Symplectic structures associated to Lie-Poisson groups

The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified and the corresponding symplectic forms are described. Thus the construction of the Kirillov symplectic form is generalized for Lie-Poisson groups.Comment: 30 page

Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations

Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and strategyproofness. In particular, we present robust versions of envy-freeness and proportionality that are not only stronger than their standard counter-parts but also have less information requirements. We then focus on cake cutting with piecewise constant valuations and present three desirable algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time, robust envy-free, and non-wasteful. It relies on parametric network flows and recent generalizations of the probabilistic serial algorithm. For the subdomain of piecewise uniform valuations, we show that it is also group-strategyproof. Then, we show that there exists an algorithm (MEA) that is polynomial-time, envy-free, proportional, and Pareto optimal. MEA is based on computing a market-based equilibrium via a convex program and relies on the results of Reijnierse and Potters [24] and Devanur et al. [15]. Moreover, we show that MEA and CCEA are equivalent to mechanism 1 of Chen et. al. [12] for piecewise uniform valuations. We then present an algorithm CSD and a way to implement it via randomization that satisfies strategyproofness in expectation, robust proportionality, and unanimity for piecewise constant valuations. For the case of two agents, it is robust envy-free, robust proportional, strategyproof, and polynomial-time. Many of our results extend to more general settings in cake cutting that allow for variable claims and initial endowments. We also show a few impossibility results to complement our algorithms.Comment: 39 page

The human mu opioid receptor: modulation of functional desensitization by calcium/calmodulin-dependent protein kinase and protein kinase C

Opioids are some of the most efficacious analgesics used in humans. Prolonged administration of opioids, however, often causes the development of drug tolerance, thus limiting their effectiveness. To explore the molecular basis of those mechanisms that may contribute to opioid tolerance, we have isolated a cDNA for the human mu opioid receptor, the target of such opioid narcotics as morphine, codeine, methadone, and fentanyl. The receptor encoded by this cDNA is 400 amino acids long with 94% sequence similarity to the rat mu opioid receptor. Transient expression of this cDNA in COS-7 cells produced high-affinity binding sites to mu-selective agonists and antagonists. This receptor displays functional coupling to a recently cloned G-protein-activated K+ channel. When both proteins were expressed in Xenopus oocytes, functional desensitization developed upon repeated stimulation of the mu opioid receptor, as observed by a reduction in K+ current induced by the second mu receptor activation relative to that induced by the first. The extent of desensitization was potentiated by both the multifunctional calcium/calmodulin-dependent protein kinase and protein kinase C. These results demonstrate that kinase modulation is a molecular mechanism by which the desensitization of mu receptor signaling may be regulated at the cellular level, suggesting that this cellular mechanism may contribute to opioid tolerance in humans

Structural and dielectric properties of Sr2_{2}TiO4_{4} from first principles

We have investigated the structural and dielectric properties of Sr$_{2}$TiO$_{4}$,the first member of the Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ Ruddlesden-Popper series, within density functional theory. Motivated by recent work in which thin films of Sr$_{2}$TiO$_{4}$ were grown by molecular beam epitaxy (MBE) on SrTiO$_{3}$ substrates, the in-plane lattice parameter was fixed to the theoretically optimized lattice constant of cubic SrTiO$_{3}$ (n=$\infty$), while the out-of-plane lattice parameter and the internal structural parameters were relaxed. The fully relaxed structure was also investigated. Density functional perturbation theory was used to calculate the zone-center phonon frequencies, Born effective charges, and the electronic dielectric permittivity tensor. A detailed study of the contribution of individual infrared-active modes to the static dielectric permittivity tensor was performed. The calculated Raman and infrared phonon frequencies were found to be in agreement with experiment where available. Comparisons of the calculated static dielectric permittivity with experiments on both ceramic powders and epitaxial thin films are discussed.Comment: 11 pages, 1 figure, 8 tables, submitted to Phys. Rev.

An efficient approach based on trust and reputation for secured selection of grid resources

Security is a principal concern in offering an infrastructure for the formation of general-purpose computational grids. A number of grid implementations have been devised to deal with the security concerns by authenticating the users, hosts and their interactions in an appropriate fashion. Resource management systems that are sophisticated and secured are inevitable for the efficient and beneficial deployment of grid computing services. The chief factors that can be problematic in the secured selection of grid resources are the wide range of selection and the high degree of strangeness. Moreover, the lack of a higher degree of confidence relationship is likely to prevent efficient resource allocation and utilisation. In this paper, we present an efficient approach for the secured selection of grid resources, so as to achieve secure execution of the jobs. This approach utilises trust and reputation for securely selecting the grid resources. To start with, the self-protection capability and reputation weightage of all the entities are computed, and based on those values, the trust factor (TF) of all the entities are determined. The reputation weightage of an entity is the measure of both the user’s feedback and other entities’ feedback. Those entities with higher TF values are selected for the secured execution of jobs. To make the proposed approach more comprehensive, a novel method is employed for evaluating the user’s feedback on the basis of the existing feedbacks available regarding the entities. This approach is proved to be scalable for an increased number of user jobs and grid entities. The experimentation portrays that this approach offers desirable efficiency in the secured selection of grid resources

Equidistribution of zeros of holomorphic sections in the non compact setting

We consider N-tensor powers of a positive Hermitian line bundle L over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed with respect to the natural measure coming from the curvature of L, as N tends to infinity. Under certain boundedness assumptions on the curvature of the canonical line bundle of X and on the Chern form of L we prove a non-compact version of this result. We give various applications, including the limiting distribution of zeros of cusp forms with respect to the principal congruence subgroups of SL2(Z) and to the hyperbolic measure, the higher dimensional case of arithmetic quotients and the case of orthogonal polynomials with weights at infinity. We also give estimates for the speed of convergence of the currents of integration on the zero-divisors.Comment: 25 pages; v.2 is a final update to agree with the published pape

More on quantum groups from the the quantization point of view

Star products on the classical double group of a simple Lie group and on corresponding symplectic grupoids are given so that the quantum double and the "quantized tangent bundle" are obtained in the deformation description. "Complex" quantum groups and bicovariant quantum Lie algebras are discused from this point of view. Further we discuss the quantization of the Poisson structure on symmetric algebra $S(g)$ leading to the quantized enveloping algebra $U_{h}(g)$ as an example of biquantization in the sense of Turaev. Description of $U_{h}(g)$ in terms of the generators of the bicovariant differential calculus on $F(G_q)$ is very convenient for this purpose. Finally we interpret in the deformation framework some well known properties of compact quantum groups as simple consequences of corresponding properties of classical compact Lie groups. An analogue of the classical Kirillov's universal character formula is given for the unitary irreducible representation in the compact case.Comment: 18 page

Randomizing world trade. II. A weighted network analysis

Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed/undirected, aggregated/disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243 [physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011

Trapped electron coupled to superconducting devices

We propose to couple a trapped single electron to superconducting structures located at a variable distance from the electron. The electron is captured in a cryogenic Penning trap using electric fields and a static magnetic field in the Tesla range. Measurements on the electron will allow investigating the properties of the superconductor such as vortex structure, damping and decoherence. We propose to couple a superconducting microwave resonator to the electron in order to realize a circuit QED-like experiment, as well as to couple superconducting Josephson junctions or superconducting quantum interferometers (SQUIDs) to the electron. The electron may also be coupled to a vortex which is situated in a double well potential, realized by nearby pinning centers in the superconductor, acting as a quantum mechanical two level system that can be controlled by a transport current tilting the double well potential. When the vortex is trapped in the interferometer arms of a SQUID, this would allow its detection both by the SQUID and by the electron.Comment: 13 pages, 5 figure

Coherent States for Quantum Compact Groups

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit and interpret the coherent state as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R--matrix formulation (generalizing this way the $q$--deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel--Weil construction) are described using the concept of coherent state. The relation between representation theory and non--commutative differential geometry is suggested.}Comment: 25 page