Penalty-based Methods for Simple Bilevel Optimization under H\"{o}lderian Error Bounds

This paper investigates simple bilevel optimization problems where the upper-level objective minimizes a composite convex function over the optimal solutions of a composite convex lower-level problem. Existing methods for such problems either only guarantee asymptotic convergence, have slow sublinear rates, or require strong assumptions. To address these challenges, we develop a novel penalty-based approach that employs the accelerated proximal gradient (APG) method. Under an $\alpha$-H\"{o}lderian error bound condition on the lower-level objective, our algorithm attains an $(\epsilon,l_F^{-\beta}\epsilon^{\beta})$-optimal solution for any $\beta>0$ within $\mathcal{O}\left(\sqrt{\frac{L_{f_1}}{\epsilon }}\right)+\mathcal{O}\left(\sqrt{\frac{l_F^{\max\{\alpha,\beta\}}L_{g_1}}{\epsilon^{\max\{\alpha,\beta\}}}}\right)$ iterations, where $l_F$, $L_{f_1}$ and $L_{g_1}$ denote the Lipschitz constants of the upper-level objective, the gradients of the smooth parts of the upper- and lower-level objectives, respectively. If the smooth part of the upper-level objective is strongly convex, the result improves further. We also establish the complexity results when both upper- and lower-level objectives are general convex nonsmooth functions. Numerical experiments demonstrate the effectiveness of our algorithms

Apoptosis of Endothelial Cells Contributes to Brain Vessel Pruning of Zebrafish During Development

During development, immature blood vessel networks remodel to form a simplified and efficient vasculature to meet the demand for oxygen and nutrients, and this remodeling process is mainly achieved via the pruning of existing vessels. It has already known that the migration of vascular endothelial cells (ECs) is one of the mechanisms underlying vessel pruning. However, the role of EC apoptosis in vessel pruning remains under debate, especially in the brain. Here, we reported that EC apoptosis makes a significant contribution to vessel pruning in the brain of larval zebrafish. Using in vivo long-term time-lapse confocal imaging of the brain vasculature in zebrafish larvae, we found that EC apoptosis was always accompanied with brain vessel pruning and about 15% of vessel pruning events were resulted from EC apoptosis. In comparison with brain vessels undergoing EC migration-associated pruning, EC apoptosis-accompanied pruned vessels were longer and showed higher probability that the nuclei of neighboring vessels’ ECs occupied their both ends. Furthermore, we found that microglia were responsible for the clearance of apoptotic ECs accompanying vessel pruning, though microglia themselves were dispensable for the occurrence of vessel pruning. Thus, our study demonstrates that EC apoptosis contributes to vessel pruning in the brain during development in a microglial cell-independent manner

Possible canonical distributions for finite systems with nonadditive energy

It is shown that a small system in thermodynamic equilibrium with a finite thermostat can have a q-exponential probability distribution which closely depends on the energy nonextensivity and the particle number of the thermostat. The distribution function will reduce to the exponential one at the thermodynamic limit. However, the nonextensivity of the system should not be neglected.Comment: 13 pages, 4 figure

Effect of Non-sodium Salt Substitution on the Properties and Flavor of Coix Starch-Myofibrillar Protein Composite Gel

Objective: To investigate the effect of calcium, magnesium and potassium salts on the properties of coix seed starch-myofibrillar protein (CSS-MP) composite gel with low sodium content. Methods: Based on the results of previous research, the effects of partial substitution of NaCl by CaCl2, MgCl2 or KCl on the gel strength, water holding capacity (WHC), rheological properties, surface hydrophobicity, sulfhydryl group content, gel microstructure and sensory evaluation of CSS-MP composite gel were investigated. Results: The texture and rheological properties of the CaCl2 substitution group were better than those of the control group (3% NaCl), and the WHC and whiteness of the KCl substitution group were not significantly different from those of the control group, but the gel strength was decreased by MgCl2 or KCl substitution. The total sulfhydryl content of the CaCl2 and MgCl2 replacement groups was significantly lower than that of the control group, and the surface hydrophobicity of the CaCl2 replacement group was significantly higher than that of the other three groups. The addition of MgCl2 promoted the formation of hydrogen bonds, enhanced the hydrophobic interaction, while CaCl2 substitution had the opposite effect. In terms of sensory properties, the substitution of 1.0% CaCl2 and 0.5% MgCl2 could attain a saltiness perception similar to 3% NaCl. However, the comprehensive sensory score showed that the substitution of the three chlorine salts caused no significant difference in sensory properties of CSS-MP composite gel. Conclusion: Calcium, magnesium and potassium salts can improve the properties of CSS-MP composite gel in different degrees. The results of this study lay a theoretical foundation for the development of low-sodium composite surimi gel products

First-principles study of electronic structures and optical properties of Cu, Ag, and Au-doped anatase TiO2

We perform first-principles calculations to investigate the band structure, density of states, optical absorption, and the imaginary part of dielectric function of Cu, Ag, and Au-doped anatase TiO2 in 72 atoms systems. The electronic structure results show that the Cu incorporation can lead to the enhancement of d states near the uppermost of valence band, while the Ag and Au doping cause some new electronic states in band gap of TiO2. Meanwhile, it is found that the visible optical absorptions of Cu, Ag, and Au-doped TiO2, are observed by analyzing the results of optical properties,.which locate in the region of 400-1000 nm. The absorption band edges of Cu, Ag, and Au-doped TiO2 shift to the long wavelength region compared with the pure TiO2. Furthermore, according to the calculated results, we propose the optical transition mechanisms of Cu, Ag, and Au-doped TiO2, respectively. Our results show that the visible light response of TiO2 can be modulated by substitutional doping of Cu, Ag, and Au.Comment: 12 pages, 6 figures, 43 reference