Properties of the Scalar Universal Equations

The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The Euler hierarchy itself is given a new interpretation in terms of the formal complex of variational calculus, and is shown to be related to the algebra of distinguished symmetries of the first source form.Comment: 15 pages, LaTeX articl

Integrin-Mediated Host Cell Invasion by Type 1–Piliated Uropathogenic Escherichia coli

Uropathogenic Escherichia coli (UPEC), the primary causative agent of urinary tract infections, typically express filamentous adhesive organelles called type 1 pili that mediate both bacterial attachment to and invasion of bladder urothelial cells. Several host proteins have previously been identified as receptors for type 1 pili, but none have been conclusively shown to promote UPEC entry into host bladder cells. Using overlay assays with FimH, the purified type 1 pilus adhesin, and mass spectroscopy, we have identified β1 and α3 integrins as key host receptors for UPEC. FimH recognizes N-linked oligosaccharides on these receptors, which are expressed throughout the urothelium. In a bladder cell culture system, β1 and α3 integrin receptors co-localize with invading type 1–piliated bacteria and F-actin. FimH-mediated bacterial invasion of host bladder cells is inhibited by β1 and α3 integrin–specific antibodies and by disruption of the β1 integrin gene in the GD25 fibroblast cell line. Phosphorylation site mutations within the cytoplasmic tail of β1 integrin that alter integrin signaling also variably affect UPEC entry into host cells, by either attenuating or boosting invasion frequencies. Furthermore, focal adhesion and Src family kinases, which propagate integrin-linked signaling and downstream cytoskeletal rearrangements, are shown to be required for FimH-dependent bacterial invasion of target host cells. Cumulatively, these results indicate that β1 and α3 integrins are functionally important receptors for type 1 pili–expressing bacteria within the urinary tract and possibly at other sites within the host

Algebraic description of spacetime foam

A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of general relativity and the commutative coordinates of its events by means of appropriate limit constructions.Comment: 34 pages, LaTeX2e, the section concerning classical spacetimes in the limit essentially correcte

HMM based scenario generation for an investment optimisation problem

This is the post-print version of the article. The official published version can be accessed from the link below - Copyright @ 2012 Springer-Verlag.The Geometric Brownian motion (GBM) is a standard method for modelling financial time series. An important criticism of this method is that the parameters of the GBM are assumed to be constants; due to this fact, important features of the time series, like extreme behaviour or volatility clustering cannot be captured. We propose an approach by which the parameters of the GBM are able to switch between regimes, more precisely they are governed by a hidden Markov chain. Thus, we model the financial time series via a hidden Markov model (HMM) with a GBM in each state. Using this approach, we generate scenarios for a financial portfolio optimisation problem in which the portfolio CVaR is minimised. Numerical results are presented.This study was funded by NET ACE at OptiRisk Systems

Integrable Generalisations of the 2-dimensional Born Infeld Equation

The Born-Infeld equation in two dimensions is generalised to higher dimensions whilst retaining Lorentz Invariance and complete integrability. This generalisation retains homogeneity in second derivatives of the field.Comment: 11 pages, Latex, DTP/93/3

Structural studies of (rac)-BIPHEN organomagnesiates and intermediates in the halogen-metal exchange of 2-Bromopyridine

Four lithium magnesiate complexes (2−5) containing the dianionic (rac)-BIPHEN ligand have been prepared and characterized using X-ray crystallography and NMR spectroscopy. (THF)3·Li2Mg{(rac)-BIPHEN}nBu2, 2, (THF)3·Li2Mg{(rac)-BIPHEN}(CH2SiMe3)2, 3, and (THF)2·Li2Mg{(rac)-BIPHEN}neoPe2, 4, have been prepared by complexation of the appropriate dialkylmagnesium compound with in situ prepared Li(rac)-BIPHEN in a mixture of hydrocarbon/THF. For all structures, the Mg centers are four-coordinate (and retain the alkyl groups); however, in 2 and 3 the two Li centers have different coordination spheres (one binding to one THF molecule, the other to two). The solid-state structures of 2 and 3 are essentially isostructural with that of 4 except that both Li atoms in this molecule have equivalent coordination spheres. The solution behaviors of these three molecules have been studied by 1H, 13C, and DOSY NMR spectroscopy. During the synthesis of 2, it was discovered that a (rac)-BIPHEN-rich (or n-butyl-free) lithium magnesiate, (THF)4Li2Mg{(rac)-BIPHEN}fo2, 2b, could be isolated. The lithium precursor to 2−5, (THF)4·Li4{(rac)-BIPHEN)}2, 1, has also been isolated. Within the molecular structure of this tetranuclear complex, there are three different Li coordination environments. Finally, 2 has already shown promise as a reagent in a halogen−metal exchange reaction with 2-bromopyridine. The structural chemistry at play in this reaction was probed by X-ray crystallography and NMR spectroscopy. The organometallic intermediate pyridyl-magnesiated 5, (THF)2·Li2Mg{(rac)-BIPHEN}(2-pyridyl)2, was isolated in high yield

A topos for algebraic quantum theory

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr's idea that the empirical content of quantum physics is accessible only through classical physics, we show how a C*-algebra of observables A induces a topos T(A) in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra. According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum S(A) in T(A), which in our approach plays the role of a quantum phase space of the system. Thus we associate a locale (which is the topos-theoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on S(A), and self-adjoint elements of A define continuous functions (more precisely, locale maps) from S(A) to Scott's interval domain. Noting that open subsets of S(A) correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos T(A).Comment: 52 pages, final version, to appear in Communications in Mathematical Physic

An ALM model for pension funds using integrated chance constraints

We discuss integrated chance constraints in their role of short-term risk constraints in a strategic ALM model for Dutch pension funds. The problem is set up as a multistage recourse model, with special attention for modeling short-term risk prompted by the development of new guidelines by the regulating authority for Dutch pension funds. The paper concludes with a numerical illustration of the importance of such short-term risk constraints