This paper presents an analytical study of the two-body tangent orbit technique by providing solution-existence conditions. The flight-direction angle is used to describe and solve this problem. Closed-form solutions are obtained for three classic problems: specified arrival flight-direction angle, specified departure flight-direction angle, and cotangent transfers. Not all of the problems admit solutions; thus, closed-form conditions for solution existence are provided by imposing a positive semilatus rectum constraint and a negative transfer-orbit energy (elliptic orbit transfer) constraint. The final solution-existence condition is then provided in terms of the true anomaly range for initial or final orbit. The singularity problem of 180 deg orbit transfer is also analyzed. Several examples are provided to verify the proposed analytical methods.
Natural language data exhibit tree-like hierarchical structures such as the hypernymhyponym relations in WordNet. FastText, as the state-of-the-art text classifier based on shallow neural network in Euclidean space, may not model such hierarchies precisely with limited representation capacity. Considering that hyperbolic space is naturally suitable for modeling tree-like hierarchical data, we propose a new model named HyperText for efficient text classification by endowing FastText with hyperbolic geometry. Empirically, we show that HyperText outperforms FastText on a range of text classification tasks with much reduced parameters.
Background
This study aimed to identify potential predictive factors for the survival of advanced non small-cell lung cancer (NSCLC) patients undergoing first-line platinum-based chemotherapy.
Methods
A total of 270 advanced NSCLC patients who underwent first-line platinum-based chemotherapy from June, 2011 to June, 2015 were enrolled. A receiver operating characteristic (ROC) curve analysis was used to evaluate the predictive value of the albumin-to-fibrinogen ratio (AFR) for overall survival (OS). The predictive factors for survival were evaluated by univariate and multivariate analyses via the Cox proportional hazards regression model. The OS and progression free survival (PFS) results were determined via the Kaplan–Meier method using the log-rank analysis.
Results
Based on the results of the ROC curve analysis, 8.02 was accepted as the cut-off AFR value for OS. The metastasis stage (M0 vs M1a/b, HR: 1.73, 95% CI: 1.15–2.59,
P
= 0.020) and AFR (≤8.02 vs > 8.02, HR: 1.80, 95% CI: 1.09–2.78,
P
= 0.025) were two independent risk factors for PFS by multivariate Cox regression analysis. The AFR (≤8.02 vs > 8.02, HR: 1.79, 95% CI: 1.11–2.59,
P
= 0.029) was a significant predictive factor for OS in advanced NSCLC patients. The PFS (
P
= 0.008) and OS (
P
= 0.003) in the high AFR group were significantly improved compared with those in the low AFR group via the Kaplan–Meier method using the log-rank analysis.
Conclusions
The AFR could be a potential effective predictive factor for the survival in advanced NSCLC patients undergoing first-line platinum-based chemotherapy.
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