Equilibrium strategy and population-size effects in lowest unique bid auctions

In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large data set of internet auctions. The theory agrees with the data with striking accuracy for small population-size N, while for larger N a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.     

Effects of refractive index changes on four-wave mixing bands in Er-doped photonic crystal fibers pumped at 976 nm

An experimental study of the effects of an auxiliary 976 nm pump signal on the four-wave mixing parametric bands generated with a 1064 nm pump in a normal dispersion Er-doped photonic crystal fiber is presented. The four-wave mixing signal and idler bands shift to shorter and longer wavelengths, respectively, with increasing 976 nm pump power. It is shown that the wavelength-dependent resonant refractive index change in the erbium-doped core under 976 nm pumping is at the origin of the effect.     

Mixing Times of Monotone Surfaces and SOS Interfaces: A Mean Curvature Approach

We consider stochastic spin-flip dynamics for: (i) monotone discrete surfaces in \({\mathbb {Z}^3}\) with planar boundary height and (ii) the one-dimensional discrete Solid-on-Solid (SOS) model confined to a box. In both cases we show almost optimal bounds O(L ²polylog(L)) for the mixing time of the chain, where L is the natural size of the system. The dynamics at a macroscopic scale should be described by a deterministic mean curvature motion such that each point of the surface feels a drift which tends to minimize the local surface tension (Spohn in J Stat Phys 71:1081–1132, 1993). Inspired by this heuristics, our approach consists in bounding the dynamics with an auxiliary one which, with very high probability, follows quite closely the deterministic mean curvature evolution. Key technical ingredients are monotonicity, coupling and an argument due to Wilson (Ann Appl Probab 14:274–325, 2004) in the framework of lozenge tiling Markov Chains. Our approach works equally well for both models despite the fact that their equilibrium maximal height fluctuations occur on very different scales (log L for monotone surfaces and \({\sqrt L}\) for the SOS model). Finally, combining techniques from kinetically constrained spin systems (Cancrini et al. in Probab Th Rel Fields 140:459–504, 2008) together with the above mixing time result, we prove an almost diffusive lower bound of order 1/L ²polylog(L) for the spectral gap of the SOS model with horizontal size L and unbounded heights.     

Core-extended rylene dyes via thiophene annulation

Annulation of thiophenes directly into the bay regions of rylene dyes through effective Stille coupling and subsequent ring-fusion under Scholl conditions leads to core-extended rylene tetracarboxylic diimides with interesting electro-optical properties.     

Determining the orientation and localization of membrane-bound peptides

Many naturally occurring bioactive peptides bind to biological membranes. Studying and elucidating the mode of interaction is often an essential step to understand their molecular and biological functions. To obtain the complete orientation and immersion depth of such compounds in the membrane or a membrane-mimetic system, a number of methods are available, which are separated in this review into four main classes: solution NMR, solid-state NMR, EPR and other methods. Solution NMR methods include the Nuclear Overhauser Effect (NOE) between peptide and membrane signals, residual dipolar couplings and the use of paramagnetic probes, either within the membrane-mimetic or in the solvent. The vast array of solid state NMR methods to study membrane-bound peptide orientation and localization includes the anisotropic chemical shift, PISA wheels, dipolar waves, the GALA, MAOS and REDOR methods and again the use of paramagnetic additives on relaxation rates. Paramagnetic additives, with their effect on spectral linewidths, have also been used in EPR spectroscopy. Additionally, the orientation of a peptide within a membrane can be obtained by the anisotropic hyperfine tensor of a rigidly attached nitroxide label. Besides these magnetic resonance techniques a series of other methods to probe the orientation of peptides in membranes has been developed, consisting of fluorescence-, infrared- and oriented circular dichroism spectroscopy, colorimetry, interface-sensitive X-ray and neutron scattering and Quartz crystal microbalance.     

Phenolic enriched extract of Baccharis trimera presents anti-inflammatory and antioxidant activities

Baccharis trimera is a plant popularly used as a tea and to treat gastrointestinal diseases and inflammatory processes as well. The total phenolic content was determined and the antioxidant and anti-inflammatory activities of six extracts (dichloromethane, ethyl acetate, butanol, aqueous, saponin and phenolic) from B. trimera were evaluated. Using carrageenan-induced pleurisy as a model of acute inflammation, the phenolic extract at 15 mg/kg decreased significantly the analyzed parameters when compared to the carrageenan group ( p < 0.05), thus showing potential anti-inflammatory activity. The total phenolic content and antioxidant activity were evaluated by the Folin-Ciocalteau and DPPH methods, respectively. Phenolic and ethyl acetate extracts presented higher antioxidant activity ( p < 0.05) than ascorbic acid. The phenolic extract also showed the highest antioxidant potential in relation to the other extracts, thus suggesting that the antioxidant and anti-inflammatory activities were due to the presence of phenolic compounds.     

A dynamical characterization of quasilinear means

The theory of dyadic iterations of two-variables continuous means is revised and extended in order to introduce the concept of base family of a continuous mean. Besides other results of interest, a new analytic characterization of quasilinear means is obtained by studying the means admitting a unique base mean.     

Polymer dynamics in the depinned phase: metastability with logarithmic barriers

We consider the stochastic evolution of a (1?+?1)-dimensional polymer in the depinned regime. At equilibrium the system exhibits a double well structure: the polymer lies (essentially) either above or below the repulsive line. As a consequence, one expects a metastable behavior with rare jumps between the two phases combined with a fast thermalization inside each phase. However, the energy barrier between these two phases is only logarithmic in the system size L and therefore the two relevant time scales are only polynomial in L with no clear-cut separation between them. The whole evolution is governed by a subtle competition between the diffusive behavior inside one phase and the jumps across the energy barriers. Our main results are: (i) a proof that the mixing time of the system lies between ${L^{\frac 5 2}}$ and ${L^{\frac 5 2 +2}}$ ; (ii) the identification of two regions associated with the positive and negative phase of the polymer together with the proof of the asymptotic exponentiality of the tunneling time between them with rate equal to a half of the spectral gap.     

Study of the thermal diffusion behavior of alkane/benzene mixtures by thermal diffusion forced rayleigh scattering experiments and lattice model calculations

In this work the thermal diffusion behavior of binary mixtures of linear alkanes (heptane, nonane, undecane, tridecane, pentadecane, heptadecane) in benzene has been investigated by thermal diffusion forced Rayleigh scattering (TDFRS) for a range of concentrations and temperatures. The Soret coefficient ST of the alkane was found to be negative for these n-alkane/benzene mixtures indicating that the alkanes are enriched in the warmer regions of the liquid mixtures. For the compositions investigated in this work, the magnitude of the Soret coefficient decreases with increasing chain length and increasing alkane content of the mixtures. The temperature dependence of the Soret coefficient depends on mixture composition and alkane chain length; the slope of ST versus temperature changes from positive to negative with increasing chain length at intermediate compositions. To study the influence of molecular architecture on the Soret effect, mixtures of branched alkanes (2-methylhexane, 3-methylhexane, 2,3-dimethylpentane, 2,4-dimethylpentane, 2,2,3-trimethylbutane, and 2,2,4-trimethylpentane) in benzene were also investigated. Our results for the Soret coefficients show that the tendency for the alkanes to move to the warmer regions of the fluid decreases with increasing degree of branching. The branching effect is so strong that for 2,2,4-trimethylpentane/benzene mixtures the Soret coefficient changes sign at high alkane content and that equimolar 2,2,3-trimethylbutane/benzene mixtures have positive Soret coefficients in the investigated temperature range. In order to investigate the effect of molecular interactions on thermal diffusion, we adapted a recently developed two-chamber lattice model to n-alkane/benzene mixtures. The model includes the effects of chain-length, compressibility, and orientation dependence of benzene-benzene interactions and yields good qualitative predictions for the Soret effect in n-alkane/benzene mixtures. For the branched isomers, we find some correlations between the moments of inertia of the molecules and the Soret coefficients. PACS numbers: 66.10.Cb, 61.25.Hq.