138,264 research outputs found
Quantum Statistics and Spacetime Topology: Quantum Surgery Formulas
To formulate the universal constraints of quantum statistics data of generic
long-range entangled quantum systems, we introduce the geometric-topology
surgery theory on spacetime manifolds where quantum systems reside, cutting and
gluing the associated quantum amplitudes, specifically in 2+1 and 3+1 spacetime
dimensions. First, we introduce the fusion data for worldline and worldsheet
operators capable of creating anyonic excitations of particles and strings,
well-defined in gapped states of matter with intrinsic topological orders.
Second, we introduce the braiding statistics data of particles and strings,
such as the geometric Berry matrices for particle-string Aharonov-Bohm,
3-string, 4-string, or multi-string adiabatic loop braiding process, encoded by
submanifold linkings, in the closed spacetime 3-manifolds and 4-manifolds.
Third, we derive new `quantum surgery' formulas and constraints, analogous to
Verlinde formula associating fusion and braiding statistics data via spacetime
surgery, essential for defining the theory of topological orders, 3d and 4d
TQFTs and potentially correlated to bootstrap boundary physics such as gapless
modes, extended defects, 2d and 3d conformal field theories or quantum
anomalies.
This article is meant to be an extended and further detailed elaboration of
our previous work [arXiv:1602.05951] and Chapter 6 of [arXiv:1602.05569]. Our
theory applies to general quantum theories and quantum mechanical systems, also
applicable to, but not necessarily requiring the quantum field theory
description.Comment: 35 pages, 3d and 4d figures, 3 tables. An extended sequel and further
detailed elaboration of [arXiv:1602.05951] and Chapter 6 of Thesis
[arXiv:1602.05569] in 201
Symmetry fractionalization and anomaly detection in three-dimensional topological phases
In a phase with fractional excitations, topological properties are enriched
in the presence of global symmetry. In particular, fractional excitations can
transform under symmetry in a fractionalized manner, resulting in different
Symmetry Enriched Topological (SET) phases. While a good deal is now understood
in regarding what symmetry fractionalization patterns are possible, the
situation in is much more open. A new feature in is the existence of
loop excitations, so to study SET phases, first we need to understand how
to properly describe the fractionalized action of symmetry on loops. Using a
dimensional reduction procedure, we show that these loop excitations exist as
the boundary between two SET phases, and the symmetry action is
characterized by the corresponding difference in SET orders. Moreover, similar
to the case, we find that some seemingly possible symmetry
fractionalization patterns are actually anomalous and cannot be realized
strictly in . We detect such anomalies using the flux fusion method we
introduced previously in . To illustrate these ideas, we use the
gauge theory with global symmetry as an example, and enumerate and
describe the corresponding SET phases. In particular, we find four
non-anomalous SET phases and one anomalous SET phase, which we show can be
realized as the surface of a system with symmetry protected topological
order.Comment: 19 pages, 8 figure
GeoZui3D: Data Fusion for Interpreting Oceanographic Data
GeoZui3D stands for Geographic Zooming User Interface. It is a new visualization software system designed for interpreting multiple sources of 3D data. The system supports gridded terrain models, triangular meshes, curtain plots, and a number of other display objects. A novel center of workspace interaction method unifies a number of aspects of the interface. It creates a simple viewpoint control method, it helps link multiple views, and is ideal for stereoscopic viewing. GeoZui3D has a number of features to support real-time input. Through a CORBA interface external entities can influence the position and state of objects in the display. Extra windows can be attached to moving objects allowing for their position and data to be monitored. We describe the application of this system for heterogeneous data fusion, for multibeam QC and for ROV/AUV monitoring
Co-evolution of RDF Datasets
Linking Data initiatives have fostered the publication of large number of RDF
datasets in the Linked Open Data (LOD) cloud, as well as the development of
query processing infrastructures to access these data in a federated fashion.
However, different experimental studies have shown that availability of LOD
datasets cannot be always ensured, being RDF data replication required for
envisioning reliable federated query frameworks. Albeit enhancing data
availability, RDF data replication requires synchronization and conflict
resolution when replicas and source datasets are allowed to change data over
time, i.e., co-evolution management needs to be provided to ensure consistency.
In this paper, we tackle the problem of RDF data co-evolution and devise an
approach for conflict resolution during co-evolution of RDF datasets. Our
proposed approach is property-oriented and allows for exploiting semantics
about RDF properties during co-evolution management. The quality of our
approach is empirically evaluated in different scenarios on the DBpedia-live
dataset. Experimental results suggest that proposed proposed techniques have a
positive impact on the quality of data in source datasets and replicas.Comment: 18 pages, 4 figures, Accepted in ICWE, 201
Exploring the assortativity-clustering space of a network's degree sequence
Nowadays there is a multitude of measures designed to capture different
aspects of network structure. To be able to say if the structure of certain
network is expected or not, one needs a reference model (null model). One
frequently used null model is the ensemble of graphs with the same set of
degrees as the original network. In this paper we argue that this ensemble can
be more than just a null model -- it also carries information about the
original network and factors that affect its evolution. By mapping out this
ensemble in the space of some low-level network structure -- in our case those
measured by the assortativity and clustering coefficients -- one can for
example study how close to the valid region of the parameter space the observed
networks are. Such analysis suggests which quantities are actively optimized
during the evolution of the network. We use four very different biological
networks to exemplify our method. Among other things, we find that high
clustering might be a force in the evolution of protein interaction networks.
We also find that all four networks are conspicuously robust to both random
errors and targeted attacks
A Bayesian fusion model for space-time reconstruction of finely resolved velocities in turbulent flows from low resolution measurements
The study of turbulent flows calls for measurements with high resolution both
in space and in time. We propose a new approach to reconstruct
High-Temporal-High-Spatial resolution velocity fields by combining two sources
of information that are well-resolved either in space or in time, the
Low-Temporal-High-Spatial (LTHS) and the High-Temporal-Low-Spatial (HTLS)
resolution measurements. In the framework of co-conception between sensing and
data post-processing, this work extensively investigates a Bayesian
reconstruction approach using a simulated database. A Bayesian fusion model is
developed to solve the inverse problem of data reconstruction. The model uses a
Maximum A Posteriori estimate, which yields the most probable field knowing the
measurements. The DNS of a wall-bounded turbulent flow at moderate Reynolds
number is used to validate and assess the performances of the present approach.
Low resolution measurements are subsampled in time and space from the fully
resolved data. Reconstructed velocities are compared to the reference DNS to
estimate the reconstruction errors. The model is compared to other conventional
methods such as Linear Stochastic Estimation and cubic spline interpolation.
Results show the superior accuracy of the proposed method in all
configurations. Further investigations of model performances on various range
of scales demonstrate its robustness. Numerical experiments also permit to
estimate the expected maximum information level corresponding to limitations of
experimental instruments.Comment: 15 pages, 6 figure
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