Wavelength dependencies in interferometric measurements of thin protein films

Summary The evaluation of the spectral modulation in reflectance measurements at thin dielectric films allows the characterisation of layers in the m-range. Diode array spectrometers make this technique a useful tool in sensor development. The variation of the optical pathlength in thin films due to change of refractive index or to change of physical thickness of a homogeneous layer has been applied to refractometry and detection of hydrocarbons by polymer swelling. More recently, the monitoring of solid-phase affinity reactions, like immunoassays has successfully been demonstrated. While the homogeneous layer concept is useful for data evaluation in the first two cases, it has its limitations for the treatment of adlayer formation as in the latter case. This is discussed with respect to results from affinity reactions carried out at optically different interference layers.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Covalent strategy for immobilization of DNA-microspots suitable for microarrays with label-free and time-resolved optical detection of hybridization

Sequence-specific detection and quantification of nucleic acids are central steps in many molecular biology procedures which have also been transferred to chip-based procedures. Hybridization-based assays can be used to quantify and discriminate between DNA target sequences down to the level of single base mismatches. Arrays of DNA probes immobilized on a support enable simultaneous testing of multiple sequences of a single sample. DNA arrays can be produced either by in-situ synthesis of oligonucleotides or by immobilization of pre-assembled DNA probes. Covalent and directed immobilization improves the reproducibility and stability of DNA arrays. This is especially interesting with repeated use of transducers or chips. Procedures are described for effective covalent immobilization of pre-assembled amino-linked oligonucleotides, by use of ink-jet techniques, on a modified and heated glass surface, with addressable surface areas ranging from 0.01 mm2 to a few mm2. Almost immediate evaporation of the spotted droplets on the heated surfaces leads to very high surface hybridization capacities. The surfaces are suitable for use with a label-free detection method - reflectometric interference spectroscopy (RIfS). It is shown that hybridization capacity and non-specific interaction at these DNA-surfaces can be characterized by use of RIfS. With a consumption of less than 80 ng mm(-2) oligonucleotide and a specific hybridization capacity of more than 300 fmol mm(-2), the activated aminodextran procedure was usually suitable for setting up a DNA array with label-free detection. Non-specific interactions with random oligomers or protein (ovalbumin) were low. Up to 150 repeated regenerations (stripping) of the surfaces by acid treatment and denaturing agents, and 50 days of storage, have been possible without significant loss of hybridization capacity.     

Operating room planning and scheduling: solving a surgical case sequencing problem

This text summarizes the PhD dissertation that was defended by the author in January 2009 under the supervision of Erik Demeulemeester at the Katholieke Universiteit Leuven (Belgium). The text is written in English and is available from the author upon request. The PhD dissertation is situated within the health care services domain and studies the impact of planning and scheduling procedures in the operating room. It incorporates an extensive review of both scientific contributions and the current operating room planning and scheduling practices of hospitals in Flanders (Belgium). The emphasis of the research, though, is directed towards the development, the testing and the application of surgery sequencing algorithms in a day-care environment.     

A second order virtual node method for elliptic problems with interfaces and irregular domains

We present a second order accurate, geometrically flexible and easy to implement method for solving the variable coefficient Poisson equation with interfacial discontinuities or on irregular domains, handling both cases with the same approach. We discretize the equations using an embedded approach on a uniform Cartesian grid employing virtual nodes at interfaces and boundaries. A variational method is used to define numerical stencils near these special virtual nodes and a Lagrange multiplier approach is used to enforce jump conditions and Dirichlet boundary conditions. Our combination of these two aspects yields a symmetric positive definite discretization. In the general case, we obtain the standard 5-point stencil away from the interface. For the specific case of interface problems with continuous coefficients, we present a discontinuity removal technique that admits use of the standard 5-point finite difference stencil everywhere in the domain. Numerical experiments indicate second order accuracy in L^∞.     

Swarming on Random Graphs

We consider a compromise model in one dimension in which pairs of agents interact through first-order dynamics that involve both attraction and repulsion. In the case of all-to-all coupling of agents, this system has a lowest energy state in which half of the agents agree upon one value and the other half agree upon a different value. The purpose of this paper is to study the behavior of this compromise model when the interaction between the N agents occurs according to an Erd?s-Rényi random graph $\mathcal{G}(N,p)$ . We study the effect of changing p on the stability of the compromised state, and derive both rigorous and asymptotic results suggesting that the stability is preserved for probabilities greater than $p_{c}=O(\frac{\log N}{N})$ . In other words, relatively few interactions are needed to preserve stability of the state. The results rely on basic probability arguments and the theory of eigenvalues of random matrices.     

Well-Posedness Theory for Aggregation Sheets

In this paper, we consider distribution solutions to the aggregation equation ${\rho_{t} + \mathrm{div}(\rho \mathbf{u} ) = 0, \; \mathbf{u} = -\nabla V * \rho}$ in ${\mathbb{R}^{d}}$ , where the density ρ concentrates on a co-dimension one manifold. We show that an evolution equation for the manifold itself completely determines the dynamics of such solutions. We refer to such solutions aggregation sheets. When the equation for the sheet is linearly well-posed, we show that the fully non-linear evolution is also well-posed locally in time for the class of bi-Lipschitz surfaces. Moreover, we show that if the initial sheet is C ¹ then the solution itself remains C ¹ as long as it remains Lipschitz. Lastly, we provide conditions on the kernel ${g(s) = -\frac{\mathrm{d}V}{\mathrm{d}s}}$ that guarantee the solution remains a bi-Lipschitz surface globally in time, and construct explicit solutions that either collapse or blow up in finite time when these conditions fail.     

Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group

We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (in the sense of full configuration interaction, with 1-10 microE(h) precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.     

Synthesis of (±)‐Nephromopsinic, (−)‐Phaseolinic,and (−)‐Dihydropertusaric Acids

The formal syntheses of (±)‐nephromopsinic acid, (−)‐phaseolinic acid, and the first total synthesis of (−)‐dihydropertusaric acid from (±)‐ and (−)‐7‐oxabicyclo[2.2.1]hept‐5‐en‐2‐one are described. These syntheses take advantage of a previously reported radical rearrangement (1,2‐acyl migration). A remarkable iodide‐mediated cleavage of a bicyclic system, followed by the introduction of the γ‐chains via a mixed Kolbe electrolysis, are the key steps of these syntheses. This approach is general and could be applied for the preparation of all kinds of paraconic acids with excellent control of the stereochemistry.