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20 pages, 7789 KB

Open AccessArticle

Simulation and Analysis of the Second-Order Memristive System in the CUDAynamics Suite

by Alexander Khanov, Maksim Gozhan, Denis Butusov, Yulia Bobrova and Valerii Ostrovskii

Algorithms 2026, 19(5), 402; https://doi.org/10.3390/a19050402 - 17 May 2026

Viewed by 247

Cycle-to-cycle variability of switching parameters inherent to memristive devices introduces significant problems in the design of neuromorphic systems and non-volatile memory. This study investigates the dynamics of a second-order memristive system incorporating capacitive effects that model parasitic charge within individual memristors, addressing both [...] Read more.

Cycle-to-cycle variability of switching parameters inherent to memristive devices introduces significant problems in the design of neuromorphic systems and non-volatile memory. This study investigates the dynamics of a second-order memristive system incorporating capacitive effects that model parasitic charge within individual memristors, addressing both the technical need for accurate analysis of complex regimes and the demand for exploratory environments. Simulations were performed using CUDAynamics, an interactive software suite developed by the authors, which utilizes parallel computing, primarily via NVIDIA Compute Unified Device Architecture (CUDA). It integrates multiple analysis tools for dynamical systems, including bifurcation diagrams, the largest Lyapunov exponent and periodicity mapping, and interactive navigation in multidimensional parameter spaces. The memristive system was discretized applying multiple integration methods with a fixed time step and various waveforms of the input signal. Analysis tools revealed well-defined regions of chaotic dynamics in the memristor resistance parameter space as functions of input signal properties. Sinusoidal and triangular waveforms produced topologically similar distributions of dynamical regimes, whereas the square waveform, mimicking digital inputs, generated distinct dynamical patterns while still preserving chaotic trajectories under specific conditions. Interactive visualization capabilities of CUDAynamics effectively demonstrate attractor evolution and hysteresis deformation, providing immediate visual feedback that significantly enhances conceptual comprehension of nonlinear feedback mechanisms. Beyond its practical implications for the design of analog and digital memristive devices, CUDAynamics offers a scalable, open-source toolkit to aid researchers and engineers in exploring complex dynamical phenomena. Full article

(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)

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13 pages, 43480 KB

Open AccessArticle

Perturbation of Highly Dispersive Solitons in Optical Metamaterials with Twin-Core Couplers and Power-Law of Self-Phase Modulation by Laplace–Adomian Decomposition

by Oswaldo González-Gaxiola, Jehan Saleh Ahmed, Lina S. Calucag and Anjan Biswas

Algorithms 2026, 19(5), 342; https://doi.org/10.3390/a19050342 - 29 Apr 2026

Viewed by 289

Abstract

This paper utilizes the Laplace–Adomian decomposition method to numerically investigate the highly dispersive bright soliton solutions in twin-core optical couplers that employ metamaterials as waveguides. The focus of the study is on the power-law self-phase modulation. The results of the simulations and the [...] Read more.

This paper utilizes the Laplace–Adomian decomposition method to numerically investigate the highly dispersive bright soliton solutions in twin-core optical couplers that employ metamaterials as waveguides. The focus of the study is on the power-law self-phase modulation. The results of the simulations and the accompanying error analysis demonstrate exceptional accuracy for this numerical approach. These findings suggest that the Laplace–Adomian decomposition method is a robust tool for tackling complex nonlinear problems in optical systems. Furthermore, the implications of this research could pave the way for advancements in the design and optimization of metamaterial-based waveguides, potentially leading to improved performance in applications, such as telecommunications and sensing technologies. Full article

(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)

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28 pages, 2251 KB

Open AccessArticle

Hierarchical Continuous Monitoring and Resource Reallocation Under Resistance to Change: A Decision-Making Framework Balancing Skill Constraints and Managerial Capacity

by Fotios Panagiotopoulos and Vassilios Chatzis

Algorithms 2026, 19(4), 293; https://doi.org/10.3390/a19040293 - 9 Apr 2026

Viewed by 354

Abstract

Organizational change is a complex process often accompanied by intense human reactions and increased uncertainty. Resistance to change (RtC) can cause critical performance declines during the organizational change period, which can delay implementation. The evolution of information systems and digital infrastructures provides immediate [...] Read more.

Organizational change is a complex process often accompanied by intense human reactions and increased uncertainty. Resistance to change (RtC) can cause critical performance declines during the organizational change period, which can delay implementation. The evolution of information systems and digital infrastructures provides immediate access to operational data and analytical tools, making it possible to continuously monitor performance and timely adjust decisions during change. Although recent approaches attempt to minimize these impacts through continuous monitoring and resource reallocation, they typically view human resource allocation as a single-level problem. In hierarchical structures where work and decision-making are distributed across levels, RtC can increase backlogs, place an excessive amount of work on managers, and result in operational issues or the failure of the change. From an algorithmic perspective, the proposed method formulates a hierarchical dynamic optimization problem with two coupled assignment layers, in which the operational output of Level 1 dynamically determines the workload processed at Level 2. Both assignment problems are solved at each time step using the Hungarian algorithm, while RtC is modelled as a time-dependent stochastic process aligned with a reference change curve, allowing employee and managerial performance to be updated dynamically over the planning horizon. In contrast to static Classical Change Management Model (CCMM), large-scale experimental results demonstrate that the new approach increases total processed workload by approximately 20%, while at the peak of resistance, the improvement reaches 56.8%. At the same time, it substantially reduces backlog accumulation, maintaining very low backlog levels (18 versus 16,424 units) within the tested setting. Finally, by applying a 50% reallocation threshold, the organization maintains 98.5% of maximum performance while avoiding 45% of the reallocations. Overall, the proposed method provides a dynamic optimization framework that combines hierarchical organizational modeling with stochastic performance updates across organizational levels. Full article

(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)

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16 pages, 326 KB

Open AccessArticle

An Explanatory CDF Manifold Algorithm for Large Telecom Datasets

by Vladislav Vasilev and Georgi Iliev

Algorithms 2026, 19(4), 269; https://doi.org/10.3390/a19040269 - 1 Apr 2026

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Abstract

In this paper we introduce the CDF manifold algorithm, which operates on datasets where a single target dimension is strictly increasing given a minimum of two or more input dimensions, which is very common in telco data. The manifold can then be used [...] Read more.

In this paper we introduce the CDF manifold algorithm, which operates on datasets where a single target dimension is strictly increasing given a minimum of two or more input dimensions, which is very common in telco data. The manifold can then be used to compute the closest upper and lower limits to a given new point, as well as its CDF. Training takes

O (n . ln [n])

steps in the best case and

O (n^{3 / 2})

in the worst case. Lookup takes

O (l n [n])

steps in the best case and

O (n^{1 / 2} ln (n))

in the worst case. The asymptotic computational cost is proven with a theorem. We compare our manifold method versus a standard dense neural network and show the asymptotic advantages both in terms of speed and accuracy. We also address potential speed gains through the use of reference points. In summary, the manifold is a non-parametric explanatory method to find the tightest data-driven upper and lower limits of the output dimension given a new unseen input. This makes it ideal for planning new site deployments where we need to find actual measurements as a baseline performance. Full article

(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)

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19 pages, 707 KB

Open AccessArticle

Performance Analysis of Half-Hyperbolic Convolution (HHC)-Type Operators via Regression-Based Metrics

by George A. Anastassiou, Seda Karateke and Metin Zontul

Algorithms 2026, 19(3), 217; https://doi.org/10.3390/a19030217 - 13 Mar 2026

Cited by 1 | Viewed by 425

Abstract

In this paper, we first introduce the adjustable half-hyperbolic (adj HH) tangent function as an activation function. We then establish both quantitative and qualitative convergence results for HH-activated convolution-type positive linear operators (PLOs) acting on the space of bounded and continuous functions on [...] Read more.

In this paper, we first introduce the adjustable half-hyperbolic (adj HH) tangent function as an activation function. We then establish both quantitative and qualitative convergence results for HH-activated convolution-type positive linear operators (PLOs) acting on the space of bounded and continuous functions on the real line. The theoretical convergence results are numerically validated by means of error decay plots obtained using Python (version 3.13). Moreover, we compare three different classes of HHC-type operators in terms of their convergence behavior and approximation performance. Finally, we conclude by discussing several potential application areas that illustrate the relevance of the presented theoretical framework. Full article

(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)

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21 pages, 5112 KB

Open AccessArticle

A Scalable Framework with Modified Loop-Based Multi-Initial Simulation and Numerical Algorithm for Classifying Brain-Inspired Nonlinear Dynamics with Stability Analysis

by Haseeba Sajjad, Adil Jhangeer and Lubomír Říha

Algorithms 2025, 18(12), 805; https://doi.org/10.3390/a18120805 - 18 Dec 2025

Viewed by 536

Abstract

The principal problem with the analysis of nonlinear dynamical systems is that it is repetitive and inefficient to simulate every initial condition and parameter configuration individually. This not only raises the cost of computation but also constrains scalability in the exploration of a [...] Read more.

The principal problem with the analysis of nonlinear dynamical systems is that it is repetitive and inefficient to simulate every initial condition and parameter configuration individually. This not only raises the cost of computation but also constrains scalability in the exploration of a large parameter space. To solve this, we restructured and extended the computational framework so that variation in the parameters and initial conditions can be automatically explored in a unified structure. This strategy is implemented in the brain-inspired nonlinear dynamical model that has three parameters and multiple coupling strengths. The framework enables detailed categorization of the system responses through statistical analysis and through eigenvalue-based assessment of the stability by considering multiple initial states of the system. These results reveal clear differences between periodic, divergent, and non-divergent behavior and show the extent to which the strength of the coupling

k_{i j}

can drive transitions to stable periodic behavior under all conditions examined. This method makes the analysis process easier, less redundant, and provides a scalable tool to study nonlinear dynamics. In addition to its computational benefits, the framework provides a general method that can be generalized to models with more parameters or more complicated network structures. Full article

(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)

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23 pages, 1181 KB

Open AccessArticle

Robust Regularized Recursive Least-Squares Algorithm Based on Third-Order Tensor Decomposition

by Radu-Andrei Otopeleanu, Constantin Paleologu, Jacob Benesty, Cristian-Lucian Stanciu, Laura-Maria Dogariu and Ruxandra-Liana Costea

Algorithms 2025, 18(12), 768; https://doi.org/10.3390/a18120768 - 5 Dec 2025

Viewed by 654

Abstract

The decomposition-based adaptive filtering algorithms have recently gained increasing interest due to their capability to reduce the parameter space. In this context, the third-order tensor (TOT) decomposition technique reformulates the conventional approach that involves a single (usually long) adaptive filter by using a [...] Read more.

The decomposition-based adaptive filtering algorithms have recently gained increasing interest due to their capability to reduce the parameter space. In this context, the third-order tensor (TOT) decomposition technique reformulates the conventional approach that involves a single (usually long) adaptive filter by using a combination of three shorter filters via the Kronecker product. This leads to a twofold gain in terms of both performance and complexity. Thus, it can be applied efficiently when operating with more complex algorithms, like the recursive least-squares (RLS) approach. In this paper, we develop an RLS-TOT algorithm with improved robustness features due to a novel regularization method that considers the contribution of the external noise and the so-called model uncertainties (which are related to the system). Simulation results obtained in the framework of echo cancelation support the performance of the proposed algorithm, which outperforms the existing RLS-TOT counterparts, as well as the conventional RLS algorithm that uses the specific regularization technique. Full article

(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)

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42 pages, 3632 KB

Open AccessArticle

Logistic Biplots for Ordinal Variables Based on Alternating Gradient Descent on the Cumulative Probabilities, with an Application to Survey Data

by Julio C. Hernández-Sánchez, Laura Vicente-González, Elisa Frutos-Bernal and José L. Vicente-Villardón

Algorithms 2025, 18(11), 718; https://doi.org/10.3390/a18110718 - 14 Nov 2025

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Abstract

Biplot methods provide a framework for the simultaneous graphical representation of both rows and columns of a data matrix. Classical biplots were originally developed for continuous data in conjunction with principal component analysis (PCA). In recent years, several extensions have been proposed for [...] Read more.

Biplot methods provide a framework for the simultaneous graphical representation of both rows and columns of a data matrix. Classical biplots were originally developed for continuous data in conjunction with principal component analysis (PCA). In recent years, several extensions have been proposed for binary and nominal data. These variants, referred to as logistic biplots (LBs), are based on logistic rather than linear response models. However, existing formulations remain insufficient for analyzing ordinal data, which are common in many social and behavioral research contexts. In this study, we extend the biplot methodology to ordinal data and introduce the ordinal logistic biplot (OLB). The proposed method estimates row scores that generate ordinal logistic responses along latent dimensions, whereas column parameters define logistic response surfaces. When these surfaces are projected onto the space defined by the row scores, they form a linear biplot representation. The model is based on a framework, leading to a multidimensional structure analogous to the graded response model used in Item Response Theory (IRT). We further examine the geometric properties of this representation and develop computational algorithms—based on an alternating gradient descent procedure—for parameter estimation and computation of prediction directions to facilitate visualization. The OLB method can be viewed as an extension of multidimensional IRT models, incorporating a graphical representation that enhances interpretability and exploratory power. Its primary goal is to reveal meaningful patterns and relationships within ordinal datasets. To illustrate its usefulness, we apply the methodology to the analysis of job satisfaction among PhD holders in Spain. The results reveal two dominant latent dimensions: one associated with intellectual satisfaction and another related to job-related aspects such as salary and benefits. Comparative analyses with alternative techniques indicate that the proposed approach achieves superior discriminatory power across variables. Full article

(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)

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30 pages, 1770 KB

Open AccessArticle

A Hybrid Numerical–Semantic Clustering Algorithm Based on Scalarized Optimization

by Ana-Maria Ifrim and Ionica Oncioiu

Algorithms 2025, 18(10), 607; https://doi.org/10.3390/a18100607 - 27 Sep 2025

Cited by 3 | Viewed by 1294

Abstract

This paper addresses the challenge of segmenting consumer behavior in contexts characterized by both numerical regularities and semantic variability. Traditional models, such as RFM-based segmentation, capture the transactional dimension but neglect the implicit meanings expressed through product descriptions, reviews, and linguistic diversity. To [...] Read more.

This paper addresses the challenge of segmenting consumer behavior in contexts characterized by both numerical regularities and semantic variability. Traditional models, such as RFM-based segmentation, capture the transactional dimension but neglect the implicit meanings expressed through product descriptions, reviews, and linguistic diversity. To overcome this gap, we propose a hybrid clustering algorithm that integrates numerical and semantic distances within a unified scalar framework. The central element is a scalar objective function that combines Euclidean distance in the RFM space with cosine dissimilarity in the semantic embedding space. A continuous parameter λ regulates the relative influence of each component, allowing the model to adapt granularity and balance interpretability across heterogeneous data. Optimization is performed through a dual strategy: gradient descent ensures convergence in the numerical subspace, while genetic operators enable a broader exploration of semantic structures. This combination supports both computational stability and semantic coherence. The method is validated on a large-scale multilingual dataset of transactional records, covering five culturally distinct markets. Results indicate systematic improvements over classical approaches, with higher Silhouette scores, lower Davies–Bouldin values, and stronger intra-cluster semantic consistency. Beyond numerical performance, the proposed framework produces intelligible and culturally adaptable clusters, confirming its relevance for personalized decision-making. The contribution lies in advancing a scalarized formulation and hybrid optimization strategy with wide applicability in scenarios where numerical and textual signals must be analyzed jointly. Full article

(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)

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22 pages, 398 KB

Open AccessArticle

An Improved Convergence Analysis of a Multi-Step Method with High-Efficiency Indices

by Santhosh George, Manjusree Gopal, Samhitha Bhide and Ioannis K. Argyros

Algorithms 2025, 18(8), 483; https://doi.org/10.3390/a18080483 - 4 Aug 2025

Viewed by 880

Abstract

A multi-step method introduced by Raziyeh and Masoud for solving nonlinear systems with convergence order five has been considered in this paper. The convergence of the method was studied using Taylor series expansion, which requires the function to be six times differentiable. However, [...] Read more.

A multi-step method introduced by Raziyeh and Masoud for solving nonlinear systems with convergence order five has been considered in this paper. The convergence of the method was studied using Taylor series expansion, which requires the function to be six times differentiable. However, our convergence study does not depend on the Taylor series. We use the derivative of F up to two only in our convergence analysis, which is presented in a more general Banach space setting. Semi-local analysis is also discussed, which was not given in earlier studies. Unlike in earlier studies (where two sets of assumptions were used), we used the same set of assumptions for semi-local analysis and local convergence analysis. We discussed the dynamics of the method and also gave some numerical examples to illustrate theoretical findings. Full article

(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)

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22 pages, 346 KB

Open AccessArticle

Two Extrapolation Techniques on Splitting Iterative Schemes to Accelerate the Convergence Speed for Solving Linear Systems

by Chein-Shan Liu and Botong Li

Algorithms 2025, 18(7), 440; https://doi.org/10.3390/a18070440 - 18 Jul 2025

Viewed by 1069

Abstract

For the splitting iterative scheme to solve the system of linear equations, an equivalent form in terms of descent and residual vectors is formulated. We propose an extrapolation technique using the new formulation, such that a new splitting iterative scheme (NSIS) can be [...] Read more.

For the splitting iterative scheme to solve the system of linear equations, an equivalent form in terms of descent and residual vectors is formulated. We propose an extrapolation technique using the new formulation, such that a new splitting iterative scheme (NSIS) can be simply generated from the original one by inserting an acceleration parameter preceding the descent vector. The spectral radius of the NSIS is proven to be smaller than the original one, and so has a faster convergence speed. The orthogonality of consecutive residual vectors is coined into the second NSIS, from which a stepwise varying orthogonalization factor can be derived explicitly. Multiplying the descent vector by the factor, the second NSIS is proven to be absolutely convergent. The modification is based on the maximal reduction of residual vector norm. Two-parameter and three-parameter NSIS are investigated, wherein the optimal value of one parameter is obtained by using the maximization technique. The splitting iterative schemes are unified to have the same iterative form, but endowed with different governing equations for the descent vector. Some examples are examined to exhibit the performance of the proposed extrapolation techniques used in the NSIS. Full article

(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)

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