50,817 research outputs found
Low-Dimensional Topology of Information Fusion
We provide an axiomatic characterization of information fusion, on the basis
of which we define an information fusion network. Our construction is
reminiscent of tangle diagrams in low dimensional topology. Information fusion
networks come equipped with a natural notion of equivalence. Equivalent
networks `contain the same information', but differ locally. When fusing
streams of information, an information fusion network may adaptively optimize
itself inside its equivalence class. This provides a fault tolerance mechanism
for such networks.Comment: 8 pages. Conference proceedings version. Will be superceded by a
journal versio
A Bayesian graph embedding model for link-based classification problems
In recent years, the analysis of human interaction data has led to the rapid development of graph embedding methods. For link-based classification problems, topological information typically appears in various machine learning tasks in the form of embedded vectors or convolution kernels. This paper introduces a Bayesian graph embedding model for such problems, integrating network reconstruction, link prediction, and behavior prediction into a unified framework. Unlike the existing graph embedding methods, this model does not embed the topology of nodes or links into a low-dimensional space but sorts the probabilities of upcoming links and fuses the information of node topology and data domain via sorting. The new model integrates supervised transaction predictors with unsupervised link prediction models, summarizing local and global topological information. The experimental results on a financial trading dataset and a retweet network dataset demonstrate that the proposed feature fusion model outperforms the tested benchmarked machine learning algorithms in precision, recall, and F1-measure. The proposed learning structure has a fundamental methodological contribution and can be extended and applied to various link-based classification problems in different fields
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
Distributing the Kalman Filter for Large-Scale Systems
This paper derives a \emph{distributed} Kalman filter to estimate a sparsely
connected, large-scale, dimensional, dynamical system monitored by a
network of sensors. Local Kalman filters are implemented on the
(dimensional, where ) sub-systems that are obtained after
spatially decomposing the large-scale system. The resulting sub-systems
overlap, which along with an assimilation procedure on the local Kalman
filters, preserve an th order Gauss-Markovian structure of the centralized
error processes. The information loss due to the th order Gauss-Markovian
approximation is controllable as it can be characterized by a divergence that
decreases as . The order of the approximation, , leads to a lower
bound on the dimension of the sub-systems, hence, providing a criterion for
sub-system selection. The assimilation procedure is carried out on the local
error covariances with a distributed iterate collapse inversion (DICI)
algorithm that we introduce. The DICI algorithm computes the (approximated)
centralized Riccati and Lyapunov equations iteratively with only local
communication and low-order computation. We fuse the observations that are
common among the local Kalman filters using bipartite fusion graphs and
consensus averaging algorithms. The proposed algorithm achieves full
distribution of the Kalman filter that is coherent with the centralized Kalman
filter with an th order Gaussian-Markovian structure on the centralized
error processes. Nowhere storage, communication, or computation of
dimensional vectors and matrices is needed; only dimensional
vectors and matrices are communicated or used in the computation at the
sensors
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