Splitting of liftings in products of probability spaces

We prove that if (X,\mathfrakA,P) is an arbitrary probability space with countably generated \sigma-algebra \mathfrakA, (Y,\mathfrakB,Q) is an arbitrary complete probability space with a lifting \rho and \hat R is a complete probability measure on \mathfrakA \hat \otimes_R \mathfrakB determined by a regular conditional probability {S_y:y\in Y} on \mathfrakA with respect to \mathfrakB, then there exist a lifting \pi on (X\times Y,\mathfrakA \hat \otimes_R \mathfrakB,\hat R) and liftings \sigma_y on (X,\hat \mathfrakA_y,\hat S_y), y\in Y, such that, for every E\in\mathfrakA \hat \otimes_R \mathfrakB and every y\in Y, [\pi(E)]^y=\sigma_y\bigl([\pi(E)]^y\bigr). Assuming the absolute continuity of R with respect to P\otimes Q, we prove the existence of a regular conditional probability {T_y:y\in Y} and liftings \varpi on (X\times Y,\mathfrakA \hat \otimes_R \mathfrakB,\hat R), \rho' on (Y,\mathfrakB,\hat Q) and \sigma_y on (X,\hat \mathfrakA_y,\hat S_y), y\in Y, such that, for every E\in\mathfrakA \hat \otimes_R \mathfrakB and every y\in Y, [\varpi(E)]^y=\sigma_y\bigl([\varpi(E)]^y\bigr) and \varpi(A\times B)=\bigcup_{y\in\rho'(B)}\sigma_y(A)\times{y}\qquadif A\times B\in\mathfrakA\times\mathfrakB. Both results are generalizations of Musia\l, Strauss and Macheras [Fund. Math. 166 (2000) 281-303] to the case of measures which are not necessarily products of marginal measures. We prove also that liftings obtained in this paper always convert \hat R-measurable stochastic processes into their \hat R-measurable modifications.Comment: Published at http://dx.doi.org/10.1214/009117904000000018 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bond breaking with auxiliary-field quantum Monte Carlo

Bond stretching mimics different levels of electron correlation and provides a challenging testbed for approximate many-body computational methods. Using the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC) method, we examine bond stretching in the well-studied molecules BH and N$_2$, and in the H$_{50}$ chain. To control the sign/phase problem, the phaseless AF QMC method constrains the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. With single Slater determinants from unrestricted Hartree-Fock (UHF) as trial wave function, the phaseless AF QMC method generally gives better overall accuracy and a more uniform behavior than the coupled cluster CCSD(T) method in mapping the potential-energy curve. In both BH and N$_2$, we also study the use of multiple-determinant trial wave functions from multi-configuration self-consistent-field (MCSCF) calculations. The increase in computational cost versus the gain in statistical and systematic accuracy are examined. With such trial wave functions, excellent results are obtained across the entire region between equilibrium and the dissociation limit.Comment: 8 pages, 3 figures and 3 tables. Submitted to JC

Stability Studies of a Mixture of Paracetamol and Ascorbic Acid, Prepared Extempore, at Elevated Temperature and Humidity Conditions

Purpose: To determine the effect of the temperature of water used for the preparation of paracetamol and ascorbic acid mixture on its stability, as well as to assess the influence of humidity on the stability of single components and their mixtures.Methods: The stability of the mixtures in aqueous medium was evaluated with the aid of UV–Vis spectrophotometer interfaced with a computer. Spectral analysis was adapted to monitor changes in the aqueous medium of a commercial paracetamol and ascorbic acid mixture, an extemporaneously prepared mixture of paracetamol and ascorbic acid, and the individual preparations of paracetamol and ascorbic acid.Results: The degradation rate was lower in commercial preparation (6.80 × 10-3 min-1), compared to that of the extemporaneously prepared ascorbic acid/paracetamol mixture (2.30 × 10-2 min-1). The decomposition of the commercial product in aqueous medium was 3.38 times slower than that of the extemporaneously prepared mixture. Ascorbic acid, tested under the same conditions as the commercial product, was unstable in aqueous solutions, with a degradation rate of 1.17×10-2 min-1. Ascorbic acid, dissolved in water, degraded completely within 4 h at room temperature, whereas paracetamol remained stable under the same conditions for 11 days.Conclusion: The individual drugs in their original form retained their stability for 72 h, but some of the mixtures, in particular, the extemporaneously prepared ones showed more rapid degradation. Extemporaneous preparation of paracetamol/ascorbic acid liquid mixtures should not be encouraged

Status of Wave and Tidal Power Technologies for the United States

This paper presents the status of marine applications for renewable energy as of 2008 from a U.S. perspective. Technologies examined include wave, tidal, and ocean current energy extraction devices

Semi-Submersible Platform and Anchor Foundation Systems for Wind Turbine Support: August 30, 2004 - May 31, 2005

This report examines the feasibility of various semi-submersible platform configurations for an offshore deep water wind turbine

Apparent multiple Delta m^2_32 in muon anti-neutrino and muon neutrino survival oscillations from non-standard interaction matter effect

Neutrinos propagating through matter may participate in forward coherent neutral-current-like scattering arising from non-standard interactions as well as from the Mikheyev-Smirnov-Wolfenstein matter potential $V_e$. We show that at fixed long baselines through matter of constant density, the non-standard interaction potential $\epsilon_{\mu\tau} V_e$ can contribute an additional term to the oscillation phase whose sign differs for \anumu versus \numu propagation in matter. Its presence can cause different apparent $\Delta m^2$ to be erroneously inferred on the basis of oscillations in vacuum, with values lying above (for \anumu) or below (for \numu) the actual $\Delta m^2_{32}$ for the case where $\epsilon_{\mu\tau}$ is predominantly real-valued and of sign opposite to $\Delta m_{32}^2$. An NSI scenario invoking only $\Re(\epsilon_{\mu\tau})$ is shown to be capable of accounting for a disparity recently reported between oscillation survival for \anumu and \numu fluxes measured at $735~\mathrm{km}$ by the MINOS experiment. Implications for mantle traversal by atmospheric neutrinos are examined. The NSI matter potential with non-maximal mixing could evade conventional atmospheric neutrino analyses which do not distinguish \numu from \anumu on an event-by-event basis.Comment: 7 pages, 5 figures. Accepted for publication in Physical Review

Influence of Liquid Paraffin, White Soft Paraffin and Initial Hydration on Viscosity of Corticosteroid Cream

Purpose: To ascertain the influence of paraffin, white soft paraffin and pre-hydrated white soft paraffin on the viscosity of a cream formulated with a corticosteroid.Methods: The formulations were prepared via homogenization with variable velocity in the range 3300 - 4000 rpm. Individual series of preparations contained the same proportion of macrogol cetostearyl alcohol, cetyl alcohol, stearyl alcohol, sorbitan stearate, propylene glycol, metyl  parahydroxybenzoate, propyl parahydroxybenzoate and water. The semi-solid preparations were assessed by viscometric and microscopic methods.Results: The viscosity of the samples measured ranged from 13050 to 15660 mPas. The particles in dispersed phase sized from 15 to 90 ìm. Within the multiple emulsion, the continuous phase included fine particles with diameter < 5 ìm. Change of the liquid paraffin used from Ondina 934 to Vara 600P significantly decreased the viscosity of the formulation. Several phases within the formulations were distinguished microscopically. Increased viscosity was observed in formulations with increasing proportion of white soft paraffin.Conclusion: Both the ratio of liquid paraffin to white soft paraffin, as well as the initial hydration of white soft paraffin influenced the viscosity of the cream as well as the diameter of particles in the dispersed phase.Keywords: Cream, Ointment, Paraffin, Emulsion, Dispersion, Viscosity, Particle diamete

Semi-supervised stochastic blockmodel for structure analysis of signed networks

© 2020 Elsevier B.V. Finding hidden structural patterns is a critical problem for all types of networks, including signed networks. Among all of the methods for structural analysis of complex network, stochastic blockmodel (SBM) is an important research tool because it is flexible and can generate networks with many different types of structures. However, most existing SBM learning methods for signed networks are unsupervised, leading to poor performance in terms of finding hidden structural patterns, especially when handling noisy and sparse networks. Learning SBM in a semi-supervised way is a promising avenue for overcoming the above difficulty. In this type of model, a small number of labelled nodes and a large number of unlabelled nodes, coupled with their network structures, are simultaneously used to train SBM. We propose a novel semi-supervised signed stochastic blockmodel and its learning algorithm based on variational Bayesian inference, with the goal of discovering both assortative (the nodes connect more densely in same clusters than that in different clusters) and disassortative (the nodes link more sparsely in same clusters than that in different clusters) structures from signed networks. The proposed model is validated through a number of experiments wherein it compared with the state-of-the-art methods using both synthetic and real-world data. The carefully designed tests, allowing to account for different scenarios, show our method outperforms other approaches existing in this space. It is especially relevant in the case of noisy and sparse networks as they constitute the majority of the real-world networks

Determining equivalent damage loading for full-scale wind turbine blade fatigue tests

This paper describes a simplified method for converting wind turbine rotor design loads into equivalent-damage, constant-amplitude loads and load ratios for both flap and lead-lag directions. It is an iterative method that was developed at the National Renewable Energy Laboratory (NREL) using Palmgren-Miner's linear damage principles. The general method is unique because it does not presume that any information about the materials or blade structural properties is precisely known. According to this method, the loads are never converted to stresses. Instead, a family of M-N curves (moment vs. cycles) is defined with reasonable boundaries for load-amplitude and slope. An optimization program iterates and converges on the constant amplitude test load and load ratio that minimizes the sensitivity to the range of M-N curves for each blade section. The authors constrained the general method to match the NedWind 25 design condition for the Standards, Measurements, and Testing (SMT) blade testing pro gram. SMT participants agreed to use the fixed S-N slope of m = 10 from the original design to produce consistent test-loads among the laboratories. Unconstrained, the general method suggests that slightly higher test loads should be used for the NedWind 25 blade design spectrum. NedWind 25 blade test loads were computed for lead-lag and flap under single-axis and two-axis loading

Status of Offshore Wind Energy Projects, Policies and Programs in the United States

This paper provides the status of the offshore wind energy project proposals in the United States and describes strategic issues faced by the U.S. wind industry