Course

3D moment invariants (3DMIs) are mathematical spatial descriptors designed to be invariant to scaling, translation and rotation. We propose to characterize the spatial distribution of positron emission tomography (PET) images using 3DMIs. We have used 3DMIs to characterize the spatial distribution of PET brain images recorded from subjects with Parkinson's Disease (PD) and healthy controls. 3DMIs were found to accurately describe the 3D texture of PET images despite changes in the size and orientation of the participating subjects in the PET scanner. In addition, we were able to find differences in the 3DMIs of PD patients distinct from those of healthy volunteers. These changes suggest that disease-related variations in the spatial distribution measured using PET can be quantitatively described with the proposed method. Therefore, this method shows great promise to extract additional information from PET data with a wealth of potential applications to disease diagnosis, staging, treatment assessment and more. The quantification of the observed disease-related changes for PD subjects is currently under way.

Tensor network algorithms are a powerful technique for the study of quantum systems in condensed matter physics. In this short series of lectures, I will present an applied perspective on tensor network algorithms. Topics to be covered will include motivation and methodology, graphical notation, Matrix Product States (MPS) and the Time-Evolving Block Decimation (TEBD) algorithm, identifying the capabilities and limitations of tensor network algorithms, the Multi-scale Entanglement Renormalisation Ansatz (MERA) and the study of systems at criticality, and the exploitation of global internal symmetries. The intent of this lecture series is to provide attendees with the necessary theoretical background to be able to understand and implement the more common tensor network algorithms.

Tensor network algorithms are a powerful technique for the study of quantum systems in condensed matter physics. In this short series of lectures, I will present an applied perspective on tensor network algorithms. Topics to be covered will include motivation and methodology, graphical notation, Matrix Product States (MPS) and the Time-Evolving Block Decimation (TEBD) algorithm, identifying the capabilities and limitations of tensor network algorithms, the Multi-scale Entanglement Renormalisation Ansatz (MERA) and the study of systems at criticality, and the exploitation of global internal symmetries. The intent of this lecture series is to provide attendees with the necessary theoretical background to be able to understand and implement the more common tensor network algorithms.