Remotely Self-Healable, Shapeable and pH-Sensitive Dual Cross-Linked Polysaccharide Hydrogels with Fast Response to Magnetic Field

The development of actuators with remote control is important for the construction of devices for soft robotics. The present paper describes a responsive hydrogel of nontoxic, biocompatible, and biodegradable polymer carboxymethyl hydroxypropyl guar with dynamic covalent cross-links and embedded cobalt ferrite nanoparticles. The nanoparticles significantly enhance the mechanical properties of the gel, acting as additional multifunctional non-covalent linkages between the polymer chains. High magnetization of the cobalt ferrite nanoparticles provides to the gel a strong responsiveness to the magnetic field, even at rather small content of nanoparticles. It is demonstrated that labile cross-links in the polymer matrix impart to the hydrogel the ability of self-healing and reshaping as well as a fast response to the magnetic field. In addition, the gel shows pronounced pH sensitivity due to pH-cleavable cross-links. The possibility to use the multiresponsive gel as a magnetic-field-triggered actuator is demonstrated

Recent Theoretical Advances in Non-Convex Optimization

Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical results on global performance guarantees of optimization algorithms for non-convex optimization. We start with classical arguments showing that general non-convex problems could not be solved efficiently in a reasonable time. Then we give a list of problems that can be solved efficiently to find the global minimizer by exploiting the structure of the problem as much as it is possible. Another way to deal with non-convexity is to relax the goal from finding the global minimum to finding a stationary point or a local minimum. For this setting, we first present known results for the convergence rates of deterministic first-order methods, which are then followed by a general theoretical analysis of optimal stochastic and randomized gradient schemes, and an overview of the stochastic first-order methods. After that, we discuss quite general classes of non-convex problems, such as minimization of α-weakly-quasi-convex functions and functions that satisfy Polyak--Lojasiewicz condition, which still allow obtaining theoretical convergence guarantees of first-order methods. Then we consider higher-order and zeroth-order/derivative-free methods and their convergence rates for non-convex optimization problems

Prenyl sulfates as alkylating reagents for mercapto amino acids

A new methodology for prenylation of thiol compounds has been developed. The approach is based on the use of prenyl sulfates as new reagents for S-prenylation of benzenethiol and cysteamine in aqueous systems. The C10-prenols geraniol and nerol that differ in the configuration (E or Z, correspondingly) of the α-isoprene unit were efficiently O-sulfated in the presence of a pyridine-SO3' complex. The obtained geranyl and neryl sulfates were tested as alkylating agents. These compounds were chosen to reveal the influence of the α-isoprene unit configuration on their alkylation (prenylation) ability. S-Geranyl cysteine was prepared to demonstrate the applicability of this method for prenylation of peptides containing mercapto amino acids