13,368 research outputs found
Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models
String-net models allow us to systematically construct and classify 2+1D
topologically ordered states which can have gapped boundaries. We can use a
simple ideal string-net wavefunction, which is described by a set of F-matrices
[or more precisely, a unitary fusion category (UFC)], to study all the
universal properties of such a topological order. In this paper, we describe a
finite computational method -- Q-algebra approach, that allows us to compute
the non-Abelian statistics of the topological excitations [or more precisely,
the unitary modular tensor category (UMTC)], from the string-net wavefunction
(or the UFC). We discuss several examples, including the topological phases
described by twisted gauge theory (i.e., twisted quantum double ).
Our result can also be viewed from an angle of holographic bulk-boundary
relation. The 1+1D anomalous topological orders, that can appear as edges of
2+1D topological states, are classified by UFCs which describe the fusion of
quasiparticles in 1+1D. The 1+1D anomalous edge topological order uniquely
determines the 2+1D bulk topological order (which are classified by UMTC). Our
method allows us to compute this bulk topological order (i.e., the UMTC) from
the anomalous edge topological order (i.e., the UFC).Comment: 32 pages, 8 figures, reference updated, some refinement
A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons
Topological orders are new phases of matter beyond Landau symmetry breaking.
They correspond to patterns of long-range entanglement. In recent years, it was
shown that in 1+1D bosonic systems there is no nontrivial topological order,
while in 2+1D bosonic systems the topological orders are classified by a pair:
a modular tensor category and a chiral central charge. In this paper, we
propose a partial classification of topological orders for 3+1D bosonic
systems: If all the point-like excitations are bosons, then such topological
orders are classified by unitary pointed fusion 2-categories, which are
one-to-one labeled by a finite group and its group 4-cocycle up to group automorphisms. Furthermore, all such 3+1D
topological orders can be realized by Dijkgraaf-Witten gauge theories.Comment: An important new result "Untwisted sector of dimension reduction is
the Drinfeld center of E" is added in Sec. IIIC; other minor refinements and
improvements; 23 pages, 10 figure
Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
Gapped domain walls, as topological line defects between 2+1D topologically
ordered states, are examined. We provide simple criteria to determine the
existence of gapped domain walls, which apply to both Abelian and non-Abelian
topological orders. Our criteria also determine which 2+1D topological orders
must have gapless edge modes, namely which 1+1D global gravitational anomalies
ensure gaplessness. Furthermore, we introduce a new mathematical object, the
tunneling matrix , whose entries are the fusion-space dimensions
, to label different types of gapped domain walls. By studying
many examples, we find evidence that the tunneling matrices are powerful
quantities to classify different types of gapped domain walls. Since a gapped
boundary is a gapped domain wall between a bulk topological order and the
vacuum, regarded as the trivial topological order, our theory of gapped domain
walls inclusively contains the theory of gapped boundaries. In addition, we
derive a topological ground state degeneracy formula, applied to arbitrary
orientable spatial 2-manifolds with gapped domain walls, including closed
2-manifolds and open 2-manifolds with gapped boundaries.Comment: 5+9 pages, 3 figures, updated references, fixed typos and
refinements, added proof for equivalence to Lagrangian subgroups in Abelian
case
A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries
We propose that, up to invertible topological orders, 2+1D fermionic
topological orders without symmetry and 2+1D fermionic/bosonic topological
orders with symmetry are classified by non-degenerate unitary braided
fusion categories (UBFC) over a symmetric fusion category (SFC); the SFC
describes a fermionic product state without symmetry or a fermionic/bosonic
product state with symmetry , and the UBFC has a modular extension. We
developed a simplified theory of non-degenerate UBFC over a SFC based on the
fusion coefficients and spins . This allows us to obtain a list
that contains all 2+1D fermionic topological orders (without symmetry). We find
explicit realizations for all the fermionic topological orders in the table.
For example, we find that, up to invertible
fermionic topological orders, there
are only four fermionic topological orders with one non-trivial topological
excitation: (1) the
fractional quantum Hall state, (2) a Fibonacci bosonic topological order
stacking with a fermionic product state, (3) the time-reversal
conjugate of the previous one, (4) a primitive fermionic topological order that
has a chiral central charge , whose only topological excitation has
a non-abelian statistics with a spin and a quantum dimension
. We also proposed a categorical way to classify 2+1D invertible
fermionic topological orders using modular extensions.Comment: 23 pages, 8 table
Person Transfer GAN to Bridge Domain Gap for Person Re-Identification
Although the performance of person Re-Identification (ReID) has been
significantly boosted, many challenging issues in real scenarios have not been
fully investigated, e.g., the complex scenes and lighting variations, viewpoint
and pose changes, and the large number of identities in a camera network. To
facilitate the research towards conquering those issues, this paper contributes
a new dataset called MSMT17 with many important features, e.g., 1) the raw
videos are taken by an 15-camera network deployed in both indoor and outdoor
scenes, 2) the videos cover a long period of time and present complex lighting
variations, and 3) it contains currently the largest number of annotated
identities, i.e., 4,101 identities and 126,441 bounding boxes. We also observe
that, domain gap commonly exists between datasets, which essentially causes
severe performance drop when training and testing on different datasets. This
results in that available training data cannot be effectively leveraged for new
testing domains. To relieve the expensive costs of annotating new training
samples, we propose a Person Transfer Generative Adversarial Network (PTGAN) to
bridge the domain gap. Comprehensive experiments show that the domain gap could
be substantially narrowed-down by the PTGAN.Comment: 10 pages, 9 figures; accepted in CVPR 201
Background Subtraction via Generalized Fused Lasso Foreground Modeling
Background Subtraction (BS) is one of the key steps in video analysis. Many
background models have been proposed and achieved promising performance on
public data sets. However, due to challenges such as illumination change,
dynamic background etc. the resulted foreground segmentation often consists of
holes as well as background noise. In this regard, we consider generalized
fused lasso regularization to quest for intact structured foregrounds. Together
with certain assumptions about the background, such as the low-rank assumption
or the sparse-composition assumption (depending on whether pure background
frames are provided), we formulate BS as a matrix decomposition problem using
regularization terms for both the foreground and background matrices. Moreover,
under the proposed formulation, the two generally distinctive background
assumptions can be solved in a unified manner. The optimization was carried out
via applying the augmented Lagrange multiplier (ALM) method in such a way that
a fast parametric-flow algorithm is used for updating the foreground matrix.
Experimental results on several popular BS data sets demonstrate the advantage
of the proposed model compared to state-of-the-arts
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