Christoph Meyer

The two-variable guarded fragment with transitive relations

We consider the restriction of the guarded fragment to the two-variable case where, in addition, binary relations may be specified as transitive. We show that (i) this very restricted form of the guarded fragment without equality is undecidable and that (ii) when allowing non-unary relations to occur only in guards, the logic becomes decidable. The latter subclass of the guarded fragments the one that occurs naturally when translating multi-modal logics of the type Kg/sub 4/ S/sub 4/ or S5 into first-order logic. We also show that the loosely guarded fragment without equality and with a single transitive relation is undecidable.

Shear force imaging of DNA in a near-field scanning optical microscope (NSOM)

A near‐field scanning optical module has been constructed as an accessory for a Nanoscope IIIa commercial scanning probe microscope. Distance feedback and topographic registration are accomplished with an uncoated optical fibre scanning tip by implementation of the shear force technique. The tip is driven by a piezoelectric actuator at a resonance frequency of 8–80 kHz. A laser diode beam is scattered by the tip and detected by a split photodiode, with lock‐in detection of the difference signal. The amplitude (r) and phase (τ) responses were characterized as a function of the calibrated tip–sample separation. Using an r cos τ feedback signal, imaging of pUC18 relaxed circular plasmid DNA spread on mica precoated with cetylpyridinium chloride was achieved. The apparent width (28 ± 5 nm) was approximately four times that achieved by scanning force measurements with the same instrument; the apparent height of the DNA (0.6 ± 0.3 nm) was similar with the two techniques. These results demonstrate the applicability of the shear force signal for imaging biological macromolecules according to topography and in conjunction with the optical signals of a near‐field scanning optical microscope (NSOM).

Novel Microscope-Based Approaches for the Investigation of Protein-Protein Interactions in Signal Transduction

In addition to the biochemical characterization of interacting proteins, the spatiotemporal localisation in situ or in vivo of the transiently associating participants of a cascade mechanism can greatly enhance our understanding of the given signal transduction process. However, the mere determination of colocalization based on fluorescent tags that are compatible with the in vivo observation does not generally suffice due to the limitation in resolution imposed by optical diffraction in conventional light microscopy.

Interferometric measurement of fluorescence excitation spectra

A Michelson interferometer has been adapted as an excitation source for fluorescence spectroscopy. A moving fringe pattern was generated by linear displacement of the movable mirror of the Michelson interferometer coupled to a xenon-arc lamp. This spectrally modulated source was monitored by a reference photomultiplier and used for exciting a Rhodamine B solution. The fluorescence emission at >645 nm was detected by a second photomultiplier. The two interferograms were acquired by a dual-channel digital oscilloscope, and their discrete Fourier transforms and corresponding power spectra were generated in a computer. The power spectrum of the emission signal represented the excitation spectrum, as was confirmed by comparison with the absorption spectrum of Rhodamine B. Thisoptical arrangement is well suited for acquiring fluorescence excitation spectra in the optical microscopy of biological specimens.

Soft Typing for Ordered Resolution

We propose a variant of ordered resolution with semantic restrictions based on interpretations which are identified by the given atom ordering and selection function. Techniques for effectively approximating validity (satisfiability) in these interpretations are presented. They are related to methods of soft typing for programming languages. The framework is shown to be strictly more general than certain previously introduced approaches. Implementation of some of our techniques in the SPASS prover has lead to encouraging experimental results.

Unification in Extension of Shallow Equational Theories

We show that unification in certain extensions of shallow equational theories is decidable. Our extensions generalize the known classes of shallow or standard equational theories. In order to prove decidability of unification in the extensions, a class of Horn clause sets called sorted shallow equational theories is introduced. This class is a natural extension of tree automata with equality constraints between brother subterms as well as shallow sort theories. We show that saturation under sorted superposition is effective on sorted shallow equational theories. So called semi-linear equational theories can be effectively transformed into equivalent sorted shallow equational theories and generalize the classes of shallow and standard equational theories.

Fluorescence SNOM of domain structures of LB films containing electron transfer systems

The morphology of a mixed monolayer consisting of a metal complex and stearic acid on mica was investigated by SNOM. In the topographic shear-force image, round domains of several micrometers diameter protruded several A from the monolayer surface. The fluorescence pattern revealed by SNOM (excitation at 488 nm, emission at 590 nm) matched the monolayer topography, and a higher fluorescence intensity was detected from the interdomain space. The photobleaching kinetics and integrated fluorescence of the different phases of the monolayer film were analyzed, yielding estimates of relative quantum yields and surface densities of the dyad.

Advanced Indexing Operations on Substitution Trees

Indexing techniques support the retrieval and maintenance of large sets of terms. There is also an indexing method called substitution tree indexing that efficiently handles sets of substitutions. We present three advanced indexing operations for substitution trees: The multi-merge for the simultaneous unification of sets of substitutions, the subsumption operation on two sets of substitutions, and the selection of ‘lightest’ substitutions of a set of substitutions. The indexing operations can be combined to obtain powerful reasoning tools for theorem provers.

Integration of Optical Techniques in Scanning Probe Microscopes

During the last 15 years scanning probe microscopes (SPM), in particular the scanning force microscope (SFM) and scanning tunneling microscope (STM), have developed into highly sophisticated instruments for the investigation of surfaces and surface structures under a broad range of environmental conditions. Applications range from imaging single atoms in ultrahigh vacuum 1, to the visualization of strands of DNA on freshly cleaved mica surfaces2, and the investigation of the activation of platelets under physiological conditions 3, 4.