Robust Inference for Univariate Proportional Hazards Frailty Regression Models

We consider a class of semiparametric regression models which are one-parameter extensions of the Cox [J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] model for right-censored univariate failure times. These models assume that the hazard given the covariates and a random frailty unique to each individual has the proportional hazards form multiplied by the frailty. The frailty is assumed to have mean 1 within a known one-parameter family of distributions. Inference is based on a nonparametric likelihood. The behavior of the likelihood maximizer is studied under general conditions where the fitted model may be misspecified. The joint estimator of the regression and frailty parameters as well as the baseline hazard is shown to be uniformly consistent for the pseudo-value maximizing the asymptotic limit of the likelihood. Appropriately standardized, the estimator converges weakly to a Gaussian process. When the model is correctly specified, the procedure is semiparametric efficient, achieving the semiparametric information bound for all parameter components. It is also proved that the bootstrap gives valid inferences for all parameters, even under misspecification. We demonstrate analytically the importance of the robust inference in several examples. In a randomized clinical trial, a valid test of the treatment effect is possible when other prognostic factors and the frailty distribution are both misspecified. Under certain conditions on the covariates, the ratios of the regression parameters are still identifiable. The practical utility of the procedure is illustrated on a non-Hodgkin's lymphoma dataset.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000053

Limits of flexural wave absorption by open lossy resonators: reflection and transmission problems

The limits of flexural wave absorption by open lossy resonators are analytically and numerically reported in this work for both the reflection and transmission problems. An experimental validation for the reflection problem is presented. The reflection and transmission of flexural waves in 1D resonant thin beams are analyzed by means of the transfer matrix method. The hypotheses, on which the analytical model relies, are validated by experimental results. The open lossy resonator, consisting of a finite length beam thinner than the main beam, presents both energy leakage due to the aperture of the resonators to the main beam and inherent losses due to the viscoelastic damping. Wave absorption is found to be limited by the balance between the energy leakage and the inherent losses of the open lossy resonator. The perfect compensation of these two elements is known as the critical coupling condition and can be easily tuned by the geometry of the resonator. On the one hand, the scattering in the reflection problem is represented by the reflection coefficient. A single symmetry of the resonance is used to obtain the critical coupling condition. Therefore the perfect absorption can be obtained in this case. On the other hand, the transmission problem is represented by two eigenvalues of the scattering matrix, representing the symmetric and anti-symmetric parts of the full scattering problem. In the geometry analyzed in this work, only one kind of symmetry can be critically coupled, and therefore, the maximal absorption in the transmission problem is limited to 0.5. The results shown in this work pave the way to the design of resonators for efficient flexural wave absorption

Elastic instability in stratified core annular flow

We study experimentally the interfacial instability between a layer of dilute polymer solution and water flowing in a thin capillary. The use of microfluidic devices allows us to observe and quantify in great detail the features of the flow. At low velocities, the flow takes the form of a straight jet, while at high velocities, steady or advected wavy jets are produced. We demonstrate that the transition between these flow regimes is purely elastic -- it is caused by viscoelasticity of the polymer solution only. The linear stability analysis of the flow in the short-wave approximation captures quantitatively the flow diagram. Surprisingly, unstable flows are observed for strong velocities, whereas convected flows are observed for low velocities. We demonstrate that this instability can be used to measure rheological properties of dilute polymer solutions that are difficult to assess otherwise.Comment: 4 pages, 4 figure

Observation of Droplet Size Oscillations in a Two-Phase Fluid under Shear Flow

Experimental observations of droplet size sustained oscillations are reported in a two-phase flow between a lamellar and a sponge phase. Under shear flow, this system presents two different steady states made of monodisperse multilamellar droplets, separated by a shear-thinning transition. At low and high shear rates, the droplet size results from a balance between surface tension and viscous stress whereas for intermediate shear rates, it becomes a periodic function of time. A possible mechanism for such kind of oscillations is discussed

Developing a methodology for carbon isotope analysis of lacustrine diatoms

Stable isotope analysis of sedimentary carbon in lakes can help reveal changes in terrestrial and aquatic carbon cycles. A method based on a single, photosynthetic organism, where host effects are minimised, should offer more precision than carbon isotope studies of bulk lake sediments. Here we report the development of a systematic method for use on fossil lacustrine diatom frustules, adapted from previous studies in marine environments. A step-wise cleaning experiment on diatomaceous lake sediments from Lake Challa, near Mount Kilimanjaro, was made to demonstrate the necessary treatment stages to remove external sedimentary carbon. Changes in soluble carbon compounds during these cleaning experiments were measured using gas chromatography/mass spectrometry (GC/MS). The mass spectrometry methods were refined to measure the small percentage of carbon in these samples and details of these methods are presented. Samples of cleaned diatoms containing <1% carbon yielded robust results. Carbon isotope analyses of diatom samples containing different species mixtures were performed and suggested that differences existed, although the effects lay within current experimental error and require further work. Unlike what was found in work on oxygen and silicon isotopes from diatom frustules, mineral contamination had no discernible impact on the diatom carbon isotope ratios from these sediments. The range of values found in the lakes investigated thus far can be interpreted with reference to the supply and nature of carbon from the catchment as well as to the demand generated from lake primary productivit

Displacement and Distance Measurement using the Change in Junction Voltage Across a Laser Diode Due to the Self-Mixing Effect

The conventional self-mixing sensing systems employ a detection scheme utilizing the photocurrent from an integrated photodiode. This work reports on an alternative way of implementing a Vertical-Cavity Surface-Emitting Laser (VCSEL) based self-mixing sensor using the laser junction voltage as the source of the self-mixing signal. We show that the same information can be obtained with only minor changes to the extraction circuitry leading to potential cost saving with reductions in component costs and complexity. The theoretical linkage between voltage and photocurrent within the self-mixing model is presented. Experiments using both photo current and voltage detection were carried out and the results obtained show good agreement with the theory. Similar error trends for both detection regimes were observed

Magnetodielectric effect in nickel nanosheet-Na-4 mica composites

Nickel nanosheets of thickness 0.6 nm were grown within the nanochannels of Na-4 mica template. The specimens show magnetodielectric effect at room temperature with a change of dielectric constant as a function of magnetic field, the electric field frequency varying from 100 to 700 kHz. A decrease of 5% in the value of dielectric constant was observed up to a field of 1.2 Tesla. This is explained by an inhomogeneous two-component composite model as theoretically proposed recently. The present approach will open up synthesis of various nanocomposites for sensor applications.Comment: 11 pages, 7 figure

Risks associated with endotoxins in feed additives produced by fermentation

Acknowledgements We thank Jordi Tarrés Call, who recorded the discussions and offered advice about procedures, and Nicole Reisinger and Gerd Schatzmayr, who provided valuable information about endotoxins in animal feeds. The Rowett Institute of Nutrition and Health is funded by the Rural and Environment Science and Analytical Services Division (RESAS) of the Scottish Government.Peer reviewedPublisher PD