凸四边形上一类具有C~2-连续的插值问题的样条解及其应用

本文讨论了一类凸四边形上的插值问题.指出这类插值问题是可解的,其解是分片二元三次多项式,且在凸四边形上是C~2-连续的.我们证明了这类插值问题的解的存在性和唯一性,给出了解样条的分片表达式及其逼近度的估计.最后还给出了一个应用实例和图形显示来说明本方法是可行的.     

Fermionic perturbation theory for the statistical mechanics of the nonlinear Schrödinger model

A fermionic perturbation theory is developed for the statistical mechanics of the nonlinear Schrödinger model. The theory is based on an interacting-fermion picture of the Bethe wave function. The inner product of the Bethe wave function is explicitly evaluated, and a simple graphical representation of it is given. The basic equations obtained for the free energy agree with those of Yang and Yang. In particular, the present theory gives a clear-cut meaning to the function of Yang and Yang: It represents a fermion energy at finite temperatures.     

Change points in heavy‐tailed multivariate time series: Methods using precision matrices

We propose two robust data‐driven techniques for detecting network structure change points between heavy‐tailed multivariate time series for situations where both the placement and number of change points are unknown. The first technique utilizes the graphical lasso method to estimate the change points, whereas the second technique utilizes the tlasso method. The techniques not only locate the change points but also estimate an undirected graph (or precision matrix) representing the relationship between the time series within each interval created by pairs of adjacent change points. An inference procedure on the edges is used in the graphs to effectively remove false‐positive edges, which are caused by the data deviating from normality. The techniques are compared using simulated multivariate t‐distributed (heavy‐tailed) time series data and the best method is applied to two financial returns data sets of stocks and indices. The results illustrate the method's ability to determine how the dependence structure of the returns changes over time. This information could potentially be used as a tool for portfolio optimization.     

Determination/estimation of an optimal replacement interval under minimal repair

In this paper the problem of estimation of an optimal replacement interval for a system which is minimally repaired at failures is studied. The problem is investigated both under a parametric and a nonparametric form of the failure intensity of the system. It is assumed that observational data from n systems are available. Some asymptotic results are shown. A graphical procedure for determining/estimating an optimal replacement interval is presented. The procedure is particularly valuable for sensitivity analyses, for example with respect to the costs involved.     

Classroom note: The area under x α by geometry

By stretching the area under the curve x ^α it is shown to be of the form x ^{α + 1} p(α). Geometry is then used to prove p(α) = 1/(α + 1).     

Schemata, Distributions and Graphical Models in Evolutionary Optimization

In this paper the optimization of additively decomposed discrete functions is investigated. For these functions genetic algorithms have exhibited a poor performance. First the schema theory of genetic algorithms is reformulated in probability theory terms. A schema defines the structure of a marginal distribution. Then the conceptual algorithm BEDA is introduced. BEDA uses a Boltzmann distribution to generate search points. From BEDA a new algorithm, FDA, is derived. FDA uses a factorization of the distribution. The factorization captures the structure of the given function. The factorization problem is closely connected to the theory of conditional independence graphs. For the test functions considered, the performance of FDA—in number of generations till convergence—is similar to that of a genetic algorithm for the OneMax function. This result is theoretically explained.     

Simultispin: A versatile graphical user interface for the simulation of solid-state continuous wave EPR spectra

Solid-state continuous wave (cw) electronic paramagnetic resonance (EPR) spectroscopy is particularly suitable for metal complex analysis. Extracting magnetic parameters by simulation is often necessary to describe the electronic structure of the studied molecular compounds that can have various electronic spin states and characterized by different parameters like g-values, hyperfine coupling or zero field splitting values. Easyspin toolbox on MATLAB is a powerful tool, but for the user, it requires spending time with coding and could discourage nonexperts. Facing this context, we have developed a graphical user interface called Simultispin, dedicated to solid-state cw-EPR spectra simulation. Some examples of experimental spectra of metal complexes (mixture of low spin and high spin Fe^III complexes, dynamic disorder of a Cu^II complex, photogeneration of a Mn^III complex), highlighting specific solid-state functions, are described and analyzed based on simulations performed with Simultispin. We hope that its ergonomy and the ease to set up a complete set of parameters to get reliable simulations could help a large EPR community to improve the efficiency of their interpretations.     

Detecting stage-wise outliers in hierarchical Bayesian linear models of repeated measures data

We propose numerical and graphical methods for outlier detection in hierarchical Bayes modeling and analyses of repeated measures regression data from multiple subjects; data from a single subject are generically called a “curve”. The first-stage of our model has curve-specific regression coefficients with possibly autoregressive errors of a prespecified order. The first-stage regression vectors for different curves are linked in a second-stage modeling step, possibly involving additional regression variables. Detection of thestage at which the curve appears to be an outlier and themagnitude and specific component of the violation at that stage is accomplished by embedding the null model into a larger parametric model that can accommodate such unusual observations. We give two examples to illustrate the diagnostics, develop a BUGS program to compute them using MCMC techniques, and examine the sensitivity of the conclusions to the prior modeling assumptions.     

Wishart Distributions on Homogeneous Cones

The classical family of Wishart distributions on a cone of positive definite matrices and its fundamental features are extended to a family of generalized Wishart distributions on a homogeneous cone using the theory of exponential families. The generalized Wishart distributions include all known families of Wishart distributions as special cases. The relationships to graphical models and Bayesian statistics are indicated.     

Graphical method for the determination of the complex NMR shift and equilibrium constant for a hetero-association accompanying self-associations

We describe a novel graphical method which, in conjunction with the previously proposed graphical determination of monomer shift, dimer shift, and dimerization constant for self-association, allows us to determine the complex shift and equilibrium constant for a hetero-association, A + B ⇌ AB, accompanying self-associations, A + A ⇌ A₂, and B + B ⇌ B₂. The merit of the new method includes the removal of the restrictions imposed on the conventional Benesi-Hildebrand (B-H) plot: (1) that the concentration of one component must be much less than that of the other; (2) that there be no accompanying self-association. The simultaneous equilibrium of the self-association of 2-pyrrolidone (A) and that of 4-methyl-α-pyrrolidone (B) and the hetero-association between A and B in acetonitrile-d₃ at 25‡C is studied. The inappropriateness of the B-H plot in dealing with this case is also pointed out.