527 research outputs found
Topological Field Theory with Haagerup Symmetry
We construct a (1+1) topological field theory (TFT) whose topological
defect lines (TDLs) realize the transparent Haagerup fusion
category. This TFT has six vacua, and each of the three non-invertible simple
TDLs hosts three defect operators, giving rise to a total of 15 point-like
operators. The TFT data, including the three-point coefficients and lasso
diagrams, are determined by solving all the sphere four-point crossing
equations and torus one-point modular invariance equations. We further verify
that the Cardy states furnish a non-negative integer matrix representation
under TDL fusion. While many of the constraints we derive are not limited to
the this particular TFT with six vacua, we leave open the construction of TFTs
with two or four vacua. Finally, TFTs realizing the Haagerup
and fusion categories can be obtained by gauging algebra
objects. This note makes a modest offering in our pursuit of exotica and the
quest for their eventual conformity.Comment: 41+11 pages, 1 figure, 3 tables; v2: corrected statements about the
literature, revised Appendix
The F-Symbols for Transparent Haagerup-Izumi Categories with G = Z_(2n+1)
The notion of a transparent fusion category is defined. For the Haagerup-Izumi fusion rings with G=Z_(2n+1) (the Z_3 case is the Haagerup H_3 fusion ring), the transparent property reduces the number of independent F-symbols from order O(n6) to O(n^2), rendering the pentagon identity practically solvable. Transparent fusion categories are constructed up to Z_(15), and the explicit F-symbols are compactly presented. The potential construction of categories for new families of fusion rings is discussed
The F-Symbols for Transparent Haagerup-Izumi Categories with G = Z_(2n+1)
The notion of a transparent fusion category is defined. For the Haagerup-Izumi fusion rings with G=Z_(2n+1) (the Z_3 case is the Haagerup H_3 fusion ring), the transparent property reduces the number of independent F-symbols from order O(n6) to O(n^2), rendering the pentagon identity practically solvable. Transparent fusion categories are constructed up to Z_(15), and the explicit F-symbols are compactly presented. The potential construction of categories for new families of fusion rings is discussed
Therapy Made Easy
In China, the rise of e-commerce has made significant impacts on a broad range of business and professional fields; psychotherapy, a profession born of the recent “psycho-boom” (xinli re 心理热), is one of them. This article, using materials collected from interviews, participant observation, and media accounts, delineates the development of Jiandan xinli (简单心理), a Beijing-based startup that features an e-commerce platform for psychotherapy services, and explicates how and why it has achieved enormous initial success. Drawing on the insights of anthropological studies of infrastructure, it argues that the platform can be conceptualised as an example of “infrastructural entrepreneurship,” a business practice taking the construction of infrastructure—in this case, for the field of psychotherapy—as its primary mission
Tailored Iterated Greedy metaheuristic for a scheduling problem in metal 3D printing
This article contributes to the additive manufacturing-based production planning literature by developing a
Mixed-Integer Linear Programming (MILP) formulation for the Identical Parallel 3D-Printing Machines Scheduling Problem considering batching, multiple build platforms of restricted sizes, and sequence-independent setup
times. Besides, a customized metaheuristic, named the Tailored Iterated Greedy (TIG) Algorithm is developed to
solve the new optimization problem. TIG’s performance is evaluated through extensive numerical analysis and
using a new testbed. It is shown that the customized computational mechanisms improve the optimization
performance; statistical analysis is supportive of the significance of the resulting improvements. The developed
mathematical model and optimization algorithm can be considered the basis for future developments in the
optimization literature of additive manufacturing
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