2,701 research outputs found
Tensor models and hierarchy of n-ary algebras
Tensor models are generalization of matrix models, and are studied as models
of quantum gravity. It is shown that the symmetry of the rank-three tensor
models is generated by a hierarchy of n-ary algebras starting from the usual
commutator, and the 3-ary algebra symmetry reported in the previous paper is
just a single sector of the whole structure. The condition for the Leibnitz
rules of the n-ary algebras is discussed from the perspective of the invariance
of the underlying algebra under the n-ary transformations. It is shown that the
n-ary transformations which keep the underlying algebraic structure invariant
form closed finite n-ary Lie subalgebras. It is also shown that, in physical
settings, the 3-ary transformation practically generates only local
infinitesimal symmetry transformations, and the other more non-local
infinitesimal symmetry transformations of the tensor models are generated by
higher n-ary transformations.Comment: 13 pages, some references updated and correcte
Exact Results in Quiver Quantum Mechanics and BPS Bound State Counting
We exactly evaluate the partition function (index) of N=4 supersymmetric
quiver quantum mechanics in the Higgs phase by using the localization
techniques. We show that the path integral is localized at the fixed points,
which are obtained by solving the BRST equations, and D-term and F-term
conditions. We turn on background gauge fields of R-symmetries for the chiral
multiplets corresponding to the arrows between quiver nodes, but the partition
function does not depend on these R-charges. We give explicit examples of the
quiver theory including a non-coprime dimension vector. The partition functions
completely agree with the mathematical formulae of the Poincare polynomials
(chi_y-genus) and the wall crossing for the quiver moduli spaces . We also
discuss exact computation of the expectation values of supersymmetric
(Q-closed) Wilson loops in the quiver theory.Comment: 40 pages, 7 figures; v2: minor corrections and references are added;
v3: references added, typos corrected, discrepancy in the non-coprime case
resolve
Mapping multiplex hubs in human functional brain network
Typical brain networks consist of many peripheral regions and a few highly
central ones, i.e. hubs, playing key functional roles in cerebral
inter-regional interactions. Studies have shown that networks, obtained from
the analysis of specific frequency components of brain activity, present
peculiar architectures with unique profiles of region centrality. However, the
identification of hubs in networks built from different frequency bands
simultaneously is still a challenging problem, remaining largely unexplored.
Here we identify each frequency component with one layer of a multiplex network
and face this challenge by exploiting the recent advances in the analysis of
multiplex topologies. First, we show that each frequency band carries unique
topological information, fundamental to accurately model brain functional
networks. We then demonstrate that hubs in the multiplex network, in general
different from those ones obtained after discarding or aggregating the measured
signals as usual, provide a more accurate map of brain's most important
functional regions, allowing to distinguish between healthy and schizophrenic
populations better than conventional network approaches.Comment: 11 pages, 8 figures, 2 table
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