High-Order Composite Likelihood Inference for Max-Stable Distributions and Processes

In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of points is a very challenging problem and current approaches typically rely on less expensive composite likelihoods constructed from small subsets of data. In this work, we explore the limits of modern state-of-the-art computational facilities to perform full likelihood inference and to efficiently evaluate high-order composite likelihoods. With extensive simulations, we assess the loss of information of composite likelihood estimators with respect to a full likelihood approach for some widely used multivariate or spatial extreme models, we discuss how to choose composite likelihood truncation to improve the efficiency, and we also provide recommendations for practitioners. This article has supplementary material online.     

Light-assisted synthesis and functionalization of silver nanoparticles with thiol derivative thioxanthones: new insights into the engineering of metal/chromophore nanoassemblies

Nanofluids are suspensions of nanometer-sized particles which significantly modify the properties of the base fluids. Nanofluids exhibit attractive properties, such as high thermal conductivity, tunable surface tension, viscosity, and rheology. Various attempts have been made to understand the mechanisms for these property modifications caused by adding nanoparticles; however, due to the lack of direct nanoscale evidence, these explanations are still controversial. This work calculated the surface tension, viscosity, and rheology of gold–water nanofluids using molecular dynamics simulations which provide a microscopic interpretation for the modified properties on the molecular level. The gold–water interaction potential parameters were changed to mimic various nanoparticle types. The results show that the nanoparticle wettability is responsible for the modified surface tension. Hydrophobic nanoparticles always tend to stay on the free surface so they behave like a surfactant to reduce the surface tension. Hydrophilic nanoparticles immersed into the bulk fluid impose strong attractive forces on the water molecules at the free surface which reduces the free surface thickness and increases the surface tension of the nanofluid. Solid-like absorbed water layers were observed around the nanoparticles which increase the equivalent nanoparticle radius and reduce the mobility of the nanoparticles within the base fluid which increases the nanofluid viscosity. The results show the water molecule solidification between two or many nanoparticles at high nanoparticle loadings, but the solidification effect is suppressed for shear rates greater than a critical shear rate; thus Newtonian nanofluids can present shear-thinning non-Newtonian behavior.     

Stability Indicating Assay Method on Vitamins: Application to their Stability Study in Parenteral Nutrition Admixtures

Vitamins are an heterogenous family of drugs with very different molecular properties. A novel method for the simultaneous quantification by LC-tandem mass spectrometry of ten water- and fat-soluble vitamins (retinol, α-tocopherol, thiamin, riboflavin, nicotinamide, pantothenic acid, pyridoxine, biotin, folic acid and ascorbic acid) in parenteral admixture without sample pre-treatment is described in this paper. The separation was achieved by reversed phase LC with a Zorbax C18 column (length 150 mm, internal diameter 4.6 mm, particle size 2.5 μm). A gradient of mobile phase was set up starting at 100% ammonium acetate solution at 10 mM, pH = 4.5 reaching a step of ammonium acetate : methanol in 15 min (65:35 v/v). The detection system combined online photodiode array and tandem mass spectrometry. Degradation studies of vitamin admixtures were performed and the method proved to be stability indicating. The LC-UV-MS-MS method was validated in accordance with the ICH guidelines. Repeatability and intermediate precision were comprised between 1.0 and 10.2% and 0.7 and 11.8%, respectively. A stability study of the vitamins mixed within three different parenteral nutrition admixtures has been performed and has shown their stability within at least 48 h.     

First trial of spatial and temporal fractionations of the delivered dose using synchrotron microbeam radiation therapy

The technical feasibility of temporal and spatial fractionations of the radiation dose has been evaluated using synchrotron microbeam radiation therapy for brain tumors in rats. A significant increase in lifespan (216%, p < 0.0001) resulted when three fractions of microbeam irradiation were applied to the tumor through three different ports, orthogonal to each other, at 24 h intervals. However, there were no long‐term survivors, and immunohistological studies revealed that 9 L tumors were not entirely ablated.     

Spectral Projections of the Complex Cubic Oscillator

We prove the spectral instability of the complex cubic oscillator \({-\frac{{\rm d}^{2}}{{\rm d}x^{2}} + ix^{3} + i \alpha x}\) for non-negative values of the parameter α, by getting the exponential growth rate of \({\|\Pi_{n}(\alpha)\|}\) , where \({\Pi_{n}(\alpha)}\) is the spectral projection associated with the nth eigenvalue of the operator. More precisely, we show that for all non-negative α $$\lim\limits_{n \to + \infty} \frac{1}{n} {\rm log}\|\Pi_{n}(\alpha)\| = \frac{\pi}{\sqrt{3}}$$ .     

Lower large deviations for the maximal flow through a domain of {\mathbb{R}^d} in first passage percolation

We consider the standard first passage percolation model in the rescaled graph ${\mathbb{Z}^d/n}$ for d??? 2, and a domain ?? of boundary ?? in ${\mathbb{R}^d}$ . Let ??¹ and ??² be two disjoint open subsets of ??, representing the parts of ?? through which some water can enter and escape from ??. We investigate the asymptotic behaviour of the flow ${\phi_n}$ through a discrete version ?? _n of ?? between the corresponding discrete sets ${\Gamma^{1}_{n}}$ and ${\Gamma^{2}_{n}}$ . We prove that under some conditions on the regularity of the domain and on the law of the capacity of the edges, the lower large deviations of ${\phi_n/ n^{d-1}}$ below a certain constant are of surface order.     

Convergence of a finite volume scheme for nonlinear degenerate parabolic equations

Summary. One approximates the entropy weak solution u of a nonlinear parabolic degenerate equation by a piecewise constant function using a discretization in space and time and a finite volume scheme. The convergence of to u is shown as the size of the space and time steps tend to zero. In a first step, estimates on are used to prove the convergence, up to a subsequence, of to a measure valued entropy solution (called here an entropy process solution). A result of uniqueness of the entropy process solution is proved, yielding the strong convergence of to{\it u}. Some on a model equation are shown. Received September 27, 2000 / Published online October 17, 2001     

On the linear wave regime of the Gross-Pitaevskii equation

We study long-wavelength asymptotics for the Gross-Pitaevskii equation corresponding to perturbations of a constant state of modulus one. We exhibit lower bounds on the first occurrence of possible zeros (vortices) and compare the solutions with the corresponding solutions to the linear wave equation or variants. The results rely on the use of the Madelung transform, which yields the hydrodynamical form of the Gross-Pitaevskii equation, as well as of an augmented system.