The Hierarchical Subspace Iteration Method for Laplace–Beltrami Eigenproblems

Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace–Beltrami operator, for example, are fundamental for methods in shape analysis and mesh processing. The Subspace Iteration Method is a robust solver for these problems. In practice, however, Lanczos schemes are often faster. In this article, we introduce the Hierarchical Subspace Iteration Method (HSIM) , a novel solver for sparse eigenproblems that operates on a hierarchy of nested vector spaces. The hierarchy is constructed such that on the coarsest space all eigenpairs can be computed with a dense eigensolver. HSIM uses these eigenpairs as initialization and iterates from coarse to fine over the hierarchy. On each level, subspace iterations, initialized with the solution from the previous level, are used to approximate the eigenpairs. This approach substantially reduces the number of iterations needed on the finest grid compared to the non-hierarchical Subspace Iteration Method. Our experiments show that HSIM can solve Laplace–Beltrami eigenproblems on meshes faster than state-of-the-art methods based on Lanczos iterations, preconditioned conjugate gradients, and subspace iterations.

Intelligent Algorithm-Based Multislice Spiral Computed Tomography to Diagnose Coronary Heart Disease

In this study, dictionary learning and expectation maximization reconstruction (DLEM) was combined to denoise 64-slice spiral CT images, and results of coronary angiography (CAG) were used as standard to evaluate its clinical value in diagnosing coronary artery diseases. 120 patients with coronary heart disease (CHD) confirmed by CAG examination were retrospectively selected as the research subjects. According to the random number table method, the patients were divided into two groups: the control group was diagnosed by conventional 64-slice spiral CT images, and the observation group was diagnosed by 64-slice spiral CT images based on the DLEM algorithm, with 60 cases in both groups. With CAG examination results as the standard, the diagnostic effects of the two CT examination methods were compared. The results showed that when the number of iterations of maximum likelihood expectation maximization (MLEM) algorithm reached 50, the root mean square error (RMSE) and peak signal to noise ratio (PSNR) values were similar to the results obtained by the DLEM algorithm under a number of iterations of 10 when the RMSE and PSNR values were 18.9121 dB and 74.9911 dB, respectively. In the observation group, 28.33% (17/60) images were of grade 4 or above before processing; after processing, it was 70% (42/60), significantly higher than the proportion of high image quality before processing. The overall diagnostic consistency, sensitivity, specificity, and accuracy (88.33%, 86.67%, 80%, and 85%) of the observation group were better than those in the control group (60.46%, 62.5%, 58.33%, and 61.66%). In conclusion, the DLEM algorithm has good denoising effect on 64-slice spiral CT images, which significantly improves the accuracy in the diagnosis of coronary artery stenosis and has good clinical diagnostic value and is worth promoting.

Research on Teaching Practice of Blended Higher Education Based on Deep Learning Route

This paper establishes a hybrid education teaching practice quality evaluation system in colleges and constructs a hybrid teaching quality evaluation model based on a deep belief network. Karl Pearson correlation coefficient and root mean square error (RMSE) indicators are used to measure the closeness and fluctuation between the effective online teaching quality evaluation results evaluated by this method and the actual teaching quality results. The experimental results show the following: (1) As the number of iterations increases, the fitting error of the DBN model decreases significantly. When the number of iterations reaches 20, the fitting error of the DBN model stabilizes and decreases to below 0.01. The experimental results show that the model used in this method has good learning and training performance, and the fitting error is low. (2) The evaluation correlation coefficients are all greater than 0.85, and the root mean square error of the evaluation is less than 0.45, indicating that the evaluation results of this method are similar to the actual evaluation level and have small errors, which can be effectively applied to online teaching quality evaluation in colleges and universities.

Weakly measured while loops: peeking at quantum states

A while loop tests a termination condition on every iteration. On a quantum computer, such measurements perturb the evolution of the algorithm. We define a while loop primitive using weak measurements, offering a trade-off between the perturbation caused and the amount of information gained per iteration. This trade-off is adjusted with a parameter set by the programmer. We provide sufficient conditions that let us determine, with arbitrarily high probability, a worst-case estimate of the number of iterations the loop will run for. As an example, we solve Grover's search problem using a while loop and prove the quadratic quantum speed-up is maintained.

Evalutation of Turbo Decoder Performance Through Software Reference Model

Turbo encoder and decoder are two important blocks of long-term evolution (LTE) systems, as they address the data encoding and decoding in a communication system. In recent years, the wireless communication has advanced to suit the user needs. The power optimization can be achieved by proposing early termination of decoding iteration where the number of iterations is made adjustable which stops the decoding as it finishes the process. Clock gating technique is used at the RTL level to avoid the unnecessary clock given to sequential circuits; here clock supplies are a major source of power dissipation. The performance of a system is affected due to the numbers of parameters, including channel noise, type of decoding and encoding techniques, type of interleaver, number of iterations, and frame length on the Matlab Simulink platform. A software reference model for turbo encoder and decoder are modeled using MATLAB Simulink. Performance of the proposed model is estimated and analyzed on various parameters like frame length, number of iterations, and channel noise.

Emphasizing the Digital Shift of Hospitality Towards Hyper-Personalization

This chapter aims to review the tech evolution in hospitality, from services to eServices, that will provide hyper-personalization in the hospitality field. In the past, the services were provided by hotels through diligent staff and supported by standardized and weak technology that was not allowed to provide personalized services by itself. Therefore, the study applied K-means and FCM clustering algorithms to cluster online travelers' reviews from TripAdvisor. The study shows that K-means clustering outperforms fuzzy c-means in this study in terms of accuracy and execution time while fuzzy c-means converge faster than K-means clustering in terms of the number of iterations. K-means achieved 93.4% accuracy, and fuzzy c-means recorded 91.3% accuracy.

A Comparison of the Effectiveness of the RRT, PRM, and Novel Hybrid RRT-PRM Path Planners

Sampling-based path planners develop paths for robots to journey to their destinations. The two main types of sampling-based techniques are the probabilistic roadmap (PRM) and the Rapidly Exploring Random Tree (RRT). PRMs are multi-query methods that construct roadmaps to find routes, while RRTs are single-query techniques that grow search trees to find paths. This investigation evaluated the effectiveness of the PRM, the RRT, and the novel Hybrid RRT-PRM methods. This novel path planner was developed to improve the performance of the RRT and PRM techniques. It is a fusion of the RRT and PRM methods, and its goal is to reduce the path length. Experiments were conducted to evaluate the effectiveness of these path planners. The performance metrics included the path length, runtime, number of nodes in the path, number of nodes in the search tree or roadmap, and the number of iterations required to obtain the path. Results showed that the Hybrid RRT-PRM method was more effective than the PRM and RRT techniques because of the shorter path length. This new technique searched for a path in the convex hull region, which is a subset of the search area near to the start and end locations. The roadmap for the Hybrid RRT-PRM could also be re-used to find pathways for other sets of initial and final positions. Keywords: Path Planning, Sampling-based algorithms, search tree, roadmap, single-query planners, multi-query planners, Rapidly Exploring Random Tree (RRT), Probabilistic Roadmap (PRM), Hybrid RRT-PRM

Novel Metaheuristic Based on Iterated Constructive Stochastic Heuristic: Dhouib-Matrix-3 (DM3)

This paper presents a new metaheuristic named Dhouib-Matrix-3 (DM3) inspired by our recently developed constructive stochastic heuristic Dhouib-Matrix-TSP2 (DM-TSP2) and characterized by only one parameter: the number of iterations. The proposed metaheuristic DM3 is an iterative algorithm in which every iteration is based on two relay hybridization techniques. At first, the constructive stochastic heuristic DM-TSP2 starts by generating a different initial basic feasible solution and then each solution is intensified by the novel procedure Far-to-Near which exchanges far cities by closer ones using three perturbation techniques: insertion, exchange, and 2-opt. Experimental results carried out on the classical travelling salesman problem using the well-known TSP-LIB benchmark instances demonstrate that our approach DM3 outclasses the simulated annealing algorithm, the genetic algorithm, and the cellular genetic algorithm. Furthermore, the proposed DM3 is statistically concurrent to the hybrid simulated annealing cellular genetic algorithm. Nevertheless, DM3 is easier to implement and needs only one parameter to identify (the maximum number of iterations).

Inverse Approach of Parameter Optimization for Nonlinear Meta-Model Using Finite Element Simulation

Accurate and efficient estimation and prediction of the nonlinear behavior of materials during plastic working is a major issue in academic and industrial settings. Studies on property meta-models are being conducted to estimate and predict plastic working results. However, accurately representing strong nonlinear properties using power-law and exponential models, which are typical meta-models, is difficult. The combination meta-model can be used to solve this problem, but the possible number of parameters increases. This causes a cost problem when using FE simulation. In this study, the accuracy of the nonlinear properties of materials and the number of iterations were compared for three typical meta-models and the proposed advanced meta-models considering stress–strain properties. A material property test was conducted using ASTM E8/E8M, and the meta-model was initialized using ASTM E646 and MATLAB Curve Fitting Toolbox. A finite element (FE) simulation was conducted for the meta-models, and the test and simulation results were compared in terms of the engineering stress–strain curve and the root-mean-square error (RMSE). In addition, an inverse method was applied for the FE simulation to estimate the true stress–strain properties, and the results were analyzed in terms of the RMSE and the number of iterations and simulations. Finally, the need for an advanced meta-model that exhibits strong nonlinearity was suggested.

Development of an enhanced scatter search algorithm using discrete chaotic Arnold’s cat map

Solving optimization problems is an ever-growing subject with an enormous number of algorithms. Examples of such algorithms are Scatter Search (SS) and genetic algorithms. Modifying and improving of algorithms can be done by adding diversity and guidance to them. Chaotic maps are quite sensitive to the initial point, which means even a very slight change in the value of the initial point would result in a dramatic change of the sequence produced by the chaotic map Arnold's Cat Map. Arnold's Cat Map is a chaotic map technique that provides long non-repetitive random-like sequences. Chaotic maps play an important role in improving evolutionary optimization algorithms and meta-heuristics by avoiding local optima and speeding up the convergence. This paper proposes an implementation of the scatter search algorithm with travelling salesman as a case study, then implements and compares the developed hyper Scatter Arnold's Cat Map Search (SACMS) method against the traditional Scatter Search Algorithm. SACMS is a hyper Scatter Search Algorithm with Arnold's Cat Map Chaotic Algorithm. Scatter Arnold's Cat Map Search shows promising results by decreasing the number of iterations required by the Scatter Search Algorithm to get an optimal solution(s). Travelling Salesman Problem, which is a popular and well-known optimization example, is implemented in this paper to demonstrate the results of the modified algorithm Scatter Arnold's Cat Map Search (SACMS). Implementation of both algorithms is done with the same parameters: population size, number of cities, maximum number of iterations, reference set size, etc. The results show improvement by the modified algorithm in terms of the number of iterations required by SS with an iteration reduction of 10–46 % and improvements in time to obtain solutions with 65 % time reduction