Small‐Noise Analysis and Symmetrization of Implicit Monte Carlo Samplers

Implicit samplers are algorithms for producing independent, weighted samples from multivariate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis suggests a symmetrization of the algorithms that leads to improved implicit sampling schemes at a relatively small additional cost. Computational experiments confirm the theory and show that symmetrization is effective for small noise sampling problems.© 2016 Wiley Periodicals, Inc.     

Exponential Growth of Ponds in Invasion Percolation on Regular Trees

In invasion percolation, the edges of successively maximal weight (the outlets) divide the invasion cluster into a chain of ponds separated by outlets. On the regular tree, the ponds are shown to grow exponentially, with law of large numbers, central limit theorem and large deviation results. The tail asymptotics for a fixed pond are also studied and are shown to be related to the asymptotics of a critical percolation cluster, with a logarithmic correction.     

Synthesis and evaluation of some variants of the Nefkens’ reagent

A series of N-substituted phthalimides have been prepared in an effort to explore synthetic variants of the Nefkens’ reagent. Three N-acylphthalimides [R = –CH₃, –CH₂CH₃, and –C(CH₃)₃] were prepared and employed for the protection of a series of representative amines. In addition, an N-methanesulfonylphthalimide and N-(diethylphosphoryl)phthalimide were also prepared. It was determined that among the phthalimides that were prepared N-propanoylphthalimide was the most effective reagent for the protection reaction.     

A new and convenient in-situ method of generating phenyl isocyanates from anilines using oxalyl chloride

A new and convenient method of generating phenyl isocyanates from anilines using oxalyl chloride is described. Acylation of a variety of substituted aniline hydrochlorides with oxalyl chloride affords the intermediate oxamic chlorides, which smoothly undergo thermal decomposition to the corresponding isocyanates.     

On the Cholesky factorization of the Gram matrix of locally supported functions

Cholesky factorization of bi-infinite and semi-infinite matrices is studied and in particular the following is proved. If a bi-infinite matrixA has a Cholesky factorization whose lower triangular factorL and its lower triangular inverse decay exponentially away from the diagonal, then the semi-infinite truncation ofA has a lower triangular Cholesky factor whose elements approach those ofL exponentially. This result is then applied to studying the asymptotic behavior of splines obtained by orthogonalizing a large finite set of B-splines, in particular identifying the limiting profile when the knots are equally spaced.The first and second authors were partially supported by Nato Grant #920209, the second author also by the Alexander von Humboldt Foundation, and the last two authors by the Italian Ministry of University and Scientific and Technological Research.     

New neutrino experiments

Following incredible recent progress in understanding neutrino oscillations, many new ambitious experiments are being planned to study neutrino properties. The most important may be to find a non-zero value of θ₁₃. The most promising way to do this appears to be to measurev _μ →v _e oscillations with anE/L near Δm _atmo ² . Future neutrino experiments are great.     

A retrospective reliability test for numeric data sets applied by example to atomic-mass values of some nuclides

 Under favorable conditions, a retrospective test for reliability of published sets of physical property data becomes possible. The test and the necessary conditions for its use are discussed. The test is applied, by example, to well-documented, periodically republished nuclidic (atomic) masses of nine low atomic number nuclides. An index of reliability is suggested and evaluated for the example. Revised: 27 November 1995     

The formation of a stable o-semidine rearrangement intermediate

Treatment of 5,6,11,12-tetrahydrodibenzo-[b, f][1,2] diazocine with dilute acids affords a spiro-1,2,3,4-tetrahydroquinoline derivative which represents the first isolated stable o-semidine rearrangement intermediate.     

Reaction kinetics in dilute solutions of chain molecules carrying randomly spaced reactive and catalytic chain substituents. II. Dependence of the ring closure probability on the solvent medium and the nature of the chain backbone

Ternary copolymers of acrylamide or methacrylamide with small proportions of comonomers carrying reactive p-nitrophenyl ester and catalytic pyridine groups in the side chains were prepared. The kinetics of the ester solvolysis was followed in highly dilute solutions, so that the rate was controlled by interaction of groups carried by the same chain backbone. Data were obtained in water and aqueous methanol and were interpreted by a computer simulation procedure in terms of the dependence of the probability of encounter between two chain substituents on their spacing along the chain backbone. This probability decreased more slowly with increasing separation of the interacting groups when the solvation of the polymer was reduced, but even in solvents approaching θ conditions the results deviated from theoretical predictions for chains without excluded volume. The formation of cyclic conformations is considerably more difficult in methacrylic than in acrylic chains, although the chain flexibility, as characterized by unperturbed chain dimensions, is very similar in the two systems.