Global Completability with Applications to Self-Consistent Quantum Tomography
Name
220_2016_2760_ReferencePDF.pdf
Size
3.56 MB
Format
Adobe PDF
Checksum (MD5)
d1283e3fed038f6d1435ec32b6bab542
Author(s)
Stark, Cyril
Date Issued
September 2016
Journal
Communications in Mathematical Physics
Publisher
Springer Berlin Heidelberg
Citation
Bagley, A. F. et al. “Endothelial Thermotolerance Impairs Nanoparticle Transport in Tumors.” Cancer Research 75.16 (2015): 3255–3267.
Version
Author's final manuscript
Abstract
Let p1,...,pN ∈ R[superscript D] be unknown vectors and let Ω ⊆ {1,...,N}[superscript 2]. Assume that the inner products p[superscript T][subscript i]p[subscript j] are fixed for all (i,j) ∈ Ω. Do these inner product constraints (up to simultaneous rotation of all vectors) determine p1,...,pN uniquely? Here we derive a necessary and sufficient condition for the uniqueness of p1,..., pN (i.e., global completability) which is applicable to a large class of practically relevant sets Ω. Moreover, given Ω, we show that the condition for global completability is universal in the sense that for almost all vectors p1,...,pN ∈ R[superscript D] the completability of p1,...,pN only depends on Ω and not on the specific values of p[superscript T][subscript i]p[subscript j] for (i,j) ∈ Ω. This work was motivated by practical considerations, namely, matrix factorization techniques and self-consistent quantum tomography.
MIT Department
Massachusetts Institute of Technology. Laboratory for Nuclear Science
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00220-016-2760-2
