Convergence criterion of Newton's method for singular systems with constant rank derivatives

AbstractThe present paper is concerned with the convergence problem of Newton's method to solve singular systems of equations with constant rank derivatives. Under the hypothesis that the derivatives satisfy a type of weak Lipschitz condition, a convergence criterion based on the information around the initial point is established for Newton's method for singular systems of equations with constant rank derivatives. Applications to two special and important cases: the classical Lipschitz condition and the Smale's assumption, are provided; the latter, in particular, extends and improves the corresponding result due to Dedieu and Kim in [J.P. Dedieu, M. Kim, Newton's method for analytic systems of equations with constant rank derivatives, J. Complexity 18 (2002) 187–209]

Geodynamic effects of subducted seamount at the Manila Trench: Insights from numerical modeling

Abstract We used numerical modeling to investigate the geodynamic effects of subducted seamounts at the Manila Trench. A series of numerical modeling experiments were conducted with variable parameters, including the activation volume (Vact) and cohesion (C), which influence lithospheric rheology, the plate convergence velocity, and the age of subducting slab. Modeling results indicate that varying the Vact and C within an appropriate range have limited effects on the geodynamic process of subduction. A lower Vact allows the slab to sink more easily and results in a steeper dip angle. A slab break-off is more likely to occur under subduction at depths of 100–300 km, while the existence of a seamount further promotes the break-off process. The convergence rate is a key parameter affecting the break-off timing and depth. In contrast, under subduction where subducted oceanic plate move faster upper plate, the model results exhibit non-break-off, steady subduction. Slab age is another factor controlling break-off, where break-off time extends with slab age. A subduction without seamount will cause a ~2 Myr delay in break-off timing. We suggest that the low-velocity zone under the Manila Trench at 17o N is the result of a break-off event due to subduction of the Zhenbei-Huangyan Seamount Chain. Further to the north, such as the location at 19o N, the absence of seamount and an older oceanic crust would favor a delay in break-off timing during subduction

Vascular changes of the choroid and their correlations with visual acuity in diabetic retinopathy

ObjectiveTo investigate changes in the choroidal vasculature and their correlations with visual acuity in diabetic retinopathy (DR).MethodsThe cohort was composed of 225 eyes from 225 subjects, including 60 eyes from 60 subjects with healthy control, 55 eyes from 55 subjects without DR, 46 eyes from 46 subjects with nonproliferative diabetic retinopathy (NPDR), 21 eyes from 21 subjects with proliferative diabetic retinopathy (PDR), and 43 eyes from 43 subjects with clinically significant macular edema (CSME). Swept-source optical coherence tomography (SS-OCT) was used to image the eyes with a 12-mm radial line scan protocol. The parameters for 6-mm diameters of region centered on the macular fovea were analyzed. Initially, a custom deep learning algorithm based on a modified residual U-Net architecture was utilized for choroidal boundary segmentation. Subsequently, the SS-OCT image was binarized and the Niblack-based automatic local threshold algorithm was employed to calibrate subfoveal choroidal thickness (SFCT), luminal area (LA), and stromal area (SA) by determining the distance between the two boundaries. Finally, the ratio of LA and total choroidal area (SA + LA) was defined as the choroidal vascularity index (CVI). The choroidal parameters in five groups were compared, and correlations of the choroidal parameters with age, gender, duration of diabetes mellitus (DM), glycated hemoglobin (HbA1c), fasting blood sugar, SFCT and best-corrected visual acuity (BCVA) were analyzed.ResultsThe CVI, SFCT, LA, and SA values of patients with DR were found to be significantly lower compared to both healthy patients and patients without DR (P < 0.05). The SFCT was significantly higher in NPDR group compared to the No DR group (P < 0.001). Additionally, the SFCT was lower in the PDR group compared to the NPDR group (P = 0.014). Furthermore, there was a gradual decrease in CVI with progression of diabetic retinopathy, reaching its lowest value in the PDR group. However, the CVI of the CSME group exhibited a marginally closer proximity to that of the NPDR group. The multivariate regression analysis revealed a positive correlation between CVI and the duration of DM as well as LA (P < 0.05). The results of both univariate and multivariate regression analyses demonstrated a significant positive correlation between CVI and BCVA (P = 0.003).ConclusionChoroidal vascular alterations, especially decreased CVI, occurred in patients with DR. The CVI decreased with duration of DM and was correlated with visual impairment, indicating that the CVI might be a reliable imaging biomarker to monitor the progression of DR

Loss of p53 Attenuates the Contribution of IL-6 Deletion on Suppressed Tumor Progression and Extended Survival in Kras-Driven Murine Lung Cancer

Interleukin-6 (IL-6) is involved in lung cancer tumorigenesis, tumor progression, metastasis, and drug resistance. Previous studies show that blockade of IL-6 signaling can inhibit tumor growth and increase drug sensitivity in mouse models. Clinical trials in non-small cell lung cancer (NSCLC) reveal that IL-6 targeted therapy relieves NSCLC-related anemia and cachexia, although other clinical effects require further study. We crossed IL-6-/- mice with KrasG12D mutant mice, which develop lung tumors after activation of mutant KrasG12D, to investigate whether IL-6 inhibition contributes to tumor progression and survival time in vivo. KrasG12D; IL-6-/- mice exhibited increased tumorigenesis, but slower tumor growth and longer survival, than KrasG12D mice. Further, in order to investigate whether IL-6 deletion contributes to suppression of lung cancer metastasis, we generated KrasG12D; p53flox/flox; IL-6-/- mice, which developed lung cancer with a trend for reduced metastases and longer survival than KrasG12D; p53flox/flox mice. Tumors from KrasG12D; IL-6-/- mice showed increased expression of TNFα and decreased expression of CCL-19, CCL-20 and phosphorylated STAT3 (pSTAT3) than KrasG12D mice; however, these changes were not present between tumors from KrasG12D; p53flox/flox; IL-6-/- and KrasG12D; p53flox/flox mice. Upregulation of pSTAT3 and phosphorylated AKT (pAKT) were observed in KrasG12D tumors with p53 deletion. Taken together, these results indicate that IL-6 deletion accelerates tumorigenesis but delays tumor progression and prolongs survival time in a Kras-driven mouse model of lung cancer. However, these effects can be attenuated by p53 deletion

Drivers of cropland abandonment in mountainous areas: A household decision model on farming scale and a case study of Southwest China

Cropland abandonment has emerged as a prevalent phenomenon in the mountainous areas of China.While there is a general understanding that this new trend is driven by the rising opportunity cost of rural labor, rigorous theoretical and empirical analyses are largely absent. This paper first develops a theoretical model to investigate household decisions on farming scale when off-farm labor market is accessible and there is heterogeneity of farmland productivity and distribution. The model is capable of explaining the hidden reasons of cropland abandonment in sloping and agriculturally less-favored locations. The model also unveils the impacts of heterogeneity of household labor on fallow decisions and the efficiency loss due to an imperfect labor market. The model is empirically tested by applying the Probit and Logit estimators to a unique household and land-plot survey dataset which contains 5258 plots of599 rural households in Chongqing, a provincial level municipality, in Southwest China. The survey shows that more than 30% of the sample plots have been abandoned, mainly since 1992. The econometric results are consistent with our theoretical expectations. This work would help policy-makers and stakeholders to identify areas with a high probability of land abandonment and farming practice which is less sustainable in the mountainous areas