Multivariable Systems Research Articles

A Comprehensive Review of MI-HFE and IPHFE Cryptosystems: Advances in Internal Perturbations for Post-Quantum Security

The RSA cryptosystem has been a cornerstone of modern public key infrastructure; however, recent advancements in quantum computing and theoretical mathematics pose significant risks to its security. The advent of fully operational quantum computers could enable the execution of Shor’s algorithm, which efficiently factors large integers and undermines the security of RSA and other cryptographic systems reliant on discrete logarithms. While Grover’s algorithm presents a comparatively lesser threat to symmetric encryption, it still accelerates key search processes, creating potential vulnerabilities. In light of these challenges, there has been an intensified focus on developing quantum-resistant cryptography. Current research is exploring cryptographic techniques based on error-correcting codes, lattice structures, and multivariate public key systems, all of which leverage the complexity of NP-hard problems, such as solving multivariate quadratic equations, to ensure security in a post-quantum landscape. This paper reviews the latest advancements in quantum-resistant encryption methods, with particular attention to the development of robust trapdoor functions. It also provides a detailed analysis of prominent multivariate cryptosystems, including the Matsumoto–Imai, Oil and Vinegar, and Polly Cracker schemes, alongside recent progress in lattice-based systems such as Kyber and Crystals-DILITHIUM, which are currently under evaluation by NIST for potential standardization. As the capabilities of quantum computing continue to expand, the need for innovative cryptographic solutions to secure digital communications becomes increasingly critical.

Machine Learning as a “Catalyst” for Advancements in Carbon Nanotube Research

The synthesis, characterization, and application of carbon nanotubes (CNTs) have long posed significant challenges due to the inherent multiple complexity nature involved in their production, processing, and analysis. Recent advancements in machine learning (ML) have provided researchers with novel and powerful tools to address these challenges. This review explores the role of ML in the field of CNT research, focusing on how ML has enhanced CNT research by (1) revolutionizing CNT synthesis through the optimization of complex multivariable systems, enabling autonomous synthesis systems, and reducing reliance on conventional trial-and-error approaches; (2) improving the accuracy and efficiency of CNT characterizations; and (3) accelerating the development of CNT applications across several fields such as electronics, composites, and biomedical fields. This review concludes by offering perspectives on the future potential of integrating ML further into CNT research, highlighting its role in driving the field forward.

Enhancing Accuracy and Efficiency in Stiff ODE Integration Using Variable Step Diagonal BBDF Approaches

Recent advancements in mathematical modelling have uncovered a growing number of systems exhibiting stiffness, a phenomenon that challenges the effectiveness of traditional numerical methods. Motivated by the need for more robust numerical techniques to address this issue, this paper presents an enhanced version of the Diagonally Block Backward Differentiation Formula (BBDF) that incorporates intermediate points, known as off-step points, to improve the accuracy and efficiency of solutions for stiff ordinary differential equations (ODEs). The new scheme leverages an adaptive step-size strategy to refine accuracy and efficiency between regular and off-grid integration steps. Theoretical analysis confirms that the proposed scheme is an A-stable and convergent method, as it satisfies the fundamental criteria of consistency, zero-stability, and A-stability. Numerical experiments on single and multivariable systems across varying time scales demonstrate significant improvements in solving stiff ODEs compared to existing techniques. Therefore, the new proposed method is an effective solver for stiff ODEs.

Experimentally-efficient data-driven rational feedforward control for multivariable systems

Feedforward control with task flexibility for MIMO systems is essential to meet the growing demands on throughput and accuracy of high-tech systems. The aim of this paper is to develop an experimentally efficient framework for data-driven tuning of rational feedforward controllers for general non-commutative MIMO systems. In the developed approach, the nonlinear terms in the non-convex optimisation problem of iterative learning control (ILC) are iteratively circumvented via approximation. This leads to a series of convex optimisation problems that can be solved offline to obtain the parameters of the rational feedforward controller. In addition, by limiting the number of offline iterations an experimentally intensive algorithm is derived, which could be beneficial in the case of severe model mismatch. A simulation study shows that the experimentally efficient approach converges fast through offline iterations and has improved convergence properties through the use of regularisation.

An analysis of the Crossbred Algorithm for the MQ Problem

The Crossbred algorithm is currently the state-of-the-art method for solving overdetermined multivariate polynomial systems over 𝔽 2 . Since its publication in 2017, several record breaking implementations have been proposed and demonstrate the power of this hybrid approach. Despite these practical results, the complexity of this algorithm and the choice of optimal parameters for it are difficult open questions. In this paper, we prove a bivariate generating series for potentially admissible parameters of the Crossbred algorithm.

Chebyshev subdivision and reduction methods for solving multivariable systems of equations

We present a new algorithm for finding isolated zeros of a system of real-valued functions in a bounded interval in Rn. It uses the Chebyshev proxy method combined with a mixture of subdivision, reduction methods, and elimination checks that leverage special properties of Chebyshev polynomials. We prove the method has quadratic convergence locally near simple zeros of the system. It also finds all nonsimple zeros, but convergence to those zeros is not guaranteed to be quadratic. We also analyze the arithmetic complexity and the numerical stability of the algorithm and provide numerical evidence in dimensions up to five that the method is both fast and accurate on a wide range of problems. Our tests show that the algorithm outperforms other standard methods on the problem of finding all real zeros in a bounded domain. Our Python implementation of the algorithm is publicly available at https://github.com/tylerjarvis/RootFinding.

Unraveling nitrogen-doped and vacancy-engineered synergistically modified molybdenum oxide promoting gallium selective adsorption

Sustainable recovery of strategic element gallium from wastewater carries great significance for economic development and environmental conservation. In this study, nitrogen-doped and vacancy-engineered synergistically modified molybdenum oxide nanowires (α-MoOx/N) were rationally designed for efficiently adsorbing gallium ions in the range of 1–200 mg/L under acidic conditions. The introduction of moderate amount of ethylenediamine induced the transition of α-MoOx to the amorphous state. Mixed-valence α-MoOx/N-0.53 (Mo(V) and Mo(VI)) with abundant active sites notably enhanced the adsorption kinetics of gallium ions, accompanied by 98.9 % of gallium ions being adsorbed within 60 min. Advantageously over most gallium adsorbents, α-MoOx/N-0.53 exhibited the maximum adsorption capacity of 464.8 mg/g (298 K), mainly attributed to the synergistic effect of electrostatic adsorption, ion exchange with H+ as well as surface complexation with Mo-O and pyridinic N. Self-enhanced adsorption mechanism and oxygen vacancies as gallium ion adsorption traps in α-MoOx/N-0.53 augmented the opportunities for capturing gallium ions. Excellent selective adsorption of gallium ions from binary and multivariate systems containing Zn2+, Al3+, Cu2+, Ni2+ and robust cyclic stability further endorse α-MoOx/N as the promising candidate for recovering gallium ions from complex wastewater.

HIV deathrate prediction by Gaidai multivariate risks assessment method.

HIV is a contagious disease with reportedly high transmissibility, being spread worldwide, with certain mortality, allegedly presenting a burden to public health worldwide. The main objective of this study was to determine excessive HIV death risks at any time within any region or country of interest. Current study presents a novel multivariate public health system bio-risk assessment approach that is particularly applicable to environmental multi-regional, biological, and public health systems, being observed over a representative period of time, yielding reliable long-term HIV deathrate assessment. Hence, the development of a new bio-statistical approach, that is, population-based, multicenter, and medical survey-based. The expansion of extreme value statistics from the univariate to the bivariate situation meets with numerous challenges. Firstly, the univariate extreme value types theorem cannot be directly extended to the bivariate (2D) case, - not to mention challenges with system dimensionality higher than 2D. Existing bio-statistical methods that process spatiotemporal clinical observations of multinational bio-processes often do not have the advantage of efficiently dealing with high regional dimensionalities and complex nonlinear inter-correlations between different national raw datasets. Hence, this study advocates the direct application of the novel bio-statistical Gaidai method to a raw unfiltered clinical data set. This investigation described the successful application of a novel bio-risk assessment approach, yielding reliable long-term HIV mortality risk assessments. The suggested risk assessment methodology may be utilized in various public bio and public health clinical applications based on available raw patient survey datasets.

Deep‐Learning Based Causal Inference: A Feasibility Study Based on Three Years of Tectonic‐Climate Data From Moxa Geodynamic Observatory

AbstractHighly sensitive laser strainmeters at Moxa Geodynamic Observatory (MGO) measure motions of the upper Earth's crust. Since the mountain overburden of the laser strainmeters installed in the gallery of the observatory is relatively low, the recorded time series are strongly influenced by local meteorological phenomena. To estimate the nonlinear effect of the meteorological variables on strain measurements in a non‐stationary environment, advanced methods capable of learning the nonlinearity and discovering causal relationships in the non‐stationary multivariate tectonic‐climate time series are needed. Methods for causal inference generally perform well in identifying linear causal relationships but often struggle to retrieve complex nonlinear causal structures prevalent in real‐world systems. This work presents a novel model invariance‐based causal discovery (CDMI) method that utilizes deep networks to model nonlinearity in a multivariate time series system. We propose to use the theoretically well‐established Knockoffs framework to generate in‐distribution, uncorrelated copies of the original data as interventional variables and test the model invariance for causal discovery. To deal with the non‐stationary behavior of the tectonic‐climate time series recorded at the MGO, we propose a regime identification approach that we apply before causal analysis to generate segments of time series that possess locally consistent statistical properties. First, we evaluate our method on synthetically generated time series by comparing it to other causal analysis methods. We then investigate the hypothesized effect of meteorological variables on strain measurements. Our approach outperforms other causality methods and provides meaningful insights into tectonic‐climate causal interactions.

A Data-Driven Predictive Control Method for Modeling Doubly-Fed Variable-Speed Pumped Storage Units

In this study, a data-driven model predictive control (MPC) method is proposed for the optimal control of a doubly-fed variable-speed pumped storage unit. This method combines modern control theory with the dynamic characteristics of the pumped storage unit to establish an accurate dynamic model based on actual operating data. In each control cycle, the MPC uses the system model to predict future system behavior and determines the optimal control input sequence by solving the constrained optimization problem, thereby effectively dealing with the nonlinearity, time-varying characteristics, and multivariable coupling problems of the system. When compared with a traditional PID control, this method significantly improves control accuracy, response speed, and system stability. The simulation results show that the proposed MPC method exhibits better steady-state error, overshoot, adjustment time, and control energy under various operating conditions, demonstrating its advantages in complex multivariable systems. This study provides an innovative solution for the efficient control of doubly-fed variable-speed pumped storage units and lays a solid foundation for the efficient utilization of new energy sources.

On the Elimination of Fast Variables from the Langevin Equation.

In a multivariable system, there are usually a number of relaxation times. When some of the relaxation times are shorter than others, the corresponding variables will decay to their equilibrium value faster than the others. After the fast variables have decayed, the system can be described with a smaller number of variables. From the theory of nonequilibrium thermodynamics, as formulated by Onsager, we know that the coefficients in the linear flux-force relations satisfy the so-called Onsager symmetry relations. The question we will address in this paper is how to eliminate the fast variables in such a way that the coefficients in the reduced description for the slow variables still satisfy the Onsager relations. As the proof that Onsager gave of the symmetry relations does not depend on the choice of the variables, it is equally valid for the subset of slow variables. Elimination procedures that lead to symmetry breaking are possible, but do not consider systems that satisfy the laws of nonequilibrium thermodynamics.

The E(G)TL Model: A Novel Approach for Efficient Data Handling and Extraction in Multivariate Systems

The E(G)TL Model: A Novel Approach for Efficient Data Handling and Extraction in Multivariate Systems

Multivariate VAR system of regional economic growth under big data

Traditional research has problems such as limited data samples, limited variable selection, and insufficient real-time analysis capabilities. With the advent of the big data era, researchers are increasingly using big data analysis to discover the laws of development. This paper combines the VAR system with big data analysis technology to study regional economic growth variables, simulate economic changes in region A, and use the Markov chain Monte Carlo algorithm and historical simulation method to analyze the process of industrial change. The model accuracy of the two algorithms is evaluated by the historical data observation loss value of the VAR post-test. The results show that at a confidence level of 0.95, the risk prediction of the historical simulation method is more accurate. The study also found that adding additional variables to the VAR system will lead to model information loss and an increase in parameters.

Optimizing multivariate alarm systems: A study on joint false alarm rate, and joint missed alarm rate using linear programming technique

In modern complex industrial systems, multiple process variables interact with one another. The role of alarm systems in ensuring the safety of these systems is of utmost importance. Consequently, there is an increasing value placed on the assessment of the performance of multivariate alarm systems. As the dimensions of the system and the number of variables grow, designing optimal parameters for the multivariate alarm system using traditional approaches such as probability density function estimation becomes increasingly convoluted. In this paper, an approximate method is proposed for calculating two indices known as the Joint False Alarm Rate (JFAR) and Joint Missed Alarm Rate (JMAR), which are used to evaluate the performance of multivariate alarm systems. These indices are computed using the multivariate Markov chain method. The Markov chain is constructed by solving an optimal Linear Programming (LP) problem. Subsequently, joint indices are defined based on steady state estimations of a multivariate Markov chain. To validate the theoretical results obtained on the JFAR and JMAR and to demonstrate the proposed performance assessment and alarm system design procedures, numerical example and an industrial case study are provided.

Statistical Identification of Independent Shocks with Kernel-based Maximum Likelihood Estimation and an Application to the Global Crude Oil Market

Independent component analysis has emerged as a promising approach for revealing structural relationships in multivariate dynamic systems, particularly in scenarios with limited knowledge of causal patterns. This article introduces a robust kernel-based maximum likelihood (KML) estimation method that accommodates the distributional characteristics of the structural sources of data variation. Our Monte Carlo study demonstrates the superior performance of the KML estimator compared to existing approaches for independence-based identification. Moreover, the proposed method enables partial identification and dimension reduction even in the presence of dependent shocks. We illustrate the benefits of our approach by applying it to the global oil market model of Kilian, highlighting its ability to capture unmodeled higher-order dependence between oil supply and speculative oil demand shocks.

Optimizing high energy density sulfur cathodes: A multivariate approach to electrode formulation and processing

Lithium-sulfur (Li-S) batteries involve complex solid-liquid-solid phase transformations during both discharging and charging processes, where cathode materials, formulation, and structure play a crucial role. Here, a design of experiments (DoE) methodology and an empirical model are developed to systematically explore the interactions and trade-offs among cathode factors and process variables, and to obtain generalizable effects estimates for the multivariate system. Compared to the conventional one-factor-at-a-time (OFAT) approach, this work demonstrates advantages in both efficiency and accuracy by allowing the data to guide future research and decisions. An optimized cathode formulation and processing parameters are predicted and validated experimentally, achieving over 1000 mAh g−1 in discharge capacity and improved cycling under practical lean electrolyte (4 µL mg−1 S) and high S-loading cathodes (>4 mg cm−2) conditions. The optimized cathode was scaled up and assembled into Li-S pouch cells, achieving 316 Wh kg−1 in cell-level energy, proving that the comprehensive and rigorous framework for optimizing complex systems with DoE leads to improved performance in a practical pouch cell system.

Enhancing HVAC multivariable system performance through hybrid modeling and direct Nyquist Array control

Enhancing HVAC multivariable system performance through hybrid modeling and direct Nyquist Array control

DBFact applied to minimum variance performance assessment for nonminimum phase multivariate systems from closed‐loop data

AbstractThis paper introduces an approach for determining a minimum variance control (MVC) benchmark for nonminimum phase (NMP) multi‐input multi‐output (MIMO) systems using closed‐loop operational data. The MVC benchmark is derived from the MVC law of DBFact factorization introduced by Lima, Trierweiler, and Farenzena. Unlike other factorization methods, DBFact offers advantages such as non‐iterative computation and ensuring internal stability of the MVC law. This approach considers the inherent directionality of NMP MIMO systems, enhancing the reliability of the control performance index. However, the original method relies on prior knowledge of the process model. To overcome this limitation, this paper proposes a method for calculating the MVC benchmark when prior knowledge is absent. It introduces a MIMO system identification strategy employing minimally invasive signal tests. The methodology is evaluated across various control conditions using a quadruple‐tank plant with additional time delays. The study emphasizes the importance of directionality in assessing MIMO system performance, particularly in evaluating individual loop performances. Results demonstrate the identification procedure's effectiveness in accurately calculating the proposed MVC benchmark, even with a mere 1% increase in output variance considered.

Risk factor analysis of medical litigation outcomes in obstetrics and gynecology: A retrospective cohort study of 344 claims in Japan

AimMedical errors are critical in obstetrics and gynecology (OB/GYN) and contribute to high litigation risks. However, few studies have examined system and diagnostic errors as potential preventable problems. This study aimed to enhance medical safety and reduce litigation by identifying and addressing key contributory factors. MethodsWe retrospectively searched the national Japanese malpractice claims database for OB/GYN cases between 1961 and 2017. We evaluated provider characteristics and background information of the patients (plaintiffs). The main outcome was litigation (acceptance or rejection) in the final judgment. Using multivariable logistic regression models, we assessed the associations between medical malpractice variables (system and diagnostic errors, facility size, situation, place, time, and clinical outcomes) and litigation outcomes (acceptance). ResultsOverall, 344 malpractice claims were analyzed. Among these, 277 (80.5 %) were obstetric, and 67 (19.5 %) were gynecological. Of the obstetric cases, 193 were perinatal, and 84 were maternal. Malpractice claims were accepted (OB-GYN losses) in 185 cases (53.8 %). In multivariable analyses, system errors (odds ratio 97.4, 95 % confidence interval 35.2–270.0), diagnostic errors (odds ratio 4.5, 95 % confidence interval 1.8–11.3), and clinic (odds ratio 2.7, 95 % confidence interval 1.2–4.8) had a significant statistical association with accepted claims. ConclusionSystem errors, diagnostic errors, and clinics were significantly associated with acceptance claims. These findings underscore the necessity of addressing modifiable factors at the physician level and within the healthcare management system to enhance patient safety and reduce litigation risks, thereby ensuring a safer and more reliable healthcare environment for patients and medical professionals.

Comparison Between Conventional PID Controller and Neural Network PID Controller Based on DC Motor Speed Control

DC motor is a multivariable, strong coupling and nonlinear controlled system, and is difficult to setting up the accurate mathematical model. So, it cannot achieve good control effect using traditional PID control method. To tackle this problem ANN based PID controller is proposed in this paper. The objective here is to compare the response of DC motor controlled by two different PID controllers.