Random Design Analysis of Ridge Regression

This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions. In particular, the analysis provides sharp results on the “out-of-sample” prediction error, as opposed to the “in-sample” (fixed design) error. The analysis also reveals the effect of errors in the estimated covariance structure, as well as the effect of modeling errors, neither of which effects are present in the fixed design setting. The proofs of the main results are based on a simple decomposition lemma combined with concentration inequalities for random vectors and matrices.     

Mechanical analogues of spin Hamiltonians and dynamics

Bloch et al. mapped the precession of the spin-half in a magnetic field of variable magnitude and direction to the rotations of a rigid sphere rolling on a curved surface utilizing SU(2)–SO(3)$\mathit{SU}(2)\text{–}\mathit{SO}(3)$ isomorphism. This formalism is extended to study the behaviour of spin–orbit interactions and the mechanical analogy for Rashba–Dresselhauss spin–orbit interaction in two dimensions is presented by making its spin states isomorphic to the rotations of a rigid sphere rolling on a ring. The change in phase of spin is represented by the angle of rotation of sphere after a complete revolution. In order to develop the mechanical analogy for the spin filter, we find that perfect spin filtration of down spin makes the sphere to rotate at some unique angles and the perfect spin filtration of up spin causes the rotations with certain discrete frequencies.     

Profiling of secondary metabolites in tissues from Rheum palmatum L. using laser microdissection and liquid chromatography mass spectrometry

Evaluating the quality of herbal medicines by morphological features is a convenient, quick, and practical method compared with other methods that mostly depend on modern instruments. Here, laser microdissection and ultra-performance liquid chromatography are combined with mass spectrometry to map the distribution of secondary metabolites in cells or tissues of a herb itself for correlating its bioactive components and morphological features. The root and rhizome of Rheum palmatum L. were taken as research target, which is the Chinese medicine, Radix et Rhizoma Rhei. According to fluorescent microscopic characteristics, 12 herbal cells or tissues of Radix et Rhizoma Rhei were separated by laser microdissection. Thirty-eight compounds were identified or tentatively characterized in the microdissected tissues. (+)-Catechin, 1-O-galloyl-2-O-cinnamoyl-β-d-glucose, and emodin were found to be the major components in most of the tissues. The brown ergastic substances found in rays of normal and anomalous vascular bundles as well as the parenchymatous cells of rhizome pith and the parenchymatous cells of root xylem contained higher than average amounts of these three components and more kinds of secondary metabolites. Overall, results suggest that Radix et Rhizoma Rhei of larger size and with conspicuous “brocaded patterns” and star spots are of higher quality as they tend to have greater contents of bioactive components. The study provides quantitative and specific criteria by which the quality of Radix et Rhizoma Rhei can be judged. This research also established a new, reliable, and practical method for direct profiling and imaging of secondary metabolites in any herbal tissue.

Enhancement of in vitro fungicidal activity of fuberidazole to Botrytis cinerea by cucurbiturils

The host–guest interaction of fuberidazole (FBZ) fungicide with cucurbituril (CB) macromolecules was characterized in pure water using UV–vis spectrophotometric and NMR techniques. The in vitro applications (at pH 5.5 in pure water) of host–guest complexes were conducted against Botrytis cinerea. While addition of CB5 to FBZ had no significant effect in vitro, mixing CB7 or CB8 with FBZ in a 1:2 ratio improved fungal growth inhibition at least threefold, when compared to the corresponding concentration of the unbound fungicide molecules. Empty CB hosts were completely inactive. Furthermore, the inhibitory activity to B. cinerea was relatively maintained down to a concentration of 5:10 μM of the CB7/8@FBZ complexes, relative to any of controls. Complexation by CB7/8 further improved the photostability of the fungicides with photostabilization factors of 7 and 3, respectively. CB7/8 bound the protonated forms of these guests very strongly but their neutral forms were significantly weaker, which reflects a complexation-induced increase of their pK _a values by 3.8 units with CB7 and 1.4 units with CB8. The present investigation constitutes an innovative, nonclassical, approach to enhance fungicides efficacy utilizing macromolecules with a potential application in crop protection technology.     

Entropy Confinement Promotes Hydrogenolysis Activity for Polyethylene Upcycling

Chemical upcycling that catalyzes waste plastics back to high-purity chemicals holds great promise in end-of-life plastics valorization. One of the main challenges in this process is the thermodynamic limitations imposed by the high intrinsic entropy of polymer chains, which makes their adsorption on catalysts unfavorable and the transition state unstable. Here, we overcome this challenge by inducing the catalytic reaction inside mesoporous channels, which possess a strong confined ability to polymer chains, allowing for stabilization of the transition state. This approach involves the synthesis of p-Ru/SBA catalysts, in which Ru nanoparticles are uniformly distributed within the channels of an SBA-15 support, using a precise impregnation method. The unique design of the p-Ru/SBA catalyst has demonstrated significant improvements in catalytic performance for the conversion of polyethylene into high-value liquid fuels, particularly diesel. The catalyst achieved a high solid conversion rate of 1106 g ⋅ g_Ru⁻¹ ⋅ h⁻¹ at 230 °C. Comparatively, this catalytic activity is 4.9 times higher than that of a control catalyst, Ru/SiO₂, and 14.0 times higher than that of a commercial catalyst, Ru/C, at 240 °C. This remarkable catalytic activity opens up immense opportunities for the chemical upcycling of waste plastics.     

Restoring coherence lost to a slow interacting mesoscopic spin bath

For a two-state quantum object interacting with a slow mesoscopic interacting spin bath, we show that a many-body solution of the bath dynamics conditioned on the quantum-object state leads to an efficient control scheme to recover the lost quantum-object coherence through disentanglement. We demonstrate the theory with the realistic problem of one electron spin in a bath of many interacting nuclear spins in a semiconductor quantum dot. The spin language can be easily generalized to a quantum object in contact with a bath of interacting multilevel quantum units with the caveat that the bath is mesoscopic and its dynamics is slow compared with the quantum object.     

Size-Mediated Recurring Spinel Sub-nanodomains in Li- and Mn-Rich Layered Cathode Materials

Li- and Mn-rich layered oxides are among the most promising cathode materials for Li-ion batteries with high theoretical energy density. Its practical application is, however, hampered by the capacity and voltage fade after long cycling. Herein, a finite difference method for near-edge structure (FDMNES) code was combined with in situ X-ray absorption spectroscopy (XAS) and transmission electron microscopy/electron energy loss spectroscopy (TEM/EELS) to investigate the evolution of transition metals (TMs) in fresh and heavily cycled electrodes. Theoretical modeling reveals a recurring partially reversible LiMn₂O₄-like sub-nanodomain formation/dissolution process during each charge/discharge, which accumulates gradually and accounts for the Mn phase transition. From the modeling of spectra and maps of the valence state over large regions of the cathodes, it was found that the phase change is size-dependent. After prolonged cycling, the TMs displayed different levels of inactivity.     

Metallo-macrocycles with labile coordination sites through self assembly: binuclear phenyl bridged bisbipyridine manganese complexes

Self assembly of phenyl bridged bisbipyridines with manganese perchlorate gave structurally different metallo-macrocycles having cis-labile coordination sites which can catalyse olefin epoxidation with peracetic acid in good yield.     

Optical strain gauge vs. traditional strain gauges for concrete elasticity modulus determination

In the field of Civil Engineering, the evaluation of concrete elasticity modulus relies heavily on traditional strain gauges like electric resistance strain gauge, demec mechanical strain and compressometer. These strain gauges work pretty well but the sample surface preparation and the strain gauge adhesion are tedious and time-consuming. On the other hand, convenient non-destructive testing methods like rebound hammer and ultrasonic pulse velocity have the disadvantage of large data scattering and low reliability. In this paper, we aim to develop a handy, reliable and cost-effective method for concrete property evaluation based on an optical technique called automatic digital image correlation (ADIC), which acts as an optical strain gauge. By incorporating an automatic searching approach, the proposed ADIC greatly expands the convergence range of normal digital image correlation (DIC) algorithms and is able to automatically determine concrete strain in real time without human interaction. After the optical strain gauge is set up, the axial concrete strain as well as the stress-strain curve is plotted in real time when the concrete sample under testing is loaded. The concrete elasticity modulus is then determined from the curve. A series of experiments have been conducted to evaluate the performance of the proposed optical strain gauge. Comparisons are also carried out between the proposed optical strain gauge and traditional strain gauges such as electronic strain gauge, compressometer and demec mechanical strain gauge, which further confirm the accuracy, convenience and reliability of the proposed technique.