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

A. Ehrenfeucht, R. McConnell
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.  ... 
doi:10.1016/0304-3975(94)90233-x fatcat:oozjnwaakraobfxrc7lrvepnw4

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

Takuo Matsuoka
2016 arXiv   pre-print
Higher 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  ... 
arXiv:1509.01582v3 fatcat:2z6gpzpekvbg5o6h47ni5temxa

Depicting qudit quantum mechanics and mutually unbiased qudit theories

André Ranchin
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.  ... 
doi:10.4204/eptcs.172.6 fatcat:5k2f4iim5jcxbppoxs5weum46a

The Origin of Structures in Generalized Gravity

Jai-Chan Hwang
1998 General Relativity and Gravitation  
In 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.  ... 
doi:10.1023/a:1018861906676 fatcat:crl53ytgpbcd3lwbkqg7xlk2be

Sporadic Homogeneous Structures [chapter]

Gregory Cherlin
2000 The Gelfand Mathematical Seminars, 1996–1999  
Lachlan's 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).  ... 
doi:10.1007/978-1-4612-1340-6_2 fatcat:hjflz7aatzbpzpi6jwmfnel22y

Novel generalization of three-dimensional Yang–Mills theory

Stephen C. Anco
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.  ... 
doi:10.1063/1.531859 fatcat:xv244zjaazdtvnszinkng52jpq

Generalized amalgamation and homogeneity [article]

Daniel Palacín
2016 arXiv   pre-print
In this paper we shall prove that any 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.  ... 
arXiv:1603.09694v3 fatcat:gqrza3hkeneonix5qbd77wymde

THREE-DIMENSIONAL TOPOLOGICAL FIELD THEORY INDUCED FROM GENERALIZED COMPLEX STRUCTURE

NORIAKI IKEDA
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.  ... 
doi:10.1142/s0217751x07037196 fatcat:7trucw5afbg7lighu3ln5exqhm

Generalizations of the Los-Tarski Preservation Theorem [article]

Abhisekh Sankaran, Bharat Adsul, Supratik Chakraborty
2013 arXiv   pre-print
Finally, we present partial results towards 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.  ... 
arXiv:1302.4350v2 fatcat:we3ock3knnaelmbrq2z3yly774

Kinetic Field Theory applied to Vector-Tensor Gravity [article]

Lavinia Heisenberg, Matthias Bartelmann
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.  ... 
arXiv:1901.01041v1 fatcat:frngfw4xdndy3mpx2ubdwfjptm

Cosmological structures in generalized gravity [article]

J. Hwang
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.  ... 
arXiv:gr-qc/9711086v1 fatcat:7gq6ybl7ezcttet6eyer2cxb2a

The exceptional generalised geometry of supersymmetric AdS flux backgrounds

Anthony Ashmore, Michela Petrini, Daniel Waldram
2016 Journal of High Energy Physics  
In all cases, one 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  ... 
doi:10.1007/jhep12(2016)146 fatcat:niad55pptzhvlbbxk4xsfj67ee

Combinations related to classes of finite and countably categorical structures and their theories [article]

Sergey V. Sudoplatov
2017 arXiv   pre-print
We consider and characterize classes 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  ... 
arXiv:1701.00205v2 fatcat:aikwec5cgfcf5lmgwbgwm3iqyy

Higher theories of algebraic structures [article]

Takuo Matsuoka
2017 arXiv   pre-print
As 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.  ... 
arXiv:1601.00301v3 fatcat:cvtrimpxwffqvmhzwe4fbvsek4

Generic separable metric structures

Alexander Usvyatsov
2008 Topology and its Applications  
We compare three notions 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.  ... 
doi:10.1016/j.topol.2007.08.023 fatcat:c6o6qhhdaveqdlamzglgt5vwdy
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