A Robust Discontinuous Phase Unwrapping Based on Least-Squares Orientation Estimator

Weighted least-squares (WLS) phase unwrapping is widely used in optical engineering. However, this technique still has issues in coping with discontinuity as well as noise. In this paper, a new WLS phase unwrapping algorithm based on the least-squares orientation estimator (LSOE) is proposed to improve phase unwrapping robustness. Specifically, the proposed LSOE employs a quadratic error norm to constrain the distance between gradients and orientation vectors. The estimated orientation is then used to indicate the wrapped phase quality, which is in terms of a weight mask. The weight mask is calculated by post-processing, including a bilateral filter, STDS, and numerical relabeling. Simulation results show that the proposed method can work in a scenario in which the noise variance is 1.5. Comparisons with the four WLS phase unwrapping methods indicate that the proposed method provides the best accuracy in terms of segmentation mean error under the noisy patterns.

A Topology-Preserving Simplification Method for 3D Building Models

Simplification of 3D building models is an important way to improve rendering efficiency. When existing algorithms are directly applied to simplify multi-component models, generally composed of independent components with strong topological dependence, each component is simplified independently. The consequent destruction of topological dependence can cause unreasonable separation of components and even result in inconsistent conclusions of spatial analysis among different levels of details (LODs). To solve these problems, a novel simplification method, which considers the topological dependence among components as constraints, is proposed. The vertices of building models are divided into boundary vertices, hole vertices, and other ordinary vertices. For the boundary vertex, the angle between the edge and component (E–C angle), denoting the degree of component separation, is introduced to derive an error metric to limit the collapse of the edge located at adjacent areas of neighboring components. An improvement to the quadratic error metric (QEM) algorithm was developed for the hole vertex to address the unexpected error caused by the QEM’s defect. A series of experiments confirmed that the proposed method could effectively maintain the overall appearance features of building models. Compared with the traditional method, the consistency of visibility analysis among different LODs is much better.

Use of water indices in the determination of thermokarst lakes according to remote sensing data

The results of application of six spectral indices (AWEI, MNDWI, NDVI, NDWI, TCW, WRI) for the isolation of thermokarst lakes in tundra landscapes of northern Yakutia are presented. To assess the accuracy of decryption of lakes, an average quadratic error (MSE) was calculated. The minimum MSE value is 0.11 km2 and corresponds to the NDWI index. An almost identical result (0.12 km2) is found in the WRI index, slightly worse (0.15 km2) one — in the NDVI index. An MNDWI index has the highest mean square error (7.02 km2). Visual analysis also showed better decryption of water bodies using the NDWI, WRI and NDVI indices, which allows the use of these indices for automatical isolatation water bodies.

Assessment of the Seismic Response of CLT Shear Walls Using the EEGBW, a Bouc–Wen Class Predictive Model

The paper presents an application of the Extended Energy-dependent Generalized Bouc–Wen model (EEGBW) to simulate the experimental cyclic response of Cross-Laminated Timber (CLT) panels. The main objectives of the paper are assessing the sensitivity of the quadratic error between experimental and numerical data to the EEGBW parameters, showing the fitting performance of the EEGBW model in matching the experimental cyclic response of CLT panels, highlighting the stability of the model in nonlinear dynamic analysis with seismic excitation. The research proves that the considered Bouc–Wen class hysteresis model can reproduce the hysteretic response of structural arrangements characterized by pinching and degradation phenomena. The model exhibits significant stability in nonlinear dynamic analysis with seismic excitation. The model’s stability and versatility endorse its application to simulate structural systems’ dynamic response when Finite Element modelling might be an impractical choice.

Quadratic Model-Based Dynamically Updated PID Control of CSTR System with Varying Parameters

In this paper, we discuss an improved version of the conventional PID (Proportional–Integral–Derivative) controller, the Dynamically Updated PID (DUPID) controller. The DUPID is a control solution which preserves the advantages of the PID controller and tends to improve them by introducing a quadratic error model in the PID control structure. The quadratic error model is constructed over a window of past error points. The objective is to use the model to give the conventional PID controller the awareness needed to battle the effects caused by the variation of the parameters. The quality of the predictions that the model is able to deliver depends on the appropriate selection of data used for its construction. In this regard, the paper discusses two algorithms, named 1D (one dimensional) and 2D (two dimensional) DUPID. Appropriate to their names, the former selects data based on one coordinate, whereas the latter selects the data based on two coordinates. Both these versions of the DUPID controller are compared to the conventional PID controller with respect to their capabilities of controlling a Continuous Stirred Tank Reactor (CSTR) system with varying parameters in three different scenarios. As a quantifying measure of the control performance, the integral of absolute error (IAE) metric is used. The results from the performed simulations indicated that the two versions of the DUPID controller improved the control performance of the conventional PID controller in all scenarios.

Magic state distillation with the ternary Golay code

The ternary Golay code—one of the first and most beautiful classical error-correcting codes discovered—naturally gives rise to an 11-qutrit quantum error correcting code. We apply this code to magic state distillation, a leading approach to fault-tolerant quantum computing. We find that the 11-qutrit Golay code can distil the ‘most magic’ qutrit state—an eigenstate of the qutrit Fourier transform known as the strange state —with cubic error suppression and a remarkably high threshold. It also distils the ‘second-most magic’ qutrit state, the Norell state, with quadratic error suppression and an equally high threshold to depolarizing noise.

Evolution Model for Epidemic Diseases Based on the Kaplan-Meier Curve Determination

We show a simple model of the dynamics of a viral process based, on the determination of the Kaplan-Meier curve P of the virus. Together with the function of the newly infected individuals I, this model allows us to predict the evolution of the resulting epidemic process in terms of the number E of the death patients plus individuals who have overcome the disease. Our model has as a starting point the representation of E as the convolution of I and P. It allows introducing information about latent patients—patients who have already been cured but are still potentially infectious, and re-infected individuals. We also provide three methods for the estimation of P using real data, all of them based on the minimization of the quadratic error: the exact solution using the associated Lagrangian function and Karush-Kuhn-Tucker conditions, a Monte Carlo computational scheme acting on the total set of local minima, and a genetic algorithm for the approximation of the global minima. Although the calculation of the exact solutions of all the linear systems provided by the use of the Lagrangian naturally gives the best optimization result, the huge number of such systems that appear when the time variable increases makes it necessary to use numerical methods. We have chosen the genetic algorithms. Indeed, we show that the results obtained in this way provide good solutions for the model.