Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

Highly unsaturated pyranone derivatives from the basidiomycete Junghuhnianitida

Four new highly unsaturated pyranone derivatives A–D (1–4), together with one known compound 5 (−)-nitidon were isolated from cultures of the fungus Junghuhnianitida. Planar structures of the new compounds were elucidated on the basis of extensive NMR spectroscopic and mass spectrometric analyses. Absolute configurations of the new compounds were determined on the basis of biosynthetic considerations and quantum chemistry theory. Compound 1 exhibited almost the same cytotoxic activities as cis-platin.     

C?H Functionalization/Asymmetric Michael Addition Cascade Enabled by Relay Catalysis: Metal Carbenoid Used for C?C Bond Formation

A combination of either ruthenium(II) or rhodium(II) complexes and quinine‐derived squaramide enables 3‐diazooxindoles, indoles, and nitroalkenes to undergo highly efficient asymmetric three‐component reactions, thus affording optically active 3,3′‐bis(indole)s through a consecutive C C bond‐forming sequence, which turned out to be applicable to the facile total synthesis of (−)‐folicanthine.     

Palladium‐Catalyzed C(sp3)?H Activation: A Facile Method for the Synthesis of 3,4‐Dihydroquinolinone Derivatives

3,4‐Dihydroquinolinones were synthesized by the palladium‐catalyzed, oxidative‐addition‐initiated activation and arylation of inert C(sp³) H bonds. Pd(OAc)₂ and P(o‐tol)₃ were used as the catalyst and ligand, respectively, to improve the efficiency of the reaction. A further advantage of this reaction is that it could be performed in air. A relatively rare seven‐membered palladacycle was proposed as a key intermediate of the catalytic cycle.     

Recombination analysis of autosomal short tandem repeats in Chinese Han families

Recombination fractions between forensic STRs can be extrapolated from the International HapMap Project, but the concordance between recombination fractions predicated from genetic maps and derived from observation of STR transmissions in families is still ambiguous for autosomal STRs because of limited family studies. Therefore, the main goal of this study is to compare recombination fractions estimated by pedigree analysis with those derived from HapMap phase SNP data. Genotypes of nine autosomal STR pairs (TPOX‐D2S1772, D5S818‐CSF1PO, D7S3048‐D7S820, D8S1132‐D8S1179, TH01‐D11S2368, vWA‐D12S391, D13S325‐D13S317, D18S51‐D18S1364, and D21S11‐PentaD) from 207 two‐generation families with two to five children (the number of families with five, four, three, and two children was 2, 3, 20, and 182, respectively) were used to analyze the recombination. The linkage analysis showed that significant linkage was observed at six STR pairs (D5S818‐CSF1PO, D8S1132‐D8S1179, TH01‐D11S2368, vWA‐D12S391, D13S325‐D13S317, and D18S51‐D18S1364) with genetic distances <36.22 cM in HapMap. Their recombination fractions calculated from family data were very close to those derived from HapMap. However, three STR pairs of TPOX‐D2S1772, D7S3048‐D7S820, and D21S11‐PentaD showed no significant linkage with genetic distances from 43.38 to 91.49 cM. Our results indicate that recombination fractions extrapolated from HapMap can provide a substitute if empirical data are unavailable for the linkage STR pair with a genetic distance spanned <36.22 cM.     

Total synthesis of Daphnodorin A

A total synthesis of Daphnodorin A, a member of the Daphnodorins, was accomplished. Key features of the synthetic strategy include construction of 2-substituted-3-functionalized benzofuran via intramolecular Heck reaction and a mild Barton–McCombie deoxygenation process mediated by triethylborane. The total synthesis provided Daphnodorin A in 19.7% or 5.6% overall yield over 7 or 15 steps.     

One-pot reaction for the concise synthesis of spiro[benzofuran-2,2′-naphthalen]-1′-one derivatives

A novel one-pot two-step protocol has been developed to synthesize various spiro[benzofuran-2,2′-naphthalen]-1′-one derivatives from the three-component reaction of tetralones, 2-hydroxyphenyl functionalized α,β-unsaturated ketones, and iodine. One C–C bond and one C–O bond have formed during this process. The notable features of this protocol are simple and mild reaction conditions, applicable to a wide range of readily available starting materials, good yields (up to 91%), and excellent stereoselectivities (up to 97:3).     

Cascade synthesis of 3-aza-bicyclo[3.1.0]hex-2-ene derivatives from N-allyl enamines

An efficient iodine-mediated cascade synthesis of 3-aza-bicyclo[3.1.0]hex-2-ene derivatives from easily prepared N-allyl enamines has been developed. The advantages of the reaction include facilitative preparation of substrates 3a–t, good functional group tolerance and transition-metal-free conditions.