Model-completion of varieties of co-Heyting algebras

It is known that exactly eight varieties of Heyting algebras have a model-completion, but no concrete axiomatisation of these model-completions were known by now except for the trivial variety (reduced to the one-point algebra) and the variety of Boolean algebras. For each of the six remaining varieties we introduce two axioms and show that 1) these axioms are satisfied by all the algebras in the model-completion, and 2) all the algebras in this variety satisfying these two axioms have a certain embedding property. For four of these six varieties (those which are locally finite) this actually provides a new proof of the existence of a model-completion, this time with an explicit and finite axiomatisation.Comment: 28 page

Investigation of Millimetre Wave Generation by stimulated Brillouin scattering for Radio Over Fibre Applications

The rising demand for greater bandwidth and increased flexibility in modern telecommunication systems has lead to increased research activities in the field of Millimetre Wave-Photonics. The combination of an optical access network and the radio propagation of high data-rate signals provides a solution to meet these demands. Such structures are also known as Radio Over Fibre Systems. They implement the optical Millimetre Wave generation in a central station and the transmission of radio waves via a remote antenna unit to the radio cell. The expected data rate is very high, due to the fact that both the optical and the radio-link provide a large transmission bandwidth. This dissertation concerns the investigation of a new and simple method for the flexible generation of Millimetre Waves for application in Radio Over Fibre systems. The method is based on the heterodyne detection of two optical waves in a photo detector. By externally amplitude modulating the optical wave, different sidebands are generated. Two of these sidebands are selected and amplified by the non-linear effect of stimulated Brillouin scattering. As a gain medium, a standard single mode fibre is used. According to the theoretical investigation, very good carrier performances are possible with this method, and a computer simulation shows little degradation in the signals during their propagation in the system. The measured results are in strong agreement with the theoretical analysis. Experimental results show that the system can be fully utilised as a Radio Over Fibre system. The thesis is divided into five main parts: Introduction – Theory – Simulation – Experiment – Conclusion. In the Introduction, an overview of the current methods of Millimetre Wave Generation, Radio Over Fibre and the nonlinear effects of Brillouin scattering is given. In the theoretical section, a differential equation system which mathematically describes the system is derived and also solved numerically. With a proof of the concept set-up, the simulated results are compared with the experimental data. In the last section the work is conclude and future tasks are discus

Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications

This paper documents nonlinear cross-sectional dependence in the term structure of U.S. Treasury yields and points out risk management implications. The analysis is based on a Kalman filter estimation of a two-factor affine model which specifies the yield curve dynamics. We then apply a broad class of copula functions for modeling dependence in factors spanning the yield curve. Our sample of monthly yields in the 1982 to 2001 period provides evidence of upper tail dependence in yield innovations; i.e., large positive interest rate shocks tend to occur under increased dependence. In contrast, the best fitting copula model coincides with zero lower tail dependence. This asymmetry has substantial risk management implications. We give an example in estimating bond portfolio loss quantiles and report the biases which result from an application of the normal dependence model.affine term structure models, nonlinear dependence, copula functions, tail dependence, value-at-risk

Codimension and pseudometric in co-Heyting algebras

In this paper we introduce a notion of dimension and codimension for every element of a distributive bounded lattice $L$. These notions prove to have a good behavior when $L$ is a co-Heyting algebra. In this case the codimension gives rise to a pseudometric on $L$ which satisfies the ultrametric triangle inequality. We prove that the Hausdorff completion of $L$ with respect to this pseudometric is precisely the projective limit of all its finite dimensional quotients. This completion has some familiar metric properties, such as the convergence of every monotonic sequence in a compact subset. It coincides with the profinite completion of $L$ if and only if it is compact or equivalently if every finite dimensional quotient of $L$ is finite. In this case we say that $L$ is precompact. If $L$ is precompact and Hausdorff, it inherits many of the remarkable properties of its completion, specially those regarding the join/meet irreducible elements. Since every finitely presented co-Heyting algebra is precompact Hausdorff, all the results we prove on the algebraic structure of the latter apply in particular to the former. As an application, we obtain the existence for every positive integers $n,d$ of a term $t_{n,d}$ such that in every co-Heyting algebra generated by an $n$-tuple $a$, $t_{n,d}(a)$ is precisely the maximal element of codimension $d$.Comment: 34 page

Entwurf einer Patternbeschreibungssprache für die Informationsextraktion in der Dokumentanalyse

Dokumentanalyse befaßt sich mit der Extraktion von relevanten Informationen aus Dokumenten, die in Papierform vorliegen. Um die gewünschten Informationen in einem Text zu finden, können verschiedene Techniken angewendet werden. Sie reichen von einfachen Suchverfahren hin zum Versuch des vollständigen Parsens eines Textes. Häufig stammen diese Techniken aus dem Bereich der NLP, wo sie zur Verarbeitung von elektronischen Texten eingesetzt werden. Unabhängig von der eingesetzten Technik benötigt man jedoch immer eine Sprache, mit der die Syntax und die Semantik der gesuchten Informationen beschrieben werden können. In diesem Dokument wird eine solche Sprache vorgestellt, die insbesondere den Erfordernissen der Dokumentanalyse Rechnung trägt, aber allerdings auch für die Verarbeitung elektronischer Texte genutzt werden kann. Derzeit wird die Sprache zur Informationsextraktion in und zur Klassifikation von deutschen Geschäftsbriefen eingesetzt

More on coupling coefficients for the most degenerate representations of SO(n)

We present explicit closed-form expressions for the general group-theoretical factor appearing in the alpha-topology of a high-temperature expansion of SO(n)-symmetric lattice models. This object, which is closely related to 6j-symbols for the most degenerate representation of SO(n), is discussed in detail.Comment: 9 pages including 1 table, uses IOP macros Update of Introduction and Discussion, References adde

TAR-RNA recognition by a novel cyclic aminoglycoside analogue

The formation of the Tat-protein/TAR-RNA complex is a crucial step in the regulation of human immunodeficiency virus (HIV)-gene expression. To obtain full-length viral transcripts the Tat/TAR complex has to recruit the positive transcription elongation factor complex (P-EFTb), which interacts with TAR through its cyclin T1 (CycT1) component. Mutational studies identified the TAR hexanucleotide loop as a crucial region for contacting CycT1. Interfering with the interaction between the Tat/CycT1 complex and the TAR-RNA is an attractive strategy for the design of anti-HIV drugs. Positively charged molecules, like aminoglycosides or peptidomimetics, bind the TAR-RNA, disrupting the Tat/TAR complex. Here, we investigate the complex between the HIV-2 TAR-RNA and a neooligoaminodeoxysaccharide by NMR spectroscopy. In contrast to other aminoglycosides, this novel aminoglycoside analogue contacts simultaneously the bulge residues required for Tat binding and the A35 residue of the hexanucleotide loop. Upon complex formation, the loop region undergoes profound conformational changes. The novel binding mode, together with the easy accessibility of derivatives for the neooligoaminodeoxysaccharide, could open the way to the design of a new class of TAR-RNA binders, which simultaneously inhibit the formation of both the Tat/TAR binary complex and the Tat/TAR/CycT1 ternary complex by obstructing both the bulge and loop regions of the RNA