A partially isochronous splitting algorithm for three-block separable convex minimization problems

During the last decade, the state-of-the-art alternating direction method of multipliers (ADMM) has successfully been used to solve many two-block separable convex minimization problems arising from several applied areas such as signal/image processing and statistical and machine learning. It however remains an interesting problem of how to implement ADMM to three-block separable convex minimization problems as required by the situation where many objective functions in the above-mentioned areas are actually more conveniently decomposed to the sum of three convex functions, due also to the observation that the straightforward extension of ADMM from the two-block case to the three-block case is apparently not convergent. In this paper, we shall introduce a new algorithm that is called a partially isochronous splitting algorithm (PISA) in order to implement ADMM for the three-block separable model. The main idea of our algorithm is to incorporate only one proximal term into the last subproblem of the extended ADMM so that the resulting algorithm maximally inherits the promising properties of ADMM. A remarkable superiority over the extended ADMM is that we can simultaneously solve two of the subproblems, thereby taking advantages of the separable structure and parallel architectures. Theoretically, we will establish the global convergence of our algorithm under standard conditions, and also the O(1/t) rate of convergence in both ergodic and nonergodic senses, where t is the iteration counter. The computational competitiveness of our algorithm is shown by numerical experiments on an application to the well-tested robust principal component analysis model.     

Approximations to fixed points of contraction semigroups in hilbert spaces

Sequences (or curves) are constructed to approximate common fixed points of a pair of nonex-pansive mappings (or contraction semigroups) in Hilbert spaces. The obtained results extend the previously known results from a single mapping to a family of mappings.     

Electrical Current in Sinai Billiards Under General Small Forces

The Lorentz gas of $\mathbb{Z}^{2}$ -periodic scatterers (or the so called Sinai billiards) can be used to model motion of electrons on a metal. We investigate the linear response for the system under various external forces (during both the flight and the collision). We give some characterizations under which the forced system is time-reversible, and derive an estimate of the electrical current generated by the forced system. Moreover, applying Pesin entropy formula and Young dimension formula, we get several characterizations of the non-equilibrium steady state of the forced system.     

Design and Use of de novo Cascades for the Biosynthesis of New Benzylisoquinoline Alkaloids

The benzylisoquinoline alkaloids (BIAs) are an important group of secondary metabolites from higher plants and have been reported to show significant biological activities. The production of BIAs through synthetic biology approaches provides a higher‐yielding strategy than traditional synthetic methods or isolation from plant material. However, the reconstruction of BIA pathways in microorganisms by combining heterologous enzymes can also give access to BIAs through cascade reactions. Most importantly, non‐natural BIAs can be generated through such artificial pathways. In the current study, we describe the use of tyrosinases and decarboxylases and combine these with a transaminase enzyme and norcoclaurine synthase for the efficient synthesis of several BIAs, including six non‐natural alkaloids, in cascades from l ‐tyrosine and analogues.     

Strain‐Induced Isomerization in One‐Dimensional Metal–Organic Chains

The ability to use mechanical strain to steer chemical reactions creates completely new opportunities for solution‐ and solid‐phase synthesis of functional molecules and materials. However, this strategy is not readily applied in the bottom‐up on‐surface synthesis of well‐defined nanostructures. We report an internal strain‐induced skeletal rearrangement of one‐dimensional (1D) metal–organic chains (MOCs) via a concurrent atom shift and bond cleavage on Cu(111) at room temperature. The process involves Cu‐catalyzed debromination of organic monomers to generate 1,5‐dimethylnaphthalene diradicals that coordinate to Cu adatoms, forming MOCs with both homochiral and heterochiral naphthalene backbone arrangements. Bond‐resolved non‐contact atomic force microscopy imaging combined with density functional theory calculations showed that the relief of substrate‐induced internal strain drives the skeletal rearrangement of MOCs via 1,3‐H shifts and shift of Cu adatoms that enable migration of the monomer backbone toward an energetically favorable registry with the Cu(111) substrate. Our findings on this strain‐induced structural rearrangement in 1D systems will enrich the toolbox for on‐surface synthesis of novel functional materials and quantum nanostructures.     

A Photolabile Semiconducting Polymer Nanotransducer for Near‐Infrared Regulation of CRISPR/Cas9 Gene Editing

Noninvasive regulation of CRISPR/Cas9 gene editing is conducive to understanding of gene function and development of gene therapy; however, it remains challenging. Herein, a photolabile semiconducting polymer nanotransducer (pSPN) is synthesized to act as the gene vector to deliver CRISPR/Cas9 plasmids into cells and also as the photoregulator to remotely activate gene editing. pSPN comprises a ¹O₂‐generating backbone grafted with polyethylenimine brushes through ¹O₂‐cleavable linkers. NIR photoirradiation spontaneously triggers the cleavage of gene vectors from pSPN, resulting in the release of CRISPR/Cas9 plasmids and subsequently initiating gene editing. This system affords 15‐ and 1.8‐fold enhancement in repaired gene expression relative to the nonirradiated controls in living cells and mice, respectively. As this approach does not require any specific modifications on biomolecular components, pSPN represents the first generic nanotransducer for in vivo regulation of CRISPR/Cas9 gene editing.     

5 nm Ordered Structures Self-Assembled by C2-Symmetric Hybrids with Polyhedral Oligomeric Silsesquioxane and Hexa-peri-Hexabenzocoronene.

Hybrids consisting of polyhedral oligomeric silsesquioxane (POSS) and hexa-peri-hexabenzocoronene (HBC) with a dumbbell topology and C₂ symmetry were designed and synthesized. They self-assemble into 5 nm ordered structures. In particular, the increased steric effect with increasing POSS units stabilizes a square columnar phase (Col_squ) which is important in nanotemplating. These hybrids containing discotic liquid crystal HBC and POSS units have an excellent etching contrast and present an approach to obtain 5 nm nanopatterns.     

Surface flatness of optical thin films evaluated by gray level co-occurrence matrix and entropy

The surface characteristics of titanium oxide films evaluated by gray level co-occurrence matrices (GLCMs) and entropy are demonstrated experimentally. A PC-based measurement system was set up to detect the interference fringe of optical coating surface as captured by a Fizeau interferometer. Titanium oxide films were prepared by an electron-beam gun evaporation method. The proposed measuring system was used to evaluate the surface flatness of titanium oxide films coated on glass substrates. The variation of entropy in titanium oxide films before and after film deposition was found to be related to the root-mean-square (rms) surface roughness. Surface characteristics of thin films were fast measured by our proposed method and the test results were verified by atomic force microscopy (AFM) and scanning electrical microscopy (SEM).     

Theoretical studies of the concentration dependences of d–d transition band,g factors,and local distortion for V4+ in Li2O–PbO–B2O3–P2O5 glasses

In this work, the g factors, d–d transition band, local distortion, and their concentration dependences for impurity V⁴⁺ in 20Li₂O–20PbO–45B₂O₃–(15 − x)P₂O₅:V₂O₅ (0 ≤ x ≤ 2.5 mol%) glasses are theoretically investigated by using perturbation formulas of g factors for a tetragonally compressed octahedral 3d¹ cluster. In the light of the cubic polynomial concentration functions for cubic field parameter D_q, covalency factor N, and relative tetragonal compression ratio ρ, the calculated concentration dependences of d–d transition band and g factors for V⁴⁺ show good agreement with the experimental data. With increasing x, N (≈0.7682–0.8165) displays the monotonously increasing trend, whereas ρ (≈6.5–4.2%) and D_q (≈1504.9–1481.1 cm⁻¹) exhibit the decreasing tendencies. The above concentration dependences can be ascribed to the modifications of the V⁴⁺–O²⁻ bonding and orbital admixtures around the impurity V⁴⁺ due to the effects of V₂O₅ doping on the stability of the glass network, the strength of local crystal fields, and the electron cloud distribution.