Higher criticism for detecting sparse heterogeneous mixtures

Higher criticism, or second-level significance testing, is a multiple-comparisons concept mentioned in passing by Tukey. It concerns a situation where there are many independent tests of significance and one is interested in rejecting the joint null hypothesis. Tukey suggested comparing the fraction of observed significances at a given \alpha-level to the expected fraction under the joint null. In fact, he suggested standardizing the difference of the two quantities and forming a z-score; the resulting z-score tests the significance of the body of significance tests. We consider a generalization, where we maximize this z-score over a range of significance levels 0<\alpha\leq\alpha_0. We are able to show that the resulting higher criticism statistic is effective at resolving a very subtle testing problem: testing whether n normal means are all zero versus the alternative that a small fraction is nonzero. The subtlety of this ``sparse normal means'' testing problem can be seen from work of Ingster and Jin, who studied such problems in great detail. In their studies, they identified an interesting range of cases where the small fraction of nonzero means is so small that the alternative hypothesis exhibits little noticeable effect on the distribution of the p-values either for the bulk of the tests or for the few most highly significant tests. In this range, when the amplitude of nonzero means is calibrated with the fraction of nonzero means, the likelihood ratio test for a precisely specified alternative would still succeed in separating the two hypotheses.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/10.1214/00905360400000026

Thermal conductivity of heterogeneous mixtures and lunar soils

The theoretical evaluation of the effective thermal conductivity of granular materials is discussed with emphasis upon the heat transport properties of lunar soil. The following types of models are compared: probabilistic, parallel isotherm, stochastic, lunar, and a model based on nonlinear heat flow system synthesis

Heterogeneous mixtures for synthetic antenna substrates

Heterogeneous mixtures have the potential to be used as synthetic substrates for antenna applications giving the antenna designer new degrees of freedom to control the permittivity and/or permeability in three dimensions such as by a smooth variation of the density of the inclusions, the height of the substrate and the manufacture the whole antenna system in one process. Electromagnetic, fabrication, environmental, time and cost advantages are potential especially when combined with nano-fabrication techniques. Readily available and cheap materials such as Polyethylene and Copper can be used in creating these heterogeneous materials. These advantages have been further explained in this thesis. In this thesis, the research presented is on canonical, numerical and measurement analysis on heterogeneous mixtures that can be used as substrates for microwave applications. It is hypothesised that heterogeneous mixtures can be used to design bespoke artificial dielectric substrates for say, patch antennas. The canonical equations from published literature describing the effective permittivity, ε_eff and effective permeability, μ_eff of heterogeneous mixtures have been extensively examined and compared with each other. Several simulations of homogenous and heterogeneous media have been carried out and an extraction/inversion algorithm applied to find their ε_eff and μ_eff. Parametric studies have been presented to show how the different variables of the equations and the simulations affect the accuracy of the results. The extracted results from the inversion process showed very good agreement with the known values of the homogenous media. Numerically and canonically computed values of ε_eff and μ_eff of various heterogeneous media were shown to have good agreement. The fabrication techniques used in creating the samples used in this research were examined, along with the different measurement methods used in characterising their electromagnetic properties via simulations and measurements. The challenges faced with these measurement methods were explained including the possible sources of error. Patch antennas were used to investigate how the performance of an antenna may be affected by heterogeneous media with metallic inclusions. The performance of the patch antenna was not inhibited by the presence of the metallic inclusions in close proximity. The patch measurement was also used as a measurement technique in determining the ε_eff of the samples

Composition measurements of crude oil and process water emulsions using thick-film ultrasonic transducers

This paper presents an experimental study to investigate the suitability of thick-film ultrasonic transducers for composition measurements in heterogeneous mixtures. Following on from earlier developments [G. Meng, A.J. Jaworski, T. Dyakowski, J.M. Hale, N.M. White, Design and testing of a thick-film dual-modality sensor for composition measurements in heterogeneous mixtures, Meas. Sci. Technol. 16(4) (2005) 942–954], focused on the design and preliminary testing of the transducers for mixtures of vegetable oil and salty water, the current paper looks in more detail into their application to industrially relevant fluids, namely crude oil and process water, which are common in oil and gas extraction and petrochemical industries. The measurements are based on the time-of-flight of the ultrasonic pressure wave in order to obtain the speed of sound. The results, showing the variation of the speed of sound with the volume fraction of crude oil, for three different temperatures, are compared with five theoretical models available in the existing literature. It is shown that the models proposed by Urick [R.J. Urick, A sound velocity method for determining the compressibility of finely divided substances, J. Appl. Phys. 18 (1947) 983–987] and by Kuster and Toks¨oz [G.T. Kuster, M.N. Toks¨oz, Velocity and attenuation of seismic waves in two-phase media. Part I. Theoretical formulations, Geophysics 39 (1974) 587–606] provide a relatively accurate prediction for the speed of sound in the media studied. Interestingly, the model developed by Povey and co-workers [V.J. Pinfield, M.J.W. Povey, Thermal scattering must be accounted for in the determination of adiabatic compressibility, J. Phys. Chem. B 101 (1997) 1110–1112] only agrees with experiment when its thermal scattering features are neglected. Overall, the results obtained demonstrate that the slim-line and compact thick-film transducers can be considered as a viable means for the composition measurements in the process conditions

Multiple Steady States in Heterogeneous Azeotropic Distillation

In this article we study multiple steady states in ternary heterogeneous azeotropic distillation. We show that in the case of infinite reflux and an infinite number of trays one can construct bifurcation diagrams on physical grounds with the distillate flow as the bifurcation parameter. Multiple steady states exist when the distillate flow varies non-monotonically along the continuation path of the bifurcation diagram. We show how the distillate and bottom product paths can be located for tray or packed columns, with or without decanter and with different types of condenser and reboiler. We derive a necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the product paths. We also locate in the composition triangle the feed compositions that lead to these multiple steady states. We show that the prediction of the existence of multiple steady states in the case of infinite reflux and an infinite number of trays has relevant implications for columns operating at finite reflux and with a finite number of trays

Quantitative spectroscopic analysis of heterogeneous mixtures: the correction of multiplicative effects caused by variations in physical properties of samples

Spectral measurements of complex heterogeneous types of mixture samples are often affected by significant multiplicative effects resulting from light scattering, due to physical variations (e.g. particle size and shape, sample packing and sample surface, etc.) inherent within the individual samples. Therefore, the separation of the spectral contributions due to variations in chemical compositions from those caused by physical variations is crucial to accurate quantitative spectroscopic analysis of heterogeneous samples. In this work, an improved strategy has been proposed to estimate the multiplicative parameters accounting for multiplicative effects in each measured spectrum, and hence mitigate the detrimental influence of multiplicative effects on the quantitative spectroscopic analysis of heterogeneous samples. The basic assumption of the proposed method is that light scattering due to physical variations has the same effects on the spectral contributions of each of the spectroscopically active chemical component in the same sample mixture. Based on this underlying assumption, the proposed method realizes the efficient estimation of the multiplicative parameters by solving a simple quadratic programming problem. The performance of the proposed method has been tested on two publicly available benchmark data sets (i.e. near-infrared total diffuse transmittance spectra of four-component suspension samples and near infrared spectral data of meat samples) and compared with some empirical approaches designed for the same purpose. It was found that the proposed method provided appreciable improvement in quantitative spectroscopic analysis of heterogeneous mixture samples. The study indicates that accurate quantitative spectroscopic analysis of heterogeneous mixture samples can be achieved through the combination of spectroscopic techniques with smart modeling methodology

Statistical Modeling of Single Target Cell Encapsulation

High throughput drop-on-demand systems for separation and encapsulation of individual target cells from heterogeneous mixtures of multiple cell types is an emerging method in biotechnology that has broad applications in tissue engineering and regenerative medicine, genomics, and cryobiology. However, cell encapsulation in droplets is a random process that is hard to control. Statistical models can provide an understanding of the underlying processes and estimation of the relevant parameters, and enable reliable and repeatable control over the encapsulation of cells in droplets during the isolation process with high confidence level. We have modeled and experimentally verified a microdroplet-based cell encapsulation process for various combinations of cell loading and target cell concentrations. Here, we explain theoretically and validate experimentally a model to isolate and pattern single target cells from heterogeneous mixtures without using complex peripheral systems.Wallace H. Coulter Foundation (Young Investigator in Bioengineering Award)National Institutes of Health (U.S.) (Grant R01AI081534)National Institutes of Health (U.S.) (Grant R21AI087107