Sparse Variational Analysis of Linear Mixed Models for Large Data Sets

It is increasingly common to be faced with longitudinal or multi-level data sets that have large numbers of predictors and/or a large sample size. Current methods of fitting and inference for mixed effects models tend to perform poorly in such settings. When there are many variables, it is appealing to allow uncertainty in subset selection and to obtain a sparse characterization of the data. Bayesian methods are available to address these goals using Markov chain Monte Carlo (MCMC), but MCMC is very computationally expensive and can be infeasible in large p and/or large n problems. As a fast approximate Bayes solution, we recommend a novel approximation to the posterior relying on variational methods. Variational methods are used to approximate the posterior of the parameters in a decomposition of the variance components, with priors chosen to obtain a sparse solution that allows selection of random effects. The method is evaluated through a simulation study, and applied to an epidemiological application.     

Noncommutative graded domains with quadratic growth

Letk be an algebraically closed field, and letR be a finitely generated, connected gradedk-algebra, which is a domain of Gelfand-Kirillov dimension two. Write the graded quotient ringQ(R) ofR asD[z,z^–1; ], for some automorphism of the division ringD. We prove thatD is a finitely generated field extension ofk of transcendence degree one. Moreover, we describeR in terms of geometric data. IfR is generated in degree one then up to a finite dimensional vector space,R is isomorphic to the twisted homogeneous coordinate ring of an invertible sheaf over a projective curveY. This implies, in particular, thatR is Noetherian, thatR is primitive when ||= and thatR is a finite module over its centre when ||<. IfR is not generated in degree one, thenR will still be Noetherian and primitive if has infinite order, butR need not be Noetherian when has finite order.Dedicated to the memory of Shimshon AmitsurOblatum 5-XI-1994 & 28-III-1995This research was supported in part by NSF grants     

Stereoelectronic effects on molecular geometries and state-energy splittings of ligated monocopper dioxygen complexes

The relative energies of side-on versus end-on binding of molecular oxygen to a supported Cu(I) species, and the singlet versus triplet nature of the ground electronic state, are sensitive to the nature of the supporting ligands and, in particular, depend upon their geometric arrangement relative to the O2 binding site. Highly correlated ab initio and density functional theory electronic structure calculations demonstrate that optimal overlap (and oxidative charge transfer) occurs for the side-on geometry, and this is promoted by ligands that raise the energy, thereby enhancing resonance, of the filled Cu dxz orbital that hybridizes with the in-plane pi* orbital of O2. Conversely, ligands that raise the energy of the filled Cu dz2 orbital foster a preference for end-on binding as this is the only mode that permits good overlap with the in-plane O2 pi*. Because the overlap of Cu dz2 with O2 pi* is reduced as compared to the overlap of Cu dxz with the same O2 orbital, the resonance is also reduced, leading to generally more stable triplet states relative to singlets in the end-on geometry as compared to the side-on geometry, where singlet ground states become more easily accessible once ligands are stronger donors. Biradical Cu(II)-O2 superoxide character in the electronic structure of the supported complexes leads to significant challenges for accurate quantum chemical calculations that are best addressed by exploiting the spin-purified M06L local density functional, single-reference completely renormalized coupled-cluster theory, or multireference second-order perturbation theory, all of which provide predictions that are qualitatively and quantitatively consistent with one another.     

Initiated Chemical Vapor Deposition and Light‐Responsive Cross‐Linking of Poly(vinyl cinnamate) Thin Films

The first vapor‐phase deposition of poly(vinyl cinnamate) (PVCin) is reported. Initiated chemical vapor deposition (iCVD) is used to synthesize PVCin thin films with an average thickness of 100 nm. Free radical polymerization and cyclization reactions compete during the deposition process, with approximately 45% of the repeat units undergoing cyclization. Exposure to UV light (λ = 254 nm) induces dimerization (cross‐linking) of the PVCin, which is quantified using spectroscopic techniques. Approximately 90% of the free cinnamate moieties are dimerized at a UV dose of 300 mJ cm⁻². PVCin is also incorporated into a copolymer with N‐isopropylacrylamide, which exhibits a characteristic change in hydrophilicity with temperature. The copolymer is selectively cross‐linked through a mask, and reversible swelling of patterns with 30 μm resolution is demonstrated by submerging the film in water.

     

A reformulation for the stochastic lot sizing problem with service-level constraints

We study the stochastic lot-sizing problem with service level constraints and propose an efficient mixed integer reformulation thereof. We use the formulation of the problem present in the literature as a benchmark, and prove that the reformulation has a stronger linear relaxation. Also, we numerically illustrate that it yields a superior computational performance. The results of our numerical study reveals that the reformulation can optimally solve problem instances with planning horizons over 200 periods in less than a minute.     

The Comparison of Electrochemical Assay and Agarose Gel Electrophoresis for the Determination of DNA Damage Induced by Kainic Acid

A possible DNA damage after interaction of kainic acid (KA) with calf thymus double stranded DNA and genomic DNA was herein determined in in vitro and in vivo conditions using; electrochemical assay and agarose gel electrophoresis. The changes in guanine signal were detected as an indicator of DNA damage in genomic DNA samples isolated from 1 or 10 mg/kg KA‐treated animals. The decreased levels of guanine signal were found as 29% and 33% by 1 and 10 mg/kg KA treatment when compared to controls, respectively. The results of gel electrophoresis confirmed DNA damage obtained in identical samples by electrochemical method.     

Model selection via adaptive shrinkage with t priors

We discuss a model selection procedure, the adaptive ridge selector, derived from a hierarchical Bayes argument, which results in a simple and efficient fitting algorithm. The hierarchical model utilized resembles an un-replicated variance components model and leads to weighting of the covariates. We discuss the intuition behind this type estimator and investigate its behavior as a regularized least squares procedure. While related alternatives were recently exploited to simultaneously fit and select variablses/features in regression models (Tipping in J Mach Learn Res 1:211–244, 2001; Figueiredo in IEEE Trans Pattern Anal Mach Intell 25:1150–1159, 2003), the extension presented here shows considerable improvement in model selection accuracy in several important cases. We also compare this estimator’s model selection performance to those offered by the lasso and adaptive lasso solution paths. Under randomized experimentation, we show that a fixed choice of tuning parameter leads to results in terms of model selection accuracy which are superior to the entire solution paths of lasso and adaptive lasso when the underlying model is a sparse one. We provide a robust version of the algorithm which is suitable in cases where outliers may exist.