Computational Difficulties Research Articles

Intelligent diagnosis system based on artificial intelligence models for predicting freezing of gait in Parkinson's disease.

Freezing of gait (FoG) is a significant issue for those with Parkinson's disease (PD) since it is a primary contributor to falls and is linked to a poor superiority of life. The underlying apparatus is still not understood; however, it is postulated that it is associated with cognitive disorders, namely impairments in executive and visuospatial functions. During episodes of FoG, patients may experience the risk of falling, which significantly effects their quality of life. This research aims to systematically evaluate the effectiveness of machine learning approaches in accurately predicting a FoG event before it occurs. The system was tested using a dataset collected from the Kaggle repository and comprises 3D accelerometer data collected from the lower backs of people who suffer from episodes of FoG, a severe indication frequently realized in persons with Parkinson's disease. Data were acquired by measuring acceleration from 65 patients and 20 healthy senior adults while they engaged in simulated daily life tasks. Of the total participants, 45 exhibited indications of FoG. This research utilizes seven machine learning methods, namely the decision tree, random forest, Knearest neighbors algorithm, LightGBM, and CatBoost models. The Gated Recurrent Unit (GRU)-Transformers and Longterm Recurrent Convolutional Networks (LRCN) models were applied to predict FoG. The construction and model parameters were planned to enhance performance by mitigating computational difficulty and evaluation duration. The decision tree exhibited exceptional performance, achieving sensitivity rates of 91% in terms of accuracy, precision, recall, and F1- score metrics for the FoG, transition, and normal activity classes, respectively. It has been noted that the system has the capacity to anticipate FoG objectively and precisely. This system will be instrumental in advancing consideration in furthering the comprehension and handling of FoG.

Properties of ground state and quench dynamics of one-dimensional contact repulsive single-spin flipped Fermi gases

Based on the exact solution method, the ground state and quench dynamics properties of one-dimensional single-spin flipped Fermi gas with repulsion interaction are studied. With the Bethe wave function, the single-body correlation function and two-body correlation function of the ground state and those between different eigen-states can be reduced into a summation of simple functions, thereby greatly reducing the computational difficulty. For the system in the ground state, the single-body correlation functions and two-body correlation functions as well as momentum distributions for spin-up particles are investigated in real space with different interaction strengths. As the interaction strength increases, the number of nodes in the single-body correlation function remains unchanged, while the amplitude of oscillation decreases. Meanwhile, the number of peaks in the two-body correlation function increases by one due to interaction, indicating that the spin-down particle behaves as a spin-up particle. The momentum distribution becomes more smooth around Fermi surface with the interaction strength increasing. The interaction quench dynamics is investigated. The system is prepared in the ground state of ideal Fermi gas, and then the interaction strength is quenched to a finite positive value. The system evolves under time-dependent Schrödinger equation. The overlap between the initial state and eigen-state of post-quench interaction strength is expressed in the form of continued multiplication. The square of the modulus of this overlap, which represents the occupation probability, is calculated. We find that the occupation probabilities of the ground state and doubly degenerated excited state always have the first and the second largest value for an arbitrary interaction strength, respectively, which means that the difference in eigenenergy between these two states gives the primary period of oscillation. For relatively large particle number (<inline-formula><tex-math id="M2">\begin{document}$ N\geqslant10$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M2.png"/></alternatives></inline-formula>), the primary period always does not change under different interaction strengths.It is found that in the case of interaction quenching, the momentum distribution and the correlation function show periodic oscillations. When the interaction strength is adjusted to a relatively small value, the oscillation periodicity is well-defined and the oscillation amplitude is small. The system can be approximated by a two-level model. When the interaction strength increases to a very large value, the oscillation periodicity worsens and the amplitude increases, but a primary period remains unchanged. Although the overall deviation is far from the initial state, it is very close to the initial state at time <inline-formula><tex-math id="M3">\begin{document}$ t=mL^2/(2\pi\hbar)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M3.png"/></alternatives></inline-formula>. This is because the difference between most energy eigenvalues is almost an integral multiple of energy unit <inline-formula><tex-math id="M4">\begin{document}$ 2\times\left(2\pi/L\right)^{2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M4.png"/></alternatives></inline-formula>.

Machine learning-inspired intelligent optimization for smart radio resource management in satellite communication networks to improve quality of service

Satellite communication networks are seeing a significant surge in traffic requirements. Nevertheless, the rise in traffic requirements is inconsistent across the service region because of the unequal distribution of consumers and fluctuations in traffic requirements during the day. Variable payload designs solve this issue by enabling the uneven allocation of payload resources to match the traffic requirement of each beam. Optimization-based Radio Resource Management (ORRM) has its high substantial efficiency demonstrated computational difficulty hinders its real-world deployment. This work explores the structure, execution, and uses of Machine Learning (ML) for resource allocation in satellite systems. The primary emphasis is on two systems: one that offers power, capacity, and beamwidth adaptability and provides temporal flexibility via beam hopping. The research examines and contrasts several ML methods suggested for these structures. The research determines whether training must be done online or offline depending on the features and needs of each ML method. The study analyzes the most suitable system structure and the pros and cons of each strategy.

Efficient Analysis of Overdispersed Data Using an Accurate Computation of the Dirichlet Multinomial Distribution.

Modeling count data using suitable statistical distributions has been instrumental for analyzing the patterns it conveys. However, failing to address critical aspects, like overdispersion, jeopardizes the effectiveness of such an analysis. In this paper, overdispersed count data is modeled using the Dirichlet Multinomial (DM) distribution by maximizing its likelihood using a fixed-point iteration algorithm. This is achieved by estimating the DM distribution parameters while comparing the recent Languasco-Migliardi (LM), and the Yu-Shaw (YS) procedures, which address the well-known computational difficulties of evaluating its log-likelihood. Experiments were conducted using multiple datasets from different domains spanning polls, images, and IoT network traffic. They all showed the superiority of the LM procedure as it succeeded at estimating the DM parameters at the designated level of accuracy in all experiments, while the YS procedure failed to produce sufficiently accurate results (or any results at all) in several experiments. Moreover, the LM procedure achieved a speedup that ranged from 2-fold to 20-fold over YS.

A new diagonalization based method for parallel-in-time solution of linear-quadratic optimal control problems

A new diagonalization technique for the parallel-in-time solution of linear-quadratic optimal control problems with time-invariant system matrices is introduced. The target problems are often derived from a semi-discretization of a Partial Differential Equation (PDE)-constrained optimization problem. The solution of large-scale time dependent optimal control problems is computationally challenging as the states, controls, and adjoints are coupled to each other throughout the whole time domain. This computational difficulty motivates the use of parallel-in-time methods. For time-periodic problems our diagonalization efficiently transforms the discretized optimality system into nt (=number of time steps) decoupled complex valued 2ny × 2ny systems, where ny is the dimension of the state space. These systems resemble optimality systems corresponding to a steady-state version of the optimal control problem and they can be solved in parallel across the time steps, but are complex valued. For optimal control problems with initial value state equations a direct solution via diagonalization is not possible, but an efficient preconditioner can be constructed from the corresponding time periodic optimal control problem. The preconditioner can be efficiently applied parallel-in-time using the diagonalization technique. The observed number of preconditioned GMRES iterations is small and insensitive to the size of the problem discretization.

Quantum Computing in Cryptographic Systems

Quantum computing represents a transformative advancement in computational power, with profound implications for cryptographic systems. This paper explores the intersection of quantum computing and cryptography, examining the potential for quantum computers to both break traditional cryptographic algorithms and enable new forms of secure communication. Classical cryptographic systems, such as RSA and ECC, rely on the computational difficulty of problems like integer factorization and discrete logarithms. However, quantum algorithms, notably Shor's algorithm, can solve these problems exponentially faster than the best-known classical algorithms, posing a significant threat to the security of current cryptographic practices. This vulnerability necessitates the development and implementation of quantum-resistant algorithms to ensure data security in a post-quantum world. The paper reviews the state-of-the-art in quantum-resistant cryptographic algorithms, including lattice-based, hash-based, code-based, and multivariate polynomial cryptography. These algorithms are analyzed for their security properties, efficiency, and practicality for real-world deployment. Additionally, the paper discusses the ongoing standardization efforts led by organizations such as NIST, which are crucial for establishing widely accepted quantum-safe cryptographic protocols. Beyond the threat posed by quantum computing, this paper also highlights the potential benefits quantum computing can bring to cryptographic systems. Quantum Key Distribution (QKD) is one such advancement, offering theoretically unbreakable encryption by leveraging the principles of quantum mechanics. QKD enables secure communication channels that are immune to any computational advances, including those of quantum computers, by ensuring that any attempt at eavesdropping can be detected. The practical implementation challenges of QKD and other quantum cryptographic protocols are also addressed, including issues related to transmission distance, error rates, and integration with existing communication infrastructures. Experimental results from recent QKD trials are presented, showcasing significant progress in extending the viability of quantum-secure communication over long distances. Furthermore, the paper delves into the hybrid approaches combining classical and quantum cryptographic techniques. These approaches aim to leverage the strengths of both paradigms to enhance security and performance. For instance, hybrid protocols might use classical encryption for bulk data transfer, supplemented by quantum techniques for key exchange, thereby ensuring robust security even against future quantum adversaries. In conclusion, while quantum computing poses substantial risks to existing cryptographic systems, it also offers novel opportunities for creating highly secure communication protocols. The transition to quantum-safe cryptography is imperative to protect sensitive information in the quantum era. This paper underscores the urgency of advancing quantum-resistant cryptographic research, promoting international collaboration for standardization, and exploring innovative applications of quantum technologies in cryptography. Continued research and development in these areas are essential to stay ahead of the evolving threat landscape and harness the full potential of quantum computing for secure communications.

Coordinated Planning of Integrated Electric and Heating System Considering the Optimal Reconfiguration of District Heating Network

The tight coupling of electric and heating systems would make it necessary to consider the coordinated planning of the energy facilities. The seasonal district heating network (DHN) reconfiguration can notably impact the planning results and offer a potential approach for better wind penetration. To address this issue, a coordinated planning of electric and heating (CPEH) model is proposed in this paper by considering the seasonally DHN reconfiguration, which is formulated as a mixed-integer linear programming problem. Considering the computation difficulties brought in by numerous operation scenarios involved in the CPEH problem, a scenario-oriented generalized Benders decomposition (S-BD) algorithm is proposed to solve the CPEH model with higher efficiency by generating feasibility and optimality cuts with a unified form. The numerical simulations and a practical case in Jilin, China, are simulated to demonstrate the efficiency of the S-BD and illustrate the potential benefits of DHN reconfiguration in enhancing wind energy penetration.

On symmetry classification of integrable evolution equations of third order

We present new results in the framework of symmetry classification of third order integrable evolution vector equations. A technique proposed by G.A. Meshkov and V.V. Sokolov allowed us to find 12 equations satisfying necessary integrability conditions. We provide a short review of all known equations of the considered type and also clarify all computational difficulties not allowing us to complete the classification problem in the general form. By imposing reasonable additional restrictions for the form of equations while classifying them we succeed to complete the calculations. The found equations possess several nontrivial conserved densities and they are likely exactly integrable. As the proof of their integrability, the Lax representation or Bäcklund autotransform could serve but finding them is a rather complicated problem requiring a sufficient motivation, for instance, an application value of some of these equations.

Propensity Score Regression for Causal Inference With Treatment Heterogeneity

Understanding how treatment effects vary on individual characteristics is critical in the contexts of personalized medicine, personalized advertising and policy design. When the characteristics are of practical interest are only a subset of full covariate, non-parametric estimation is often desirable; but few methods are available due to the computational difficult. Existing non-parametric methods such as the inverse probability weighting methods have limitations that hinder their use in many practical settings where the values of propensity scores are close to 0 or 1. We propose the propensity score regression (PSR) that allows the non-parametric estimation of the heterogeneous treatment effects in a wide context. PSR includes two non-parametric regressions in turn, where it first regresses on the propensity scores together with the characteristics of interest, to obtain an intermediate estimate; and then, regress the intermediate estimates on the characteristics of interest only. By including propensity scores as regressors in the non-parametric manner, PSR is capable of substantially easing the computational difficulty while remain (locally) insensitive to any value of propensity scores. We present several appealing properties of PSR, including the consistency and asymptotical normality, and in particular the existence of an explicit variance estimator, from which the analytical behaviour of PSR and its precision can be assessed. Simulation studies indicate that PSR outperform existing methods in varying settings with extreme values of propensity scores. We apply our method to the national 2009 flu survey (NHFS) data to investigate the effects of seasonal influenza vaccination and having paid sick leave across different age groups.

Multirate Modeling and Predictive Control for WBG-Device-Based High-Switching-Frequency Power Converters

With the growth of wide bandgap devices, it is necessary to exploit the high switching frequency benefits to improve the power converter's performance, thus requiring a higher sampling/interrupt frequency in digital signal processors. However, such a short interrupt time duration imposes big computational difficulty in the execution of programming code, especially using the model predictive control (MPC). Thus, most of the existing MPCs are applied with switching frequencies below 20 kilohertz, which cannot exploit the full potential of the wide bandgap device-based power converters. To solve this challenge, this article proposes a multi-rate MPC scheme, where the trigger of interrupt and switching device transition can be performed at different rates. Compared to conventional MPCs, the main uniqueness of the proposed multi-rate MPC is that the high-dimension control sequence is solved and applied within each interrupt interval. Therefore, the increased switching frequency objective can be easily achieved with a low sampling/interrupt frequency configuration, which also significantly relieves the digital execution of the heavy interrupt tasks. The proposed method shows a more optimized control input and higher computational efficiency over the multi-rate finite-control-set MPC counterpart. A silicon carbide inverter-fed AC motor drive system is used to verify the proposed multi-rate MPC. The results show the improved system performance with the combined advantages of both the high switching frequency and MPC strategy.

Arithmetic Optimization Algorithm with Adaptive Neuro-Fuzzy Interference System for Predicting Financial Crisis

Financial technology (Fintech) is paramount in driving advanced technologies, economies, society, and several other sectors. Smart Fintech is the new-generation Fintech, primarily stimulated and endowed by compuational technology. Smart Fintech syndicates DSAI and renovates economies and finance for dynamic, smart, customized, automated services and systems, economies and financial companies, and the industry. The strength and development of the country’s economies are assessed by the correct forecasting. Financial crisis prediction (FCP) has the substantial consequence on the economies. Previous studies mainly emphasise statistical, DL, and ML methodologies for predicting the financial well-being of the business. Therefore, this article develops a new Arithmetic Optimization Algorithm with Adaptive Neuro-Fuzzy Interference System (AOA-ANFIS) technique for Predicting Financial Crisis. The presented AOA-ANFIS technique aims to predict the presence of financial crises or not. The model incorporates three major elements: Arithmetic Optimization Algorithm (AOA) for feature selection, Adaptive Neuro-Fuzzy Inference System (ANFIS) as the classification algorithm, and Bat Optimization Algorithm (BOA) for parameter tuning. The AOA feature selection model effectively detects the important attributes from a large proportion of financial indicators, augmenting the model's prediction capability while decreasing computational difficulty. Subsequently, the ANFIS classifier exploits the features selected for capturing the intricate non-linear relations intrinsic in financial data, permitting accurate crisis calculation. Additionally, the BOA parameter tuning model augments the ANFIS model's parameters, ensuring robustness and optimum performance. Experimental outcomes on varied financial databases validate the higher efficiency of the AOA-ANFIS technique over underlying processes, demonstrating its effectiveness in forecasting financial crises with great reliability and precision.

Numerical implementation of the hypoplastic model for SPH analysis of soil structure development in extremely large deformation

The extremely large deformation of soil is a significant challenge due to the dynamic changes in soil structure, but it is poorly understood owing to inadequate effective numerical methods. This paper presents a numerical method for analysing the responses of sand-like granular soil undergoing extremely large deformation. The proposed method utilizes the Smoothed Particle Hydrodynamics (SPH) technique, which is a meshfree particle-based approach capable of circumventing the computational difficulties associated with mesh distortion. The Gudehus-Bauer (G-B) hypoplastic model, which can capture the pressure- and density- dependent mechanical behaviour of granular soil, is implemented into the in-house developed SPH code. Concerning the characteristics of large deformation, the Green-Naghdi rate is applied in this study to achieve objective stress integration. An adaptive explicit stress integration scheme, termed Modified Euler automatic Substepping with Error Control (M-E-SEC) is utilized to handle the time integration of the SPH equation system. Additionally, a stability correction method is introduced to suppress the breakdown problem that occurs at low-stress states. The effectiveness of the proposed method is validated by experimental data. Furthermore, several numerical examples are presented to elucidate the evolution of shear band structures in granular soils subject to extremely large deformation levels.

A Current Noise Cancellation Method Based on Fractional Linear Prediction for Bearing Fault Detection.

The stator current in an induction motor contains a large amount of information, which is unrelated to bearing faults. This information is considered as the noise component for the detection of bearing faults. When there is noise information in the current signal, it can affect the detection of motor bearing faults and lead to the possibility of false alarms. Therefore, to accomplish an effective bearing fault detection, all or some of these noise components must be properly eliminated. This paper proposes the use of fractional linear prediction (FLP) as a noise elimination method in bearing fault diagnosis, which makes these noise components the predictable components and this bearing fault information the unpredictable components. The basis of the FLP is to eliminate noise components in the current signal by predicting predictable components through linear prediction theory and optimal prediction order. Meanwhile, this paper adopts the FLP model with limited memory samples. After determining the optimal number of memories, only the fractional derivative order parameter needs to be optimized, which greatly reduces the computational complexity and difficulty in parameter optimization. In addition, this paper uses spectral analysis of the current signals through experimental simulation to compare the FLP method with the linear prediction (LP) method and the time-shifting (TS) method that have been successfully applied to bearing fault diagnosis. Based on the analysis results, the FLP method can better extract fault features and achieve better bearing fault diagnosis results, verifying the effectiveness and superiority of the FLP method in the field of bearing fault diagnosis. Additionally, the predictive performance of thevFLP and LP was compared based on experimental data, verifying the advantages of the FLP method in predictive performance, indicating that this method has a better noise cancellation effect.

Symmetric and asymmetric buckling of rotating eccentric annular plate

The thermo-induced buckling, including the symmetric and asymmetric buckling, of rotating eccentric annular plate is investigated. And the splitting phenomenon in buckling caused by structural eccentricity is at the core of the present paper. To overcome the computational difficulty resulted from the irregular physical field of the eccentric annular plate, the transformed differential quadrature method is adopted to solve the governing equations. The governing equations and boundary conditions are discretized directly in the physical domain by utilizing the conformal mapping. The combined effects of eccentricity, boundary conditions, geometric dimensions, and rotational motion on the buckling of annular plate are discussed through parameter studies. The eccentricity leads to the splitting of asymmetric buckling of eccentric annular plate. With the increase of eccentricity, this phenomenon becomes more obvious. Meanwhile, the variation tendency of critical buckling temperature rise is closely related to the number of pitch diameter in buckling mode. The sequence of symmetric and asymmetric buckling appears is affected by the boundary conditions. To a certain extent, the rotational motion inhibits the splitting phenomenon in buckling arose from the eccentricity.

Graphene-based phononic crystal lenses: Machine learning-assisted analysis and design

The advance of artificial intelligence and graphene-based composites brings new vitality into the conventional design of acoustic lenses which suffers from high computation cost and difficulties in achieving precise desired refractive indices. This paper presents an efficient and accurate design methodology for graphene-based gradient-index phononic crystal (GGPC) lenses by combing theoretical formulations and machine learning methods. The GGPC lenses consist of two-dimensional phononic crystals possessing square unit cells with graphene-based composite inclusions. The plane wave expansion method is exploited to obtain the dispersion relations of elastic waves in the structures and then establish the data sets of the effective refractive indices in structures with different volume fractions of graphene fillers in composite materials and filling fractions of inclusions. Based on the database established by the theoretical formulation, genetic programming, a superior machine learning algorithm, is introduced to generate explicit mathematical expressions to predict the effective refractive indices under different structural information. The design of GGPC lenses is conducted with the assistance of the machine learning prediction model, and it will be illustrated by several typical design examples. The proposed design method offers high efficiency, accuracy as well as the ability to achieve inverse design of GGPC lenses, thus significantly facilitating the development of novel phononic crystal lenses and acoustic energy focusing.

Batch process monitoring based on sequential phase division multiway sparse weighted neighborhood preserving embedding

Batch processes are often characterized by multiphase and different batch durations, which vary from phase to phase presenting multiple local neighborhood features. In this paper, a sequential phase division-multiway sparse weighted neighborhood preserving embedding method is proposed for monitoring batch processes more sensitively. First, batches with uneven durations are synchronized, and the phases are automatically determined in chronological order. Secondly, the nearest neighbors are computed at each phase and the optimal sparse representation (SR) is obtained based on the nearest neighbors. This improves the robustness of the algorithm to noise and outliers, and solves the problem of computational difficulties associated with global SR based. Thirdly, the distance values of the neighbor elements are considered to fully extract the neighbor structure when the optimal SR is calculated. Finally, after dimension reduction, T 2 and squared prediction error statistics are established in feature space and residual space respectively for fault detection. The effectiveness of the method is verified by a multiphase numerical simulation example and the penicillin fermentation process.

Sparse successive approximation for nonlinear [formula omitted] and [formula omitted] optimal control problems under residual errors

Successive approximation techniques are effective approaches to solve the Hamilton–Jacobi–Bellman (HJB)/Hamilton–Jacobi–Isaacs (HJI) equations in nonlinear H2 and H∞ optimal control problems (OCPs), but residual errors in the solving process may destroy its convergence property, and related numerical methods also pose computational burden and difficulties. In this paper, the HJB/HJI partial differential equations (PDEs) for infinite-horizon nonlinear H2 and H∞ OCPs are handled in a unified formulation, and a sparse successive approximation method is proposed. Taking advantage of successive approximation techniques, the nonlinear HJB/HJI PDEs are transformed into sequences of easily solvable linear PDEs, to which the solutions can be computed point-wise by handling simple initial value problems. Extra constraints are also incorporated in the solving process to guarantee the convergence under residual errors. The sparse grid based collocation points and basis functions are then employed to enable efficient numerical implementation. The performance of the proposed method is also numerically demonstrated in simulations.

(Q, S, R)-Dissipativity Analysis of Large-Scale Networked Systems

This brief investigates the (Q,S,R)-dissipativity of large-scale networked systems in the discrete-time case. The networked system consists of a large number of subsystems, each of which can have different dynamic characteristics, and the connections among subsystems are arbitrary. When the number of subsystems is large, the traditional analysis method based on lumped description may have computational difficulties. To solve this problem, some computationally attractive conditions are derived, which essentially depend on the block-diagonal structure of the system parameter matrices and the sparseness of the subsystem connection matrix. Numerical simulations illustrate that compared with the existing results, the conditions suggested in this brief have higher computational efficiency in the dissipative analysis of large-scale networked systems.

Investigation of compressible flow under low Mach number in an enclosed square cavity with a novel non-Boussinesq algorithm

Natural convection is widely observed in various scales of natural phenomena and industrial applications. The low Mach number (i.e., low-velocity) natural convection, especially under large temperature differences and significant density and pressure fluctuations, is of great research significance in industrial fields such as nuclear engineering. The Boussinesq approximation based on the incompressible Navier–Stokes (NS) equation is not fully descriptive due to the neglect of coupling effects among temperature, density, and pressure. As for numerical algorithms based on the compressible Navier–Stokes equation, they often suffer from high computational costs and convergence difficulties. In this paper, a novel numerical algorithm based on the decoupled and stabilized Lattice Boltzmann multiphase model with a complete physical description and clear conceptual framework is proposed. It couples the equation of state and the temperature equation, considering the full effects of gravity, pressure, and temperature-dependent density on flow disturbances, and it recovers the complete compressible NS equation. Taking the natural convection in an enclosed cavity as an example, the non-dimensional numbers governing the fluid system are identified by Buckingham π theorem; thus, a new thermal expansion number is proposed to connect the pressure effect. The accuracy and reliability of the numerical algorithm are validated by comparing it with standard benchmarks. On this basis, the proposed algorithm enables a unified physical description from low to high Rayleigh numbers and from small to large temperature differences. By analyzing the flow and heat transfer characteristics of natural convection under different Rayleigh numbers, temperature differences, and thermal expansion numbers, this study reveals the coupled physical mechanisms of low Mach number flow from small to large temperature differences, from low to high Rayleigh numbers and under different thermal expansion numbers.

Privacy-Preserving Range Query Quantum Scheme With Single Photons in Edge-Based Internet of Things

Range query in cloud-based outsourcing applications is an important data search service, but it can suffer from privacy disclosure. In this paper, we generalize and redefine privacy-preserving range query in edge-based Internet of Things (IoT). Furthermore, to enhance security and privacy of sensitive data, we introduce quantum cryptographic technologies and present a novel quantum approach to solve the problem. First, we present a feasible protocol for Quantum Secret Permutating (QSP) with single photons, which will be later utilized in the final scheme as a basic block. Second, we generalize traditional privacy-preserving range query to a secure one-sided two-party computation, i.e., specific dot product. Third, we present a synchronously grouping strategy based on Quantum Key Distribution (QKD) to reduce the complexity and improve the efficiency of solving this two-party computation, so that it can easily get the desired result by repeatedly using feasible quantum privacy query group by group. Finally, adopting our previously proposed quantum protocols, we design privacy-preserving range query quantum scheme in edge-based IoT. Compared with the classical related schemes, our proposed quantum scheme has higher security, because the security of our proposed protocols is based on the basic physical principles of quantum mechanics, instead of unproven computational difficulty assumptions.