Efficient Computational Scheme Research Articles

Adaptive region algorithm based on a ternary optical computer

The adaptive region algorithm is an improved compression algorithm based on Huffman coding. Because of the large number of rules for dividing regions in the algorithm, there are problems such as high computing costs, slow speed, and low compression efficiency. To address these problems, this paper investigates the adaptive region algorithm based on a ternary optical computer (TOC) combined with the characteristics of a ternary optical computer, such as many data bits, high parallelism, and three-valued coding. According to the characteristics of TOC three-valued coding, this paper designs a three-valued character coding scheme that can effectively shorten the coding length of characters by changing the original coding rules and further improve the compression efficiency of the adaptive region algorithm. Furthermore, in conjunction with the advantages of TOC enabling parallel computation, this paper presents an efficient computational scheme capable of effectively improving computational efficiency during the process of region partitioning. Through case studies, the compression efficiency and computational efficiency of the adaptive region algorithm implemented on TOC and an electronic computer were analyzed, respectively. It was found that the compression efficiency of the TOC-based algorithm is 50.4%, while that of the electronic-computer-based algorithm is only 36%. In the comparison of computational efficiency, the computational time complexity of TOC is O(n), whereas that of the electronic computer (EC) is O(n2). Finally, it is concluded through experimental validation that the TOC-based adaptive region compression algorithm performs well in terms of computational performance and compression efficiency, giving full play to the three-valued coding characteristics of TOC-based as well as the advantages of being able to realize parallel computation.

The Dynamics of the Hubbard Model Through Stochastic Calculus and Girsanov Transformation

As a typical quantum many body problem, we consider the time evolution of density matrix elements in the Bose-Hubbard model. For an arbitrary initial state, these quantities can be obtained from an SDE or stochastic differential equation system. To this SDE system, a Girsanov transformation can be applied. This has the effect that all the information from the initial state moves into the drift part, into the mean field part, of the transformed system. In the large N limit with g=UN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g=UN$$\\end{document} fixed, the diffusive part of the transformed system vanishes and as a result, the exact quantum dynamics is given by an ODE system which turns out to be the time dependent discrete Gross Pitaevskii equation. For the two site Bose-Hubbard model, the GP equation reduces to the mathematical pendulum and the difference of expected number of particles at the two lattice sites is equal to the velocity of that pendulum which is either oscillatory or it can have rollovers which then corresponds to the self trapping or insulating phase. As a by-product, we also find an equivalence of the mathematical pendulum with a quartic double well potential. Collapse and revivals are a more subtle phenomenom, in order to see these the diffusive part of the SDE system or quantum corrections have to be taken into account. This can be done with an approximation and collapse and revivals can be reproduced, numerically and also through an analytic calculation. Since expectation values of Fresnel or Wiener diffusion processes, we write the density matrix elements exactly in this way, can be obtained from parabolic second order PDEs, we also obtain various exact PDE representations. The paper has been written with the goal to come up with an efficient calculation scheme for quantum many body systems and as such the formalism is generic and applies to arbitrary dimension, arbitrary hopping matrices and, with suitable adjustments, to fermionic models.

An efficient computational scheme for solving coupled time-fractional Schrödinger equation via cubic B-spline functions.

The time fractional Schrödinger equation contributes to our understanding of complex quantum systems, anomalous diffusion processes, and the application of fractional calculus in physics and cubic B-spline is a versatile tool in numerical analysis and computer graphics. This paper introduces a numerical method for solving the time fractional Schrödinger equation using B-spline functions and the Atangana-Baleanu fractional derivative. The proposed method employs a finite difference scheme to discretize the fractional derivative in time, while a θ-weighted scheme is used to discretize the space directions. The efficiency of the method is demonstrated through numerical results, and error norms are examined at various values of the non-integer parameter, temporal directions, and spatial directions.

Efficient and Privacy-Preserving Cloud-Assisted Two-Party Computation Scheme in Heterogeneous Networks

Efficient and Privacy-Preserving Cloud-Assisted Two-Party Computation Scheme in Heterogeneous Networks

An efficient polynomial-based verifiable computation scheme on multi-source outsourced data

With the development of cloud computing, users are more inclined to outsource complex computing tasks to cloud servers with strong computing capacity, and the cloud returns the final calculation results. However, the cloud is not completely trustworthy, which may leak the data of user and even return incorrect calculations on purpose. Therefore, it is important to verify the results of computing tasks without revealing the privacy of the users. Among all the computing tasks, the polynomial calculation is widely used in information security, linear algebra, signal processing and other fields. Most existing polynomial-based verifiable computation schemes require that the input of the polynomial function must come from a single data source, which means that the data must be signed by a single user. However, the input of the polynomial may come from multiple users in the practical application. In order to solve this problem, the researchers have proposed some schemes for multi-source outsourced data, but these schemes have the common problem of low efficiency. To improve the efficiency, this paper proposes an efficient polynomial-based verifiable computation scheme on multi-source outsourced data. We optimize the polynomials using Horner’s method to increase the speed of verification, in which the addition gate and the multiplication gate can be interleaved to represent the polynomial function. In order to adapt to this structure, we design the corresponding homomorphic verification tag, so that the input of the polynomial can come from multiple data sources. We prove the correctness and rationality of the scheme, and carry out numerical analysis and evaluation research to verify the efficiency of the scheme. The experimental indicate that data contributors can sign 1000 new data in merely 2 s, while the verification of a delegated polynomial function with a power of 100 requires only 18 ms. These results confirm that the proposed scheme is better than the existing scheme.

A fast and efficient numerical algorithm for image segmentation and denoising

<abstract><p>Image segmentation is the process of partitioning an image into homogenous regions, and represents one of the most fundamental and important procedures in image processing. Image denoising is a process to remove unwanted noise from a digital image, enhancing its visual quality. Various algorithms, like non-local means and deep learning-based approaches, have been developed to remove noise while preserving important image details. Currently, the prevalent application of pattern recognition technology is achieved through the implementation of image segmentation algorithms. In this study, we present a new, highly efficient, and fast computational scheme specifically developed for a phase-field mathematical model of image segmentation. The numerical methodology is based on an operator splitting method (OSM). The split operators are solved by using closed-form analytic solutions and a finite difference method (FDM) with an alternating direction explicit (ADE) method. To show the notable efficiency and rapid computational performance of the proposed computational algorithm, we conduct a series of numerical experiments. Through these computational tests, we confirm a significant contribution to the advancement of methodologies employed in the critical domain of image processing.</p></abstract>

EG-STC: An Efficient Secure Two-Party Computation Scheme Based on Embedded GPU for Artificial Intelligence Systems

EG-STC: An Efficient Secure Two-Party Computation Scheme Based on Embedded GPU for Artificial Intelligence Systems

Improvement of the transitional technology from open pit to underground mining of magnetite quartzite

The paper analyzes the disadvantages of the technology of iron ore open pit mining and current environmental problems of open pit mining. The paper also addresses problems of possible displacement and strains of rocks in the classical open pit mining method with extraction of minerals exclusively by open pit mining, studies current transitional technologies from open pit to integrated open pit-underground and subsequent underground mining, and presents an improved methodology for studying the stress-strain state of the massif during transition from open pit mining to integrated open pit-underground and subsequent underground mining. There are studied, developed and proposed options of environmentally friendly technologies of integrated open pit-underground mining with mining waste disposal in the worked-out space of underground mines and open pits, highly efficient calculation schemes for studying the stress-strain state of a rock massif during transition from open pit to underground mining with formation of protective barrier pillars, an option with the development of the lower room of stage II under protection of an ore pillar left within the contours of the upper room of stage I, and an option with the development of the lower room of stage II under protection of an artificial pillar made of the consolidating backfill in the upper room of stage I. The stress-strain state of the massif and possibilities of forming internal waste rock dumps when applying integrated open pit-underground mining technologies are studied and substantiated. Transition technologies from open pit to underground mining of iron ore raw materials under the bottom of an operating open pit are developed and proposed on the example of Kryvyi Rih iron ore basin.

Accurate error estimation for model reduction of nonlinear dynamical systems via data-enhanced error closure

Accurate error estimation is crucial in model order reduction, to obtain small reduced-order models as well as to certify their accuracy when deployed in downstream applications such as digital twins. In existing a posteriori error estimation approaches, knowledge about the time integration scheme is mandatory, e.g., the residual-based error estimators proposed for the reduced basis method. This poses a challenge when automatic ordinary differential equation solver libraries are used to perform the time integration. To address this, we present a data-enhanced approach for a posteriori error estimation. Our new formulation enables residual-based error estimators to be independent of any time integration method. To achieve this, we introduce a corrected reduced-order model which takes into account a data-driven closure term for improved accuracy. The closure term, subject to mild assumptions, is related to the local truncation error of the corresponding time integration scheme. We propose efficient computational schemes for approximating the closure term, at the cost of a modest amount of training data. Furthermore, the new error estimator is incorporated within a greedy process to obtain parametric reduced-order models. Numerical results on three different systems show the accuracy of the proposed error estimation approach and its ability to produce ROMs that generalize well.

Benchmark Study of the Electronic States of the LiRb Molecule: Ab Initio Calculations with the Fock Space Coupled Cluster Approach.

Accurate potential energy curves (PECs) are determined for the twenty-two electronic states of LiRb. In contrast to previous studies, the applied approach relies on the first principle calculations involving correlation among all electrons. The current methodology is founded on the multireference coupled cluster (CC) scheme constructed within the Fock space (FS) formalism, specifically for the (2,0) sector. The FS methodology is established within the framework of the intermediate Hamiltonian formalism and offers an intruder-free, efficient computational scheme. This method has a distinctive feature that, when applied to the doubly ionized system, provides the characteristics of the neutral case. This proves especially beneficial when investigating PECs in situations where a closed-shell molecule dissociates into open-shell fragments, yet its double positive ion forms closed-shell species. In every instance, we successfully computed continuous PECs spanning the entire range of interatomic distances, from the equilibrium to the dissociation limit. Moreover, the spectroscopic characteristic of various electronic states is presented, including relativistic effects. Relativistic corrections included at the third-order Douglas-Kroll level have a non-negligible effect on the accuracy of the determined spectroscopic constants.

Polyatomic radiative association by quasiclassical trajectory calculations: Formation of HCN and HNC molecules in H + CN collisions.

We have developed the polyatomic extension of the established [M. Gustafsson, J. Chem. Phys. 138, 074308 (2013)] classical theory of radiative association in the absence of electronic transitions. The cross section and the emission spectrum of the process is calculated by a quasiclassical trajectory method combined with the classical Larmor formula which can provide the radiated power in collisions. We have also proposed a Monte Carlo scheme for efficient computation of ro-vibrationally quantum state resolved cross sections for radiative association. Besides the method development, the global potential energy and dipole surfaces for H + CN collisions have been calculated and fitted to test our polyatomic semiclassical method.

MAGIC-GPS global variance reduction method for large-scale shielding calculation

We propose a Method of Automatic Generation Importance by Calculation with Growth Population Scheme (MAGIC-GPS) for efficient and accurate shielding calculation. The new method adopts a Growth Population Scheme (GPS) in the reciprocal iteration process of flux and importance for the Monte Carlo fixed-source calculation. Mathematical derivation is performed to prove that the GPS scheme is conducive to a rapid flux distribution convergence and can improve the Figure of Merit (FOM) of the Monte Carlo deep-penetration simulation. The effectivity of the MAGIC-GPS method is tested by a single concrete rod model, the H.B. Robinson-2 reactor benchmark (HBR2) and the China Fusion Engineering Test Reactor (CFETR). The results show that the MAGIC-GPS method can accelerate the Monte Carlo deep-penetration simulation, and the faster the population of particles increases, the better the acceleration. The MAGIC-GPS method is helpful for large-scale shielding calculation.

Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models.

Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem due to the absence of closed-form solutions to the marginal likelihood. The Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach can be employed to jointly sample models and coefficients, but the effective design of the trans-dimensional jumps of RJMCMC can be challenging, making it hard to implement. Alternatively, the marginal likelihood can be derived conditional on latent variables using a data-augmentation scheme (e.g., Pólya-gamma data augmentation for logistic regression) or using other estimation methods. However, suitable data-augmentation schemes are not available for every generalised linear model and survival model, and estimating the marginal likelihood using a Laplace approximation or a correlated pseudo-marginal method can be computationally expensive. In this paper, three main contributions are presented. Firstly, we present an extended Point-wise implementation of Adaptive Random Neighbourhood Informed proposal (PARNI) to efficiently sample models directly from the marginal posterior distributions of generalised linear models and survival models. Secondly, in light of the recently proposed approximate Laplace approximation, we describe an efficient and accurate estimation method for marginal likelihood that involves adaptive parameters. Additionally, we describe a new method to adapt the algorithmic tuning parameters of the PARNI proposal by replacing Rao-Blackwellised estimates with the combination of a warm-start estimate and the ergodic average. We present numerous numerical results from simulated data and eight high-dimensional genetic mapping data-sets to showcase the efficiency of the novel PARNI proposal compared with the baseline add-delete-swap proposal.

An adaptive divided-difference perturbation method for solving stochastic problems

Most stochastic problems are based on the independent and symmetrically distributed random variables. Using this principle, in this study, we propose an efficient calculation scheme to obtain the statistical moments based on high-order stochastic perturbation (SP) expansion. This solves the long-existing problem of the SP method, namely, the low calculation efficiency of statistical moments using high-order perturbation expansion, and the complexity of the calculation format. The scheme involves adopting the divided-difference method to approximate the partial derivative items of the SP method. The proposed method, which is similar to the collocation point method, only requires the deterministic calculation result for each node in the divided-difference method. In addition, as the adoption of high-order perturbation expansion is limited in multidimensional random problems due to the curse of dimensionality, an adaptive partial derivative items selection method is proposed in this paper to efficiently and reasonably ignore the expansion items that have an insignificant influence on statistical moments. This considerably improves the calculation efficiency of the statistical moments. Finally, the adaptive divided-difference perturbation (ADDP) method proposed in this paper is compared with the quasi-Monte Carlo method and the adaptive sparse grid methods using three numerical examples. The results prove that the ADDP method not only has high efficiency but also leads to significant improvements in the accuracy of statistical moments.

Computational Analysis of the Fractional Riccati Differential Equation with Prabhakar-type Memory

The key objective of the current work is to examine the behavior of the nonlinear fractional Riccati differential equation associated with the Caputo–Prabhakar derivative. An efficient computational scheme, that is, a mixture of homotopy analysis technique and sumudu transform, is used to solve the nonlinear fractional Riccati differential equation. The convergence and uniqueness analysis for the solution of the implemented technique is shown. In addition, the numerical consequences are demonstrated in the form of graphical representations to verify the reliability of the applied method in obtaining the solution to the mathematical model with Prabhakar-type memory.

Selectivity of Electrochemical Ion Insertion into Manganese Dioxide Polymorphs

The ion insertion redox chemistry of manganese dioxide has diverse applications in energy storage, catalysis, and chemical separations. Unique properties derive from the assembly of Mn-O octahedra into polymorphic structures that can host protons and nonprotonic cations in interstitial sites. Despite many reports on individual ion-polymorph couples, much less is known about the selectivity of electrochemical ion insertion in MnO2. In this work, we use density functional theory to holistically compare the electrochemistry of AxMnO2 (where A = H+, Li+, Na+, K+, Mg2+, Ca2+, Zn2+, Al3+) in aqueous and nonaqueous electrolytes. We develop an efficient computational scheme demonstrating that Hubbard-U correction has a greater impact on calculating accurate redox energetics than choice of exchange-correlation functional. Using PBE+U, we find that for nonprotonic cations, ion selectivity depends on the oxygen coordination environments inside a polymorph. When H+ is present, however, the driving force to form hydroxyl bonds is usually stronger. In aqueous electrolytes, only three ion-polymorph pairs are thermodynamically stable within water's voltage stability window (Na+ and K+ in α-MnO2, and Li+ in λ-MnO2), with all other ion insertion being metastable. We find Al3+ may insert into the δ, R, and λ polymorphs across the full 2-electron redox of MnO2 at high voltage; however, electrolytes for multivalent ions must be designed to impede the formation of insoluble precipitates and facilitate cation desolvation. We also show that small ions coinsert with water in α-MnO2 to achieve greater coordination by oxygen, while solvation energies and kinetic effects dictate water coinsertion in δ-MnO2. Taken together, these findings explain reports of mixed ion insertion mechanisms in aqueous electrolytes and highlight promising design strategies for safe, high energy density electrochemical energy storage, desalination batteries, and electrocatalysts.

The DLR ThermoFluid Stream Library

This paper introduces the DLR Thermofluid Stream Library: a free open-source library for the robust modeling of complex thermofluid architectures. Designed to be easy to use, easy to adapt, and enriched by a number of examples, this library contains the fundamental components for many different applications, such as thermal management of electric cars, power plants, or building physics. Different from many previous software implementations, the library exploits a new computational concept on the basis of the fluid inertance that derives the mass flow balance in such a manner that large non-linear equations systems in implicit form can be avoided. Hence, there is a reliable and efficient computational scheme for simulation and initialization. Although this scheme is explained in detail in previous publications, this paper focuses on the implementational aspects of the library, explaining its structure, the underlying equations of key components and providing basic examples. In addition to the practical value of the library, we also aim to display the underlying thought driving the design of the software.

Multi-scale computational method for nonlinear dynamic thermo-mechanical problems of composite materials with temperature-dependent properties

For most of materials, the properties of the materials are usually dependent on the temperature, which causes the nonlinear physical and mechanical material behaviors. In this paper, an innovative multi-scale computational method is developed for efficiently simulating nonlinear dynamic thermo-mechanical problems of composite materials. The nonlinearities of these multi-scale problems were caused by the temperature-dependent properties of each component material in the composites and the heterogeneities of composite materials are taken into account by periodic distributions of representative unit cells on the micro-scale. Firstly, a second-order two-scale (SOTS) computational model for accurately analyzing nonlinear dynamic thermo-mechanical behaviors of composite materials is established based on multi-scale asymptotic analysis and Taylor series method. The proposed SOTS computational model includes the first-order and second-order auxiliary cell problems on micro-scale, homogenized problem on macro-scale and macro–micro coupled SOTS asymptotic solutions. Then we theoretically explain the crucial importance of developing the SOTS solutions by the error analysis in the point-wise sense. Next, a rigorous error analysis with an explicit rate of the SOTS approximate solutions is given under some simplifications and assumptions in the integral sense. In addition, a multi-scale numerical algorithm is proposed in detail to effectively simulate these nonlinear multi-scale problems. Finally, several typical numerical examples are carried out to confirm the effectiveness and correctness of the proposed multi-scale numerical algorithm, especially for large-scale engineering structures. This study offers an efficient and high-accuracy multi-scale computational scheme that enables the effective simulation and analysis of nonlinear dynamic thermo-mechanical problems of composite materials with temperature-dependent properties.

Numerical approximation of the square phase-field crystal dynamics on the three-dimensional objects

In the natural world, the phase field transition on the surface of a three-dimensional (3D) object is common. The square phase-field crystal (SPFC) equation is an effective model for describing the phase transition from liquid to solid with lattice structure. This study aims to present an efficient and practical computational scheme to simulate the SPFC dynamics on arbitrary surfaces. The surface is represented by the zero level-set of a singed distance function. The closest point method and appropriate pseudo-Neumann boundary condition are used to make the numerical solution to be constant along the normal direction to the arbitrary surface. In this sense, the calculations are transformed into a 3D discrete narrow computational band domain embedding the arbitrary surface and the finite difference method (FDM) is adopted to discretize the governing equation in 3D space. To maintain second-order spatial accuracy, the standard seven-point discrete Laplacian operator is applied to replace the discrete surface Laplace–Beltrami operator. We treat the nonlinear term in a totally explicit form and utilize the stabilization technique to suppress the stiffness of the numerical scheme. Therefore, we avoid solving any nonlinear equation or linear equation with variable coefficients. In each time step, we only need to update the linear system with constant coefficients. The proposed numerical scheme is highly efficient and its implementation is simple. Various numerical experiments demonstrate that the proposed numerical scheme not only achieves the expected accuracy but also works well for the simulations of phase transition and crystallization on surfaces with smooth and sharp shapes.

Effect of rotation in NMR diffusion experiments on micron-sized particles: A generalized theoretical treatment

We have recently developed an analytical framework to interpret the results of pulsed field gradient (PFG) NMR experiments on solution samples of micron-sized amyloid fibrils [Angew. Chem. Int. Ed. 60 (2021) 15445–15451. https://doi.org/10.1002/anie.202102408]. Here we generalize this result by reporting a rigorous theoretical model of such experiments, implemented in a form of efficient computational scheme. In particular, the new treatment fully accounts for the anisotropy of fibrils’ translational diffusion and takes into consideration the finite length of the gradient pulses. The results hold not only for the historic spin-echo sequence, but also for the widely used stimulated echo experiment. We have found that fibrils’ rotation can attenuate the echo by a factor comparable with that of translation. However, contrary to some recent claims, the rotational mechanism cannot lead to an apparent fast-diffusion situation.