16,424 research outputs found
The role of religious institutions in community governance affairs: how are communities governed beyond the district level?
Ahmad Idrees Rahman
Exact results on the quench dynamics of the entanglement entropy in the toric code
We study quantum quenches in the two-dimensional Kitaev toric code model and
compute exactly the time-dependent entanglement entropy of the non-equilibrium
wave-function evolving from a paramagnetic initial state with the toric code
Hamiltonian. We find that the area law survives at all times. Adding disorder
to the toric code couplings makes the entanglement entropy per unit boundary
length saturate to disorder-independent values at long times and in the
thermodynamic limit. There are order-one corrections to the area law from the
corners in the subsystem boundary but the topological entropy remains zero at
all times. We argue that breaking the integrability with a small magnetic field
could change the area law to a volume scaling as expected of thermalized states
but is not sufficient for forming topological entanglement due to the presence
of an excess energy and a finite density of defects.Comment: 14 pages, 7 figures, published versio
Randomized Robust Subspace Recovery for High Dimensional Data Matrices
This paper explores and analyzes two randomized designs for robust Principal
Component Analysis (PCA) employing low-dimensional data sketching. In one
design, a data sketch is constructed using random column sampling followed by
low dimensional embedding, while in the other, sketching is based on random
column and row sampling. Both designs are shown to bring about substantial
savings in complexity and memory requirements for robust subspace learning over
conventional approaches that use the full scale data. A characterization of the
sample and computational complexity of both designs is derived in the context
of two distinct outlier models, namely, sparse and independent outlier models.
The proposed randomized approach can provably recover the correct subspace with
computational and sample complexity that are almost independent of the size of
the data. The results of the mathematical analysis are confirmed through
numerical simulations using both synthetic and real data
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