An Exploration of Pathologies of Multilevel Principal Components Analysis in Statistical Models of Shape

3D facial surface imaging is a useful tool in dentistry and in terms of diagnostics and treatment planning. Between-groups PCA (bgPCA) is a method that has been used to analyse shapes in biological morphometrics, although various “pathologies” of bgPCA have recently been proposed. Monte Carlo (MC) simulated datasets were created here in order to explore “pathologies” of multilevel PCA (mPCA), where mPCA with two levels is equivalent to bgPCA. The first set of MC experiments involved 300 uncorrelated normally distributed variables, whereas the second set of MC experiments used correlated multivariate MC data describing 3D facial shape. We confirmed previous results of other researchers that indicated that bgPCA (and so also mPCA) can give a false impression of strong differences in component scores between groups when there is none in reality. These spurious differences in component scores via mPCA reduced strongly as the sample sizes per group were increased. Eigenvalues via mPCA were also found to be strongly effected by imbalances in sample sizes per group, although this problem was removed by using weighted forms of covariance matrices suggested by the maximum likelihood solution of the two-level model. However, this did not solve problems of spurious differences between groups in these simulations, which was driven by very small sample sizes in one group here. As a “rule of thumb” only, all of our experiments indicate that reasonable results are obtained when sample sizes per group in all groups are at least equal to the number of variables. Interestingly, the sum of all eigenvalues over both levels via mPCA scaled approximately linearly with the inverse of the sample size per group in all experiments. Finally, between-group variation was added explicitly to the MC data generation model in two experiments considered here. Results for the sum of all eigenvalues via mPCA predicted the asymptotic amount for the total amount of variance correctly in this case, whereas standard “single-level” PCA underestimated this quantity.

THE PROBLEM OF OPTIMIZING BUS ROUTE USING GEOINFORMATION ENVIRONMENT

The public transport system is characterized by a complex transport network, intersecting routes and fragmented stopping points. In this regard, the functioning of the transport system to ensure optimal planning of bus transportation is an urgent task. A solution to this problem can be a multi-level model that allows you to represent network objects at several spatial levels, calculate the exact time delay, and meet the needs of planning bus trips with various optimization criteria

Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom–Diatomic Molecule Coexistence

A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT.

Research on Real-Time Model of Turboshaft Engine with Surge Process

The main data source for the verification of surge detection methods still rely on test rigs of the compressor or the whole engine, which makes the development of models of the whole engine surge process an urgent need to replace the high-cost and high-risk surge test. In this paper, a novel real-time surge model based on the surge mechanism is proposed. Firstly, the turboshaft engine component level model (CLM) and the classic surge dynamic model, Moore-Greitzer (MG) model is established. Then the stability of the MG model is analyzed and the compressor characteristics in the classical MG model are extended to establish the extended MG model. Finally, this paper considers the coupling relationship of the compressor’s rotor speed, mass flow and pressure between CLM and the extended MG model to establish the real-time model of the turboshaft engine with surge process. The simulation results show that this model can realize the whole surge process of the turboshaft engine under multiple operating states. The change characteristics of the rotor speed, compressor outlet pressure, mass flow, exhaust gas temperature and other parameters are consistent with the test data, which means that the model proposed can be further applied to the research of surge detection and anti-surge control.

Predicting Future Diameter Distributions Given Current Stand Attributes

This study discussed four methods to project a diameter distribution from age A1 to age A2. Method 1 recovers parameters of the distribution at age A2 from stand attributes at that age. Method 2 uses a stand-level model to grow the quadratic mean diameter, and then recovers the distribution parameters from that prediction. Method 3 grows the diameter distribution by assuming tree-level survival and diameter growth functions. Method 4 first converts the diameter distribution at age A1 into a list of individual trees before growing these trees to age A2. In a numerical example employing the Weibull distribution, methods 3 and 4 produced better results based on two types of error indices and the relative predictive error for each diameter class. Method 4 is a novel method that converts a diameter distribution into a list of individual-trees, and in the process, successfully links together diameter distribution, individual-tree, and whole stand models.

Integrated optimization of production planning and scheduling in uncertain re-entrance environment for fixed-position assembly workshops

For the fixed-position assembly workshop, the integrated optimization problem of production planning and scheduling in the uncertain re-entrance environment is studied. Based on the situation of aircraft assembly workshops, the characteristics of fixed-position assembly workshop with uncertain re-entrance are abstracted. As the re-entrance repetition obeys some type of probability distribution, the expected value is used to describe the repetition, and a bi-level stochastic expected value programming model of integrated production planning and scheduling is constructed. Recursive expressions for start time and completion time of assembly classes and teams are confirmed. And the relation between the decision variable in the lower-level model of scheduling and the overtime and earliness of assembly classes and teams in the upper-level model of production planning is identified. Addressing the characteristics of bi-level programming model, an alternate iteration method based on Improved Genetic Algorithm (AI-IGA) is proposed to solve the models. Elite Genetic Algorithm (EGA) is introduced for the upper-level model of production planning, and Genetic Simulated Annealing Algorithm based on Stochastic Simulation Technique (SS-GSAA) is developed for the lower-level model of scheduling. Results from our experiments demonstrate that the proposed method is feasible for production planning and optimization of the fixed-position assembly workshop with uncertain re-entrance. And algorithm comparison verifies the effectiveness of the proposed algorithm.

Eliciting patients’ healthcare goals and concerns: Do questions influence responses?

There is increasing interest in asking patients questions before their visits to elicit goals and concerns, which is part of the move to support the concept of coproducing care. The phrasing and delivery of such questions differs across settings and is likely to influence responses. This report describes a study that (i) used a three-level model to categorize the goals and concerns elicited by two different pre-visit questions, and (ii) describes associations between responses elicited and the phrasing and delivery of the two questions. The questions were administered to patients with rheumatic disease, and patients with inflammatory bowel disease (IBD). Paper-based responses from 150 patients with rheumatic disease and 338 patients with IBD were analyzed (163 paper, 175 electronic). The goals and concerns elicited were primarily disease or symptom-specific. The specific goal and concern examples featured in one pre-visit question were more commonly reported in responses to that question, compared to the question without examples. Questions completed electronically before the visit were associated with longer responses than those completed on paper in the waiting room. In conclusion, how and when patients’ goals and concerns are elicited appears to have an impact on responses and warrants further investigation.

Design of the Capacitive Dual-Mass Micromechanical Gyroscope

Development of micromechanical inertial sensors have made it possible to use them in the navigation and motion control systems. This application area imposes strict requirements on sensors. One of the ways to meet the requirements and to improve the gyroscope characteristics is to apply a dual- or multi-mass architecture of a gyroscope sensing element. This paper presents the results of dual-mass micromechanical gyroscope with a measurement range of ±450°/s design. The complex design method, including simulation at the system level, model refinement based on the results of finite element modelling, and modelling of individual electronic blocks at the circuit level, is described.