Controlling the supramolecular assembly of redox-active dendrimers at molecular printboards by scanning electrochemical microscopy

Redox-active ferrocenyl (Fc)-functionalized poly(propylenimine) (PPI) dendrimers solubilized in aqueous media by complexation of the Fc end groups with beta-cyclodextrin (betaCD) were immobilized at monolayers of betaCD on glass ("molecular printboards") via multiple host-guest interactions. The directed immobilization of the third-generation dendrimer-betaCD assembly G3-PPI-(Fc)16-(betaCD)16 at the printboard was achieved by supramolecular microcontact printing. The redox activity of the patterned dendrimers was mapped by scanning electrochemical microscopy (SECM) in the positive feedback mode using [IrCl(6)](3-) as a mediator. Local oxidation of the Fc-dendrimers by the microelectrode-generated [IrCl(6)](2-) resulted in an effective removal of the Fc-dendrimers from the host surface since the oxidation of Fc to the oxidized form (Fc+) leads to a concomitant loss of affinity for betaCD. Thus, SECM provided a way not only to image the surface, but also to control the binding of the Fc-terminated dendrimers at the molecular printboard. Additionally, the electrochemical desorption process could be monitored in time as the dendrimer patterns were gradually erased upon multiple scans.     

Proteomics in cancer research: methods and application of array-based protein profiling technologies

With the human genome sequence now determined, the field of molecular medicine is moving beyond genomics to proteomics, the large-scale analysis of proteins.It is now possible to examine the expression of more than 1000 proteins using mass spectrometry technology coupled with various separation methods.Microarray technology is a new and efficient approach, for extracting relevant biomedical data and has a wide range of applications. It provides a versatile tool to study protein-protein, protein-nucleic acid, protein-lipid, enzyme-substrate and protein-drug interactions.This review paper will explore the key themes in proteomics and their application in clinical cancer research.     

The attenuated ray transform for connections and Higgs fields

We show that for a simple surface with boundary the attenuated ray transform in the presence of a unitary connection and a skew-Hermitian Higgs field is injective modulo the natural obstruction for functions and vector fields. We also show that the connection and the Higgs field are uniquely determined by the scattering relation modulo a gauge transformation. The proofs involve a Pestov type energy identity for connections together with holomorphic gauge transformations which arrange the curvature of the connection to have definite sign.     

Continuous functions with impermeable graphs

We construct a Hölder continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We conclude that this function has impermeable graph—one of the key concepts introduced in this paper—and we present further examples of functions both with permeable and impermeable graphs. Moreover, we show that typical (in the sense of Baire category) continuous functions have permeable graphs. The first example function is subsequently used to construct an example of a continuous function on the plane which is intrinsically Lipschitz continuous on the complement of the graph of a Hölder continuous function with impermeable graph, but which is not Lipschitz continuous on the plane. As another main result, we construct a continuous function on the unit interval which coincides in a set of Hausdorff dimension 1 with every function of total variation smaller than 1 which passes through the origin.     

Finite Element Solution of Conical Diffraction Problems

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R ² coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.     

Completely prime L-filters,irreducible L-filters and sobriety

In this paper, for a frame L, we characterize modified sobriety in stratified L-topological spaces and strong L-topological spaces internally using certain classes of stratified L-filters. While the first characterization using completely prime L-filters is trivial and applies to all stratified L-topological spaces, the other one using irreducible L-filters generalizes an approach of R.E. Ho?mann to the lattice-valued case but is restricted to either the case that the lattice is a complete Boolean algebra or to the case of completely distributive lattices and strong L-topological spaces.     

On Quasi-Interpolation with Non-uniformly Distributed Centers on Domains and Manifolds

The paper studies quasi-interpolation by scaled shifts of a smooth and rapidly decaying function. The centers are images of a smooth mapping of the hZⁿ-lattice in R^s, sn, and the scaling parameters are proportional to h. We show that for a large class of generating functions the quasi-interpolants provide high order approximations up to some prescribed accuracy. Although in general the approximants do not converge as h tends to zero, the remaining saturation error is negligible in numerical computations if a scalar parameter is suitably chosen. The lack of convergence is compensated for by a greater flexibility in the choice of generating functions used in numerical methods for solving operator equations.