83 research outputs found
Reoptimization of Some Maximum Weight Induced Hereditary Subgraph Problems
The reoptimization issue studied in this paper can be described as follows: given an instance I of some problem Π, an optimal solution OPT for Π in I and an instance I′ resulting from a local perturbation of I that consists of insertions or removals of a small number of data, we wish to use OPT in order to solve Π in I', either optimally or by guaranteeing an approximation ratio better than that guaranteed by an ex nihilo computation and with running time better than that needed for such a computation. We use this setting in order to study weighted versions of several representatives of a broad class of problems known in the literature as maximum induced hereditary subgraph problems. The main problems studied are max independent set, max k-colorable subgraph and max split subgraph under vertex insertions and deletion
Topological Quantum Field Theories and Operator Algebras
We review "quantum" invariants of closed oriented 3-dimensional manifolds
arising from operator algebras.Comment: For proceedings of "International Workshop on Quantum Field Theory
and Noncommutative Geometry", Sendai, November 200
The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants
We determine the Nakayama automorphism of the almost Calabi-Yau algebra A
associated to the braided subfactors or nimrep graphs associated to each SU(3)
modular invariant. We use this to determine a resolution of A as an A-A
bimodule, which will yield a projective resolution of A.Comment: 46 pages which constitutes the published version, plus an Appendix
detailing some long calculations. arXiv admin note: text overlap with
arXiv:1110.454
Online Multi-Coloring with Advice
We consider the problem of online graph multi-coloring with advice.
Multi-coloring is often used to model frequency allocation in cellular
networks. We give several nearly tight upper and lower bounds for the most
standard topologies of cellular networks, paths and hexagonal graphs. For the
path, negative results trivially carry over to bipartite graphs, and our
positive results are also valid for bipartite graphs. The advice given
represents information that is likely to be available, studying for instance
the data from earlier similar periods of time.Comment: IMADA-preprint-c
On local boundary CFT and non-local CFT on the boundary
The holographic relation between local boundary conformal quantum field
theories (BCFT) and their non-local boundary restrictions is reviewed, and
non-vacuum BCFT's, whose existence was conjectured previously, are constructed.Comment: 16 pages. Contribution to "Rigorous Quantum Field Theory", Symposium
in honour of J. Bros, Paris, July 2004. Based on joint work math-ph/0405067
with R. Long
Algebraic conformal quantum field theory in perspective
Conformal quantum field theory is reviewed in the perspective of Axiomatic,
notably Algebraic QFT. This theory is particularly developped in two spacetime
dimensions, where many rigorous constructions are possible, as well as some
complete classifications. The structural insights, analytical methods and
constructive tools are expected to be useful also for four-dimensional QFT.Comment: Review paper, 40 pages. v2: minor changes and references added, so as
to match published versio
Localized Endomorphisms of the Chiral Ising Model
Based on the treatment of the chiral Ising model by Mack and Schomerus, we
present examples of localized endomorphisms and
. It is shown that they lead to the same
superselection sectors as the global ones in the sense that unitary equivalence
and holds. Araki's formalism of the selfdual CAR algebra is
used for the proof. We prove local normality and extend representations and
localized endomorphisms to a global algebra of observables which is generated
by local von Neumann algebras on the punctured circle. In this framework, we
manifestly prove fusion rules and derive statistics operators.Comment: 41 pages, latex2
How to remove the boundary in CFT - an operator algebraic procedure
The relation between two-dimensional conformal quantum field theories with
and without a timelike boundary is explored.Comment: 18 pages, 2 figures. v2: more precise title, reference correcte
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