A Flexibly Conditional Screening Approach via a Nonparametric Quantile Partial Correlation

Considering the influence of conditional variables is crucial to statistical modeling, ignoring this may lead to misleading results. Recently, Ma, Li and Tsai proposed the quantile partial correlation (QPC)-based screening approach that takes into account conditional variables for ultrahigh dimensional data. In this paper, we propose a nonparametric version of quantile partial correlation (NQPC), which is able to describe the influence of conditional variables on other relevant variables more flexibly and precisely. Specifically, the NQPC firstly removes the effect of conditional variables via fitting two nonparametric additive models, which differs from the conventional partial correlation that fits two parametric models, and secondly computes the QPC of the resulting residuals as NQPC. This measure is very useful in the situation where the conditional variables are highly nonlinearly correlated with both the predictors and response. Then, we employ this NQPC as the screening utility to do variable screening. A variable screening procedure based on NPQC (NQPC-SIS) is proposed. Theoretically, we prove that the NQPC-SIS enjoys the sure screening property that, with probability going to one, the selected subset can recruit all the truly important predictors under mild conditions. Finally, extensive simulations and an empirical application are carried out to demonstrate the usefulness of our proposal

A Flexibly Conditional Screening Approach via a Nonparametric Quantile Partial Correlation

Considering the influence of conditional variables is crucial to statistical modeling, ignoring this may lead to misleading results. Recently, Ma, Li and Tsai proposed the quantile partial correlation (QPC)-based screening approach that takes into account conditional variables for ultrahigh dimensional data. In this paper, we propose a nonparametric version of quantile partial correlation (NQPC), which is able to describe the influence of conditional variables on other relevant variables more flexibly and precisely. Specifically, the NQPC firstly removes the effect of conditional variables via fitting two nonparametric additive models, which differs from the conventional partial correlation that fits two parametric models, and secondly computes the QPC of the resulting residuals as NQPC. This measure is very useful in the situation where the conditional variables are highly nonlinearly correlated with both the predictors and response. Then, we employ this NQPC as the screening utility to do variable screening. A variable screening procedure based on NPQC (NQPC-SIS) is proposed. Theoretically, we prove that the NQPC-SIS enjoys the sure screening property that, with probability going to one, the selected subset can recruit all the truly important predictors under mild conditions. Finally, extensive simulations and an empirical application are carried out to demonstrate the usefulness of our proposal

Multidimensional Control of Repeating Unit/Sequence/Topology for One-Step Synthesis of Block Polymers from Monomer Mixtures

Synchronously and thoroughly adjusting the chemical structure difference between two blocks of the diblock copolymer is very useful for designing materials but difficult to achieve via self-switchable alternating copolymerization. Here, we report self-switchable alternating copolymerization from a mixture of two different cyclic anhydrides, epoxides, and oxetanes, where a simple alkali metal carboxylate catalyst switches between ring-opening alternating copolymerization (ROCOP) of cyclic anhydrides/epoxides and ROCOP of cyclic anhydrides/oxetanes, resulting in the formation of a perfect block tetrapolymer. By investigating the reactivity ratio of these comonomers, a reactivity gradient was established, enabling the precise synthesis of block copolymers with synchronous adjustment of each unit's chemical structure/sequence/topology. Consequently, a diblock tetrapolymer with two glass transition temperatures (T-g) can be easily produced by adjusting the difference in chemical structures between the two blocks

Polyether/Polythioether Synthesis via Ring-Opening Polymerization of Epoxides and Episulfides Catalyzed by Alkali Metal Carboxylates

Alkali metal carboxylates were evaluated as simple and green catalysts for the ring-opening polymerization (ROP) of various epoxides (e.g., alkyl-substituted epoxides and glycidyl ethers) and episulfides (alkyl-substituted episulfides and thioglycidyl ethers). The thus-produced functional polyethers (end-functionalized polyethers, block copolyethers, polyether- polyester block copolymers, topologically unique polyethers, and isotactic-enriched polyethers) and polythioethers featured well-defined structures and controlled molecular weights (Mn,SEC = 1.0-32 kg mol-1). The most effective catalyst was identified as cesium pivalate, and the variation of carboxylate moieties and alkali metal cations enabled the tuning of acid/base character-istics and thus allowed one to control polymerization behavior and expand the scope of functional monomers and initiators. Kinetic analysis confirmed the controlled/living nature of the polymerization process, while mechanistic studies revealed that carboxylate moieties did not directly initiate the ring-opening of epoxide monomers via nucleophilic attack but rather activated the alcohol initiators/chain ends via H-bonding and thus rendered the corresponding OH groups sufficiently nucleophilic to attack the alkali metal cation-activated epoxides

Smart Access to Sequentially and Architecturally Controlled Block Polymers via a Simple Catalytic Polymerization System

Self-switchable polymerization is an attractive strategy for precisely controlling the microstructures and monomer sequences of polymers. To date, catalysts for the polymerization are generally limited to metal complex catalysts and some organocatalysts. In this article, we report that simple, inexpensive, and environmentally benign alkali metal carboxylate catalysts smartly switch between the ring-opening alternating copolymerization of epoxides with cyclic anhydrides and the ring-opening polymerization of cyclic esters to create a single synthetic step and thus achieve sequence-controlled multiblock polyesters. This polymerization system shows extremely high effectiveness and versatility for different combinations of epoxides, cyclic anhydrides, cyclic esters, and initiators. As a result, various types of complex block copolymers, such as AB diblocks, BAB triblocks, star copolymers, hyperbranched copolymers, and CAB triblocks, can be simply prepared and postpolymerization modification can be performed. As a proof of concept, polyester-based elastomers and adhesives were successfully synthesized via one-step procedures by reasonably designing the monomer structures of triblock copolymers, showing great potential for industrial applications of polyesters

Synthesis of hyperbranched polyesters via the ring-opening alternating copolymerisation of epoxides with a cyclic anhydride having a carboxyl group

Hyperbranched polyesters (HBPEs) are well-known interesting materials used in many fields. However, the known synthetic approaches for HBPEs lack versatility. Herein, we report a novel synthetic approach for an HBPE via ring-opening alternating copolymerisation (ROAC) using epoxides and trimellitic anhydride (TA) as the latent difunctional and trifunctional monomers, respectively. Caesium pivalate-catalysed ROACs of TA and excess epoxides were performed in the presence of an alcohol initiator at 80 degrees C in bulk. The obtained products, together with their linear counterparts (i.e., poly(phthalic anhydride-alt-epoxide) s), were characterised by NMR, viscometry, and light scattering. The results supported the successful synthesis of hyperbranched poly(TA-alt-epoxide)s. The versatility of the present HBPE synthesis was demonstrated by applying a range of alcohol initiators, such as typical diol and functional alcohols (e.g., poly (ethylene glycol) as a mono-alcohol or diol, and azido-/alkene-functionalised alcohols as another mono-alcohol), leading to HBPE-based block copolymers and functional HBPEs. Various epoxides, such as mono- and disubstituted alkylene oxides, glycidyl ether, and glycidyl amine, were found to be applicable in the present polymerisation system, which successfully produced HBPEs with different properties depending on the resulting backbone structure of the polymer

Varying-Coefficient Semiparametric Model Averaging Prediction

Forecasting and predictive inference are fundamental data analysis tasks. Most studies employ parametricapproaches making strong assumptions about the data generating process. On the other hand, while nonparametric modelsare applied, it is sometimes found in situations involving low signal to noise ratios or large numbers of covariates that theirperformance is unsatisfactory. We propose a new varying-coefficient semiparametric model averaging prediction (VC-SMAP)approach to analyze large data sets with abundant covariates. Performance of the procedure is investigated with numericalexamples. Even though model averaging has been extensively investigated in the literature, very few authors have consideredaveraging a set of semiparametric models. Our proposed model averaging approach provides more flexibility than parametricmethods, while being more stable and easily implemented than fully multivariate nonparametric varying-coefficient models.We supply numerical evidence to justify the effectiveness of our methodology

Safety Verification of Nonlinear Systems with Bayesian Neural Network Controllers

Bayesian neural networks (BNNs) retain NN structures with a probability distribution placed over their weights. With the introduced uncertainties and redundancies, BNNs are proper choices of robust controllers for safety-critical control systems. This paper considers the problem of verifying the safety of nonlinear closed-loop systems with BNN controllers over unbounded-time horizon. In essence, we compute a safe weight set such that as long as the BNN controller is always applied with weights sampled from the safe weight set, the controlled system is guaranteed to be safe. We propose a novel two-phase method for the safe weight set computation. First, we construct a reference safe control set that constraints the control inputs, through polynomial approximation to the BNN controller followed by polynomial-optimization-based barrier certificate generation. Then, the computation of safe weight set is reduced to a range inclusion problem of the BNN on the system domain w.r.t. the safe control set, which can be solved incrementally and the set of safe weights can be extracted. Compared with the existing method based on invariant learning and mixed-integer linear programming, we could compute safe weight sets with larger radii on a series of linear benchmarks. Moreover, experiments on a series of widely used nonlinear control tasks show that our method can synthesize large safe weight sets with probability measure as high as 95% even for a large-scale system of dimension 7