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Cadmium Zinc Telluride, or CZT, cameras offer dual-isotope imaging capabilities impossible to duplicate using any other preclinical molecular imaging system. This new technology will enable the investigation of multiple biological processes in parallel and open new areas in research and drug development. The dual-isotope capability is due to the improved energy resolution of CZT (4.5% for 99m Tc), which is 2-3 times better than in existing systems. This improved energy resolution allows for the rejection of more scattered photons, yielding higher contrast images. In addition, CZT provides increased sensitivity compared to traditional pixellated NaI(Tl) systems due to the absence of any escape peaks. These properties combine to give a higher sensitivity detector with significantly improved contrast. The present work demonstrates the use of CZT in dual-isotope imaging of mice using two radiopharmaceuticals with very close energy peaks. These included 99m Tc-labelled MDP (bone agent) and 123 I (thyroid) and a mouse bone ( 99m Tc-MDP) image with a 57 Co fiducial marker. The results show the first ever simultaneous 99m Tc / 123 I mouse images. The individual isotope peaks showed significant separation and yielded an image with the thyroid (2-3 mm) clearly distinguished from the bone structure. GM-I's new FLEX Triumph™ Pre-clinical system is the first in the field to offer CZT SPECT detectors.

We develop the theoretical foundations of a network distance that has recently been applied to various subfields of topological data analysis, namely persistent homology and hierarchical clustering. While this network distance has previously appeared in the context of finite networks, we extend the setting to that of compact networks. The main challenge in this new setting is the lack of an easy notion of sampling from compact networks; we solve this problem in the process of obtaining our results. The generality of our setting means that we automatically establish results for exotic objects such as directed metric spaces and Finsler manifolds. We identify readily computable network invariants and establish their quantitative stability under this network distance. We also discuss the computational complexity involved in precisely computing this distance, and develop easily-computable lower bounds by using the identified invariants. By constructing a wide range of explicit examples, we show that these lower bounds are effective in distinguishing between networks. Finally, we provide a simple algorithm that computes a lower bound on the distance between two networks in polynomial time and illustrate our metric and invariant constructions on a database of random networks and a database of simulated hippocampal networks. CONTENTS1. Introduction 1.1. Contributions and organization of the paper 1.2. Related literature 1.3. Notation and basic terminology 2. Networks, isomorphism, and network distances 2.1. The second network distance 2.2. Special families: dissimilarity networks and directed metric spaces 2.3. Two families of examples: the directed circles 2.3.1. The general directed circle 2.3.2. The directed circles with finite reversibility 3. The case of compact networks 3.1. Compact networks and finite sampling 3.1.1. Proofs of result in §3.1 3.2. Compact networks and weak isomorphism 4. Invariants of networks 4.1. Quantitative stability of invariants of networks 5. Computational aspects 5.1. The complexity of computing d N

We define a metric-the Network Gromov-Wasserstein distance-on weighted, directed networks that is sensitive to the presence of outliers. In addition to proving its theoretical properties, we supply easily computable network invariants that approximate this distance by means of lower bounds. CONTENTS 1. Introduction 1.1. Motivation and related literature 1.2. Organization of the paper 1.3. Notation and basic terminology 2. The structure of measure networks 2.1. Couplings and the distortion functional 2.2. Interval representation and continuity of distortion 2.3. Optimality of couplings in the network setting 2.4. The Network Gromov-Wasserstein distance 2.5. The Network Gromov-Prokhorov distance 3. Invariants and lower bounds 3.1. Global invariants 3.2. Local invariants 3.3. Distribution-valued invariants: local and global pushforwards 4. Discussion References