Cubically convergent methods for selecting the regularization parameters in linear inverse problems

AbstractWe present three cubically convergent methods for choosing the regularization parameters in linear inverse problems. The detailed algorithms are given and the convergence rates are estimated. Our basic tools are Tikhonov regularization and Morozov's discrepancy principle. We prove that, in comparison with the standard Newton method, the computational costs for our cubically convergent methods are nearly the same, but the number of iteration steps is even less. Numerical experiments for an elliptic boundary value problem illustrate the efficiency of the proposed algorithms

Finite- and Large- Sample Inference for Model and Coefficients in High-dimensional Linear Regression with Repro Samples

In this paper, we present a new and effective simulation-based approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in which we conduct statistical inference by creating and studying the behavior of artificial samples that are obtained by mimicking the sampling mechanism of the data. We obtain confidence sets for (a) the true model corresponding to the nonzero coefficients, (b) a single or any collection of regression coefficients, and (c) both the model and regression coefficients jointly. We also extend our approaches to drawing inferences on functions of the regression coefficients. The proposed approach fills in two major gaps in the high-dimensional regression literature: (1) lack of effective approaches to address model selection uncertainty and provide valid inference for the underlying true model; (2) lack of effective inference approaches that guarantee finite-sample performances. We provide both finite-sample and asymptotic results to theoretically guarantee the performances of the proposed methods. In addition, our numerical results demonstrate that the proposed methods are valid and achieve better coverage with smaller confidence sets than the existing state-of-art approaches, such as debiasing and bootstrap approaches

Extension of the Lower Load Limit in Dieseline Compression Ignition Mode

AbstractA study to extend the low load limit of the mixture of commercial gasoline and diesel in the compression mode is performed on a single cylinder diesel engine. The additional measures, like intake heating, rebreathing, negative valve overlap, are not employed. By adopting boosting, sweeping the injection pressure and varying the fuel octane number, the minimum fuelling rate and the minimum IMEP gained is compared. Besides, the thermal efficiency and emission results at these operation points are also discussed.The results illustrate that the high intake pressure, the low injection pressure and the low fuel octane number are very effective to extend low load limit. With these strategies, gasoline-type fuels can get the lowest load 0.07MPa IMEP (0.14MPa intake pressure and 20MPa injection pressure) and successfully replace diesel at low load operation points in the compression mode. Increasing the intake pressure and reducing the injection pressure can significantly reduce the minimum fuelling rate and then the minimum IMEP. The minimum IMEP (0.34MPa) of the calibration point on the original engine at test speed (1600rpm) can be achieved by G80 without boosting.The combustion efficiency is influenced by the intake pressure and the injection pressure, however, the ISFC is more dependent on the engine load rather than other factors. If there is more over-lean mixture in cylinder when adjusting the experimental conditions, CO and HC emissions are higher. To satisfy the Euro VI regulation on NOx (<0.4g/kWh), a small amount of EGR is needed to control NOx emission

An Optimal Allocation Model of Public Transit Mode Proportion for the Low-Carbon Transportation

Public transit has been widely recognized as a potential way to develop low-carbon transportation. In this paper, an optimal allocation model of public transit mode proportion (MPMP) has been built to achieve the low-carbon public transit. Optimal ratios of passenger traffic for rail, bus, and taxi are derived by running the model using typical data. With different values of traffic demand, construction cost, travel time, and accessibilities, MPMP can generate corresponding optimal ratios, benefiting decision impacts analysis and decision makers. Instead of considering public transit as a united system, it is separated into units in this paper. And Shanghai is used to test model validity and practicality

Study on Evaluation Models of Highway Safety Based on Catastrophe Theory

Evaluating safety performance of first-class highways in China is important due to their high mortality rates. Traditional models for statistical crash prediction and traffic conflict techniques require long periods of data collection which is time-consuming and labor-intensive. This paper introduces a safety evaluation method based on catastrophe theory for highways in China. The method firstly divides the highway into multiple road sections and uses video-based road detection (VRD) system to collect video data of existing road conditions. Then, experienced drivers and experts are invited to watch the collected videos to establish a multilayer safety index system and assign values to bottom indexes. By applying catastrophe theory, a general safety index is derived, which indicates the relative safety level of a road section. Finally, all road sections can be ranked based on the general safety index. A case study shows encouraging results where (1) the safety index is highly correlated with real mortality rates and (2) the safety index successfully identifies most dangerous road sections. The proposed method can be considered as a promising supplementary safety evaluation method that could help traffic engineers to better understand safety implications of first-class highways in China