Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators

Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the theory are described as matrix models. This allow us to make a link with non-commutative geometry and to look at the issue of the semi-classical limit of LQG from a new perspective. This work is thought as part of a bigger project of describing quantum geometry in quantum information terms.Comment: 16 pages, revtex, 3 figure

Fourier Duality as a Quantization Principle

The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally compact groups. Kac algebras -- and the duality they incorporate -- are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest non-trivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no more complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems.Comment: LaTeX 2.09 with NFSS or AMSLaTeX 1.1. 97Kb, 43 pages, no figures. requires subeqnarray.sty, amssymb.sty, amsfonts.sty. Final version with (few) text and (crucial) typos correction

Topology at the Planck Length

A basic arbitrariness in the determination of the topology of a manifold at the Planck length is discussed. An explicit example is given of a `smooth' change in topology from the 2-sphere to the 2-torus through a sequence of noncommuting geometries. Applications are considered to the theory of D-branes within the context of the proposed $M$(atrix) theory.Comment: Orsay Preprint 97/34, 17 pages, Late

Projective Fourier Duality and Weyl Quantization

The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras.Comment: LaTeX 2.09 with NFSS or AMSLaTeX 1.1. 102Kb, 44 pages, no figures. requires subeqnarray.sty, amssymb.sty, amsfonts.sty. Final version with text improvements and crucial typos correction

Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and Simulation

We investigate the effective conductivity ($\sigma_e$) of a class of amorphous media defined by the level-cut of a Gaussian random field. The three point solid-solid correlation function is derived and utilised in the evaluation of the Beran-Milton bounds. Simulations are used to calculate $\sigma_e$ for a variety of fields and volume fractions at several different conductivity contrasts. Relatively large differences in $\sigma_e$ are observed between the Gaussian media and the identical overlapping sphere model used previously as a `model' amorphous medium. In contrast $\sigma_e$ shows little variability between different Gaussian media.Comment: 15 pages, 14 figure

Worms take to the slo lane: a perspective on the mode of action of emodepside

The cyclo-octapdepsipeptide anthelmintic emodepside exerts a profound paralysis on parasitic and free-living nematodes. The neuromuscular junction is a significant determinant of this effect. Pharmacological and electrophysiological analyses in the parasitic nematode Ascaris suum have resolved that emodepside elicits a hyperpolarisation of body wall muscle, which is dependent on extracellular calcium and the efflux of potassium ions. The molecular basis for emodepside’s action has been investigated in forward genetic screens in the free-living nematode Caenorhabditis elegans. Two screens for emodepside resistance, totalling 20,000 genomes, identified several mutants of slo-1, which encodes a calcium-activated potassium channel homologous to mammalian BK channels. Slo-1 null mutants are more than 1000-fold less sensitive to emodepside than wild-type C. elegans and tissue-specific expression studies show emodepside acts on SLO-1 in neurons regulating feeding and motility as well as acting on SLO-1 in body wall muscle. These genetic data, combined with physiological measurements in C. elegans and the earlier physiological analyses on A. suum, define a pivotal role for SLO-1 in the mode of action of emodepside. Additional signalling pathways have emerged as determinants of emodepside’s mode of action through biochemical and hypothesis-driven approaches. Mutant analyses of these pathways suggest a modulatory role for each of them in emodepside’s mode of action; however, they impart much more modest changes in the sensitivity to emodepside than mutations in slo-1. Taken together these studies identify SLO-1 as the major determinant of emodepside’s anthelmintic activity. Structural information on the BK channels has advanced significantly in the last 2 years. Therefore, we rationalise this possibility by suggesting a model that speculates on the nature of the emodepside pharmacophore within the calcium-activated potassium channels

Structure-property correlations in model composite materials

We investigate the effective properties (conductivity, diffusivity and elastic moduli) of model random composite media derived from Gaussian random fields and overlapping hollow spheres. The morphologies generated in the models exhibit low percolation thresholds and give a realistic representation of the complex microstructure observed in many classes of composites. The statistical correlation functions of the models are derived and used to evaluate rigorous bounds on each property. Simulation of the effective conductivity is used to demonstrate the applicability of the bounds. The key morphological features which effect composite properties are discussed

Immunomagnetic microbeads for screening with flow cytometry and identification with nano-liquid chromatography mass spectrometry of ochratoxins in wheat and cereal

Multi-analyte binding assays for rapid screening of food contaminants require mass spectrometric identification of compound(s) in suspect samples. An optimal combination is obtained when the same bioreagents are used in both methods; moreover, miniaturisation is important because of the high costs of bioreagents. A concept is demonstrated using superparamagnetic microbeads coated with monoclonal antibodies (Mabs) in a novel direct inhibition flow cytometric immunoassay (FCIA) plus immunoaffinity isolation prior to identification by nano-liquid chromatography–quadrupole time-of-flight-mass spectrometry (nano-LC-Q-ToF-MS). As a model system, the mycotoxin ochratoxin A (OTA) and cross-reacting mycotoxin analogues were analysed in wheat and cereal samples, after a simple extraction, using the FCIA with anti-OTA Mabs. The limit of detection for OTA was 0.15 ng/g, which is far below the lowest maximum level of 3 ng/g established by the European Union. In the immunomagnetic isolation method, a 350-times-higher amount of beads was used to trap ochratoxins from sample extracts. Following a wash step, bound ochratoxins were dissociated from the Mabs using a small volume of acidified acetonitrile/water (2/8 v/v) prior to separation plus identification with nano-LC-Q-ToF-MS. In screened suspect naturally contaminated samples, OTA and its non-chlorinated analogue ochratoxin B were successfully identified by full scan accurate mass spectrometry as a proof of concept for identification of unknown but cross-reacting emerging mycotoxins. Due to the miniaturisation and bioaffinity isolation, this concept might be applicable for the use of other and more expensive bioreagents such as transport proteins and receptors for screening and identification of known and unknown (or masked) emerging food contaminants

Skyrmionic order and magnetically induced polarization change in lacunar spinel compounds GaV4_{4}S8_{8} and GaMo4_{4}S8_{8}: comparative theoretical study

We show how low-energy electronic models derived from the first-principles electronic structure calculations can help to rationalize the magnetic properties of two lacunar spinel compounds GaM4S8 with light (M=V) and heavy (M=Mo) transition-metal elements, which are responsible for different spin-orbit interaction strength. In the model, each magnetic lattice point was associated with the M4S4 molecule, and the model itself was formulated in the basis of molecular Wannier functions constructed for three magnetic t2 bands. The effects of rhombohedral distortion, spin-orbit interaction, band filling, and the screening of Coulomb interactions in the t2 bands are discussed in details. The electronic model is further treated in the superexchange approximation, which allows us to derive an effective spin model for the energy and electric polarization ($P$) depending on the relative orientation of spins in the bonds, and study the properties of this model by means of classical Monte Carlo simulations with the emphasis on the possible formation of the skyrmionic phase. While isotropic exchange interactions clearly dominate in GaV4S8, all types of interactions -- isotropic, antisymmetric, and symmetric anisotropic -- are comparable in the case of GaMo4S8. Particularly, large uniaxial exchange anisotropy has a profound effect on the properties of GaMo4S8. On the one hand, it raises the Curie temperature by opening a gap in the spectrum of magnon excitations. On the other hand, it strongly affects the skyrmionic phase by playing the role of a molecular field, which facilitates the formation of skyrmions, but makes them relatively insensitive to the external magnetic field in the large part of the phase diagram. We predict reversal of the magnetic dependence of $P$ in the case of GaMo4S8 caused by the reversal of direction of the rhombohedral distortion.Comment: 13 pages, 9 figure