Zero-temperature properties of randomly self-interacting polymers

We study the zero-temperature behavior of several simple models for randomly self-interacting polymers in one and 1+1 dimensions. Results are based on exact enumeration and closed-form expressions.     

Universal Components of Random Nodal Sets

We give, as L grows to infinity, an explicit lower bound of order \({L^{\frac{n}{m}}}\) for the expected Betti numbers of the vanishing locus of a random linear combination of eigenvectors of P with eigenvalues below L. Here, P denotes an elliptic self-adjoint pseudo-differential operator of order \({m > 0}\), bounded from below and acting on the sections of a Riemannian line bundle over a smooth closed n-dimensional manifold M equipped with some Lebesgue measure. In fact, for every closed hypersurface \({\Sigma}\) of \({\mathbb{R}^n}\), we prove that there exists a positive constant \({p_\Sigma}\) depending only on \({\Sigma}\), such that for every large enough L and every \({x \in M}\), a component diffeomorphic to \({\Sigma}\) appears with probability at least \({p_\Sigma}\) in the vanishing locus of a random section and in the ball of radius \({L^{-\frac{1}{m}}}\) centered at x. These results apply in particular to Laplace–Beltrami and Dirichlet-to-Neumann operators.     

A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface

We report on an exact vector (polarized) radiative transfer (VRT) model for coupled atmosphere and ocean systems. This VRT model is based on the successive order of scattering (SOS) method, which virtually takes all the multiple scattering processes into account, including atmospheric scattering, oceanic scattering, reflection and transmission through the rough ocean surface. The isotropic Cox–Munk wave model is used to derive the ref and transmission matrices for the rough ocean surface. Shadowing effects are included by the shadowing function. We validated the SOS results by comparing them with those calculated by two independent codes based on the doubling/adding and Monte Carlo methods. Two error analyses related to the ocean color remote sensing are performed in the coupled atmosphere and ocean systems. One is the scalar error caused by ignoring the polarization in the whole system. The other is the error introduced by ignoring the polarization of the light transmitted through the ocean interface. Both errors are significant for the cases studied. This code fits for the next generation of ocean color study because it converges fast for absorbing medium as, for instance, ocean.     

Synthesis of fluorinated malonamides and use in L/L extraction of f-elements

Synthesis of new fluorinated tertiary malonamides (F-malonamides) was accomplished, and their liquid/liquid (L/L) extraction properties with f-elements were investigated. These molecules are fluorinated analogues of well known extractants used in several processes designed towards the treatment of nuclear wastes, and the efficient separation of lanthanides from minor actinides; however, the synthesis of F-malonamides deserved a modification of the general synthetic route commonly employed to prepare H-malonamides. Extraction of neodymium from various aqueous media into both fluorous and classical solvents was studied, which revealed an opposite trend between F-malonamides and H-malonamides: L/L extraction ability is very sensitive to the nitrogen atoms substitution pattern, and the most efficient F-malonamide is compound 3 (R₁ = Me), whereas the best H-malonamide is compound 5 (R₁ = Bu, DMDBTDMA).     

Selective and Wash-Resistant Fluorescent Dihydrocodeinone Derivatives Allow Single-Molecule Imaging of μ-Opioid Receptor Dimerization

μ-Opioid receptors (μ-ORs) play a critical role in the modulation of pain and mediate the effects of the most powerful analgesic drugs. Despite extensive efforts, it remains insufficiently understood how μ-ORs produce specific effects in living cells. We developed new fluorescent ligands based on the μ-OR antagonist E-p-nitrocinnamoylamino-dihydrocodeinone (CACO), that display high affinity, long residence time and pronounced selectivity. Using these ligands, we achieved single-molecule imaging of μ-ORs on the surface of living cells at physiological expression levels. Our results reveal a high heterogeneity in the diffusion of μ-ORs, with a relevant immobile fraction. Using a pair of fluorescent ligands of different color, we provide evidence that μ-ORs interact with each other to form short-lived homodimers on the plasma membrane. This approach provides a new strategy to investigate μ-OR pharmacology at single-molecule level.     

Sharper asset ranking from total drawdown durations

The total duration of drawdowns is shown to provide a moment-free, unbiased, efficient and robust estimator of Sharpe ratios both for Gaussian and heavy-tailed price returns. We then use this quantity to infer an analytic expression of the bias of moment-based Sharpe ratio estimators as a function of the return distribution tail exponent. The heterogeneity of tail exponents at any given time among assets implies that our new method yields significantly different asset rankings than those of moment-based methods, especially in periods large volatility. This is fully confirmed by using 20 years of historical data on 3449 liquid US equities.