Separable and additive representations of binary gambles of gains

Two approaches are taken to a new utility representation of binary gambles that is called “ratio rank-dependent utility.” Both are based on known axiomatizations of a ranked-additive representation of consequence pairs (x, y) in binary gambles (x, C; y) of gains with C held fixed and of a separable one of the special gambles (x, C; e), where e denotes the status quo. The axiomatized version imposes the condition of status-quo event commutativity to get a functional equation that leads to the result. The other assumes, but does not axiomatize, a separable representation of the (C; y) portion of the gamble. These assumptions lead to two difficult functional equations that are solved in the mathematical literature, but the former only under the assumption that the function is twice differentiable. Three behavioral conditions are shown to force this new utility representation to reduce to the standard rank-dependent utility one for gains. They are co-monotonic trade-off consistency, ranked bisymmetry, and segregation, the latter requiring the addition of an operation of joint receipt.     

Modulation of Relaxivity,Suspension Stability,and Biodistribution of Dendronized Iron Oxide Nanoparticles as a Function of the Organic Shell Design

Nanoparticles (NPs) with a mean diameter of 10 nm are functionalized with three dendrons: D1 a PEGylated PAMAM dendron of generation 0.5, D2 a hydrophilic oligoethyleneglycol‐derivatized dendron (D2) displaying a phosphonic acid at the focal point, and D2–2P the same dendron than D2 but with two phosphonic acid anchoring agents. Their grafting is confirmed by IR spectroscopy and elemental analysis. All dendronized NPs are stable over a long period of time in suspensions in water and in different physiological media and display a mean hydrodynamic diameter smaller than 50 nm whatever the molecule architecture. NMRD profiles and relaxivity measurements highlight the influence of the molecule architecture on the water diffusion close to the magnetic core thus influencing the relaxation properties at low magnetic field. The high hydrophilic architecture of the dendron D2 by contrast to dendron D1 allows maintaining the colloidal stability in different conditions while ensuring a very good accessibility of water molecule close to the magnetic core. Coupling of a fluorescent dye on dendrons have allowed investigating the biodistribution of dendronized NPs, which are found to be quickly eliminated through urinary and hepatobiliary pathways within 4 h. Furthermore, no enhanced permeation and retention effect in tumors can be observed.     

Zeolite GdNaY nanoparticles with very high relaxivity for application as contrast agents in magnetic resonance imaging

In this paper we explore Gd(3+)-doped zeolite NaY nanoparticles for their potential application as a contrast agent in magnetic resonance imaging (MRI). The nanoparticles have an average size of 80-100 nm, as determined by TEM and XRD. A powdered sample loaded with La3+ was characterised by means of multinuclear solid-state NMR spectroscopy. The NMR dispersion (NMRD) profiles obtained from aqueous suspensions of samples with Gd3+ doping ratios of 1.3-5.4 wt% were obtaining at different temperatures. The relaxivity increases drastically as the Gd3+ loading decreases, with values ranging between 11.4 and 37.7 s-1 mM-1 at 60 MHz and 37 degrees C. EPR spectra of aqueous suspensions of the samples suggest that an interaction between neighbouring Gd3+ ions within the same particle produces a significant increase in the transversal electronic relaxation rates in samples with a high Gd3+ content. The experimental NMRD and EPR data are explained with the use of a model that considers the system as a concentrated aqueous solution of Gd3+ in the interior of the zeolite that is in exchange with the bulk water outside the zeolite. The results obtained indicate that the Gd3+ ion is immobilised in the interior of the zeolite and that the relaxivity is mainly limited by the relatively slow diffusion of water protons from the pores of the zeolite channels into the bulk water.     

On the rational approximation of Markov functions,with applications to the computation of Markov functions of Toeplitz matrices

Numerical Algorithms - We investigate the problem of approximating the matrix function f(A) by r(A), with f a Markov function, r a rational interpolant of f, and A a symmetric Toeplitz matrix. In a...     

Infrared near-field microscopy with the Vanderbilt free electron laser: overview and perspectives

Scanning near-field optical microscopy (SNOM) makes it routinely possible to overcome the fundamental diffraction limit of standard (far-field) microscopy. Recently, aperture-based infrared SNOM performed in the spectroscopic mode, using the Vanderbilt University free electron laser, started delivering spatially-resolved information on the distribution of chemical species and on other laterally-fluctuating properties. The practical examples presented here show the great potential of this new technique both in materials science and in life sciences.     

Dysprosium Complexes and Their Micelles as Potential Bimodal Agents for Magnetic Resonance and Optical Imaging

Six diethylene triamine pentaacetic acid (DTPA) bisamide derivatives functionalized with p‐toluidine (DTPA‐BTolA), 6‐aminocoumarin (DTPA‐BCoumA), 1‐naphthalene methylamine (DTPA‐BNaphA), 4‐ethynylaniline (DTPA‐BEthA), p‐dodecylaniline (DTPA‐BC₁₂PheA) and p‐tetradecyl‐aniline (DTPA‐BC₁₄PheA) were coordinated to dysprosium(III) and the magnetic and optical properties of the complexes were examined in detail. The complexes consisting of amphiphilic ligands (DTPA‐BC₁₂PheA and DTPA‐BC₁₄PheA) were further assembled into mixed micelles. Upon excitation into the ligand levels, the complexes display characteristic Dy^III emission with quantum yields of 0.3–0.5 % despite the presence of one water molecule in the first coordination sphere. A deeper insight into the energy‐transfer processes has been obtained by studying the photophysical properties of the corresponding Gd^III complexes. Since the luminescence quenching effect is decreased by the intervention of non‐ionic surfactant, quantum yields up to 1 % are obtained for the micelles. The transverse relaxivity r₂ per Dy^III ion at 500 MHz and 310 K reaches a maximum value of 27.4 s^?1 mM ^?1 for Dy‐DTPA‐BEthA and 36.0 s^?1 mM ^?1 for the Dy‐DTPA‐BC₁₂PheA assemblies compared with a value of 0.8 s^?1 mM ^?1 for Dy‐DTPA. The efficient T₂ relaxation, especially at high magnetic field strengths, is sustained by the high magnetic moment of the dysprosium ion, the coordination of water molecules with slow water exchange kinetics and long rotational correlation times. These findings open the way to the further development of bimodal optical and magnetic resonance imaging probes starting from single lanthanide compounds.     

A heterobimetallic ruthenium-gadolinium complex as a potential agent for bimodal imaging

Trinuclear heterobimetallic Ln(III)-Ru(II) complexes (Ln = Eu, Gd) based on a 1,10-phenanthroline ligand bearing a diethylenetriaminepentaacetic acid (DTPA) core have been synthesized and fully characterized by a range of experimental techniques. The (17)O NMR and proton nuclear magnetic relaxation dispersion (NMRD) measurements of Gd(III)-Ru(II) show that, in comparison to the parent Gd-DTPA, this complex exhibits improved relaxivity, which is the result of an increase of the rotational correlation time. Relaxometry and ultrafiltration experiments indicate that the 1,10-phenanthroline ligand has a high affinity for noncovalent binding to human serum albumin, which results in a high relaxivity r(1) of 14.3 s(-1) mM(-1) at 20 MHz and 37 °C. Furthermore, the Ln(III)-Ru(II) complexes (Ln = Eu, Gd) show an intense light absorption in the visible spectral region due to metal-to-ligand charge transfer (MLCT) transitions. Upon excitation into the MLCT band at 440 nm, the complexes exhibit a bright-red luminescence centered at 610 nm, with a quantum yield of 4.7%. The luminescence lifetime equals 540 ns and is therefore long enough to exceed the fluorescent background. Monometallic lanthanide complexes have also been synthesized, and the Eu(III) analogue shows a characteristic red luminescence with a quantum yield of 0.8%. Taking into account the relaxometric and luminescent properties, the developed Gd(III)-Ru(II) complex can be considered as a potential in vitro bimodal imaging agent.