We perform a series of high-resolution 2D hydrodynamical simulations of equal-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) accretion disks to study whether these binaries can be driven to merger by the surrounding gas. We find that the gravitational softening adopted for the BBH has a profound impact on this result. When the softening is less than 10% of the binary separation, we show that, in agreement with recent simulations of isolated equal-mass binaries, prograde BBHs expand in time rather than contract. Eventually, however, the binary separation becomes large enough that the tidal force of the central AGN disrupts them. Only when the softening is relatively large do we find that prograde BBHs harden. We determine through detailed analysis of the binary torque, that this dichotomy is due to a loss of spiral structure in the circum-single disks orbiting each black hole when the softening is a significant fraction of the binary separation. Properly resolving these spirals—both with high resolution and small softening—results in a significant source of binary angular momentum. Only for retrograde BBHs do we find consistent hardening, regardless of softening, as these BBHs lack the important spiral structure in their circum-single disks. This suggests that the gas-driven inspiral of retrograde binaries can produce a population of compact BBHs in the gravitational-wave-emitting regime in AGN disks, which may contribute a large fraction to the observed BBH mergers.

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Electronic wave-functions in the adiabatic representation acquire nontrivial geometric phases (GPs) when corresponding potential energy surfaces undergo conical intersection (CI). These GPs have profound effects on the nuclear quantum dynamics and cannot be eliminated in the adiabatic representation without changing the physics of the system. To define dynamical effects arising from the GP presence the nuclear quantum dynamics of the CI containing system is compared with that of the system with artificially removed GP. We explore a new construction of the system with removed GP via a modification of the diabatic representation for the original CI containing system. Using an absolute value function of diabatic couplings we remove the GP while preserving adiabatic potential energy surfaces and CI. We assess GP effects in dynamics of a two-dimensional linear vibronic coupling model both for ground and excited state dynamics. Results are compared with those obtained with a conventional removal of the GP by ignoring double-valued boundary conditions of the real electronic wave-functions. Interestingly, GP effects appear similar in two approaches only for the low energy dynamics. In contrast with the conventional approach, a new approach does not have substantial GP effects in the ultra-fast excited state dynamics.

ObjectivesThe accurate assessment of lymph node metastases (LNMs) and the preoperative nodal (N) stage are critical for the precise treatment of patients with gastric cancer (GC). The diagnostic performance, however, of current imaging procedures used for this assessment is sub-optimal. Our aim was to investigate the value of preoperative 18F-FDG PET/CT radiomic features to predict LNMs and the N stage.MethodsWe retrospectively collected clinical and 18F-FDG PET/CT imaging data of 185 patients with GC who underwent total or partial radical gastrectomy. Patients were allocated to training and validation sets using the stratified method at a fixed ratio (8:2). There were 2,100 radiomic features extracted from the 18F-FDG PET/CT scans. After selecting radiomic features by the random forest, relevancy-based, and sequential forward selection methods, the BalancedBagging ensemble classifier was established for the preoperative prediction of LNMs, and the OneVsRest classifier for the N stage. The performance of the models was primarily evaluated by the AUC and accuracy, and validated by the independent validation methods. Analysis of the feature importance and the correlation were also conducted. We also compared the predictive performance of our radiomic models to that with the contrast-enhanced CT (CECT) and 18F-FDG PET/CT.ResultsThere were 185 patients—127 men, 58 women, with the median age of 62, and an age range of 22–86 years. One CT feature and one PET feature were selected to predict LNMs and achieved the best performance (AUC: 82.2%, accuracy: 85.2%). This radiomic model also detected some LNMs that were missed in CECT (19.6%) and 18F-FDG PET/CT (35.7%). For predicting the N stage, four CT features and one PET feature were selected (AUC: 73.7%, accuracy: 62.3%). Of note, a proportion of patients in the validation set whose LNMs were incorrectly staged by CECT (57.4%) and 18F-FDG PET/CT (55%) were diagnosed correctly by our radiomic model.ConclusionWe developed and validated two machine learning models based on the preoperative 18F-FDG PET/CT images that have a predictive value for LNMs and the N stage in GC. These predictive models show a promise to offer a potentially useful adjunct to current staging approaches for patients with GC.