A study of comparability in amplified fragment length polymorphism profiling using a simple model system

A simple amplified fragment length polymorphism (AFLP) model, using the bacteriophage lambda genome, was developed to test the reproducibility of this technique in an international comparative study. Using either non-selective or selective primers, nine fragments or subsets of two or three fragments, respectively, were predicted using in silico software. Under optimized conditions, all predicted fragments were experimentally generated. The reproducibility of the AFLP model was tested by submitting both "unknown" DNA template that had been restricted and ligated with AFLP linkers (R/L mixture) and corresponding primer pairs to nine laboratories participating in the study. Participants completed the final PCR step and then used either slab gel electrophoresis or CE to detect the AFLP fragments. The predicted fragments were identified by the majority of participants with size estimates consistently up to 3 base pair (bp) larger for slab gel electrophoresis than for CE. Shadow fragments, 3 bp larger than the predicted fragments, were often observed by study participants and organizers. The nine AFLP fragments exhibited relative intensities ranging from less than 3% to 22% and, apart from the two weakest fragments, with a % CV of 16 to 25. Fragments containing the highest guanine-cytosine (GC) content of 50-56% showed the greatest stability in the AFLP profiles.     

CesA protein is included in the terminal complex of <Emphasis Type="Italic">Acetobacter</Emphasis>

Cellulose is a major biopolymer on the earth that is produced by cellulose synthase in the cell membrane of living organisms. Cellulose synthase is a hetero-subunit complex composed of several different protein subunits, and is visualized as a supermolecular complex called a “terminal complex” by electron microscopy. Such supermolecular organization of an enzyme complex is believed to be important for the fiber formation or crystallization of cellulose microfibrils in cellulose biosynthesis. In the case of the cellulose-producing bacterium Acetobacter, it is hypothesized that the enzyme complex includes at least six subunits given its genetic constitution. However, to date, only three of these molecules have been experimentally confirmed as the subunits included in the terminal complex: CesB, CesD, and ccp2. In this study, we used fluorescence immuno-microscopy to show that CesA protein, the catalytic subunit, is included in the terminal complex of Acetobacter. Furthermore we discuss the obtained microscopic data for improving our understanding of the molecular organization of the bacterial cellulose synthase complex.     

Epoc group: transformable protecting group with gold(iii)-catalyzed fluorene formation

This study presents the novel concept of a transformable protecting group, which changes its properties through structural transformation. Based on this concept, we developed a 2-(2-ethynylphenyl)-2-(5-methylfuran-2-yl)-ethoxycarbonyl (Epoc) group. The Epoc group was transformed into an Fmoc-like structure with gold(iii)-catalyzed fluorene formation and was removable under Fmoc-like mild basic conditions post-transformation even though it was originally stable under strongly basic conditions. As an application for organic synthesis, the Epoc group provides the novel orthogonality of gold(iii)-labile protecting groups in solid-phase peptide synthesis. In addition, the high turnover number of fluorene formation in aqueous media is suggestive of the applicability of the Epoc group to biological systems.

A protecting group removable with gold(iii)-catalyzed fluorene formation and the subsequent addition of piperidine was developed.     

Anionic Sublattices in Halide Solid Electrolytes: A Case Study with the High-Pressure Phase of Li3ScCl6

The Li₃MX₆ compounds (M=Sc, Y, In; X=Cl, Br) are known as promising ionic conductors due to their compatibility with typical metal oxide cathode materials. In this study, we have successfully synthesized γ-Li₃ScCl₆ using high pressure for the first time in this family. Structural analysis revealed that the high-pressure polymorph crystallizes in the polar and chiral space group P6₃mc with hexagonal close-packing (hcp) of anions, unlike the ambient-pressure α-Li₃ScCl₆ and its spinel analog with cubic closed packing (ccp) of anions. Investigation of the known Li₃MX₆ family further revealed that the cation/anion radius ratio, r_M/r_X, is the factor that determines which anion sublattice is formed and that in γ-Li₃ScCl₆, the difference in compressibility between Sc and Cl exceeds the ccp r_M/r_X threshold under pressure, enabling the ccp-to-hcp conversion. Electrochemical tests of γ-Li₃ScCl₆ demonstrate improved electrochemical reduction stability. These findings open up new avenues and design principles for lithium solid electrolytes, enabling routes for materials exploration and tuning electrochemical stability without compositional changes or the use of coatings.     

Baxter-Guttmann-Jensen conjecture for power series in directed percolation problem

A probabilistic model of a flow of fluid through a random medium,percolation model, provides a typical example of statistical mechanical problems which are easy to describe but difficult to solve. While the percolation problem on undirected planar lattices is exactly solved as a limit of the Potts models, there still has been no exact solution for the directed lattices. The most reliable method to provide good approximations is a numerical estimation using finite power-series expansion data of the infinite formal power series for percolation probability. In order to calculate higher-order terms in power series, Baxter and Guttmann [6] and Jensen and Guttmann [33] proposed an extrapolation procedure based on an assumption that thecorrection terms, which show the difference between the exact infinite power series and approximate finite series, are expressed as linear combinations of the Catalan numbers.In this paper, starting from a brief review on the directed percolation problem and the observation by Baxter, Guttmann, and Jensen, we state some theorems in which we explain the reason why the combinatorial numbers appear in the correction terms of power series. In the proof of our theorems, we show several useful combinatorial identities for the ballot numbers, which become the Catalan numbers in a special case. These identities ensure that a summation of products of the ballot numbers with polynomial coefficients can be expanded using the ballot numbers. There is still a gap between our theorems and the Baxter-Guttmann-Jensen observation, and we also give some conjectures.As a generalization of the percolation problem on a directed planar lattice, we present two topics at the end of this paper: The friendly walker problem and the stochastic cellular automata in higher dimensions. We hope that these two topics as well as the directed percolation problem will be of much interest to researchers of combinatorics.     

Numerical Analysis of the Allen-Cahn Equation with Coarse Meshes

In this paper, we consider the finite difference semi-discretization of the Allen-Cahn equation with the diffuse interface parameter $\varepsilon$. While it is natural to make the mesh size parameter $h$ smaller than $\varepsilon$, it is desirable that $h$ is as big as possible in view of computational costs. In fact, when $h$ is bigger than $\varepsilon$ (i.e., the mesh is relatively coarse), it is observed that the numerical solution does not move at all. The purpose of this paper is to clarify the mechanism of this phenomenon. We will prove that the numerical solution converges to that of the ordinary equation without the diffusion term if $h$ is bigger than $\varepsilon$. Numerical examples are presented to support the result.     

The Stein phenomenon for monotone incomplete multivariate normal data

We establish the Stein phenomenon in the context of two-step, monotone incomplete data drawn from , a (p+q)-dimensional multivariate normal population with mean and covariance matrix . On the basis of data consisting of n observations on all p+q characteristics and an additional N−n observations on the last q characteristics, where all observations are mutually independent, denote by the maximum likelihood estimator of . We establish criteria which imply that shrinkage estimators of James-Stein type have lower risk than under Euclidean quadratic loss. Further, we show that the corresponding positive-part estimators have lower risk than their unrestricted counterparts, thereby rendering the latter estimators inadmissible. We derive results for the case in which is block-diagonal, the loss function is quadratic and non-spherical, and the shrinkage estimator is constructed by means of a nondecreasing, differentiable function of a quadratic form in . For the problem of shrinking to a vector whose components have a common value constructed from the data, we derive improved shrinkage estimators and again determine conditions under which the positive-part analogs have lower risk than their unrestricted counterparts.     

Hausdorff measures and packing measures of limit sets of CIFSs of generalized complex continued fractions

ABSTRACT

We consider a certain family of CIFSs of the generalized complex continued fractions with a complex parameter space. We show that for each CIFS of the family, the Hausdorff measure of the limit set of the CIFS with respect to the Hausdorff dimension is zero and the packing measure of the limit set of the CIFS with respect to the Hausdorff dimension is positive (main result). This is a new phenomenon of infinite CIFSs which cannot hold in finite CIFSs. We prove the main result by showing some estimates for the unique conformal measure of each CIFS of the family and by using some geometric observations.     

Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem

In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel is adopt to provide a stable solution when the measurement data contain noises. Numerical results indicate that the proposed method is stable, efficient, and accurate.