Nonlocal games and quantum permutation groups

We present a strong connection between quantum information and the theory of quantum permutation groups. Specifically, we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the theory of quantum groups, and then show that this is equivalent to the previously defined notion of quantum isomorphism corresponding to perfect quantum strategies to the isomorphism game. Moreover, we show that two connected graphs X and Y are quantum isomorphic if and only if there exists x is an element of V(X) and y is an element of V(Y) that are in the same orbit of the quantum automorphism group of the disjoint union of X and Y. This connection links quantum groups to the more concrete notion of nonlocal games and physically observable quantum behaviours. In this work, we exploit this by using ideas and results from quantum information in order to prove new results about quantum automorphism groups of graphs, and about quantum permutation groups more generally. In particular, we show that asymptotically almost surely all graphs have trivial quantum automorphism group. Furthermore, we use examples of quantum isomorphic graphs from previous work to construct an infinite family of graphs which are quantum vertex transitive but fail to be vertex transitive, answering a question from the quantum permutation group literature. Our main tool for proving these results is the introduction of orbits and orbitals (orbits on ordered pairs) of quantum permutation groups. We show that the orbitals of a quantum permutation group form a coherent configuration/algebra, a notion from the field of algebraic graph theory. We then prove that the elements of this quantum orbital algebra are exactly the matrices that commute with the magic unitary defining the quantum group. We furthermore show that quantum isomorphic graphs admit an isomorphism of their quantum orbital algebras which maps the adjacency matrix of one graph to that of the other. We hope that this work will encourage new collaborations among the communities of quantum information, quantum groups, and algebraic graph theory. (C) 2020 Elsevier Inc. All rights reserved

Radiographic film dosimetry for IMRT fields in the near‐surface buildup region

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135573/1/acm20087.pd

Flame Retardant Effect of Aerogel and Nanosilica on Engineered Polymers

Aerogels are typically manufactured vIa high temperature and pressure-critical-point drying of a colloidal metal oxide gel filled with solvents. Aerogel materials derived from silica materials represent a structural morphology (amorphous, open-celled nanofoams) rather than a particular chemical constituency. Aerogel is not like conventional foams in that it is a porous material with extreme microporosity and composed of individual features only a few nanometers in length with a highly porous dendriticlike structure. This unique substance has unusual properties such as low thermal conductivity, refractive index and sound suppression; in addition to its exceptional ability to capture fast moving dust. The highly porous nature of the aerogel's structure provides large amounts of surface area per unit weight. For instance, a silica aerogel material with a density of 100 kilograms per cubic meters can have surface areas of around 800 to 1500 square meters per gram depending on the precursors and process utilized to produce it. To take advantage of the unique properties of silica aerogels, especially the ultra light weight and low thermal conductivity, their composites with various engineering polymers were prepared and their flammability was investigated by Cone Calorimetry. The flammability of various polystyrene/silica aerogel nanocomposites were measured. The combination of these nanocomposites with a NASA patented flame retardant SINK were also studied. The results were compared with the base polymer to show the differences between composites with different forms of silica

Perfect Strategies for Non-Local Games

We describe the main classes of non-signalling bipartite correlations in terms of states on operator system tensor products. This leads to the introduction of another new class of games, called reflexive games, which are characterised as the hardest non-local games that can be won using a given set of strategies. We provide a characterisation of their perfect strategies in terms of operator system quotients. We introduce a new class of non-local games, called imitation games, in which the players display linked behaviour, and which contain as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and unique games. We associate a C*-algebra C * (G) to any imitation game G, and show that the existence of perfect quantum commuting (resp. quantum, local) strategies of G can be characterised in terms of properties of this C*algebra. We single out a subclass of imitation games, which we callmirror games, and provide a characterisation of their quantum commuting strategies that has an algebraic flavour, showing in addition that their approximately quantum perfect strategies arise from amenable traces on the encoding C*-algebra

Biological-Effect Modeling of Radioimmunotherapy for Non-Hodgkins Lymphoma: Determination of Model Parameters

Treatment with Tositumomab and 131I tositumomab anti-CD20 radioimmunotherapy (Bexxar) yields a nonradioactive antibody antitumor response (the so-called cold effect) and a radiation response. Numerical parameter determination by least-squares (LS) fitting was implemented for more accurate parameter estimates in equivalent biological-effect calculations. Methods: One hundred thirty-two tumors in 37 patients were followed using five or six SPECT/CT studies per patient, three each (typical) post-tracer (0.2 GBq) and post-therapy (?3 GBq) injections. The SPECT/CT data were used to calculate position- and time-dependent dose rates and antibody concentrations for each tumor. CT-defined tumor volumes were used to track tumor volume changes. Combined biological-effect and cell-clearance models were fit to tumor volume changes. Optimized parameter values determined using LS fitting were compared to previous fitted values that were determined by matching calculated to measured tumor volume changes using visual assessment. Absorbed dose sensitivity (α) and cold-effect sensitivity (?p) parameters were the primary fitted parameters, yielding equivalent biological-effect (E) values. Results: Individual parameter uncertainties were approximately 10% and 30% for α and ?p, respectively. LS versus previously fit parameter values were highly correlated, although the averaged α value decreased and the averaged ?p value increased for the LS fits compared to the previous fits. Correlation of E with 2-month tumor shrinkage data was similar for the two fitting techniques. The LS fitting yielded improved fit quality and likely improved parameter estimation.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140326/1/cbr.2012.1467.pd

Accuracy of rapid radiographic film calibration for intensity‐modulated radiation therapy verification

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135342/1/acm20086.pd