Topologically Massive Gauge Theories and their Dual Factorised Gauge Invariant Formulation

There exists a well-known duality between the Maxwell-Chern-Simons theory and the self-dual massive model in 2+1 dimensions. This dual description has been extended to topologically massive gauge theories (TMGT) in any dimension. This Letter introduces an unconventional approach to the construction of this type of duality through a reparametrisation of the master theory action. The dual action thereby obtained preserves the same gauge symmetry structure as the original theory. Furthermore, the dual action is factorised into a propagating sector of massive gauge invariant variables and a sector with gauge variant variables defining a pure topological field theory. Combining results obtained within the Lagrangian and Hamiltonian formulations, a new completed structure for a gauge invariant dual factorisation of TMGT is thus achieved.Comment: 1+7 pages, no figure

Delocalization transition for the Google matrix

We study the localization properties of eigenvectors of the Google matrix, generated both from the World Wide Web and from the Albert-Barabasi model of networks. We establish the emergence of a delocalization phase for the PageRank vector when network parameters are changed. In the phase of localized PageRank, a delocalization takes place in the complex plane of eigenvalues of the matrix, leading to delocalized relaxation modes. We argue that the efficiency of information retrieval by Google-type search is strongly affected in the phase of delocalized PageRank.Comment: 4 pages, 5 figures. Research done at http://www.quantware.ups-tlse.fr

Invariance quantum groups of the deformed oscillator algebra

A differential calculus is set up on a deformation of the oscillator algebra. It is uniquely determined by the requirement of invariance under a seven-dimensional quantum group. The quantum space and its associated differential calculus are also shown to be invariant under a nine generator quantum group containing the previous one.Comment: 13 pages, Late

Out-of-plane spin polarization from in-plane electric and magnetic fields

We show that the joint effect of spin-orbit and magnetic fields leads to a spin polarization perpendicular to the plane of a two-dimensional electron system with Rashba spin-orbit coupling and in-plane parallel dc magnetic and electric fields, for angle-dependent impurity scattering or nonparabolic energy spectrum, while only in-plane polarization persists for simplified models. We derive Bloch equations, describing the main features of recent experiments, including the magnetic field dependence of static and dynamic responses.Comment: 5 pages and 1 figure in main text, 5 pages in appendi

Harmonic Measure and Winding of Conformally Invariant Curves

The exact joint multifractal distribution for the scaling and winding of the electrostatic potential lines near any conformally invariant scaling curve is derived in two dimensions. Its spectrum f(alpha,lambda) gives the Hausdorff dimension of the points where the potential scales with distance $r$ as $H \sim r^{\alpha}$ while the curve logarithmically spirals with a rotation angle phi=lambda ln r. It obeys the scaling law f(\alpha,\lambda)=(1+\lambda^2) f(\bar \alpha)-b\lambda^2 with \bar \alpha=\alpha/(1+\lambda^2) and b=(25-c)/{12}$, and where f(\alpha)\equiv f(\alpha,0) is the pure harmonic measure spectrum, and c the conformal central charge. The results apply to O(N) and Potts models, as well as to {\rm SLE}_{\kappa}.Comment: 3 figure

Strategy bifurcation and spatial inhomogeneity in a simple model of competing sellers

We present a simple one-parameter model for spatially localised evolving agents competing for spatially localised resources. The model considers selling agents able to evolve their pricing strategy in competition for a fixed market. Despite its simplicity, the model displays extraordinarily rich behavior. In addition to ``cheap'' sellers pricing to cover their costs, ``expensive'' sellers spontaneously appear to exploit short-term favorable situations. These expensive sellers ``speciate'' into discrete price bands. As well as variety in pricing strategy, the ``cheap'' sellers evolve a strongly correlated spatial structure, which in turn creates niches for their expensive competitors. Thus an entire ecosystem of coexisting, discrete, symmetry-breaking strategies arises.Comment: 6 pages, 6 figures, epl2; 1 new figure, include nash equilibrium analysis, typo fixe

Inverse problem and Bertrand's theorem

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical equation. This permit a particulary compact and elegant proof of Bertrand's theorem.Comment: 11 pages, 3 figure

Fixed-point elimination in the intuitionistic propositional calculus

It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras are not complete as lattices. The reason is that these extremal fixed-points are definable by formulas of the IPC. Consequently, the $\mu$-calculus based on intuitionistic logic is trivial, every $\mu$-formula being equivalent to a fixed-point free formula. We give in this paper an axiomatization of least and greatest fixed-points of formulas, and an algorithm to compute a fixed-point free formula equivalent to a given $\mu$-formula. The axiomatization of the greatest fixed-point is simple. The axiomatization of the least fixed-point is more complex, in particular every monotone formula converges to its least fixed-point by Kleene's iteration in a finite number of steps, but there is no uniform upper bound on the number of iterations. We extract, out of the algorithm, upper bounds for such n, depending on the size of the formula. For some formulas, we show that these upper bounds are polynomial and optimal

Fifteen days of 3200m simulated hypoxia marginally regulates markers for protein synthesis and degradation in human skeletal muscle

Chronic hypoxia leads to muscle atrophy. The molecular mechanisms responsible for this phenomenon are not well defined in vivo. We sought to determine how chronic hypoxia regulates molecular markers of protein synthesis and degradation in human skeletal muscle and whether these regulations were related to the regulation of the hypoxia-inducible factor (HIF) pathway. Eight young male subjects lived in a normobaric hypoxic hotel (FiO2 14.1%, 3,200 m) for 15 days in well-controlled conditions for nutrition and physical activity. Skeletal muscle biopsies were obtained in the musculus vastus lateralis before (PRE) and immediately after (POST) hypoxic exposure. Intramuscular hypoxia-inducible factor-1 alpha (HIF-1α) protein expression decreased (-49%, P=0.03), whereas hypoxia-inducible factor-2 alpha (HIF-2α) remained unaffected from PRE to POST hypoxic exposure. Also, downstream HIF-1α target genes VEGF-A (-66%, P=0.006) and BNIP3 (-24%, P=0.002) were downregulated, and a tendency was measured for neural precursor cell expressed, developmentally Nedd4 (-47%, P=0.07), suggesting lowered HIF-1α transcriptional activity after 15 days of exposure to environmental hypoxia. No difference was found on microtubule-associated protein 1 light chain 3 type II/I (LC3b-II/I) ratio, and P62 protein expression tended to increase (+45%, P=0.07) compared to PRE exposure levels, suggesting that autophagy was not modulated after chronic hypoxia. The mammalian target of rapamycin complex 1 pathway was not altered as Akt, mammalian target of rapamycin, S6 kinase 1, and 4E-binding protein 1 phosphorylation did not change between PRE and POST. Finally, myofiber cross-sectional area was unchanged between PRE and POST. In summary, our data indicate that moderate chronic hypoxia differentially regulates HIF-1α and HIF-2α, marginally affects markers of protein degradation, and does not modify markers of protein synthesis or myofiber cross-sectional area in human skeletal muscle