Fuzzy clustering using multiple Gaussian kernels with optimized-parameters

In this paper, we propose a new kernel-based fuzzy clustering algorithm which tries to find the best clustering results using optimal parameters of each kernel in each cluster. It is known that data with nonlinear relationships can be separated using one of the kernel-based fuzzy clustering methods. Two common fuzzy clustering approaches are: clustering with a single kernel and clustering with multiple kernels. While clustering with a single kernel doesn’t work well with “multiple-density” clusters, multiple kernel-based fuzzy clustering tries to find an optimal linear weighted combination of kernels with initial fixed (not necessarily the best) parameters. Our algorithm is an extension of the single kernel-based fuzzy c-means and the multiple kernel-based fuzzy clustering algorithms. In this algorithm, there is no need to give “good” parameters of each kernel and no need to give an initial “good” number of kernels. Every cluster will be characterized by a Gaussian kernel with optimal parameters. In order to show its effective clustering performance, we have compared it to other similar clustering algorithms using different databases and different clustering validity measures.     

A Fluorescent and Phosphorescent Nanoporous Solid: Crystalline Calix[4]arene

Calix[4]arene forms elongated nanoporous microcrystals. The pores are linear nano-channels (1.7 nm diameter) arranged in a honeycomb network. The crystals luminesce at room temperature according to a variety of processes that include monomer fluorescence (lifetime of ca. 1.1 ns), dimer fluorescence (lifetime of ca. 5.4 ns), and monomer phosphorescence (lifetime of ca. 2 s). The dimers result from pi-orbital overlap of adjacent phenol groups from neighboring nano-channels, with C-C distances of ca. 4 A.     

Multigrid solvers in reconfigurable hardware

The problem of finding the solution of partial differential equations (PDEs) plays a central role in modeling real world problems. Over the past years, Multigrid solvers have showed their robustness over other techniques, due to its high convergence rate which is independent of the problem size. For this reason, many attempts for exploiting the inherent parallelism of Multigrid have been made to achieve the desired efficiency and scalability of the method. Yet, most efforts fail in this respect due to many factors (time, resources) governed by software implementations. In this paper, we present a hardware implementation of the V-cycle Multigrid method for finding the solution of a 2D-Poisson equation. We use Handel-C to implement our hardware design, which we map onto available field programmable gate arrays (FPGAs). We analyze the implementation performance using the FPGA vendor's tools. We demonstrate the robustness of Multigrid over other similar iterative solvers, such as Jacobi and successive over relaxation (SOR  ), in both hardware and software. We compare our findings with a C++$\mathrm{C}++$ version of each algorithm. The obtained results show better performance when compared to existing software versions.     

Finite Rank Commutators and Semicommutators of Quasihomogeneous Toeplitz Operators

We study finite rank semicommutators and commutators of Toeplitz operators on the Bergman space with quasihomogeneous symbols. We show that in this context, the situation is different from the case of harmonic Toeplitz operators. Submitted: July 23, 2007. Accepted: December 4, 2007.     

Synthesis of the tricyclic core of colchicine via a dienyne tandem ring-closing metathesis reaction

The synthesis of the tricyclic framework of colchicine has been achieved using a tandem ring-closing metathesis reaction of dienynes as the key step. In this process, both seven-membered rings B and C were formed in one step. Oxidation of tertiary allylic alcohol derived from the tandem metathesis product furnished an intermediate in the total synthesis of colchicine.     

Powers and roots of Toeplitz operators

We study the commutativity of two Toeplitz operators whose symbols are quasihomogeneous functions. We give a relationship between this commutativity and the roots (or powers) of the Toeplitz operators. We use this to characterize Toeplitz operators with symbols in which commute with Toeplitz operators whose symbols are of the form .

     

A Structural Study of Epoxidized Natural Rubber (ENR-50) and Its Cyclic Dithiocarbonate Derivative Using NMR Spectroscopy Techniques

A structural study of epoxidized natural rubber (ENR-50) and its cyclic dithiocarbonate derivative was carried out using NMR spectroscopy techniques. The overlapping ¹H-NMR signals of ENR-50 at δ 1.56, 1.68-1.70, 2.06, 2.15-2.17 ppm were successfully assigned. In this work, the ¹³C-NMR chemical shift assignments of ENR-50 were consistent to the previously reported work. A cyclic dithiocarbonate derivative of ENR-50 was synthesized from the reaction of purified ENR-50 with carbon disulfide (CS₂), in the presence of 4-dimethylaminopyridine (DMAP) as catalyst at reflux temperature. The cyclic dithiocarbonate formation involved the epoxide ring opening of the ENR-50. This was followed by insertion of the C-S moiety of CS₂ at the oxygen attached to the quaternary carbon and methine carbon of epoxidized isoprene unit, respectively. The bands due to the C=S and C-O were clearly observed in the FTIR spectrum while the ¹H-NMR spectrum of the derivative revealed the peak attributed to the methylene protons had split. The ¹³C-NMR spectrum of the derivative further indicates two new carbon peaks arising from the >C=S and quaternary carbon of cyclic dithiocarbonate. All other ¹H- and ¹³C-NMR chemical shifts of the derivative remain unchanged with respect to the ENR-50.     

Stereospecific hydride transfer under NCI/OH− conditions. 2—Origins of the C2H4O elimination from stereoisomeric alkoxyketal derivatives1

A new stereospecific intramolecular hydride transfer, induced by an alkoxide, has been demonstrated under NCI/OH^? conditions using unimolecular and collision-induced decomposition spectra.     

Production, purification, and biochemical characterization of two beta-glucosidases from Sclerotinia sclerotiorum

The filamentous fungus Sclerotinia sclerotiorum produces beta-glucosidases in liquid culture with a variety of carbon sources, including cellulose (filter paper), xylan, barley straw, oat meal, and xylose. Analysis by native polyacrylamide gel electrophoresis (PAGE) followed by an activity staining with the specific chromogenic substrate, 5-bromo 4-chloro 3-indolyl beta-1,4 glucoside (X-glu) showed that two extracellular beta-glucosidases, designated as beta-glu1 and beta-glu2, were in the filter paper culture filtrate. Only one enzyme designated as beta-glu x was revealed by the same method in the xylose culture filtrate. Beta-glu1 and beta-glu2 were purified to homogeneity. The purification procedure consist of a common step of anion-exchange chromatography on DEAE-Sepharose CL6B, both high-performance liquid chromatography (HPLC) anion-exchange and gel filtration columns for beta-glu1 and only HPLC gel filtration for beta-glu2. Beta-glu1 has a molecular mass of 196 kDa and 96.5 kDa, as estimated by gel filtration and sodium dodecyl sulfate (SDS)-PAGE, respectively, suggesting that the native enzyme may consist of two identical subunits. The same analysis showed that beta-glu2 is a monomeric protein with an apparent molecular mass of about 76.5 kDa. Beta-glu1 and beta-glu2 hydrolyses PNPGlc and cellobiose, with apparent Km values respectively for PNPGlc and cellobiose of 0.1 and 1.9 mM for beta-glu1 and 2.8 and 8 mM for beta-glu2. Both enzymes exhibit the same temperature and pH optima for PNPGlc hydrolysis (60 degrees C and pH 5.0). beta-glu1 was stable over a pH range of 3-8 and kept 50% of its activity after 30 min of heating at 60 degrees C without substrate. It was further characterized by studying the effect of some cations and various reagents on its activity.