Sequential procedures for nonparametric kernel regression

In a nonparametric setting, the functional form of the relationship between the response variable and the associated predictor variables is unspecified; however it is assumed to be a smooth function. The main aim of nonparametric regression is to highlight an important structure in data without any assumptions about the shape of an underlying regression function. In regression, the random and fixed design models should be distinguished. Among the variety of nonparametric regression estimators currently in use, kernel type estimators are most popular. Kernel type estimators provide a flexible class of nonparametric procedures by estimating unknown function as a weighted average using a kernel function. The bandwidth which determines the influence of the kernel has to be adapted to any kernel type estimator. Our focus is on Nadaraya-Watson estimator and Local Linear estimator whic h belong to a class of kernel type regression estimators called local polynomial kernel estimators. A closely related problem is the determination of an appropriate sample size that would be required to achieve a desired confidence level of accuracy for the nonparametric regression estimators. Since sequential procedures allow an experimenter to make decisions based on the smallest number of observations without compromising accuracy, application of sequential procedures to a nonparametric regression model at a given point or series of points is considered. The motivation for using such procedures is: in many applications the quality of estimating an underlying regression function in a controlled experiment is paramount; thus, it is reasonable to invoke a sequential procedure of estimation that chooses a sample size based on recorded observations that guarantees a preassigned accuracy. We have employed sequential techniques to develop a procedure for constructing a fixed-width confidence interval for the predicted value at a specific point of the independent variable. These fixed-width confidence intervals are developed using asymptotic properties of both Nadaraya-Watson and local linear kernel estimators of nonparametric kernel regression with data-driven bandwidths and studied for both fixed and random design contexts. The sample sizes for a preset confidence coefficient are optimized using sequential procedures, namely two-stage procedure, modified two-stage procedure and purely sequential procedure. The proposed methodology is first tested by employing a large-scale simulation study. The performance of each kernel estimation method is assessed by comparing their coverage accuracy with corresponding preset confidence coefficients, proximity of computed sample sizes match up to optimal sample sizes and contrasting the estimated values obtained from the two nonparametric methods with act ual values at given series of design points of interest. We also employed the symmetric bootstrap method which is considered as an alternative method of estimating properties of unknown distributions. Resampling is done from a suitably estimated residual distribution and utilizes the percentiles of the approximate distribution to construct confidence intervals for the curve at a set of given design points. A methodology is developed for determining whether it is advantageous to use the symmetric bootstrap method to reduce the extent of oversampling that is normally known to plague Stein's two-stage sequential procedure. The procedure developed is validated using an extensive simulation study and we also explore the asymptotic properties of the relevant estimators. Finally, application of our proposed sequential nonparametric kernel regression methods are made to some problems in software reliability and finance

Dynamic compression of foam supported plates impacted by high velocity soil

The response of back-supported buffer plates comprising a solid face sheet and foam core backing impacted by a column of high velocity particles (sand slug) is investigated via a lumped parameter model and coupled discrete/continuum simulations. The buffer plate is either resting (unattached) or attached to a rigid stationary foundation. The lumped parameter model is used to construct maps of the regimes of behaviour with axes of the ratio of the height of the sand slug to core thickness and the normalised core strength. Four regimes of behaviour are identified based on whether the core compression ends prior to the densification of the sand slug or vice versa. Coupled discrete/continuum simulations are also reported and compared with the lumped parameter model. While the model predicted regimes of behaviour are in excellent agreement with numerical simulations, the lumped parameter model is unable to predict the momentum transmitted to the supports as it neglects the role of elasticity in both the buffer plate and the sand slug. The numerical calculations show that the momentum transfer is minimised for intermediate values of the core strength when the so-called “soft-catch” mechanism is at play. In this regime the bounce-back of the sand slug is minimised which reduces the momentum transfer. For high values of the core strength, the response of the buffer plate resembles a rigid plate with nearly no impulse mitigation while at low values of core strength, a slap event occurs when the face sheet impinges against the foundation due to full densification of the foam core. This slap event results in a significant enhancement of the momentum transfer to the foundation. The results demonstrate that appropriately designed buffer plates have potential as impulse mitigators in landmine loading situations

Fabrication of CdS/CdTe-based thin film solar cells using an electrochemical technique

Thin film solar cells based on cadmium telluride (CdTe) are complex devices which have great potential for achieving high conversion efficiencies. Lack of understanding in materials issues and device physics slows down the rapid progress of these devices. This paper combines relevant results from the literature with new results from a research programme based on electro-plated CdS and CdTe. A wide range of analytical techniques was used to investigate the materials and device structures. It has been experimentally found that n-, i- and p-type CdTe can be grown easily by electroplating. These material layers consist of nano- and micro-rod type or columnar type grains, growing normal to the substrate. Stoichiometric materials exhibit the highest crystallinity and resistivity, and layers grown closer to these conditions show n - p or p - n conversion upon heat treatment. The general trend of CdCl2 treatment is to gradually change the CdTe material’s n-type electrical property towards i-type or p-type conduction. This work also identifies a rapid structural transition of CdTe layer at 385 ± 5 °C and a slow structural transition at higher temperatures when annealed or grown at high temperature. The second transition occurs after 430 °C and requires more work to understand this gradual transition. This work also identifies the existence of two different solar cell configurations for CdS/CdTe which creates a complex situation. Finally, the paper presents the way forward with next generation CdTe-based solar cells utilising low-cost materials in their columnar nature in graded bandgap structures. These devices could absorb UV, visible and IR radiation from the solar spectrum and combine impact ionisation and impurity photovoltaic (PV) effect as well as making use of IR photons from the surroundings when fully optimised

The use of common bean (Phaseolus vulgaris ) traditional varieties and their mixtures with commercial varieties to manage bean fly (Ophiomyia spp .) infestations in Uganda

The bean fly (Ophiomyia spp.) is considered the most economically damaging field insect pest of common beans in Uganda. Despite the use of existing pest management approaches, reported damage has remained high. Forty-eight traditional and improved common bean varieties currently grown in farmers’ fields were evaluated for resistance against bean fly. Data on bean fly incidence, severity and root damage from bean stem maggot were collected. Generalized linear mixed model (GLMM) revealed significant resistance to bean fly in the Ugandan traditional varieties. A popular resistant traditional variety and a popular susceptible commercial variety were selected from the 48 varieties and evaluated in pure and mixed stands. The incidence of bean fly infestation on both varieties in mixtures with different arrangements (systematic random versus rows), and different proportions within each of the two arrangements, was measured and analysed using GLMMs. The proportion of resistant varieties in a mixture and the arrangement type significantly decreased bean fly damage compared to pure stands, with the highest decrease in damage registered in the systematic random mixture with at least 50 % of resistant variety. The highest reduction in root damage, obvious 21 days after planting, was found in systematic random mixtures with at least 50 % of the resistant variety. Small holder farmers in East Africa and elsewhere in the world have local preferences for growing bean varieties in genetic mixtures. These mixtures can be enhanced by the use of resistant varieties in the mixtures to reduce bean fly damage on susceptible popular varieties

A new direct detection electron scattering experiment to search for the X17 particle

A new electron scattering experiment (E12-21-003) to verify and understand the nature of hidden sector particles, with particular emphasis on the so-called X17 particle, has been approved at Jefferson Lab. The search for these particles is motivated by new hidden sector models introduced to account for a variety of experimental and observational puzzles: excess in $e^+e^-$ pairs observed in multiple nuclear transitions, the 4.2$\sigma$ disagreement between experiments and the standard model prediction for the muon anomalous magnetic moment, and the small-scale structure puzzle in cosmological simulations. The aforementioned X17 particle has been hypothesized to account for the excess in $e^+e^-$ pairs observed from the $^8$Be M1, $^4$He M0, and, most recently, $^{12}$C E1 nuclear transitions to their ground states observed by the ATOMKI group. This experiment will use a high resolution electromagnetic calorimeter to search for or set new limits on the production rate of the X17 and other hidden sector particles in the $3 - 60$ MeV mass range via their $e^+e^-$ decay (or $\gamma\gamma$ decay with limited tracking). In these models, the $1 - 100$ MeV mass range is particularly well-motivated and the lower part of this range still remains unexplored. Our proposed direct detection experiment will use a magnetic-spectrometer-free setup (the PRad apparatus) to detect all three final state particles in the visible decay of a hidden sector particle for an effective control of the background and will cover the proposed mass range in a single setting. The use of the well-demonstrated PRad setup allows for an essentially ready-to-run and uniquely cost-effective search for hidden sector particles in the $3 - 60$ MeV mass range with a sensitivity of 8.9$\times$10$^{-8}$ - 5.8$\times$10$^{-9}$ to $\epsilon^2$, the square of the kinetic mixing interaction constant between hidden and visible sectors.Comment: 6 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:2108.1327

Impact of spatial perception on place making in open spaces of middle class housing schemes around Colombo

Mass housing is used to provide not only a home but a social structure for communities. People celebrate their lifestyle using available spaces in these mass housings. This research aims to understand how spatial perception act on the placemaking process in this open spaces. This research mainly focuses on middle income housing which ensure the applicability of outcome to a broader spectrum. These communities may override designer’s idea for a space and built their own. It is pertinent to create a middle ground between these informal place making process and formal design practice of professionals. Research was carried out by analyzing the activities in these open spaces through a photographic survey. Then different case studies were compared to accomplish the outcome. According to research findings dwellers prefer a more centralized establishment plus close proximity of nodes. When dwellers can experience the open space as one whole it act positively. When open spaces of a housing scheme failed to depict a sense of territoriality it becomes vulnerable to negative social influences. These patterns were clearly visible in all three case studies