4 research outputs found
Algorithm 950: Ncpol2sdpa---Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables
A hierarchy of semidefinite programming (SDP) relaxations approximates the
global optimum of polynomial optimization problems of noncommuting variables.
Generating the relaxation, however, is a computationally demanding task, and
only problems of commuting variables have efficient generators. We develop an
implementation for problems of noncommuting problems that creates the
relaxation to be solved by SDPA -- a high-performance solver that runs in a
distributed environment. We further exploit the inherent sparsity of
optimization problems in quantum physics to reduce the complexity of the
resulting relaxations. Constrained problems with a relaxation of order two may
contain up to a hundred variables. The implementation is available in Python.
The tool helps solve problems such as finding the ground state energy or
testing quantum correlations.Comment: 17 pages, 3 figures, 1 table, 2 algorithms, the algorithm is
available at http://peterwittek.github.io/ncpol2sdpa
PERICLES Deliverable 4.3:Content Semantics and Use Context Analysis Techniques
The current deliverable summarises the work conducted within task T4.3 of WP4, focusing on the extraction and the subsequent analysis of semantic information from digital content, which is imperative for its preservability. More specifically, the deliverable defines content semantic information from a visual and textual perspective, explains how this information can be exploited in long-term digital preservation and proposes novel approaches for extracting this information in a scalable manner. Additionally, the deliverable discusses novel techniques for retrieving and analysing the context of use of digital objects. Although this topic has not been extensively studied by existing literature, we believe use context is vital in augmenting the semantic information and maintaining the usability and preservability of the digital objects, as well as their ability to be accurately interpreted as initially intended.PERICLE