Best linear unbiased prediction for linear combinations in general mixed linear models

The general mixed linear model can be written as . In this paper, we mainly deal with two problems. Firstly, the problem of predicting a general linear combination of fixed effects and realized values of random effects in a general mixed linear model is considered and an explicit representation of the best linear unbiased predictor (BLUP) is derived. In addition, we apply the resulting conclusion to several special models and offer an alternative to characterization of BLUP. Secondly, we recall the notion of linear sufficiency and consider it as regards the BLUP problem and characterize it in several different ways. Further, we study the concepts of linear sufficiency, linear minimal sufficiency and linear completeness, and give relations among them. Finally, four concluding remarks are given.     

Weakly dependent chains with infinite memory

We prove the existence of a weakly dependent strictly stationary solution of the equation _Xt=F(_Xt−1,_Xt−2,_Xt−3,…;_ξt)$X_t=F(X_{t-1},X_{t-2},X_{t-3},\dots ;{\xi }_t)$ called a chain with infinite memory. Here the innovations  _ξt${\xi }_t$ constitute an independent and identically distributed sequence of random variables. The function F$F$ takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments, the rate of decay of the Lipschitz coefficients of the function F$F$ and the weak dependence properties. From these weak dependence properties, we derive strong laws of large number, a central limit theorem and a strong invariance principle.     

Moufang sets of mixed type F4

Moufang sets were introduced by Jacques Tits in order to understand isotropic linear algebraic groups of relative rank one, but the notion is more general. We describe a new class of Moufang sets, arising from so‐called mixed groups of type ${\mathsf{F}}_4$ in characteristic 2, obtained as the fixed point set under a suitable involution.     

Parallel and bootstrapped stochastic approximation

Parallelization of stochastic approximation procedures can reduce computation and total observation time of a system. Concerning the number of all observations used by the pure sequential and the suggested parallel method a weak invariance principle implies the asymptotic equivalence of both methods. A loglog invariance principle and a rate of a.s. convergence result describe the pathwise properties. Due to the parallel design asymptotic confidence regions can readily be constructed either by computing the bootstrap distribution or the Gaussian limit distribution determined by the empirical covariance     

Influence of stereoelectronic effects on the 1JC─F spin–spin coupling constant in fluorinated heterocyclic compounds

The Perlin effect and its analog for fluorinated compounds (the fluorine Perlin-like effect) manifest on one-bond C─H (C─F for the fluorine Perlin-like effect) spin–spin coupling constants (SSCCs) in six-membered rings. These effects can be useful to probe the stereochemistry (axial or equatorial) of the C─H and C─F bonds, respectively. The origin of these effects has been debatable in the literature as being due to hyperconjugative interactions, dipolar effects, and induced current density. Accordingly, a variety of model compounds has been used to probe such effects since the cyclohexanone carbonyl group and the endocyclic heteroatom lone pairs play different roles on the above-mentioned effects. Thus, the ¹J_C─F SSCC in fluorinated lactams and lactones were theoretically studied to gain further insight on the nature of the fluorine Perlin-like effect. In addition, because the intramolecular α-effect has recently gained attention for its importance in the reactivity and stereoelectronic interactions in peroxide compounds, some fluorinated 1,2-dioxanes and 1,2-dithianes were studied to evaluate the role of the α-effect on the behavior of ¹J_C─F SSCCs. Differently from fluorinated ketones and ethers, the fluorine Perlin-like effect in the amides and esters cannot be explained by hyperconjugative or dipolar interactions alone, because the resonance in these groups affect the ¹J_C─F values. The O─O and S─S-containing systems exhibit a strong fluorine Perlin-like effect, but unlike the α-effect, this behavior cannot be explained neither by hyperconjugation nor by dipolar interactions alone; the spatial proximity of the C─F and O─O/S─S bonds is proposed to affect the magnitude of the ¹J_C─F SSCC.     

Impact of fluorine on the phase behavior of bis-p-tolyl propane in supercritical CO2, 1,1-difluoroethane,and 1,1,1,2-tetrafluoroethane

Fluorine substitution on a solute can have a significant effect on solute solubility in a given solvent and fluorine substitution on a solvent can also have a significant effect on solvent quality. The effect of fluorine is demonstrated with the phase behavior data for bis(p-tolyl)propane (BTP) compared to bis(p-tolyl)hexafluoropropane (BTHFP) in supercritical carbon dioxide, 1,1-difluoroethane (F152a), and 1,1,1,2-tetrafluoroethane (F134a). Semifluorinated BTHFP is more soluble than non-fluorinated BTP in all three solvents, especially CO₂. The CO₂–BTP system exhibits solid solubility behavior while the CO₂–BTHFP system exhibits liquid–liquid–vapor (LLV) behavior near the critical point of CO₂. Although the two dipolar hydrofluorocarbons (HFC) are better solvents than CO₂ for these two aromatic solid compounds, F152a is the superior HFC solvent, especially for BTP, because F152a has a smaller molar volume and a larger effective dipole moment than F134a. LLV behavior is also observed for the F134a–BTP system near the critical point of F134a although the F134a–BTHFP, F152a–BTP, and F152a–BTHFP systems all appear to exhibit type-I phase behavior and no liquid–liquid immiscibility near the respective critical points.     

New Diterpenoid Alkaloids from Delphinium Souliei Franch

Inourpreviouspapers'-',wehavereportedtheisolationandelucidationofaseriesofnewditerpenoidalkaloidsfromDelphinillnlsolllieiFranch.ContinuedphytochemcalinvestigationsontheconstituentsofthisplanthaveledtotheisolationoftwoothernewditerpenoidalkaloidssoulineE(l)andsoulineF(2).SoulineE(2.6mg)wasobtainedascolorlesscrystals,mpf77-78'C(fromethanol).[a]."8.0(c=0.05,CHCI;).itsmolecularformulaC,=H;,NO,wasderivedfromHkEIMS(M-f361.2613,cafe.361.2608).TheiHnmrspectrum(400MHz)exhibitedthefollowingsign…     

Biomarkers for ischemic stroke subtypes: A protein-protein interaction analysis

According to the Trial of Org 10172 in Acute Stroke Treatment, ischemic stroke is classified into five subtypes. However, the predictive biomarkers of ischemic stroke subtypes are still largely unknown. The utmost objective of this study is to map, construct and analyze protein-protein interaction (PPI) networks for all subtypes of ischemic stroke, and to suggest the predominant biological pathways for each subtypes. Through 6285 protein data retrieved from PolySearch2 and STRING database, the first PPI networks for all subtypes of ischemic stroke were constructed. Notably, F2 and PLG were identified as the critical proteins for large artery atherosclerosis (LAA), lacunar, cardioembolic, stroke of other determined etiology (SOE) and stroke of undetermined etiology (SUE). Gene ontology and DAVID analysis revealed that GO:0030193 regulation of blood coagulation and GO:0051917 regulation of fibrinolysis were the important functional clusters for all the subtypes. In addition, inflammatory pathway was the key etiology for LAA and lacunar, while FOS and JAK2/STAT3 signaling pathways might contribute to cardioembolic stroke. Due to many risk factors associated with SOE and SUE, the precise etiology for these two subtypes remained to be concluded.