Stochastic Primal-Dual Coordinate Method for Nonlinear Convex Cone Programs

Block coordinate descent (BCD) methods and their variants have been widely used in coping with large-scale nonconstrained optimization problems in many fields such as imaging processing, machine learning, compress sensing and so on. For problem with coupling constraints, Nonlinear convex cone programs (NCCP) are important problems with many practical applications, but these problems are hard to solve by using existing block coordinate type methods. This paper introduces a stochastic primal-dual coordinate (SPDC) method for solving large-scale NCCP. In this method, we randomly choose a block of variables based on the uniform distribution. The linearization and Bregman-like function (core function) to that randomly selected block allow us to get simple parallel primal-dual decomposition for NCCP. The sequence generated by our algorithm is proved almost surely converge to an optimal solution of primal problem. Two types of convergence rate with different probability (almost surely and expected) are also obtained. The probability complexity bound is also derived in this paper

An Augmented Lagrangian Approach to Conically Constrained Non-monotone Variational Inequality Problems

In this paper we consider a non-monotone (mixed) variational inequality model with (nonlinear) convex conic constraints. Through developing an equivalent Lagrangian function-like primal-dual saddle-point system for the VI model in question, we introduce an augmented Lagrangian primal-dual method, to be called ALAVI in the current paper, for solving a general constrained VI model. Under an assumption, to be called the primal-dual variational coherence condition in the paper, we prove the convergence of ALAVI. Next, we show that many existing generalized monotonicity properties are sufficient -- though by no means necessary -- to imply the above mentioned coherence condition, thus are sufficient to ensure convergence of ALAVI. Under that assumption, we further show that ALAVI has in fact an $o(1/\sqrt{k})$ global rate of convergence where $k$ is the iteration count. By introducing a new gap function, this rate further improves to be $O(1/k)$ if the mapping is monotone. Finally, we show that under a metric subregularity condition, even if the VI model may be non-monotone the local convergence rate of ALAVI improves to be linear. Numerical experiments on some randomly generated highly nonlinear and non-monotone VI problems show practical efficacy of the newly proposed method

Ototoxicity of polystyrene nanoplastics in mice, HEI-OC1 cells and zebrafish

Polystyrene nanoplastics are a novel class of pollutants. They are easily absorbed by living organisms, and their potential toxicity has raised concerns. However, the impact of polystyrene nanoplastics on auditory organs remains unknown. Here, our results showed that polystyrene nanoplastics entered the cochlea of mice, HEI-OC1 cells, and lateral line hair cells of zebrafish, causing cellular injury and increasing apoptosis. Additionally, we found that exposure to polystyrene nanoplastics resulted in a significant elevation in the auditory brainstem response thresholds, a loss of auditory sensory hair cells, stereocilia degeneration and a decrease in expression of Claudin-5 and Occludin proteins at the blood-lymphatic barrier in mice. We also observed a significant decrease in the acoustic alarm response of zebrafish after exposure to polystyrene nanoplastics. Mechanistic analysis revealed that polystyrene nanoplastics induced up-regulation of the Nrf2/HO-1 pathway, increased levels of malondialdehyde, and decreased superoxide dismutase and catalase levels in cochlea and HEI-OC1 cells. Furthermore, we observed that the expression of ferroptosis-related indicators GPX4 and SLC7A11 decreased as well as increased expression of ACLS4 in cochlea and HEI-OC1 cells. This study also revealed that polystyrene nanoplastics exposure led to increased expression of the inflammatory factors TNF-α, IL-1β and COX2 in cochlea and HEI-OC1 cells. Further research found that the cell apoptosis, ferroptosis and inflammatory reactions induced by polystyrene nanoplastics in HEI-OC1 cells was reversed through the pretreatment with N-acetylcysteine, a reactive oxygen species inhibitor. Overall, our study first discovered and systematically revealed the ototoxicity of polystyrene nanoplastics and its underlying mechanism

In Situ Pah Sensors

The detection of organic pollutants and their concentrations in soil, water, and air is essential for adequate environmental monitoring and analysis. There are recent needs for developing near-real-time environmental sensing and monitoring platforms for water quality with innovative algorithms to aid in natural/anthropogenic hazard responses (e.g., the Deepwater Horizon oil spill incident in 2010 and West Virginia chemical spill in 2014) and ecosystem restoration assessment. Among the many hydrophobic organic compounds, polycyclic aromatic hydrocarbons (PAHs) have been of great concern because of their carcinogenic and mutagenic properties—particularly four- to six-ring compounds [1, 2]. PAHs are neutral, nonpolar, and hydrophobic organic molecules comprised of two or more fused benzene rings. They are essentially insoluble and have very low vapor pressures; therefore, their measurement in aquatic environments is challenging, and the procedures for in situ sensors for PAHs have not yet been thoroughly explored