Complex Parameters Research Articles

On numerical stability of continued fractions

The paper considers the numerical stability of the backward recurrence algorithm (BR-algorithm) for computing approximants of the continued fraction with complex elements. The new method establishes sufficient conditions for the numerical stability of this algorithm and the error bounds of the calculation of the $n$th approximant of the continued fraction with complex elements. It follows from the obtained conditions that the numerical stability of the algorithm depends not only on the rounding errors of the elements and errors of machine operations but also on the value sets and the element sets of the continued fraction. The obtained results were used to study the numerical stability of the BR-algorithm for computing the approximants of the continued fraction expansion of the ratio of Horn's confluent functions $\mathrm{H}_7$. Bidisc and bicardioid regions are established, which guarantee the numerical stability of the BR-algorithm. The obtained result is applied to the study of the numerical stability of computing approximants of the continued fraction expansion of the ratio of Horn's confluent function $\mathrm{H}_7$ with complex parameters. In addition, the analysis of the relative errors arising from the computation of approximants using the backward recurrence algorithm, the forward recurrence algorithm, and Lenz's algorithm is given. The method for studying the numerical stability of the BR-algorithm proposed in the paper can be used to study the numerical stability of the branched continued fraction expansions and numerical branched continued fractions with elements in angular and parabolic domains.

Variational Bayesian Estimation of Quantile Nonlinear Dynamic Latent Variable Models with Possible Nonignorable Missingness

Our study presents an innovative variational Bayesian parameter estimation method for the Quantile Nonlinear Dynamic Latent Variable Model (QNDLVM), particularly when dealing with missing data and nonparametric priors. This method addresses the computational inefficiencies associated with the traditional Markov chain Monte Carlo (MCMC) approach, which struggles with large datasets and high-dimensional parameters due to its prolonged computation times, slow convergence, and substantial memory consumption. By harnessing the deterministic variational Bayesian framework, we convert the complex parameter estimation into a more manageable deterministic optimization problem. This is achieved by leveraging the hierarchical structure of the QNDLVM and the principle of efficiently optimizing approximate posterior distributions within the variational Bayesian framework. We further optimize the evidence lower bound using the coordinate ascent algorithm. To specify propensity scores for missing data manifestations and covariates, we adopt logistic and probit models, respectively, with conditionally conjugate mean field variational Bayes for logistic models. Additionally, we utilize Bayesian local influence to analyze the Ecological Momentary Assessment (EMA) dataset. Our results highlight the variational Bayesian approach’s notable accuracy and its ability to significantly alleviate computational demands, as demonstrated through simulation studies and practical applications.

A Novel Hybrid Approach for Global Maximum Power Point Tracking in Standalone PV Systems

The efficiency of Photo-Voltaic (PV) systems is highly dependent on their ability to accurately track the Global Maximum Power Point (GMPP) under varying environmental conditions. Traditional Maximum Power Point Tracking (MPPT) methods often struggle with issues such as slow tracking speed, susceptibility to local maxima, and the need for complex parameter tuning, particularly in dynamically changing environments with Partial Shading Conditions (PSCs) and rapid irradiation changes. To address these challenges, this study introduces a hybrid approach that combines a modified Rao algorithm with the Perturb and Observe (P&O) method. The modified Rao algorithm was employed in the initial tracking stages to quickly locate the global vicinity, benefiting from its simplicity and the absence of algorithm-specific parameters, whereas the P&O method ensured precise tracking in the final stages. The performance of the proposed method was assessed on a PV array subjected to PSCs and compared with several well-known MPPT algorithms, such as Gray Wolf Optimization (GWO), JayaDE, and the Slime Mould Algorithm (SMO). The proposed approach was implemented and analyzed using the MATLAB/Simulink software.

Computational thrombosis modeling based on multiphase porous media theory for prognostic evaluation of aortic dissection after stenting

Accurately and rapidly predicting the occurrence and progression of false lumen thrombosis in patients undergoing thoracic endovascular aortic repair (TEVAR) is crucial for optimizing patient recovery. Traditional models for predicting false lumen thrombosis often lack the ability to capture phase interface changes, and their complex parameters and algorithms result in a long computation time. This study introduces a multiphase porous media approach that can accurately and rapidly predict thrombus formation in aortic dissection patients at different postoperative stages. The approach employed the Darcy–Brinkman–Stokes equation to model the interaction between the thrombotic and fluid phases and incorporated a novel porosity equation to explicitly capture phase interface dynamics. Additionally, the hemodynamic parameters associated with thrombus formation were updated to enhance the physical accuracy of the algorithm while reducing its computational complexity. Using patient-specific models derived from computed tomography angiography datasets, our algorithm demonstrated excellent predictive performance in real patients. The predicted thrombus morphology in the third and sixth months postoperatively closely matched the actual imaging data, with discrepancies in thrombus volume remaining within a ±10% range at each postoperative stage. Moreover, the algorithm significantly improved computational convergence, reducing the computation time to 30 minutes and enhancing the computational efficiency by 80% compared to traditional methods. By integrating the porous media framework, this approach offers a valuable tool for rapid clinical diagnosis and the prediction of post-TEVAR recovery.

Enhancing crop yield and carbon sequestration and greenhouse gas emission mitigation through different organic matter input in the Bohai Rim region: An estimation based on the DNDC-RF framework

ContextComprehending the intricacies of crop growth and its impact on greenhouse gas (GHG) emissions is crucial for food security and agricultural resilience to climate change. Research questionAgroecosystem models are instrumental in this endeavor, yet their regional applicability remains constrained. MethodsIn our study, we conducted a rigorous verification of the DNDC (DeNitrification-DeComposition) model across eight representative sites in the Bohai Rim region and determined its efficacy in accurately simulating crop yield, soil organic carbon (SOC), and nitrous oxide (N2O) emissions. We developed a coupled framework, DNDC-RF (DeNitrification-DeComposition-Random Forest), using the RF algorithm in conjunction with DNDC simulation results across fertilization and climate scenarios. Employing the DNDC-RF, we quantitatively evaluated the impact of diverse fertilization strategies on yield and net GHG (including SOC and N2O emissions) under future climate scenarios, spanning the period from 2008 to 2100. ResultsThe DNDC-RF framework accurately predicts SOC, yield, and N2O with high R2 and LCCC, lower RMSE and MAE. Under the RCP4.5 scenario, spring maize yields exhibited a reduction under conventional fertilization measures. However, with organic matters input could achieve the yield increase, particularly additional manure input (9.6 kg C ha−1 yr−1). Summer maize yields were projected to increase under future climate change, with the fastest increase occurring under the RCP8.5 scenario with additional manure input (26 kg C ha−1 yr−1). Wheat yields also increased under future climate change, with the highest growth rate observed with straw return under the RCP8.5 (17.1 kg C ha−1 yr−1). Under different fertilization practices, spring maize fields exhibited a net GHG sink. The best performance was observed with additional manure input and straw return under RCP4.5 and RCP8.5, respectively. In contrast, conventional fertilization in winter wheat-summer maize fields resulted in a net GHG source under both RCP4.5 and RCP8.5. However, the application of organic matter mitigated the net GHG emissions, with additional manure input resulting in the largest increase rate of the net GHG sink. ConclusionsDNDC-RF framework can quickly and effectively solve the difficulties of DNDC model in regional scale prediction (such as complex parameter setting, difficult to accurately and quickly simulate at regional scale and time series), and can accurately simulate regional crop yield, SOC change and N2O emission. With the input of organic matter, the projected yields of maize and wheat are expected to increase, and the field’s ability to act as a net GHG sink could be enhanced. SignificanceOur findings have important scientific significance and practical value for promoting the sustainable development of regional agriculture and formulating effective regional agricultural management measures.

Resilient fast convolutional sparse filtering with convergence directivity for the bearing fault diagnosis

The fast nonlinear convolutional sparse filtering (FNCSF), which detects fault features 42 h earlier than traditional methods in the intelligent maintenance system dataset and takes only 0.12 s, is widely considered a powerful tool for early fault diagnosis. However, random shocks caused by the structure or external interference pose challenges to the extraction accuracy of FNCSF. In addition, the extraction reliability of FNCSF is affected by computational instability and complex parameter settings. To address the above defects, resilient fast convolutional sparse filtering (RFCSF) is proposed in this study. First, the collected vibration signal is normalized by Z-score to eliminate the scale variability of the nonlinear transformation. Then, the frequency components of the signal are evenly divided by the initialized filters to indicate the convergence direction of fault and improve random shock resistance and extraction stability. Next, the nonlinear [Formula: see text] norm, which can effectively distinguish fault features from irrelevant disturbances, is regarded as the target of blind deconvolution. In the process of deconvolution, the filter converging to random shocks and noise is adaptively eliminated to improve the extraction efficiency and intelligence. Finally, the filtered signal is envelope demodulated to obtain fault information. In the simulation analysis, features under noise with −16 dB and random shocks with 50 m/s2 are accurately extracted by RFCSF with parameters robustness. Several experimental cases demonstrate that RFCSF with these advantages is a promising feature extraction tool.

Flow-augmentation I: Directed graphs

We show a flow-augmentation algorithm in directed graphs: There exists a randomized polynomial-time algorithm that, given a directed graph G , two vertices s , t ∈ V ( G ), and an integer k , adds (randomly) to G a number of arcs such that for every minimal st -cut Z in G of size at most k , with probability 2 − poly( k ) the set Z becomes a minimum st -cut in the resulting graph. We also provide a deterministic counterpart of this procedure. The directed flow-augmentation tool allows us to prove fixed-parameter tractability of a number of problems parameterized by the cardinality of the deletion set whose parameterized complexity status was repeatedly posed as open problems: (1) Chain SAT , defined by Chitnis, Egri, and Marx [ESA’13, Algorithmica’17], (2) a number of weighted variants of classic directed cut problems, such as Weighted st -Cut or Weighted Directed Feedback Vertex Set . By proving that Chain SAT is FPT, we confirm a conjecture of Chitnis, Egri, and Marx that, for any graph H , if the List H -Coloring problem is polynomial-time solvable, then the corresponding vertex-deletion problem is fixed-parameter tractable.

Adaptive pruning-based Newton's method for distributed learning

Newton's method leverages curvature information to boost performance, and thus outperforms first-order methods for distributed learning problems. However, Newton's method is not practical in large-scale and heterogeneous learning environments, due to obstacles such as high computation and communication costs of the Hessian matrix, sub-model diversity, staleness of training, and data heterogeneity. To overcome these obstacles, this paper presents a novel and efficient algorithm named Distributed Adaptive Newton Learning (DANL), which solves the drawbacks of Newton's method by using a simple Hessian initialization and adaptive allocation of training regions. The algorithm exhibits remarkable convergence properties, which are rigorously examined under standard assumptions in stochastic optimization. The theoretical analysis proves that DANL attains a linear convergence rate while efficiently adapting to available resources and keeping high efficiency. Furthermore, DANL shows notable independence from the condition number of the problem and removes the necessity for complex parameter tuning. Experiments demonstrate that DANL achieves linear convergence with efficient communication and strong performance across different datasets.

On the Activation Energy of Termination in Radical Polymerization, as Studied at Low Conversion.

The chain-length-dependent nature of the termination reaction in radical polymerization (RP) renders the overall termination rate coefficient, <kt>, a complex parameter in the usual situation where the radical chain-length distribution is non-uniform. This applies also for the activation energy of termination, Ea(<kt>), which we subject to detailed mechanistic investigation for the first time. The experimental side of this work measures Ea(<kt>) for the dilute-solution, low-conversion, chemically initiated homopolymerization of styrene (ST), methyl methacrylate (MMA), butyl methacrylate, and dodecyl methacrylate. Values of 25-39 kJ mol-1 are obtained, consistent with strong chain-length-dependent termination (CLDT) for short chains. On other hand, the reanalysis of analogous bulk polymerization data for ST and MMA finds Ea(<kt>) values of 18-24 kJ mol-1, consistent with weak CLDT for long chains. Both these results are as expected from the so-called composite model for CLDT. A simple analytic framework for understanding and predicting Ea(<kt>) values is presented for the standard RP situation of continuous initiation. All the results of this work can be rationalized via this framework, which clearly establishes that Ea(<kt>) is determined by far more than just the Ea of radical diffusion. This framework is extended to activation energy for the number-average degree of polymerization, Ea(DPn), which we measure and successfully scrutinize via our CLDT model. In the final section of this work, we make interesting, testable predictions about Ea(<kt>) and/or Ea(DPn) in various RP systems of different natures to those studied here, most notably, systems involving acrylates, continuous photoinitiation, or dominant chain transfer.

Nonstationary Control Parameter Prediction for Underwater Gliders Utilizing an Innovative Transformer-Based Model

As a new type of unmanned autonomous marine observation platform, underwater gliders (UGs) offer advantages such as low energy consumption and long operational ranges. However, during the gliding process, the complex marine environment often leads to abrupt changes in short-term control parameters, complicating the data and rendering them more challenging to predict. This typically poses difficulties in adjusting control parameters based on human experience, thereby significantly reducing UG control efficiency. To address this issue, this paper proposes a novel method termed DFFormer, aimed at enhancing the predictive accuracy of the rudder angles during UG motion. The proposed method integrates discrete wavelet transform (DWT) for rudder angle signal decomposition and employs a fast Fourier transform-based attention mechanism (FFT-Attention) to effectively capture and analyze its frequency- and time-domain characteristics. Notably, the method leverages a Transformer architecture to process the decomposed signals through multiple parallel pathways, substantially improving the capability to forecast the complex and variable control parameters of UGs. The effectiveness and practicality of the proposed method are demonstrated through actual sea trials. The experimental results indicate that the proposed method surpasses traditional approaches in terms of accuracy and computational efficiency, exhibiting superior performance in predicting UG control parameters and, to some extent, enhancing their heading-keeping ability.

Automatic Modulation Recognition Based on Multimodal Information Processing: A New Approach and Application

Automatic modulation recognition (AMR) has wide applications in the fields of wireless communications, radar systems, and intelligent sensor networks. The existing deep learning-based modulation recognition models often focus on temporal features while overlooking the interrelations and spatio-temporal relationships among different types of signals. To overcome these limitations, a hybrid neural network based on a multimodal parallel structure, called the multimodal parallel hybrid neural network (MPHNN), is proposed to improve the recognition accuracy. The algorithm first preprocesses the data by parallelly processing the multimodal forms of the modulated signals before inputting them into the network. Subsequently, by combining Convolutional Neural Networks (CNN) and Bidirectional Gated Recurrent Unit (Bi-GRU) models, the CNN is used to extract spatial features of the received signals, while the Bi-GRU transmits previous state information of the time series to the current state to capture temporal features. Finally, the Convolutional Block Attention Module (CBAM) and Multi-Head Self-Attention (MHSA) are introduced as two attention mechanisms to handle the temporal and spatial correlations of the signals through an attention fusion mechanism, achieving the calibration of the signal feature maps. The effectiveness of this method is validated using various datasets, with the experimental results demonstrating that the proposed approach can fully utilize the information of multimodal signals. The experimental results show that the recognition accuracy of MPHNN on multiple datasets reaches 93.1%, and it has lower computational complexity and fewer parameters than other models.

Revisiting model complexity: Space-time correction of high dimensional variable sets in climate model simulations

Multivariate bias correction (BC) models are well-known to correct more statistical attributes in climate model simulations. However, their inherent complexity and excessive parameters can introduce higher uncertainty into future climate simulations. In contrast, univariate BC models, with fewer parameters, are limited to correcting certain attributes. An issue that has not been investigated in-depth is the impact ofan increased number of variables in the multivariate BC has on the bias-corrected climate models’ stability. This study compares the performance of a multivariate BC approach, Multivariate Recursive Nested Bias Correction (MRNBC), and a univariate BC approach, Continuous Wavelet-based Bias Correction (CWBC), as the number of variables to be corrected increases, known as the “curse of dimensionality” (CoD). The analysis uses high-resolution climate model outputs for both current and future simulations of sea surface temperature and precipitation in the Niño 3.4 region. Results show both BC models effectively correct current climate biases. As the number of variables increases, CWBC remains robust and produces sensible future simulations, while MRNBC’s complexity leads to deterioration in standard deviations and spatial cross-correlation. CWBC, based on univariate correction, isrelatively unaffected by the CoD.

Material design-for-X: A decision-making tool applied for high-performance applications

As the need for enhanced material performance continues to escalate in several sectors, addressing complex parameters such as economic feasibility, ease of manufacturing, and production volume, rises the need for multi-domain decision-making tools. In order to explore and streamline this process, this study employed the novel Material Design-for-eXcellence methodology to investigate polymer material selection in aeronautical and power transformer components, using additive manufacturing. The study assessed the X’s selected (mechanical, thermal, physical, cost, dielectric, and environmental) by assigning weights to these factors, and identifying the optimal materials for each application. In the aeronautical context, PEI+GF30 was chosen as the best solution, attaining an overall effectiveness of 79 %, primarily due to its exceptional mechanical characteristics. The use of a thermoplastic can lead to lighter components while ensuring the same technical performance, enabling longer flight duration. Conversely, in the energy sector for power transformers, PSU obtained a 78 % score, largely attributable to its outstanding dielectric properties. The application of additive methods on transformers’ insulating parts leads to optimized channels for the mineral oil, enhancing its thermal and dielectric performance. The obtained results underscored the importance of tailored material selection approaches, adjusted to specific application requirements. The importance of comprehending and adapting to diverse contexts for effective material design and implementation is also highlighted.

Fast parameter optimization for high-fidelity crystal plasticity simulation using active learning

Crystal plasticity (CP) simulation is a powerful tool for studying and understanding the mechanical behavior of materials. A critical aspect of this method is the accurate determination of CP parameters, which ensures that the constitutive model accurately represents the real deformation behavior of a material, especially in high-fidelity simulations. However, identifying these parameters poses a significant challenge due to the high computational cost and the difficulty of finding optimal solutions within a vast and complex parameter space. To address these challenges, we propose a fast search strategy that leverages active learning (AL) and experimental data to accelerate the optimization of CP parameters. Using the Al-Cu eutectic materials as a case study, we introduced a quantitative index, C ecp, to measure the consistency between simulated and experimental stress-strain curves. We demonstrated that Gaussian process regression (GPR) serves as the most appropriate surrogate model for relating CP parameters and C ecp based on our dataset. After only six iterations guided by AL, the optimal CP parameters were successfully identified, resulting in a high-fidelity CP model for analyzing the mechanical behavior of Al-Cu eutectic materials. The machine learning-enhanced strategy is far superior to traditional methods in terms of both efficiency and accuracy. It advances our understanding of the macro-micro relationships of materials and accelerates the material design process.

On MAX–SAT with cardinality constraint

We consider the weighted MAX–SAT problem with an additional constraint that at mostk variables can be set to true. We call this problem k–WMAX–SAT. This problem admits a (1−1e)-factor approximation algorithm in polynomial time [Sviridenko, Algorithmica (2001)] and it is proved that there is no (1−1e+ϵ)-factor approximation algorithm in f(k)⋅no(k) time for Maximum Coverage, the unweighted monotone version of k–WMAX–SAT [Manurangsi, SODA 2020]. Therefore, we study two restricted versions of the problem in the realm of parameterized complexity.1.When the input is an unweighted 2–CNF formula (the problem is called k–MAX–2SAT), we design an efficient polynomial-size approximate kernelization scheme. That is, we design a polynomial-time algorithm that given a 2–CNF formula ψ and ϵ>0, compresses the input instance to a 2–CNF formula ψ⋆ such that any c-approximate solution of ψ⋆ can be converted to a c(1−ϵ)-approximate solution of ψ in polynomial time.2.When the input is a planar CNF formula, i.e., the variable-clause incidence graph is a planar graph, we show the following results:•There is an FPT algorithm for k–WMAX–SAT on planar CNF formulas that runs in 2O(k)⋅(C+V) time.•There is a polynomial-time approximation scheme for k–WMAX–SAT on planar CNF formulas that runs in time 2O(1ϵ)⋅k⋅(C+V). The above-mentioned C and V are the number of clauses and variables of the input formula respectively.

Statistical-based modeling strategy for entrance skin dose estimation in patient undergoing body interventional radiology.

Interventional radiology (IR) provides significant advancements in diagnostic and therapeutic procedures, yet concerns persist regarding radiological risks such as erythema, burns, and epilation. Direct dose measurements observed difficulties regarding the perturbation of the detector probe in X-ray images during fluoroscopy-guided procedures, high-cost expenses, and non-compliant patients. This study aims to develop a statistical-based model for estimating entrance skin dose (ESD) in body IR procedures using patient radiation-dose recording data. Models are categorized into vascular and non-vascular procedures. This study demonstrates that the simplified models are sufficient in estimating patient ESDs for both IR groups, with a 95% confidence interval. This user-friendly method enables radiologists to calculate doses without complex parameters such as the backscatter factor and mass-energy absorption coefficient, as required in conventional calculation methods. It not only does this support to radiologists in effectively refining treatment protocols, but also enables patients to monitor their received doses immediately after treatment ends.

The parameterized complexity of the survivable network design problem

In the well-known Survivable Network Design Problem (SNDP), we are given an undirected graph G with edge costs, a set R of terminal vertices, and an integer demand ds,t for every terminal pair s,t∈R. The task is to compute a subgraph H of G of minimum cost, such that for every terminal pair s,t∈R there are at least ds,t disjoint paths between s and t in H. Depending on the type of disjointness, we obtain several variants of SNDP that have been widely studied in the literature: if the paths are required to be edge-disjoint we obtain EC-SNDP, while if they must be internally vertex-disjoint we obtain VC-SNDP. Another important case is the element-connectivity variant (LC-SNDP), where the paths must be disjoint on edges and non-terminals, i.e., they may only share terminals. In this work we shed light on the parameterized complexity of the above problems. We consider several natural parameters, which include the solution size ℓ, the sum of demands D, the number of terminals k, and the maximum demand dmax.

Determination of the kinetic parameters of complex condensed phase reactions using a nonlinear model

This research introduces a novel nonlinear model that can be used in the modified Friedman method to determine activation energy via linear regression with a trial-and-error approach. Its application in a simulated reaction enhanced precision in activation energy determination and accurately captured the trend in activation energy variation with temperature compared to quadratic regression. The nonlinear model can also predict nonlinearity in compensation effect relationships, aiding in the assessment of pre-exponential factor, rate constant, and conversion function in complex reactions, ensuring more precise results compared to linear model. By incorporating random noise into the simulated reaction’s isoconversional kinetic data, which follows a normal distribution, we observed that both nonlinear and quadratic regressions produce comparable activation energy values. However, the nonlinear compensation effect approach yields more precise results for the pre-exponential factor, rate constant, and conversion function compared to the linear model in the presence of random errors. The novel approach based on the nonlinear model was applied, in conjunction with the linear and quadratic Friedman methods featuring linear compensation effect, to compute the kinetic parameters of a polymer coating on a commercial optical fiber as well as a polyethylene. Gnu Octave/MATLAB codes were also made available for estimating the kinetic parameters of complex reactions exhibiting a single peak in reaction rate curves using the linear, quadratic, and nonlinear Friedman methods, along with the application of linear and nonlinear compensation effects. These codes can be customized by users to estimate the kinetic parameters of their own kinetic data.

Research on lane detection algorithms based on GTNs

Abstract. Lane detection technology plays an important role in the lane departure warning and adaptive cruise control functions of autonomous vehicle systems. Traditional lane line detection includes experimental steps such as preyreatment, color space conversion, feature extraction, and lane line tracking, but there are still some problems such as recognition accuracy in complex environments and parameter adjustment dependency. To overcome these limitations, this study uses a novel method that can directly predict the parameters of the lane shape model, thus avoiding complex post-processing steps. This research method uses the network structure based on Graph Transformer Networks (GTNS) to capture richer structural information and contextual relationships, thereby improving the accuracy of detection. In terms of feature extraction, Graph Transformer Networks is used to accurately capture the structural information of the lane through the attention mechanism. At the same time, the results in the later stage show that our method has better advantages in accuracy and speed. In short, this optimization scheme not only improves the detection speed but also ensures a certain degree of accuracy. The method will perform better in the future after further optimization such as multi-sensor fusion and real-time optimization.

On the Analytic Continuation of Appell’s Hypergeometric Function F2 to Some Symmetric Domains in the Space C2

The paper considers the problem of representation and extension of Appell’s hypergeometric functions by a special family of functions—branched continued fractions. Here, we establish new symmetric domains of the analytical continuation of Appell’s hypergeometric function F2 with real and complex parameters, using their branched continued fraction expansions whose elements are polynomials in the space C2. To do this, we used a technique that extends the domain of convergence of the branched continued fraction, which is already known for a small domain, to a larger domain, as well as the PC method to prove that it is also the domain of analytical continuation. A few examples are provided at the end to illustrate this.