New Robust Projection to Latent Structure

In many actual nonlinear systems, especially near the equilibrium point, linearity is the primary feature and nonlinearity is the secondary feature. For the system that deviates from the equilibrium point, the secondary nonlinearity or local structure feature can also be regarded as the small uncertainty part, just as the nonlinearity can be used to represent the uncertainty of a system (Wang et al. 2019). So this chapter also focuses on how to deal with the nonlinearity in PLS series method, but starts from an different view, i.e., robust PLS. Here the system nonlinearity is considered as uncertainty and a new robust $$\mathrm{L}_1$$ L 1 -PLS is proposed.

Comparisons of Propensity Score Methods for Time to Event Outcomes: Evaluation through Simulations and Oral Squamous Cell Carcinoma Case Study

Introduction & Objective: In observational studies, it is recommended to use propensity score (PS) methods or covariate adjustment for confounding effect adjustment. However, few guidelines are available regarding the choice of PS approaches or covariate adjustment for the best performance in a particular data. In this study, we compared different PS methods and conventional covariate adjustment to investigate the treatment effect for the overall population on time-to-event outcomes. Methods: In the Monte Carlo simulations, we compared the hazard ratio (HR) and precision estimated using covariate adjustment and eight different PS approaches, including matching, stratification, and inverse probability of treatment weighting (IPTW). In the Oral Squamous-Cell Carcinoma Cancer case study, we applied the aforementioned PS approaches to compare the effect of receiving post-operative radiation therapy (PORT) and having engraftable tumors on different time-to-event clinical outcomes. Results: In the simulations, both IPTW and covariate adjustment produced unbiased HR estimates with small uncertainty. In the case study, covariate adjustment showed that patients with engraftable tumors were twice as likely to have local/regional recurrence (HR 1.98 [1.23, 3.18], p-value<0.005) and any recurrence or death (HR 2.02 [1.38, 2.96], p-value<0.001); patients received PORT were twice as likely to develop either local, regional, or distance recurrence (HR 2.12 [1.32, 3.41], p-value<0.005). Results produced by IPTW were consistent with covariate adjustment method (within ± 0.1 differences). Conclusion: Covariate adjustment and the IPTW method performed well across simulations and the case study. In practice, care should be taken to select the most suitable method when estimating the treatment, exposure or intervention effect on time-to-event outcomes.

Impact of Flow Variation on Hydropower Projects in Budhigandaki River Basin of Nepal

Daily flow data from 1964 to 2015 of Budhigandaki River at Arughat were analyzed to assess the impact of flow variation at different time scales to the run of the river (RoR) type of hydropower projects. The data show very high inter-annual variation in daily, monthly and seasonal flows. The long term annual average flow at Arughat was 160 m3/s and varies from 120 to 210 m3/s. The long-term averages of loss in flow for both dry and wet seasons based on daily flows for three design discharges (Q90, Q60 and Q40) were found to be respectively -0.72, -1.76 and -1.54 m3/s for dry season and 0.0, -0.27 and -2.26 m3/s for wet season. Although long-term average loss is small, uncertainty increases with the increase in design discharge. The long-term dry season power loss is about 3 % for the RoR projects of the basin however, its annual variation is large. There is a probability of losing the quantum of energy generation by nearly 40% in some years and gaining by about 30 % in some other years in dry season. The impact of flow variation on power production was negative in both dry and wet seasons for RoR projects of Budhigandaki basin. This study concludes that uncertainty arising from daily flow variation should be assessed while estimating energy generation in hydropower projects. Intra-annual flow variation is, thus, to be taken into consideration while calculating the power generated by the RoR plants; and it should be reflected in power purchase agreement.

The uncertainty of flood frequency analyses in hydrodynamic model simulations

Assessing the risk of a historical-level flood is essential for regional flood protection and resilience establishment. However, due to the limited spatiotemporal coverage of observations, the impact assessment relies on model simulations and is thus subject to uncertainties from cascade physical processes. This study assesses the flood hazard map with uncertainties subject to different combinations of runoff inputs, variables for flood frequency analysis and fitting distributions based on estimations by the CaMa-Flood global hydrodynamic model. Our results show that deviation in the runoff inputs is the most influential source of uncertainties in the estimated flooded water depth and inundation area, contributing more than 80 % of the total uncertainties investigated in this study. Global and regional inundation maps for floods with 1-in-100 year return periods show large uncertainty values but small uncertainty ratios for river channels and lakes, while the opposite results are found for dry zones and mountainous regions. This uncertainty is a result of increasing variation at tails among various fitting distributions. In addition, the uncertainty between selected variables is limited but increases from the regular period to the rarer floods, both for the water depth at points and for inundation area over regions. The uncertainties in inundation area also lead to uncertainties in estimating the population and economy exposure to the floods. In total, inundation accounts for 9.1 % [8.1 %–10.3 %] of the land area for a 1-in-100 year flood, leading to 13.4 % [12.1 %–15 %] of population exposure and 13.1 % [11.8 %–14.7 %] of economic exposure for the globe. The flood exposure and uncertainties vary by continent and the results in Africa have the largest uncertainty, probably due to the limited observations to constrain runoff simulations, indicating a necessity to improve the performance of different hydrological models especially for data-limited regions.

On the Surface Residual Stress Measurement in Magnesium Alloys Using X-Ray Diffraction

X-ray penetration in magnesium alloys is significant due to the low X-ray mass attenuation coefficient. To measure the surface residual stresses in magnesium alloys, a correction needs to be made to account for penetration depth. The residual stresses in as-received and shot peened AZ31B-H24 rolled sheet samples were measured using two-dimensional X-ray diffraction (2D-XRD) method. The electro-polishing layer removal method was used to find the residual stress pattern at the surface and through the depth. The results show that the corrected residual stresses in a few tens of micrometers layer from the surface differ from the raw stresses. To better estimate the residual stress distribution in the surface, the grazing-incidence X-ray diffraction (GIXD) technique was applied. Additionally, micrographs of the lateral cross-section of the peened specimens confirmed the presence of microcracks in this region, causing the residual stresses to vanish. Due to the low X-ray absorption coefficient of Mg alloys, this study shows how a small uncertainty in a single raw measurement leads to high uncertainty in the corrected residual stresses. The results were corroborated with the hole drilling method of residual stress measurements. The corrected X-ray diffraction (XRD) results are in close agreement with the hole drilling and GIXD results.

Hybrid two-mode squeezing of microwave and optical fields using optically pumped graphene layers

A measurable quadrature of a squeezed quantum state manifests a small uncertainty below the Heisenberg limit. This phenomenon has the potential to enable several extraordinary applications in quantum information, metrology and sensing, and other fields. Several techniques have been implemented to realize squeezed electromagnetic states, including microwave fields and optical fields. However, hybrid squeezed modes (that incorporate both microwave and optical fields) have not yet been proposed despite their vital functionality to combine the two worlds of quantum superconducting systems and photonics systems. In this work, for the first time, we propose a novel approach to achieve two-mode squeezing of microwave and optical fields using graphene based structure. The proposed scheme includes a graphene layered structure that is driven by a quantum microwave voltage and subjected to two optical fields of distinct frequencies. By setting the optical frequency spacing equal to the microwave frequency, an interaction occurs between the optical and microwave fields through electrical modulation of the graphene conductivity. We show that significant hybrid two-mode squeezing, that includes one microwave field and one optical field, can be achieved. Furthermore, the microwave frequency can be tuned over a vast range by modifying the operation parameters.

A Precise Benchmark for Cluster Scaling Relations: Fundamental Plane, Mass Plane and IMF in the Coma Cluster from Dynamical Models

We study a sample of 148 early-type galaxies in the Coma cluster using SDSS photometry and spectra, and calibrate our results using detailed dynamical models for a subset of these galaxies, to create a precise benchmark for dynamical scaling relations in high-density environments. For these galaxies, we successfully measured global galaxy properties, modeled stellar populations, and created dynamical models, and support the results using detailed dynamical models of 16 galaxies, including the two most massive cluster galaxies, using data taken with the SAURON IFU. By design, the study provides minimal scatter in derived scaling relations due to the small uncertainty in the relative distances of galaxies compared to the cluster distance. Our results demonstrate low (≤55% for 90th percentile) dark matter fractions in the inner 1Re of galaxies. Owing to the study design, we produce the tightest, to our knowledge, IMF-σe relation of galaxies, with a slope consistent with that seen in local galaxies. Leveraging our dynamical models, we transform the classical Fundamental Plane of the galaxies to the Mass Plane. We find that the coefficients of the mass plane are close to predictions from the virial theorem, and have significantly lower scatter compared to the Fundamental plane. We show that Coma galaxies occupy similar locations in the (M* - Re) and (M* - σe) relations as local field galaxies but are older. This, and the fact we find only three slow rotators in the cluster, is consistent with the scenario of hierarchical galaxy formation and expectations of the kinematic morphology-density relation.

Bayesian inversion and visualization of hierarchical geostatistical models

&lt;p&gt;Geostatistical inversion methods estimate the spatial distribution of heterogeneous soil properties (here: hydraulic conductivity) from indirect information (here: piezometric heads). Bayesian inversion is a specific approach, where prior assumptions (or prior models) are combined with indirect measurements to predict soil parameters and their uncertainty in form of a posterior parameter distribution. Posterior distributions depend heavily on prior models, as prior models describe the spatial structure of heterogeneity. The most common prior is the stationary multi-Gaussian model, which expresses that close-by points are more correlated than distant points. This is a good assumption for single-facies systems. For multi-facies systems, multiple-point geostatistical (MPS) methods are widely used. However, these typically only distinguish between several facies and do not represent the internal heterogeneity inside each facies.&lt;/p&gt;&lt;p&gt;We combine these two approaches to a joint hierarchical model, which results in a multi-facies system with internal heterogeneity in each facies. Using this model, we propose a tailored Gibbs sampler, a kind of Markov Chain Monte Carlo (MCMC) method, to perform Bayesian inversion and sample from the resulting posterior parameter distribution. We test our method on a synthetic channelized flow scenario for different levels of data available: A highly informative setting (with many measurements) where we recover the synthetic truth with relatively small uncertainty invervals, and a weakly informative setting (with only a few measurements) where the synthetic truth cannot be recovered that clearly. Instead, we obtain a multi-modal posterior. We investigate the multi-modal posterior using a clustering algorithm. Clustering algorithms are a common machine learning approach to find structures in large data sets. Using this approach, we can split the multi-modal posterior into its modes and can assign probabilities to each mode. A visualization of this clustering and the according probabilities enables researchers and engineers to intuitively understand complex parameter distributions and their uncertainties.&lt;/p&gt;

EVALUATION OF THE ELECTRICAL CAPACITANCE TOMOGRAPHY SYSTEM FOR MEASUREMENT USING 3D SENSOR

Further tests of EVT4 data acquisition system for electrical capacitance tomography are presented. The modular system, which can have up to 32 channels with an individual analogue to digital converter, was designed to ensure small uncertainty of capacitance measurement at high speed of imaging. The system’s performance in the context of 3D imaging was experimentally verified. In particular, we show that the measurement of changes in capacitance due to a small change of an electric permittivity distribution for the most distant electrodes in a suitably designed 3D sensor is possible using our system. Cross-plane measurements together with the measurements for the pairs of most distant electrodes are essential for accurate reconstruction of 3D distributions. Due to sensitivity of capacitance measurements obtained in the hardware, the measurements for all electrode pairs can be used in the inverse problem – the system of equations can be extended. Although the numerical condition number of a matrix of such a system is high, image reconstruction is possible from the data obtained in our system. The results of 3D image reconstruction for simple test objects are shown.