Multivariate Problem Research Articles

Robust Tensor Completion via Capped Frobenius Norm.

Tensor completion (TC) refers to restoring the missing entries in a given tensor by making use of the low-rank structure. Most existing algorithms have excellent performance in Gaussian noise or impulsive noise scenarios. Generally speaking, the Frobenius-norm-based methods achieve excellent performance in additive Gaussian noise, while their recovery severely degrades in impulsive noise. Although the algorithms using the lp -norm ( ) or its variants can attain high restoration accuracy in the presence of gross errors, they are inferior to the Frobenius-norm-based methods when the noise is Gaussian-distributed. Therefore, an approach that is able to perform well in both Gaussian noise and impulsive noise is desired. In this work, we use a capped Frobenius norm to restrain outliers, which corresponds to a form of the truncated least-squares loss function. The upper bound of our capped Frobenius norm is automatically updated using normalized median absolute deviation during iterations. Therefore, it achieves better performance than the lp -norm with outlier-contaminated observations and attains comparable accuracy to the Frobenius norm without tuning parameter in Gaussian noise. We then adopt the half-quadratic theory to convert the nonconvex problem into a tractable multivariable problem, that is, convex optimization with respect to (w.r.t.) each individual variable. To address the resultant task, we exploit the proximal block coordinate descent (PBCD) method and then establish the convergence of the suggested algorithm. Specifically, the objective function value is guaranteed to be convergent while the variable sequence has a subsequence converging to a critical point. Experimental results based on real-world images and videos exhibit the superiority of the devised approach over several state-of-the-art algorithms in terms of recovery performance. MATLAB code is available at https://github.com/Li-X-P/Code-of-Robust-Tensor-Completion.

Improved Newton-Raphson method with simplified Jacobian matrix and optimized iteration rate for power flow calculation of power system

With high penetration of renewable energy and novel loads connected to the distribution network, the voltage fluctuation becomes more severe and frequent, which may cause over- and under-voltage. The distribution system operator should calculate the power flow and validate the state to optimize the distribution network. Power flow calculation is the solution to the multivariate nonlinear problem, and the Newton-Raphson method is an effective algorithm for solving nonlinear problems. However, calculating the Jacobian matrix is a crucial process of the Newton-Raphson method, which is time-consuming. Therefore, this paper proposed an improved Newton-Raphson method, which simplifies and decreases the iterations of the calculation process of the Jacobian matrix to improve the calculation rate. To verify the effectiveness of the proposed method, the power flow of the IEEE 33-node power distribution system is calculated by the improved Newton-Raphson method and the conventional Newton-Raphson method.

Cryptographic Protocols Resilient to Quantum Attacks: Advancements in Post-Quantum Cryptography

New developments in quantum computing have made people worry that current security methods could be broken by quantum attacks. Some mathematical problems are hard to solve, which is how traditional encryption methods like RSA and ECC keep their secrets safe. However, quantum computers might be able to solve these issues a lot faster than regular computers, which makes these methods less safe. Because of this threat, experts have been working hard to make post-quantum cryptography methods that quantum computers can't break. These methods are made to stand up to the strength of quantum algorithms and protect the privacy, integrity, and validity of private data even when quantum attackers are present. Lattice-based cryptography is a potential method for post-quantum encryption. Its security comes from the difficulty of certain lattice problems. Lattice-based methods are thought to be safe from threats from both traditional and quantum computers because they offer good security promises. Lattice-based cryptography is a flexible way to build different types of cryptographic primitives, like encryption, digital signatures, and key sharing protocols. The study of code-based cryptography, which is based on how hard it is to decode some error-correcting codes, is another important advance. Code-based methods have been around for a long time and have been studied a lot, which makes them a good choice for security after quantum computing. Code-based cryptography is also easy to use and has strong security features, which makes it a good choice for real-world situations. Multivariate polynomial cryptography is another possible choice for cryptography after quantum computing. The safety of this method depends on how hard it is to solve systems of multivariate polynomial problems. Multivariate polynomial methods might not be as secure as lattice-based or code-based cryptography, but they are interesting options for some situations and places with limited resources.

A critical review on the influence of operating parameters and feedstock characteristics on microwave pyrolysis of biomass.

Biomass pyrolysis is the most effective process to convert abundant organic matter into value-added products that could be an alternative to depleting fossil fuels. A comprehensive understanding of the biomass pyrolysis is essential in designing the experiments. However, pyrolysis is a complex process dependent on multiple feedstock characteristics, such as biomass consisting of volatile matter, moisture content, fixed carbon, and ash content, all of which can influence yield formation. On top of that, product composition can also be affected by the particle size, shape, susceptors used, and pre-treatment conditions of the feedstock. Compared to conventional pyrolysis, microwave-assisted pyrolysis (MAP) is a novel thermochemical process that improves internal heat transfer. MAP experiments complicate the operation due to additional governing factors (i.e. operating parameters) such as heating rate, temperature, and microwave power. In most instances, a single parameter or the interaction of parameters, i.e. the influence of other parameter integration, plays a crucial role in pyrolysis. Although various studies on a few operating parameters or feedstock characteristics have been discussed in the literature, a comprehensive review still needs to be provided. Consequently, this review paper deconstructed biomass and its sources, including microwave-assisted pyrolysis, and discussed the impact of operating parameters and biomass properties on pyrolysis products. This paper addresses the challenge of handling multivariate problems in MAP and delivers solutions by application of the machine learning technique to minimise experimental effort. Techno-economic analysis of the biomass pyrolysis process and suggestions for future research are also discussed.

Competitive pricing for ride-sourcing platforms with MARL

With the advancement of autonomous driving, the competition between shared autonomous vehicles (SAVs) and the existing human-driven vehicles (HVs) ride-sourcing platforms has emerged as a prominent research area within the fields of transportation and management. Solving the pricing problem, considering the competition between HV and SAV platforms, is critical for the platform’s operation. The competitive pricing problem is hard to solve since it is a partially observable Markov decision process (POMDP), that is, only the strategies of other platforms (such as price and wage) are observable, while their states are unobservable. It is also a multivariable sequential problem pricing since spatial-temporal pricing varies with region and time. To tackle this complex problem, this paper implements the multi-agent reinforcement learning (MARL) approach of multi-agent deep deterministic policy gradient (MADDPG) to an mesoscopic simulation system. The simulation replicates the intricate dynamics within a competitive environment where SAV and HV platforms coexist. MADDPG effectively resolves the competitive pricing issue using data derived from simulation. The findings indicate that the SAV platform secures greater profits with a smaller fleet, as it eliminates the need to compensate drivers. Meanwhile, for the same reason, even with fewer vehicles, the SAV platform can set lower prices to attract more passengers and thereby generate higher profits. We further evaluate the efficacy of dynamic pricing versus spatial-temporal pricing and discover that spatial-temporal pricing yields greater profits.

Auto-Ignited Combustion Control in an Engine Equipped with Multiple Boosting Devices

<div>The combustion timing of auto-ignited combustion is determined by composition, temperature, and pressure of cylinder charge. Thus, for a successful auto-ignition, those key variables must be controlled within tight target ranges, which is challenging due to (i) nature of coupling between those variables, and (ii) complexity of managing multiple actuators in the engine. In this article, a control strategy that manages multiple actuators of a boosted homogeneous charge compression ignition (HCCI) engine is developed to maintain robust auto-ignited combustion. The HCCI engine being considered is equipped with multiple boosting devices including a supercharger and a turbocharger in addition to conventional actuators and sensors. Since each boosting device has its own pros and cons, harmonizing those boosting devices is crucial for successful transient operation. To address the multi-variable transient control problem, speed-gradient control methodology is applied to minimize coupling between boosting devices. Simulation results show that the control strategy overcomes turbo lag by utilizing the supercharger during transient. The controller developed is still appliable to manage multiple boosting devices with conventional engines as well as HCCI engine.</div>

Prediction of Dust Emissions in Highway Subgrade-Filling Construction Based on Deep Neural Network

Dust pollution can harm the urban environment and the health of citizens. Each stage in highway construction generates unorganized dust emissions to varying degrees, which complicates their quantification. To precisely forecast dust emissions during the construction of highway subgrades and reduce the associated pollution risks, this study introduces a predictive model based on a deep neural network (DNN) for dust emissions during highway subgrade-filling operations. Dust concentration is treated as a nonlinear multivariate problem, with predictive indicators encompassing particulate matter 2.5 (PM2.5), particulate matter 10 (PM10), ground surface temperature, wind speed, air temperature, surface pressure, and relative humidity. Using a DNN model, this study forecasts the concentrations of PM2.5 and PM10 at highway construction sites. Based on a highway project in Hebei Province, this study predicts dust-emission concentrations via field monitoring conducted using self-developed equipment. The model’s predictions exhibit a small mean-absolute-percentage error and root-mean-square error compared with the actual values, and the model’s accuracy significantly surpasses that of conventional regression models. Accurate forecasting can facilitate the timely control of dust concentrations at construction sites, thus facilitating more environmentally friendly and efficient construction. Doi: 10.28991/HIJ-2024-05-02-03 Full Text: PDF

A multi-stage framework for coordinated scheduling of networked microgrids in active distribution systems with hydrogen refueling and charging stations

Due to the increase in electric energy consumption and the significant growth in the number of electric vehicles (EV) at the level of the distribution network, new networks have started using new fuels such as hydrogen to improve environmental indicators and at the same time better efficiency from the excess capacity of renewable resources. In this article, the services that can be provided by hydrogen refueling stations and charging electric vehicles in the optimal performance of microgrids have been investigated. The model proposed in this paper includes a two-stage stochastic framework for scheduling resources in microgrids, especially hydrogen refueling stations and electric vehicle charging. In this model, two main goals of cost minimization and greenhouse gas emissions are considered. In the proposed framework and in the first stage, the service range of microgrids is determined precisely according to the electrical limitations of distribution systems in emergency situations. Then, in the second stage, the problem of energy management in each microgrid will be solved centrally. In this situation, various indicators including the output energy of renewable sources, smart charging of hydrogen and electric vehicle charging stations (EV/FCV) and flexible loads (FL) are evaluated. The final mathematical model is implemented as a multivariate integer multiple linear problem (MILP) using the GUROBI solver in GAMS software. The simulation results on the modified IEEE 118-Bus network show the positive effect of the presence of flexible loads and smart charging strategies by charging stations. Also, the numerical derivation shows that the operating costs of the entire system can be reduced by 4.77% and the use of smart charging strategies can reduce greenhouse gas emissions by 49.13%.

Spatiotemporal Mechanism-Based Spacetimeformer Network for InSAR Deformation Prediction and Identification of Retrogressive Thaw Slumps in the Chumar River Basin

The increasing incidence of retrogressive thaw slumps (RTSs) in permafrost regions underscores the need for detailed spatial and temporal analysis using InSAR technology to monitor and predict dynamic changes in the process of RTSs. Nevertheless, current InSAR deformation forecasting methods employing deep learning strategies such as the traditional long short-term memory (LSTM) and recent transformer models encounter difficulties in effectively capturing temporal features. Moreover, they are limited in their ability to directly integrate spatial information. In this paper, an innovative deep learning approach named Spacetimeformer is proposed for predicting medium- and short-term InSAR deformation of RTSs in the Chumar River area. This method employs a transformer architecture with a spatiotemporal attention mechanism, which enhances the long-term prediction capabilities of time series models and dynamic spatial modeling. It is applicable to multivariate InSAR spatiotemporal deformation prediction problems. The findings include a list of 72 RTSs compiled based on derived InSAR deformation maps and Sentinel-2 optical images, of which 64 have an average deformation rate exceeding 10 mm/year, indicating signs of permafrost degradation. The density distribution of the displacement maps predicted by the Spacetimeformer model aligned well with the InSAR deformation maps obtained from the small baseline subset (SBAS) method, with the overall prediction deviation controlled within 20 mm. In addition, the point-scale prediction results were compared with LSTM and transformer models. This study indicates that the Spacetimeformer network achieved good results in predicting the deformation of RTSs, with a root mean square error of 1.249 mm. The Spacetimeformer method for deformation prediction with the spacetime mechanism presented in this study can serve as a general framework for multivariate deformation prediction based on InSAR results. It can also quantitatively assess the spatial deformation characteristics and deformation trends of RTSs.

Mathematical and computationalmodeling of migrations, population spread, and Location-dependent carrying capacities

In single-variable calculus, differential equation models for population dynamics are of high importance and by developing these ordinary differential equation (ODE) models, a practical and intelligible approach can be created to partial differential equations (PDEs). This paper researches focus on PDE models for migrations, population spread and location-dependent carrying capacities. However, logistic equation from which the PDE models develop include the diffusion equation, traveling wave equation, and building blocks with location-dependent parameters. This methodology is suitable for multivariable calculus lecture, evaluation task, and problem activity. The text is accompanied by interactive examples, and the article is formatted to be used as a CDF document in which some of the input can be hidden.

Optimal multivariate mixture: a genetic algorithm approach

AbstractThe Optimal Multivariate Mixture Problem (OMMP) consists of finding an optimal mixture which, starting from a set of elements (items) described by a set of variables (features), is as close as possible to an ideal solution. This problem has numerous applications spanning various fields, including food science, agriculture, chemistry, materials science, medicine, and pharmaceuticals. The OMMP is a class of optimization problems that can be addressed using traditional Operations Research (OR) approaches. However, it can also be effectively tackled using meta-heuristic techniques within Artificial Intelligence (AI). This paper aims to present an Artificial Intelligence perspective. It proposes a Genetic Algorithm (GA) for Optimal Multivariate Mixture (GA-OMM), a novel improved version of a GA whose modified genetic operators prove to improve the exploration efficiency. Here, the algorithm is described in its general framework, and a test case 8-items 5-features is conducted to evaluate efficiency by exploring various combinations of hyperparameters. Test cases are also set up for the previous version, as well as a linear programming (LP) approach. The data experiments indicate that the proposed GA is efficient, converges towards the global optimum, consistently outperforms its predecessor, and delivers highly competitive results. In particular, GA-OMM shows an average fitness of GA-OMMP/LP and standard deviation with an order of magnitude ranging between $$10^{-8}$$ 10 - 8 to $$10^{-4}$$ 10 - 4 . Moreover, it consistently outperforms its predecessor, which exhibits similar values around $$10^{-3}$$ 10 - 3

EGame-flow: psychometric properties of the scale in the Mexican context

PurposeThe present study examined the psychometric properties of the EGame- flow scale in a Mexican sample, presenting evidence of construct validity (exploratory factor analysis and confirmatory factor analysis), reliability (Cronbach’s alpha and McDonald’s omega) and discriminant validity (mean variance extracted).Design/methodology/approachParticipants: Of the 255 Mexican participants in the non-probabilistic sample who had previously interacted with the LOST logistics simulator, 166 (65%) were men and 89 (35%) were women; their ages ranged from 22 to 45. The statistical packages SPSS 25, JASP 0.16 and AMOS 23 facilitated the corresponding analyses. First, we calculated the means and standard deviations of the scale items. Next, we performed an exploratory factor analysis to examine the measurement model’s internal structure and a confirmatory factor analysis to confirm the structure proposed in the exploratory factor analysis. To analyze the internal structure of the measurement model so that the estimates were not affected by multivariate normality problems, we utilized the AMOS bootstrap method (with 500 repetitions, 95% CI), the maximum likelihood (MV) estimation method, and the fit indices: X2, p (chi-square and associated likelihood), Tucker–Lewis index (TLI), standardized statistical mean square residual (SRMR), comparative fit index (CFI) and root mean Square error approximation (RMSEA) with its confidence interval, the values of X2 with p < 0.001; TLI, CFI, AGFI = 0.95; RMSEA and SRMR = 0.08 (Byrne, 2016). Finally, we estimated the reliability of the measurement model with Cronbach’s alpha (a), McDonald’s omega (ω) coefficient and the mean variance extracted (VME).FindingsAn exploratory factor analysis with the MV method and obliminal rotation showed a good fit of the data to the model, which aligns with the significance of the Barlette sphericity test (X2 = 8443.2, p < 0.000) and the Kaiser–Meyer-Olkin (KMO) value of 0.94. The indices confirmed the fit of the data to the six-dimensional model for measuring the users' level of enjoyment of online games (X2 = 678.2 gl = 411, p = 0.000; SRMR = 0.05; TLI = 0.95, CFI = 0.95 and RMSEA = 0.05, IC 90% [0.04, 0.05]).Research limitations/implicationsThe self-reporting format of the scale increases the social desirability of the responses, but the sample only collects information from a specific geographic location, so these findings cannot extrapolate to populations with very marked cultural differences. Finally, the study did not measure other validity evidence, such as predictive and concurrent validity, which should be considered in future studies.Practical implicationsFrom a practical perspective, the study offers a measurement scale with fewer items and robust psychometric evidence that ensures the fit of the data to the EGame-flow measurement scale. Further research must continue to learn about the behavior of the EGame-flow scale in different samples that new evidence of psychometric properties continues to appear and that other factors associated with the users' gaming enjoyment experience are analyzed.Originality/valueThe value and originality of the study lie in the type of evidence of psychometric properties that the instrument has and particularly in the style of sample in which the study is carried out, in this case, in the context of Mexico, where there are not enough instruments that measure the flow experience of users.

Tractability of Multivariate Approximation Problem on Euler and Wiener Integrated Processes

This paper examines the tractability of multivariate approximation problems under the normalized error criterion for a zero-mean Gaussian measure in an average-case setting. The Gaussian measure is associated with a covariance kernel, which is represented by the tensor product of one-dimensional kernels corresponding to Euler and Wiener integrated processes with non-negative and nondecreasing smoothness parameters {rd}d∈N. We give matching sufficient and necessary conditions for various concepts of tractability in terms of the asymptotic properties of the regularity parameters, except for (s, 0)-WT.

Updated Ostrowski inequalities over a spherical shell

Here we present general multivariate mixed Ostrowski type inequalities over spherical shells and balls. We cover the radial and not necessarily radial cases. The proofs derive by the use of some estimates coming out of some new trigonometric and hyperbolic Taylor’s formulae ([2]) and reducing the multivariate problem to a univariate one via general polar coordinates.

Kernel-Based Multivariate Nonparametric CUSUM Multi-Chart for Detection of Abrupt Changes

In many cases, it is difficult to obtain precise distributional information on multivariate sequences. Therefore, there is a need to propose nonparametric methods for monitoring multivariate sequences. This article discusses the multivariate change detection problem and utilizes the kernel function as the statistic to construct the nonparametric Multivariate Cumulative Sum multi-chart, under the assumption that there is prior information about the abrupt changes. Through theoretical and numerical analysis, we show that the proposed control chart is more effective compared to other existing control charts. The good monitoring effect of this method demonstrates a strong potential for application.

Comparative Analysis of Weather Forecasting Using LSTM, BiLSTM, and CLSTM Networks

Weather prediction plays vital role in the evaluation of various processes and phenomenon for the betterment of society. Weather forecasting depends on many parameters hence, it’s a multivariable prediction problem. Behavior of data involved in the prediction are in majority of time stochastics hence, conventional mathematical approaches are failed to predict accurate data. Classical computational methods fail in predicting chaotic data due to its limitation to have know-how about behavior of data. Artificial Intelligence and Data Processing techniques is appealing investigators due to its efficiency to predict data based on its learning capability, without any know-how about the behavior of data. In this paper, Artificial Intelligence based approach LSTM, BiLSTM, and CLSTM are used to predict time series weather data prediction. Data considered are Pressure, Humidity, Temperature, and Maximum wind speed as input data. Neural Network based approaches are used to predict Average wind speed based on above inputs. The performance of above Artificial based approaches is compared to predict time series Average wind speed. MATLAB is used as software tool to implement Artificial Intelligence approaches. It has been observed that CLSTM algorithm outperformed other two algorithms LSTM and BiLSTM algorithm.

Sleep stage prediction using multimodal body network and circadian rhythm.

Quality sleep plays a vital role in living beings as it contributes extensively to the healing process and the removal of waste products from the body. Poor sleep may lead to depression, memory deficits, heart, and metabolic problems, etc. Sleep usually works in cycles and repeats itself by transitioning into different stages of sleep. This study is unique in that it uses wearable devices to collect multiple parameters from subjects and uses this information to predict sleep stages and sleep patterns. For the multivariate multiclass sleep stage prediction problem, we have experimented with both memoryless (ML) and memory-based models on seven database instances, that is, five from the collected dataset and two from the existing datasets. The Random Forest classifier outclassed the ML models that are LR, MLP, kNN, and SVM with accuracy (ACC) of 0.96 and Cohen Kappa 0.96, and the memory-based model long short-term memory (LSTM) performed well on all the datasets with the maximum attained accuracy of 0.88 and Kappa 0.82. The proposed methodology was also validated on a longitudinal dataset, the Multiethnic Study of Atherosclerosis (MESA), with ACC and Kappa of 0.75 and 0.64 for ML models and 0.86 and 0.78 for memory-based models, respectively, and from another benchmarked Apple Watch dataset available on Physio-Net with ACC and Kappa of 0.93 and 0.93 for ML and 0.92 and 0.87 for memory-based models, respectively. The given methodology showed better results than the original work and indicates that the memory-based method works better to capture the sleep pattern.

A rational approach for the scantling design of GRP pleasure crafts

In various fields of industrial engineering, including naval architecture, structural design is considered one of the most challenging steps by designers as it shall accommodate all other design aspects, likely already defined in earlier steps. Moreover, structures need to comply with specific requirements, i.e. limit states, while also performing in accordance with user's demands in terms of mission profile. In a goal-based design perspective, limit state criteria have to be defined accounting for both, structural robustness, functional and operational demands. Construction feasibility is an issue as well, further constraining the scantling design. Balancing construction needs, ship performances and structural aspects is not always an easy task.The environment in which a ship operates is indeed complex and verification of safety and robustness is usually carried out in accordance with classification societies and other rules, possibly applying direct calculations whenever applicable rules do not provide suitable solutions. At the same time, the asset needs to fulfill various attributes specified by the owner. As a matter of facts, the scantling design is mathematically a multivariate and over-constrained problem whose feasible solutions are in fact rather few. In the case of composite pleasure craft hull structures, while the number of design variables increases, feasibility constraints also largely reduce the design space.To address these challenges, designers may nowadays exploit new procedures able to reduce structural weight, though ensuring that the asset performs safely and adequately meeting client's requirements. To achieve this, designers may combine a more rational design philosophy with currently available numerical problem-solving applications to obtain a rational trade-off among all actually feasible solutions, which are relatively few.Thus, the objective of this study is to present a dependable numerical method for determining the scantling while reducing the weight of hull composite structures of pleasure crafts. This method aims to provide the most suitable, high-performing, and safe layout in the quickest and easiest possible manner. It turns out that counterintuitive, yet feasible and fit-for-purpose, structural lay-outs can be obtained.

Метод генерации уникальных вариантов для математических задач

The article poses the problem of creating generators for unique multivariate mathematical problems. Types of methods of obtaining random numbers are considered. A comparative analysis of the standard generator used by developers with the generator providing the possibility to create sets of numbers occurring once among the required range of values is carried out. A specific example is provided that requires the application of unique problem sets and parameters. The examples are accompanied by formulas in general form, listings of the proposed algorithms of functions in JavaScript, a brief verbal description of the result of the functions. Attention is paid to the generation of numbers without zero, to the peculiarities of development, taking into account the choice of the best interval for a wide range of values of generated numbers, excluding the use of loops and reducing risks. The article explains a method of description of the result of generation of numbers in JSON format, which can be used when transferring the obtained sets between different programming languages.

Метод генерации уникальных вариантов для математических задач

The article poses the problem of creating generators for unique multivariate mathematical problems. Types of methods of obtaining random numbers are considered. A comparative analysis of the standard generator used by developers with the generator providing the possibility to create sets of numbers occurring once among the required range of values is carried out. A specific example is provided that requires the application of unique problem sets and parameters. The examples are accompanied by formulas in general form, listings of the proposed algorithms of functions in JavaScript, a brief verbal description of the result of the functions. Attention is paid to the generation of numbers without zero, to the peculiarities of development, taking into account the choice of the best interval for a wide range of values of generated numbers, excluding the use of loops and reducing risks. The article explains a method of description of the result of generation of numbers in JSON format, which can be used when transferring the obtained sets between different programming languages.