Series Expansion Algorithm Research Articles

Analysis of pseudo-random number generators in QMC-SSE method

In the quantum Monte Carlo (QMC) method, the pseudo-random number generator (PRNG) plays a crucial role in determining the computation time. However, the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process. Here, we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion (SSE) algorithm. To quantitatively compare them, we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms. After testing several representative observables of the Heisenberg model in one and two dimensions, we recommend the linear congruential generator as the best choice of PRNG. Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.

Optimization design of all-angle negative refraction phononic crystals at a specified frequency

All-angle negative refraction (AANR) is an effective way to achieve negative refraction in phononic crystals (PnCs). It is difficult to achieve AANR using a traditional heuristic design. In this work, we propose a novel topology optimization framework for optimizing the material distribution of air/solid PnCs to achieve AANR at a specified frequency. The optimization goal is to minimize the curvature at a specific point of the equal-frequency contours (EFCs), and the Kriging-based material-field series expansion (KG-MFSE) algorithm is adopted to solve the complicated optimization problem. To ensure the connectivity of the air domain inside the unit cell, the virtual temperature technique is employed, and the filtering and threshold projection are used to control the minimum length scale of the air domain. Numerical examples show that the proposed optimization framework is effective for the material design of AANR PnCs, and several optimized design samples were fabricated with additive manufacturing. The corresponding negative refraction is verified through numerical simulation and experiment.

Probabilistic Network Topology Prediction for Active Planning: An Adaptive Algorithm and Application

This article tackles the problem of active planning to achieve cooperative localization for multirobot systems under measurement uncertainty in GNSS-limited scenarios. Specifically, we address the issue of accurately predicting the probability of a future connection between two robots equipped with range-based measurement devices. Due to the limited range of the equipped sensors, edges in the network connection topology will be created or destroyed as the robots move with respect to one another. Accurately predicting the future existence of an edge, given imperfect state estimation and noisy actuation, is therefore a challenging task. An adaptive power series expansion (or APSE) algorithm is developed based on current estimates and control candidates. Such an algorithm applies the power series expansion formula of the quadratic positive form in a normal distribution. Finite-term approximation is made to realize the computational tractability. Further analyses are presented to show that the truncation error in the finite-term approximation can be theoretically reduced to a desired threshold by adaptively choosing the summation degree of the power series. Several sufficient conditions are rigorously derived as the selection principles. Finally, extensive simulation results and comparisons, with respect to both single and multirobot cases, validate that a formally computed and therefore more accurate probability of future topology can help improve the performance of active planning under uncertainty.

Bond-disordered Heisenberg antiferromagnets on a square lattice

The ground-state magnetic properties of bond-disordered spin-1/2 Heisenberg Antiferromagnets on a square lattice are investigated using the Stochastic Series Expansion algorithm. We modify the distribution of the previous work and introduce the normalized standard deviation of the exchange coupling to characterize the magnitude of the disorder. By examining the magnetic properties in various distributions with the normalized standard deviation description, we find that the antiferromagnetism follows the same trend in weak disorder and vanishes at a finite value. And we also analyze the data in perspective of the logarithm of exchange coupling's standard deviation.

Sign-problem free quantum stochastic series expansion algorithm on a quantum computer

A quantum implementation of the Stochastic Series Expansion (SSE) Monte Carlo method is proposed, and is shown to offer significant advantages over classical implementations of SSE. In particular, for problems where classical SSE encounters the sign problem, the cost of implementing a Monte Carlo iteration scales only linearly with system size in quantum SSE, while it may scale exponentially with system size in classical SSE. In cases where classical SSE can be efficiently implemented, quantum SSE still offers an advantage by allowing for more general observables to be measured.

Evidence-Theory-Based Kinematic Uncertainty Analysis of a Dual Crane System With Epistemic Uncertainty

Abstract An evidence-theory-based interval perturbation method (ETIPM) and an evidence-theory-based subinterval perturbation method (ETSPM) are presented for the kinematic uncertainty analysis of a dual cranes system (DCS) with epistemic uncertainty. A multiple evidence variable (MEV) model that consists of evidence variables with focal elements (FEs) and basic probability assignments (BPAs) is constructed. Based on the evidence theory, an evidence-based kinematic equilibrium equation with the MEV model is equivalently transformed to several interval equations. In the ETIPM, the bounds of the luffing angular vector (LAV) with respect to every joint FE are calculated by integrating the first-order Taylor series expansion and interval algorithm. The bounds of the expectation and variance of the LAV and corresponding BPAs are calculated by using the evidence-based uncertainty quantification (UQ) method. In the ETSPM, the subinterval perturbation method (SIPM) is introduced to decompose original FE into several small subintervals. By comparing results yielded by the ETIPM and ETSPM with those by the evidence theory-based Monte Carlo method (ETMCM), numerical examples show that the accuracy and computational time of the ETSPM are higher than those of the ETIPM, and the accuracy of the ETIPM and ETSPM can be significantly improved with the increase of the number of FEs and subintervals.

High level synthesis strategies for ultra fast and low latency matrix inversion implementation for massive MIMO processing

In this paper, we discuss the implementation strategies of an explicit matrix inversion technique based on the recursive Gram matrix inversion update (RGMIU) algorithm. These strategies are explicitly chosen to optimize the design for high throughput dictated by the enhanced mobile broad band (eMBB) use case and by the low latency imposed by the ultra-reliable low-latency communications (URLLCs) use case. The RGMIU algorithm is recently proposed to implement the zero forcing (ZF) problem encountered in massive multiple-input multiple-output (MIMO) detection task. We therefore compare and analyse the performance in terms of symbol error rate (SER) against popular implicit and explicit methods such as optimized coordinate descent (OCD), Gauss-Seidel (GS) and Neumann series expansion (NSE) algorithms. To determine the optimal word length, a fixed-point analysis shows that 16 bits are enough to reach a floating-point precision. We, thereafter, use Vivado High-Level Synthesis tools and optimization directives to implement the RGMIU algorithm based on three strategies to infer key insights and design trade-offs from the resource's utilization, latency, throughput and energy efficiency.

Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations

The quantum-critical properties of the transverse-field Ising model with algebraically decaying interactions are investigated by means of stochastic series expansion quantum Monte Carlo, on both the one-dimensional linear chain and the two-dimensional square lattice. We extract the critical exponents $\nu$ and $\beta$ as a function of the decay exponent of the long-range interactions. For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range Gaussian universality classes, as well as the intermediate regime with continuously varying critical exponents. In the long-range Gaussian regime, we treat the effect of dangerous irrelevant variables on finite-size scaling forms. For antiferromagnetic and therefore competing Ising interactions, the stochastic series expansion algorithm displays growing auto-correlation times leading to a reduced performance. Nevertheless, our results are consistent with the nearest-neighbor Ising universality for all investigated interaction ranges both on the linear chain and the square lattice.

Fractional residual series for conformable time‐fractional Sawada–Kotera–Ito, Lax, and Kaup–Kupershmidt equations of seventh order

The purpose of the present work is to analyze and investigate the analytical solution of the seventh‐order fractional Sawada–Kotera–Ito, Lax, and Kaup–Kupershmidt equations under the conformable derivatives. Using the residual series expansion algorithm, the posed fractional models are studied analytically and numerically. Simultaneously, convergence analysis and error estimation are performed for the proposed technique. For this purpose, an advanced numerical algorithm is designed to handle the complexity of nonlinear fractional terms. Some experiments are provided to support theoretical analysis in a one‐dimensional finite compact regime in light of the conformable sense. Eventually, numerical comparison is performed with other existing techniques along with some two‐ and three‐dimensional representative graphs. Physical interpretation of the solution behaviors is discussed as well for various α values in an adequate time duration. Comparative results indicate the superiority and great flexibility of the presented method for fractional evolution systems arising in nonlinear wave propagation phenomena.

REFINED TAYLOR SERIES EXPANSION-BASED PREDICTION OF THE OVERALL SURVIVAL FOR NONSMALL CELL LUNG CANCER PATIENTS OF CLINICAL STAGE IIIA-N2 AFTER VARIOUS TREATMENTS: TAIWAN POPULATION-BASED STUDY OF 2655 CASES FROM 2010 TO 2017

The overall survival (OS) prediction for nonsmall cell lung carcinoma (NSCLC) patients of clinical IIIA-N2 stage undergone various treatments was investigated through a refined Taylor series expansion algorithm. The model was created according to a population-based study in Taiwan. The proposed prediction algorithm is based on the well-known hit and target model adopted for analyzing the cell death from the microscopic viewpoint. It also implies the application of the Taylor series expansion to the population-based survey dataset. In the proposed algorithm, the basic degradation of a patient’s health is represented via a specific function comprising a single exponential term exp([Formula: see text]). The refined algorithm successfully predicted NSCLC IIIA-N2 patients’ OS rate. A total of 127,301 patients were collected from 2010 to 2017. Then, 2655 patients were recognized as effective events and classified into eight classes according to various medical treatments, namely surgical operation, radiotherapy, and chemotherapy. For each class of patients, the average life was evaluated, according to Taylor’s expansion algorithm, and the average derived life range spread from 3.51 to 7.81 years. An index of life gain with specific treatment was defined according to the Taguchi optimization analysis. The life gains provided by the surgical operation, chemotherapy, and radiotherapy were 2.74, 1.18, and 0.48 years. The surgical operation was the most beneficial treatment, which is in concert with recommendations of European experts. A similar finding was also reflected in four out of eight classes, which included the surgical operation in the treatment plans of most Taiwanese hospitals.

Permutation matrix representation quantum Monte Carlo

We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of the quantum partition function in its off-diagonal terms and is both parameter-free and Trotter error-free. In our approach, the quantum dimension consists of products of elements of a permutation group. As such, it allows for the study of a very wide variety of models on an equal footing. To demonstrate the utility of our technique, we use it to clarify the emergence of the sign problem in the simulations of non-stoquastic physical models. We showcase the flexibility of our algorithm and the advantages it offers over existing state-of-the-art by simulating transverse-field Ising model Hamiltonians and comparing the performance of our technique against that of the stochastic series expansion algorithm. We also study a transverse-field Ising model augmented with randomly chosen two-body transverse-field interactions.

An Implementation of Interactive Application for the Synthesis of Communication Systems with Antenna Arrays

Introduction. Modern radar and communications systems contain phased array antennas. One of the synthesis problems of such systems is the formulation of requirements for components, modules and units which are comprised in it. To solve this problem, one needs to build a coverage area and to analyze an impact of characteristics of its parts. The quality of analysis and synthesis of such complex systems can be enhanced by use of interactive data visualization, which requires a fairly quick calculation of characteristics.Aim. Development of an interactive application for increasing the synthesis capabilities of communication systems containing antenna arrays and for improving the characteristics of systems of interest.Materials and methods. To accelerate the calculation of radiation patterns, the antenna array pattern in a form suitable for the fast Fourier transform algorithm was used. To find the required amplitude-phase distributions, Kotelnikov series expansion and genetic algorithm were used.Results. In the developed application, amplitude-phase distribution, directivity pattern of a linear equidistant array and coverage area were displayed. An interactive change of the amplitude-phase distribution at radiation elements and synthesized radiation patterns in given directions were possible. With introduction of changes to the radiation pattern, the amplitude-phase distribution and the array radiation pattern itself changed in directions other than the specified one. The coverage area was rebuilt when any of the characteristics changes. If necessary, the coverage area display could be turned off. The paper provides an example of using the application in the synthesis of a communication system with an aircraft.Conclusion. The use of the developed application allows one to extend the capabilities and significantly reduce the analysis and synthesis time of the communication secondary radar systems with antenna arrays too. Besides, the application is used for training specialists for industry enterprises.

Topology optimization using material-field series expansion and Kriging-based algorithm: An effective non-gradient method

Topology optimization is now a very effective and important tool for designing the layouts of various structural and multidisciplinary problems, but most existing methods require information about the sensitivity of the performance function with respect to an enormous number of design variables. This paper presents an efficient non-gradient approach to the topology optimization of structures when no information is available about design sensitivity. Based on the material-field series expansion (MFSE), the problem of topology optimization is constructed as a constrained minimization model with the series expansion coefficients as the design variables, thereby involving a considerable reduction of design variables. The Kriging-based optimization algorithm incorporating two infill criteria is used to solve the optimization problem. A special strategy of (i) using a self-adjusting design domain and (ii) remodeling the surrogate function is proposed to improve the searching efficiency of the Kriging-based algorithm. Several examples are given in the form of linear, nonlinear, and fluid topology optimization problems to demonstrate the effectiveness and applicability of the proposed Kriging-based MFSE method.

Novel indoor positioning system based on ultra-wide bandwidth

To tackle challenges such as interference and poor accuracy of indoor positioning systems, a novel scheme based on ultra-wide bandwidth (UWB) technology is proposed. First, we illustrate a distance measuring method between two UWB devices. Then, a Taylor series expansion algorithm is developed to detect coordinates of the mobile node using the location of anchor nodes and the distance between them. Simulation results show that the observation error under our strategy is within 15 cm, which is superior to existing algorithms. The final experimental data in the hardware system mainly composed of STM32 and DW1000 also confirms the performance of the proposed scheme.

Study on the improvement of ultra-wideband localization accuracy in narrow and long space

PurposeWireless network localization technology is very popular in recent years and has attracted worldwide attention. The purpose of this paper is to improve the localization accuracy of ultra-wideband (UWB) with lower localization error taking into consideration the special real environment with the closed long and narrow space.Design/methodology/approachThe principle of multidimensional scaling (MDS), particle swarm optimization (PSO) and Taylor series expansion algorithm (Taylor-D) were introduced. A novel positioning algorithm, MDS-PSO-Taylor was proposed to minimize the localization error. MDS-PSO algorithm provided a more accurate preliminary coordinate by applying the PSO algorithm so that the Taylor-D was used for further enhancing the localization accuracy.FindingsExperimental results manifested that the proposed algorithm, providing small localization error value and higher positioning accuracy, can effectively reduce errors and achieve better performance in terms of the considerable improvement of localization accuracy.Originality/valueThe presented study with the real environment test attempts to demonstrate the proposed algorithm is hopeful to be applied to the underground environment for in the future.

Overall Survival Prediction for Colon Cancer Patients of 0–IV Stages With and Without Surgical Operation Through a Revised Taylor Series Expansion Algorithm: A Population-Based Study in Taiwan

This study was aimed to predict the overall survival of colon cancer patients at various (0–IV) stages and provided a robust assessment of the expediency of a surgical operation for such patients. The proposed prediction algorithm was based on the well-known hit and target model adopted for analyzing the cell death from the microscopic viewpoint and implied the application of the Taylor series expansion to the population-based survey dataset (in particular, to the population-based study of colon cancer patients in Taiwan covering the period from 2007 to 2016). In the proposed algorithm, the fundamental degradation of patient's health was represented by a specific function comprising a single exponential term exp(–αt), which was multiplied by an additional term P(αt) that specified the recovery effect of a particular therapy. The revised algorithm successfully predicted the colon cancer patients' overall survival at stages 0–IV and evaluated the expediency necessity of surgical operation for patients at various stages as well. For the above population-based survey dataset, the calculated lethal frequency and average residual life of colon cancer patients who undergone surgical operation amounted to {0.029, 0.036, 0.058, 0.077, 0.236} yr–1 and {34.5, 27.8, 17.2, 13.0, 4.2} yr for stages 0–IV, respectively, while those for the respective groups of patients with no surgical operation was assessed as {0.116, 0.181, 0.256, 0.203, 0.504} yr–1 and {8.6, 5.5, 3.9, 4.9, 2.0} yr, respectively. The proposed algorithm was also applied to interpret the overall survival of lung cancer patients at stages III and IV and exhibited a partial agreement with the actual collected data.

Survival rate prediction of breast cancer patients of 0-IV stages with and without radiotherapy via a revised Taylor series expansion algorithm: A population-based study in Taiwan

BACKGROUND: The morbidity of breast cancer has continuously achieved a global topicality. In particular, during the last decade several ten thousand female adults in Taiwan have been confirmed as breast cancer patients.OBJECTIVE: To predict the survival rate of breast cancer patients at various (0-IV) stages and provide efficient assessment of proposed radiotherapy for patients.METHODS: The prediction algorithm proposed is based on the revised hit and target model and implies the application of Taylor series expansion to the population-based survey dataset. The proposed algorithm features a specific function comprising a single simple exponential term to imply the fundamental degradation of patient’s health multiplied by an additional term , which specifies the recovery effect of a particular therapy.RESULTS: Its calculated values for breast cancer patients who undergone radiotherapy at different stages 0-IV were {0.0029, 0.0066, 0.0178, 0.0475, 0.1785} yr, respectively, while those for corresponding groups of patients with no radiotherapy were assessed as {0.0072, 0.0137, 0.0264, 0.0913, 0.2425} yr.CONCLUSIONS: The revised algorithm successfully interpreted the breast cancer patients’ survival rate at stages 0-IV and evaluated the necessity of radiotherapy for patients at various stages as well.

Estimation of ionospheric delay of NavIC/IRNSS signals using the Taylor Series Expansion

The delay in Navigation with Indian Constellation (NavIC)/Indian Regional Navigation Satellite System (IRNSS) signals due to the ionosphere are decisive because it leads to significant changes in the positional accuracy of the system. In this paper, we try to estimate the ionospheric time delay (ionodelay) precisely using the local Taylor Series Expansion (TSE) algorithm for a single frequency NavIC/IRNSS system. The performance of the local TSE algorithm is examined by considering two cases. In case I, the TSE was validated under the influence of an intense geomagnetic storm (8 September 2017) by considering NavIC/IRNSS data from the Indian equatorial and Equatorial Ionization Anomaly (EIA) regions. In case II, based on the quiet and disturbed days data, the local TSE model was examined at different locations in the local area (<10 km) using two NavIC/IRNSS receivers (i.e. reference and rover). The results of ionodelay and positional accuracy (Three Dimensional Distance Root Mean Square [3DRMS], Circular Error Probability [CEP], and Spherical Error Probability [SEP]) of NavIC/IRNSS for both the cases indicates that the single frequency local TSE algorithm performs the same as the reference dual frequency model, where as the global eight coefficient Klobuchar and the regional Grid Ionospheric Vertical Error (GIVE) model behaves differently. Therefore, the single-frequency TSE model improves the performance of the NavIC/IRNSS receiver in the local area, and the mathematical coefficient computation and additional frequency hardware cost have been reduced, with the acceptance of a maximum 0.8 m of errors.

Ultra-wideband pose detection method based on TDOA positioning model for boom-type roadheader

In deep and dangerous coal seam tunnelling, the autonomous navigation control system (ANCS) of the boom-type roadheader is the core that realises unattended work. The remote pose detection of the boom-type roadheader is the key task of the ANCS. In this study, an ultra-wide band (UWB) pose detection system (UPDS) for boom-type roadheaders is designed which realises the remote measurement of position and attitude parameters (heading, roll, and pitch angles) of the boom-type roadheader in a narrow and long enclosed roadway space. Based on the time difference-of-arrival (TDOA) positioning model, three UPDS positioning algorithms are proposed: Indirect positioning algorithm (IPA-D), Taylor series expansion algorithm (Taylor-D), and Chan positioning algorithm (Chan-D). A complete calculation process is deduced from the three UDPS positioning algorithms. Their accuracies are analysed based on the measured data of a P440 UWB ranging module in a narrow and long roadway. The positioning accuracy of IPA-D behaves better than those of Taylor-D and Chan-D: Within 95 m of the roadway, IPA-D can achieve values at a centimetre scale and the positioning error increases with increasing measurement distance. The calculated UPDS attitude angle error based on IPA-D increases with increasing measurement distance of up to 95 m; The roll angle error is approximately 0.05°, and the pitch and heading angles are approximately 0.15°. The presented UPDS meets the accuracy requirements for the pose detection of boom-type roadheaders in a fully mechanised excavation face and provides a reliable theoretical basis for ANCSs of boom-type roadheaders.

Two-step melting of three-sublattice order in S = 1 easy-axis triangular lattice antiferromagnets

We consider $S=1$ triangular lattice Heisenberg antiferromagnets with a strong single-ion anisotropy $D$ that dominates over the nearest-neighbour antiferromagnetic exchange $J$. In this limit of small $J/D$, we study low temperature ($T \sim J \ll D$) properties of such magnets by employing a low-energy description in terms of hard-core bosons with nearest neighbour repulsion $V \approx 4J + J^2/D$ and nearest neighbour unfrustrated hopping $t \approx J^2/2D$. Using a cluster Stochastic Series Expansion (SSE) algorithm to perform sign-problem-free quantum Monte Carlo (QMC) simulations of this effective model, we establish that the ground-state three-sublattice order of the easy-axis spin-density $S^z(\vec{r})$ melts in zero field ($B=0$) in a {\em two-step} manner via an intermediate temperature phase characterized by power-law three-sublattice order with a temperature dependent exponent $\eta(T) \in [\frac{1}{9}, \frac{1}{4}]$. For $\eta(T) < \frac{2}{9}$ in this phase, we find that the uniform easy-axis susceptibility of an $L \times L$ sample diverges as $\chi_L \sim L^{2-9 \eta}$ at $B=0$, consistent with a recent prediction that the thermodynamic susceptibility to a uniform field $B$ along the easy axis diverges at small $B$ as $\chi_{\rm easy-axis}(B) \sim B^{-\frac{4-18\eta}{4-9\eta}}$ in this regime.