Benchmarking treewidth as a practical component of tensor network simulations.

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on the tensor ranks and the order in which they are contracted. Unfortunately, computing optimal contraction sequences (orderings) in general is known to be a computationally difficult (NP-complete) task. In 2005, Markov and Shi showed that optimal contraction sequences correspond to optimal (minimum width) tree decompositions of a tensor network's line graph, relating the contraction sequence problem to a rich literature in structural graph theory. While treewidth-based methods have largely been ignored in favor of dataset-specific algorithms in the prior tensor networks literature, we demonstrate their practical relevance for problems arising from two distinct methods used in quantum simulation: multi-scale entanglement renormalization ansatz (MERA) datasets and quantum circuits generated by the quantum approximate optimization algorithm (QAOA). We exhibit multiple regimes where treewidth-based algorithms outperform domain-specific algorithms, while demonstrating that the optimal choice of algorithm has a complex dependence on the network density, expected contraction complexity, and user run time requirements. We further provide an open source software framework designed with an emphasis on accessibility and extendability, enabling replicable experimental evaluations and future exploration of competing methods by practitioners.

Sensitivity and specificity of the empirical lymphocyte genome sensitivity (LGS) assay: implications for improving cancer diagnostics.

Lymphocyte responses from 208 individuals: 20 with melanoma, 34 with colon cancer, and 4 with lung cancer (58), 18 with suspected melanoma, 28 with polyposis, and 10 with COPD (56), and 94 healthy volunteers were examined. The natural logarithm of the Olive tail moment (OTM) was plotted for exposure to UVA through 5 different agar depths (100 cell measurements/depth) and analyzed using a repeated measures regression model. Responses of patients with cancer plateaued after treatment with different UVA intensities, but returned toward control values for healthy volunteers. For precancerous conditions and suspected cancers, intermediate responses occurred. ROC analysis of mean log OTMs, for cancers plus precancerous/suspect conditions vs. controls, cancer vs. precancerous/suspect conditions plus controls, and cancer vs. controls, gave areas under the curve of 0.87, 0.89, and 0.93, respectively (P<0.001). Optimization allowed test sensitivity or specificity to approach 100% with acceptable complementary measures. This modified comet assay could represent a stand-alone test or an adjunct to other investigative procedures for detecting cancer.

Bilateral pyoderma gangrenosum complicating minimal access cranial suspension face lift.

We present the case of a previously healthy 53-year-old woman upon whom a minimal access cranial suspension (MACS) face lift and bilateral upper and lower blepharoplasty were performed. Her preauricular wounds recurrently broke down postoperatively, and after surgically excluding stitch granuloma, a diagnosis of pyoderma gangrenosum was made. The wound breakdown resolved with topical steroid treatment. Our case highlights the need to be aware of pyoderma gangrenosum to avoid unnecessary surgery.