Quantum Cuntz-Krieger algebras

Motivated by the theory of Cuntz-Krieger algebras we define and study C∗-algebras associated to directed quantum graphs. For classical graphs the C∗-algebras obtained this way can be viewed as free analogues of Cuntz-Krieger algebras, and need not be nuclear. We study two particular classes of quantum graphs in detail, namely the trivial and the complete quantum graphs. For the trivial quantum graph on a single matrix block, we show that the associated quantum Cuntz-Krieger algebra is neither unital, nuclear nor simple, and does not depend on the size of the matrix block up to KK-equivalence. In the case of the complete quantum graphs we use quantum symmetries to show that, in certain cases, the corresponding quantum Cuntz-Krieger algebras are isomorphic to Cuntz algebras. These isomorphisms, which seem far from obvious from the definitions, imply in particular that these C∗-algebras are all pairwise non-isomorphic for complete quantum graphs of different dimensions, even on the level of KK-theory. We explain how the notion of unitary error basis from quantum information theory can help to elucidate the situation. We also discuss quantum symmetries of quantum Cuntz-Krieger algebras in general

Prediction of left lobe hypertrophy after right lobe radioembolization of the liver using a clinical data model with external validation

In cirrhotic patients with hepatocellular carcinoma (HCC), right-sided radioembolization (RE) with Yttrium-90-loaded microspheres is an established palliative therapy and can be considered a “curative intention” treatment when aiming for sequential tumor resection. To become surgical candidate, hypertrophy of the left liver lobe to > 40% (future liver remnant, FLR) is mandatory, which can develop after RE. The amount of radiation-induced shrinkage of the right lobe and compensatory hypertrophy of the left lobe is difficult for clinicians to predict. This study aimed to utilize machine learning to predict left lobe liver hypertrophy in patients with HCC and cirrhosis scheduled for right lobe RE, with external validation. The results revealed that machine learning can accurately predict relative and absolute volume changes of the left liver lobe after right lobe RE. This prediction algorithm could help to estimate the chances of conversion from palliative RE to curative major hepatectomy following significant FLR hypertrophy

Highly selective, reversible water activation by P,N-cooperativity in pyridyl-functionalized phosphinines

Tetrapyridyl-functionalized phosphinines were prepared and structurally characterized. The donor-functionalized aromatic phosphorus heterocycles react highly selectively and even reversibly with water. Calculations reveal P,N-cooperativity for this process, with the flanking pyridyl groups serving to kinetically enhance the formal oxidative addition process of H2O to the low-coordinate phosphorus atom via H-bonding. Subsequent tautomerization forms 1,2-dihydrophosphinine derivatives, which can be quantitatively converted back to the phosphinine by applying vacuum, even at room temperature. This process can be repeated numerous times, without any sign of decomposition of the phosphinine. In the presence of CuI·SMe2, dimeric species of the type ([Cu2I2(phosphinine)]2) are formed, in which each phosphorus atom shows the less common μ2-bridging 2e−-lone-pair-donation to two Cu(i)-centres. Our results demonstrate that fully unsaturated phosphorus heterocycles, containing reactive P = C double bonds, are interesting candidates for the activation of E-H bonds, while the aromaticity of such compounds plays an appreciable role in the reversibility of the reaction, supported by NICS calculations