fatcat:crl53ytgpbcd3lwbkqg7xlk2be
*a*class*of**generalized*gravity*theories*with*general*couplings between*the*scalar field and*the*scalar curvature in*the*Lagrangian, we can describe*the*quantum*generation*and*the*classical evolution ...*of*both*the*scalar and tensor*structures*in*a*simple and unified manner. ... Acknowledgments This work was supported in part by*the*KOSEF Grant No. 95-0702-04-01-3 and through*the*SRC program*of*SNU-CTP. ...##
###
Sporadic Homogeneous Structures
[chapter]

2000
*
The Gelfand Mathematical Seminars, 1996–1999
*

Lachlan's

doi:10.1007/978-1-4612-1340-6_2
fatcat:hjflz7aatzbpzpi6jwmfnel22y
*theory*provides*a*hierarchy*of*classifications in which*structures*which are "sporadic" in one context reappear as members*of*infinite families at later stages. ... Every finite*structure*is accounted for at some level in this hierarchy, but for*structures*associated with familiar primitive permutation groups*the*combinatorial problem*of*locating that level precisely ... In*the*long run*the*most*general*form*of*this*theory*would be*a**structural*analysis*of*large*k*-closed permutation groups*of*bounded rank (with both*k*and*the*bound on rank taken as fixed). ...##
###
Novel generalization of three-dimensional Yang–Mills theory

1997
*
Journal of Mathematical Physics
*

*The*

*theories*describe

*a*

*generalization*

*of*three-dimensional Yang-Mills

*theory*featuring

*a*novel nonlinear gauge symmetry and field equations for Lie-algebra valued vector potential fields. ...

*A*gauge covariant formulation

*of*

*the*new

*theories*is given which utilizes

*the*covariant derivative and curvature from

*the*geometrical formulation

*of*Yang-Mills

*theory*. ... As

*a*consequence, in

*the*SU(

*2*) case,

*the*nonlinear

*structure*

*of*

*the*

*generalization*is unique. Extension

*of*

*the*SU(

*2*) case to

*the*

*general*nonabelian case

*of*

*the*

*generalization*is considered in Sec. ...

##
###
Generalized amalgamation and homogeneity
[article]

2016
*
arXiv
*
pre-print

In this paper we shall prove that any

arXiv:1603.09694v3
fatcat:gqrza3hkeneonix5qbd77wymde
*2*-transitive finitely homogeneous*structure*with*a*supersimple*theory*satisfying*a**generalized*amalgamation property is*a*random*structure*. ... In particular, this adapts*a*result*of*Koponen for binary homogeneous*structures*to arbitrary ones without binary relations. ... For instance,*the*random graph, or more*generally**a*random*structure*in*the*sense*of*Definition 4.1, is an archetypical example*of**a**structure*with*a*first-order simple, even supersimple,*theory*. ...##
###
THREE-DIMENSIONAL TOPOLOGICAL FIELD THEORY INDUCED FROM GENERALIZED COMPLEX STRUCTURE

2007
*
International Journal of Modern Physics A
*

*The*

*theory*is invariant under

*the*diffeomorphism on

*the*world volume and

*the*b-transformation on

*the*

*generalized*complex

*structure*. ... We construct

*a*three-dimensional topological sigma model which is induced from

*a*

*generalized*complex

*structure*on

*a*target

*generalized*complex manifold. ... Acknowledgements We would like to thank

*K*. -I. Izawa for valuable comments and discussions. ...

##
###
Generalizations of the Los-Tarski Preservation Theorem
[article]

2013
*
arXiv
*
pre-print

Finally, we present partial results towards

arXiv:1302.4350v2
fatcat:we3ock3knnaelmbrq2z3yly774
*generalizing*to*theories*,*the*substructural version*of**the*Los-Tarski theorem and in*the*process, we give*a*preservation theorem that provides*a*semantic characterization ... We present new preservation theorems that semantically characterize*the*∃^*k*∀^* and ∀^*k*∃^* prefix classes*of*first order logic, for each natural number*k*. ... Preservation under*k*-ary Covered Extensions*The*classical notion*of*"extension*of**a**structure*" can be naturally*generalized*to extension*of**a*collection*of**structures*as follows. ...##
###
Kinetic Field Theory applied to Vector-Tensor Gravity
[article]

2019
*
arXiv
*
pre-print

*The*formation

*of*cosmic

*structures*is an important diagnostic for both

*the*dynamics

*of*

*the*cosmological model and

*the*underlying

*theory*

*of*gravity. ... At

*the*linear level

*of*these

*structures*, certain degeneracies remain between different cosmological models and alternative gravity

*theories*. ... ACKNOWLEDGEMENTS LH is supported by

*the*Swiss National Science Foundation and

*the*European Unions Horizon 2020 Research Council Grant. ...

##
###
Cosmological structures in generalized gravity
[article]

1997
*
arXiv
*
pre-print

*of*both

*the*scalar and tensor

*structures*in

*a*simple and unified manner. ... In

*a*class

*of*

*generalized*gravity

*theories*with

*general*couplings between

*the*scalar field and

*the*scalar curvature in

*the*Lagrangian, we describe

*the*quantum

*generation*and

*the*classical evolution processes ... Acknowledgments This work was supported by

*the*KOSEF, Grant No. 95-0702-04-01-3 and through

*the*SRC program

*of*SNU-CTP. ...

##
###
The exceptional generalised geometry of supersymmetric AdS flux backgrounds

2016
*
Journal of High Energy Physics
*

In all cases, one

doi:10.1007/jhep12(2016)146
fatcat:niad55pptzhvlbbxk4xsfj67ee
*structure*defines*a*"generalised Reeb vector" that*generates**a*Killing symmetry*of**the*background corresponding to*the*R-symmetry*of**the*dual field*theory*, and in addition encodes*the*... In particular, we give*the*complete analysis*of**the**generic*AdS_5 M-*theory*backgrounds. We also briefly discuss*the**structure**of**the*moduli space*of*solutions. ... DW is supported by*the*STFC Consolidated Grant ST/L00044X/1,*the*EPSRC Programme Grant EP/K034456/1 "New Geometric*Structures*from String*Theory*" and*the*EPSRC Standard Grant EP/N007158/1 "Geometry for ...##
###
Combinations related to classes of finite and countably categorical structures and their theories
[article]

2017
*
arXiv
*
pre-print

We consider and characterize classes

arXiv:1701.00205v2
fatcat:aikwec5cgfcf5lmgwbgwm3iqyy
*of*finite and countably categorical*structures*and their*theories*preserved under E-operators and P-operators. ... We describe e-spectra and families*of*finite cardinalities for*structures*belonging to closures with respect to E-operators and P-operators. ...*The**theory*T*k**of*resulting*generic**structure*M*k*satisfiesĉ P (T*k*) = {*k*} since each realization*a**of*p ∞ (x) forces*k*realizations*of*p ∞ (x) consisting*of*E*k*(*a*) and any two realizations*of*p ∞ (x ...##
###
Higher theories of algebraic structures
[article]

2017
*
arXiv
*
pre-print

As

arXiv:1601.00301v3
fatcat:cvtrimpxwffqvmhzwe4fbvsek4
*a*result, (coloured) morphism between n-*theories*is*a*"graded" and "enriched"*generalization**of*(n-1)-*theory*. ... Indeed, theorization turns out to produce more*general*kinds*of**structure*than*the*process*of*categorification in*the*sense*of*Louis Crane does. ... I am grateful to*the*participants*of*my informal talks on this work for many helpful comments and questions, especially to Shō Saitō, Kōtarō Kawatani, Isamu Iwanari, Hiroyuki Minamoto, Norihiko Minami. ...##
###
Generic separable metric structures

2008
*
Topology and its Applications
*

We compare three notions

doi:10.1016/j.topol.2007.08.023
fatcat:c6o6qhhdaveqdlamzglgt5vwdy
*of**genericity**of*separable metric*structures*. ... Our analysis provides*a**general*model theoretic technique*of*showing that*structures*are*generic*in descriptive set theoretic (topological) sense and in measure theoretic sense. ... Acknowledgements*The*author thanks C. Ward Henson and*the*anonymous referee for very helpful comments and suggestions. ...
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