Appoximation-assisted [sic] estimation of eigenvectors under quadratic loss

Improved estimation of eigen vector of covariance matrix is considered under uncertain prior information (UPI) regarding the parameter vector. Like statistical models underlying the statistical inferences to be made, the prior information will be susceptible to uncertainty and the practitioners may be reluctant to impose the additional information regarding parameters in the estimation process. A very large gain in precision may be achieved by judiciously exploiting the information about the parameters which in practice will be available in any realistic problem. Several estimators based on preliminary test and the Stein-type shrinkage rules are constructed. The expressions for the bias and risk of the proposed estimators are derived and compared with the usual estimators. We demonstrate that how the classical large sample theory of the conventional estimator can be extended to shrinkage and preliminary test estimators for the eigenvector of a covariance matrix. It is established that shrinkage estimators are asymptotically superior to the usual sample estimators. For illustration purposes, the method is applied to three datasets

Finite elements software and applications

The contents of this thesis are a detailed study of the software for the finite element method. In the text, the finite element method is introduced from both the engineering and mathematical points of view. The computer implementation of the method is explained with samples of mainframe, mini- and micro-computer implementations. A solution is presented for the problem of limited stack size for both mini- and micro-computers which possess stack architecture. Several finite element programs are presented. Special purpose programs to solve problems in structural analysis and groundwater flow are discussed. However, an efficient easy-to-use finite element program for general two-dimensional problems is presented. Several problems in groundwater flow are considered that include steady, unsteady flows in different types of aquifers. Different cases of sinks and sources in the flow domain are also considered. The performance of finite element methods is studied for the chosen problems by comparing the numerical solutions of test problems with analytical solutions (if they exist) or with solutions obtained by other numerical methods. The polynomial refinement of the finite elements is studied for the presented problems in order to offer some evidence as to which finite element simulation is best to use under a variety of circumstances

Entropy generation for MHD natural convection in enclosure with a micropolar fluid saturated porous medium with Al2O3Cu water hybrid nanofluid

This contribution gives a numerical investigation of buoyancy-driven flow of natural convection heat transfer and entropy generation of non-Newtonian hybrid nanofluid (Al2O3-Cu) within an enclosure square porous cavity. Hybrid nanofluids represent a novel type of enhanced active fluids. During the current theoretical investigation, an actual available empirical data for both thermal conductivity and dynamic viscosity of hybrid nanofluids are applied directly. Numerical simulation have been implemented for solid nanoparticles, the volumetric concentration of which varies from 0.0% (i.e., pure fluid) to 0.1% of hybrid nanofluids. Heat and sink sources are situated on a part of the left and right sides of the cavity with length B, while the upper and bottom horizontal sides are kept adiabatic. The stated partial differential equations describing the flow are mutated to a dimensionless formulas, then solved numerically via the help of an implicit finite difference approach. The acquired computations are given in terms of streamlines, isotherms, isomicrorotations, isoconcentraions, local Began number, total entropy, local and mean Nusselt numbers. The data illustrates that variations of ratio of the average Nusselt number to the average Nusselt of pure fluid Num+ is a decreasing function of Ha and φ, while e+ is an increasing function of Ha and φ parameters of hybrid nanofluid

Novel Green Micro-Synthesis of Graphene-Titanium Dioxide Nano- Composites with Photo-Electrochemical Properties

Background: Graphene-Titanium dioxide nano-composite forms a very promising material in the field of photo-electrochemical research. Methods: In this study, a novel environment-friendly synthesis method was developed to produce well-distributed anatase nano-titanium dioxide spherical particles on the surface of graphene sheets. This novel method has great advantages over previously developed methods of producing graphenetitanium dioxide nanocomposites (GTNCs). High calcination temperature 650°C was used in the preparation of nano titanium dioxide, and chemical exfoliation for graphene synthesis and GTNC was performed by our novel method of depositing titanium dioxide nanoparticles on graphene sheets using a Y-shaped micro-reactor under a controlled pumping rate with minimal use of chemicals. Results: The physiochemical and crystallographic properties of the GTNC were confirmed by TEM, XRD, FTIR and EDX measurements, confirming process repeatability. Spherical nano-titanium dioxide was produced in the anatase phase with very high crystallinity and small particle diameters ranging from 9 nm to 25 nm, also the as prepared graphene (RGO) exhibited minimal flake folding and a high carbon content of 81.28% with a low oxygen-to-carbon atomic ratio of 0.172 and GTNCs produced by our novel method had a superior loading content, a homogeneous distribution and a 96.6% higher content of titanium dioxide particles on the graphene sheets compared with GTNCs prepared with the one-pot method. Conclusion: For its photoelectrochemical properties, chronoamperometry showed that GTNC sample (2) had a higher peak current of 60 μA compared with that of GTNC sample (1), which indicates that the separation and transfer of electron-hole pairs are better in the case of GTNC sample (2) and according to the LSV results, the generation of photocurrent in the samples can be observed through multiple on-off cycles, which indicates that the electrodes are stable and that the photocurrent is quite reversible

Similarity Solution for Unsteady MHD Flow Near a Stagnation Point of a Three-Dimensional Porous Body with Heat and Mass Transfer, Heat Generation/Absorption and Chemical Reaction

The problem of unsteady mixed convection heat and mass transfer near the stagnation point of a three-dimensional porous body in the presence of magnetic field, chemical reaction and heat source or sink is analyzed. An efficient, iterative, tri-diagonal implicit finite difference method is used to solve the transformed similarity equations in the boundary layer. Three cases were considered, namely, accelerating flow, decelerating flow and the steady-state case. The obtained results are presented in graphical and tabulated forms to illustrate the influence of the different physical parameters such as the magnetic field parameter, transpiration parameter, unsteadiness parameter, ratio of velocity gradients at the edge of the boundary layer parameter, heat generation/absorption parameter and the chemical reaction parameter on the velocity components in the x-and y- directions, temperature and concentration distributions, as well as the skin-friction coefficients and Nusselt and Sherwood numbers

Automated grade classification of oral epithelial dysplasia using morphometric analysis of histology images

Oral dysplasia is a pre-malignant stage of oral epithelial carcinomas, e.g., oral squamous cell carcinoma, where significant changes in tissue layers and cells can be observed under the microscope. However, malignancy can be reverted or cured using proper medication or surgery if the grade of malignancy is assessed properly. The assessment of correct grade is therefore critical in patient management as it can change the treatment decisions and prognosis for the dysplastic lesion. This assessment is highly challenging due to considerable inter- and intraobserver variability in pathologists’ agreement, which highlights the need for an automated grading system that can predict more accurate and reliable grade. Recent advancements have made it possible for digital pathology (DP) and artificial intelligence (AI) to join forces from the digitization of tissue slides into images and using those images to train and predict more accurate grades using complex AI models. In this regard, we propose a novel morphometric approach exploiting the architectural features in dysplastic lesions i.e., irregular epithelial stratification where we measure the widths of different layers of the epithelium from the boundary layer i.e., keratin projecting inwards to the epithelium and basal layers to the rest of the tissue section from a clinically significant viewpoint

The Capaciousness of No: Affective Refusals as Literacy Practices

© 2020 The Authors. Reading Research Quarterly published by Wiley Periodicals, Inc. on behalf of International Literacy Association The authors considered the capacious feeling that emerges from saying no to literacy practices, and the affective potential of saying no as a literacy practice. The authors highlight the affective possibilities of saying no to normative understandings of literacy, thinking with a series of vignettes in which children, young people, and teachers refused literacy practices in different ways. The authors use the term capacious to signal possibilities that are as yet unthought: a sense of broadening and opening out through enacting no. The authors examined how attention to affect ruptures humanist logics that inform normative approaches to literacy. Through attention to nonconscious, noncognitive, and transindividual bodily forces and capacities, affect deprivileges the human as the sole agent in an interaction, thus disrupting measurements of who counts as a literate subject and what counts as a literacy event. No is an affective moment. It can signal a pushback, an absence, or a silence. As a theoretical and methodological way of thinking/feeling with literacy, affect proposes problems rather than solutions, countering solution-focused research in which the resistance is to be overcome, co-opted, or solved. Affect operates as a crack or a chink, a tiny ripple, a barely perceivable gesture, that can persist and, in doing so, hold open the possibility for alternative futures

Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder

We study the statistics of thermodynamic quantities in two related systems with quenched disorder: A (1+1)-dimensional planar lattice of elastic lines in a random potential and the 2-dimensional random bond dimer model. The first system is examined by a replica-symmetric Bethe ansatz (RBA) while the latter is studied numerically by a polynomial algorithm which circumvents slow glassy dynamics. We establish a mapping of the two models which allows for a detailed comparison of RBA predictions and simulations. Over a wide range of disorder strength, the effective lattice stiffness and cumulants of various thermodynamic quantities in both approaches are found to agree excellently. Our comparison provides, for the first time, a detailed quantitative confirmation of the replica approach and renders the planar line lattice a unique testing ground for concepts in random systems.Comment: 16 pages, 14 figure

Supernova Neutrinos, Neutrino Oscillations, and the Mass of the Progenitor Star

We investigate the initial progenitor mass dependence of the early-phase neutrino signal from supernovae taking neutrino oscillations into account. The early-phase analysis has advantages in that it is not affected by the time evolution of the density structure of the star due to shock propagation or whether the remnant is a neutron star or a black hole. The initial mass affects the evolution of the massive star and its presupernova structure, which is important for two reasons when considering the neutrino signal. First, the density profile of the mantle affects the dynamics of neutrino oscillation in supernova. Second, the final iron core structure determines the features of the neutrino burst, i.e., the luminosity and the average energy. We find that both effects are rather small. This is desirable when we try to extract information on neutrino parameters from future supernova-neutrino observations. Although the uncertainty due to the progenitor mass is not small for intermediate $\theta_{13}$ ($10^{-5} \lesssim \sin^{2}{2 \theta_{13}} \lesssim 10^{-3}$), we can, nevertheless, determine the character of the mass hierarchy and whether $\theta_{13}$ is very large or very small.Comment: 8 pages, 15 figure