Mathematics, Volume 12, Issue 9 (May-1 2024) – 135 articles

Electro-hydraulic actuators have witnessed significant development over recent years due to their remarkable abilities to perform complex and dynamic movements. Integrating such an actuator in humanoids is highly beneficial, leading to a humanoid capable of performing complex tasks requiring high force. This highlights the importance of safety, especially since high power output and safe interaction seem to be contradictory; the greater the robot’s ability to generate high dynamic movements, the more difficult it is to achieve safety, as this requires managing a large amount of motor energy before, during, and after the collision. No matter what technology or algorithm is used to achieve safety, none can be implemented without a stable control system. Hence, one of the main parameters remains the quality and reliability of the robot’s control architecture through handling a huge amount of data without system failure. This paper addresses the development of a stable control architecture that ensures, in later stages, that the safety algorithm is implemented correctly. The optimum control architecture to utilize and ensure the maximum benefit of electro-hydraulic actuators in humanoid robots is one of the important subjects in this field. For a stable and safe functioning of the humanoid, the development of the control architecture and the communication between the different components should adhere to some requirements such as stability, robustness, speed, and reduced complexity, ensuring the easy addition of numerous components. This paper presents the developed control architecture for an underdeveloped electro-hydraulic actuated humanoid. The proposed solution has the advantage of being a distributed, real-time, open-source, modular, and adaptable control architecture, enabling simple integration of numerous sensors and actuators to emulate human actions and safely interact with them. The contribution of this paper is an enhancement of the updated rate compared to other humanoids by 20% and by 40 % in the latency of the master. The results demonstrate the potential of using EtherCAT fieldbus and open-source software to develop a stable robot control architecture capable of integrating safety and security algorithms in later stages. Full article

In this paper, we explore the trade-offs between public and private investment in autonomous driving technologies. Utilizing an evolutionary game model, we delve into the complex interaction mechanisms between governments and auto manufacturers, focusing on how strategic decisions impact overall outcomes. Specifically, we predict that governments may opt for strategies such as constructing and maintaining infrastructure for Roadside Infrastructure-based Vehicles (RIVs) or subsidizing high-level Autonomous Driving Vehicles (ADVs) without additional road infrastructure. Manufacturers’ choices involve deciding whether to invest in RIVs or ADVs, depending on governmental policies and market conditions. Our simulation results, based on scenarios derived from existing economic data and forecasts on technology development costs, suggest that government subsidy policies need to dynamically adjust in response to manufacturers’ shifting strategies and market behavior. This dynamic adjustment is crucial as it addresses the evolving economic environment and technological advancements, ensuring that subsidies effectively incentivize the desired outcomes in autonomous vehicle development. The findings of this paper could serve as valuable decision-making tools for governments and auto manufacturers, guiding investment strategies that align with the dynamic landscape of autonomous driving technology. Full article

This paper concentrates on examining the characterization of nonlinear mixed bi-skew Lie triple *- derivations within an *-algebra denoted by $\mathcal{A}$ which contains a nontrivial projection with a unit I. Additionally, we expand this investigation to applications by describing these derivations within prime *-algebras, von Neumann algebras, and standard operator algebras. Full article

Load forecast is the foundation of power system operation and planning. The forecast results can guide the power system economic dispatch and security analysis. In order to improve the accuracy of load forecast, this paper proposes a forecasting model based on the combination of the cuckoo search (CS) algorithm and the long short-term memory (LSTM) neural network. Load data are specific data with time series characteristics and periodicity, and the LSTM algorithm can control the information added or discarded through the forgetting gate, so as to realize the function of forgetting or memorizing. Therefore, the use of the LSTM algorithm for load forecast is more effective. The CS algorithm can perform global search better and does not easily fall into local optima. The CS-LSTM forecasting model, where CS algorithm is used to optimize the hyper-parameters of the LSTM model, has a better forecasting effect and is more feasible. Simulation results show that the CS-LSTM model has higher forecasting accuracy than the standard LSTM model, the PSO-LSTM model, and the GA-LSTM model. Full article

With the development of artificial intelligence (AI), deep learning is widely used in various industries. At CRYPTO 2019, researchers used deep learning to analyze the block cipher for the first time and constructed a differential neural network distinguisher to meet a certain accuracy. In this paper, a mixture differential neural network distinguisher using ResNet is proposed to further improve the accuracy by exploring the mixture differential properties. Experiments are conducted on SIMON32/64, and the accuracy of the 8-round mixture differential neural network distinguisher is improved from 74.7% to 92.3%, compared with that of the previous differential neural network distinguisher. The prediction accuracy of the differential neural network distinguisher is susceptible to the choice of the specified input differentials, whereas the mixture differential neural network distinguisher is less affected by the input difference and has greater robustness. Furthermore, by combining the probabilistic expansion of rounds and the neutral bit, the obtained mixture differential neural network distinguisher is extended to 11 rounds, which can realize the 12-round actual key recovery attack on SIMON32/64. With an appropriate increase in the time complexity and data complexity, the key recovery accuracy of the mixture differential neural network distinguisher can be improved to 55% as compared to 52% of the differential neural network distinguisher. The mixture differential neural network distinguisher proposed in this paper can also be applied to other lightweight block ciphers. Full article

In this paper, we study the average Kolmogorov $\sigma$–widths and the average linear $\sigma$–widths of multivariate isotropic and anisotropic Besov classes in Orlicz spaces and give the weak asymptotic estimates of these two widths. At the same time, we also give the asymptotic property of the optimal recovery of isotropic Besov classes in Orlicz spaces. Full article

In this article, we mainly generalize the results in the literature for a fractional q-difference equation. Our study considers a more comprehensive type of fractional $\left(p,q\right)$-difference system of nonlinear equations. By the Banach contraction mapping principle, we obtain a unique solution. By Krasnoselskii’s fixed-point theorem, we prove the existence of solutions. In addition, finite stability has been established too. The main results in the literature have been proven to be a particular corollary of our work. Full article

Selecting features associated with patient-centered outcomes is of major relevance yet the importance given depends on the method. We aimed to compare stepwise selection, least absolute shrinkage and selection operator, random forest, Boruta, extreme gradient boosting and generalized maximum entropy estimation and suggest an aggregated evaluation. We also aimed to describe outcomes in people with chronic obstructive pulmonary disease (COPD). Data from 42 patients were collected at baseline and at 5 months. Acute exacerbations were the aggregated most important feature in predicting the difference in the handgrip muscle strength (dHMS) and the COVID-19 lockdown group had an increased dHMS of 3.08 kg (CI95 ≈ [0.04, 6.11]). Pack-years achieved the highest importance in predicting the difference in the one-minute sit-to-stand test and no clinical change during lockdown was detected. Charlson comorbidity index was the most important feature in predicting the difference in the COPD assessment test (dCAT) and participants with severe values are expected to have a decreased dCAT of 6.51 points (CI95 ≈ [2.52, 10.50]). Feature selection methods yield inconsistent results, particularly extreme gradient boosting and random forest with the remaining. Models with features ordered by median importance had a meaningful clinical interpretation. Lockdown seem to have had a negative impact in the upper-limb muscle strength. Full article

In this paper, the scale mixture of the Gleser (SMG) distribution is introduced. This new distribution is the product of a scale mixture between the Gleser (G) distribution and the Beta$(a,1)$ distribution. The SMG distribution is an alternative to distributions with two parameters and a heavy right tail. We study its representation and some basic properties, maximum likelihood inference, and Fisher’s information matrix. We present an application to a real dataset in which the SMG distribution shows a better fit than two other known distributions. Full article

A PLS-based quality prediction method is proposed for batch processes using two-dimensional extended windows. To realize the adoption of information in the directions of sampling time and batch, a newly defined region of support (ROS), called the k-i-back-extended region of support (KIBROS), is proposed; it establishes an extended window by adding two regions of data to the traditional ROS to include all possible important data for quality prediction. Based on the new ROS, extended windows are established, and different models are proposed using the extended windows for batch process quality prediction. Furthermore, using the typical injection molding batch process as an example, the proposed quality prediction method is experimentally verified, proving that the proposed methods have higher prediction accuracy than the traditional method and that the prediction stability is also improved. Full article

Let $(M,\nabla ,g)$ be a statistical manifold and $TM$ be its tangent bundle endowed with a twisted Sasaki metric G. This paper serves two primary objectives. The first objective is to investigate the curvature properties of the tangent bundle $TM$. The second objective is to explore conformal vector fields and Ricci, Yamabe, and gradient Ricci–Yamabe solitons on the tangent bundle $TM$ according to the twisted Sasaki metric G. Full article

Searching over a sorted list is a classical problem in computer science. Binary Search takes at most $⌊{\log }_{2}n⌋+1$ tries to find an item in a sorted list of size n. Interpolation Search achieves an average time complexity of $\mathsf{O}\left(\log \log n\right)$ for uniformly distributed data. Hybrids of Binary Search and Interpolation Search are also available to handle data with unknown distributions. This paper analyzes the computation cost of these methods and shows that interpolation can significantly affect their performance—accordingly, a new method, Interpolation Once Binary Search (IOBS), is proposed. The experimental results show that IOBS outperforms the hybrids of Binary Search and Interpolation Search for nonuniformly distributed data. Full article

This research stems from the increasing use of hand gestures in various applications, such as sign language recognition to electronic device control. The focus is the importance of accuracy and robustness in recognizing hand gestures to avoid misinterpretation and instruction errors. However, many experiments on hand gesture recognition are conducted in limited laboratory environments, which do not fully reflect the everyday use of hand gestures. Therefore, the importance of an ideal background in hand gesture recognition, involving only the signer without any distracting background, is highlighted. In the real world, the use of hand gestures involves various unique environmental conditions, including differences in background colors, varying lighting conditions, and different hand gesture positions. However, the datasets available to train hand gesture recognition models often lack sufficient variability, thereby hindering the development of accurate and adaptable systems. This research aims to develop a robust hand gesture recognition model capable of operating effectively in diverse real-world environments. By leveraging deep learning-based image augmentation techniques, the study seeks to enhance the accuracy of hand gesture recognition by simulating various environmental conditions. Through data duplication and augmentation methods, including background, geometric, and lighting adjustments, the diversity of the primary dataset is expanded to improve the effectiveness of model training. It is important to note that the utilization of the green screen technique, combined with geometric and lighting augmentation, significantly contributes to the model’s ability to recognize hand gestures accurately. The research results show a significant improvement in accuracy, especially with implementing the proposed green screen technique, underscoring its effectiveness in adapting to various environmental contexts. Additionally, the study emphasizes the importance of adjusting augmentation techniques to the dataset’s characteristics for optimal performance. These findings provide valuable insights into the practical application of hand gesture recognition technology and pave the way for further research in tailoring techniques to datasets with varying complexities and environmental variations. Full article

This paper provides a computationally efficient and novel four-step methodological approach for predicting volatility estimators derived from bitcoin prices. In the first step, open, high, low, and close bitcoin prices are transformed into volatility estimators using Brownian motion assumptions and logarithmic transformations. The second step determines the optimal number of time-series lags required for converting the series into an autoregressive model. This selection process utilizes random forest regression, evaluating the importance of each lag using the Mean Decrease in Impurity (MDI) criterion and optimizing the number of lags considering an 85% cumulative importance threshold. The third step of the developed methodological approach fits the Elastic Net Regression (ENR) to the volatility estimator’s dataset, while the final fourth step assesses the predictive accuracy of ENR, compared to decision tree (DTR), random forest (RFR), and support vector regression (SVR). The results reveal that the ENR prevails in its predictive accuracy for open and close prices, as these prices may be linear and less susceptible to sudden, non-linear shifts typically seen during trading hours. On the other hand, SVR prevails for high and low prices as these prices often experience spikes and drops driven by transient news and intra-day market sentiments, forming complex patterns that do not align well with linear modelling. Full article

This study investigates the integration of quantum circuits with classical neural networks for enhancing credit scoring for small- and medium-sized enterprises (SMEs). We introduce a hybrid quantum–classical model, focusing on the synergy between quantum and classical rather than comparing the performance of separate quantum and classical models. Our model incorporates a quantum layer into a traditional neural network, achieving notable reductions in training time. We apply this innovative framework to a binary classification task with a proprietary real-world classical credit default dataset for SMEs in Singapore. The results indicate that our hybrid model achieves efficient training, requiring significantly fewer epochs (350) compared to its classical counterpart (3500) for a similar predictive accuracy. However, we observed a decrease in performance when expanding the model beyond 12 qubits or when adding additional quantum classifier blocks. This paper also considers practical challenges faced when deploying such models on quantum simulators and actual quantum computers. Overall, our quantum–classical hybrid model for credit scoring reveals its potential in industry, despite encountering certain scalability limitations and practical challenges. Full article

The main objective of this research is to establish a new formulation and mathematical model based on graph theory to create dynamic equations and provide clarity on the fundamental formulation. We have employed graph theory as a new approach to develop a new representation and formulate the vertical dynamics of a motorcycle with four degrees of freedom, including a suspension and tire model. We have outlined the principal procedural steps required to generate the mathematical and dynamic equations. This systematic approach ensures clarity and precision in our formulation process and representation. Subsequently, we implemented the dynamics equations to examine the dynamic behavior of both the sprung and unsprung masses’ vertical displacements, while considering the varying conditions of the road profile. Full article

This paper explores the application of Random Matrix Theory (RMT) as a methodological enhancement for portfolio selection within financial markets. Traditional approaches to portfolio optimization often rely on historical estimates of correlation matrices, which are particularly susceptible to instabilities. To address this challenge, we combine a data preprocessing technique based on the Hilbert transformation of returns with RMT to refine the accuracy and robustness of correlation matrix estimation. By comparing empirical correlations with those generated through RMT, we reveal non-random properties and uncover underlying relationships within financial data. We then utilize this methodology to construct the correlation network dependence structure used in portfolio optimization. The empirical analysis presented in this paper validates the effectiveness of RMT in enhancing portfolio diversification and risk management strategies. This research contributes by offering investors and portfolio managers with methodological insights to construct portfolios that are more stable, robust, and diversified. At the same time, it advances our comprehension of the intricate statistical principles underlying multivariate financial data. Full article

The Least Absolute Shrinkage and Selection Operator (LASSO) regression technique has proven to be a valuable tool for fitting and reducing linear models. The trend of applying LASSO to compositional data is growing, thereby expanding its applicability to diverse scientific domains. This paper aims to contribute to this evolving landscape by undertaking a comprehensive exploration of the $L^1$-norm for the penalty term of a LASSO regression in a compositional context. This implies first introducing a rigorous definition of the compositional $L^p$-norm, as the particular geometric structure of the compositional sample space needs to be taken into account. The focus is subsequently extended to a meticulous data-driven analysis of the dimension reduction effects on linear models, providing valuable insights into the interplay between penalty term norms and model performance. An analysis of a microbial dataset illustrates the proposed approach. Full article

In this paper, we consider the Cauchy problem for a three-component Novikov system on the line. We give a construction of the initial data $({\rho }_0,u_0,v_0)\in B_{p,\infty }^{\sigma -1}\left(\mathbb{R}\right)\times B_{p,\infty }^{\sigma }\left(\mathbb{R}\right)\times B_{p,\infty }^{\sigma }\left(\mathbb{R}\right)$ with $\sigma >max\left\{3+\frac{1}{p},\frac{7}{2}\right\},1\le p\le \infty$, such that the corresponding solution to the three-component Novikov system starting from $({\rho }_0,u_0,v_0)$ is discontinuous at $t=0$ in the metric of $B_{p,\infty }^{\sigma -1}\left(\mathbb{R}\right)\times B_{p,\infty }^{\sigma }\left(\mathbb{R}\right)\times B_{p,\infty }^{\sigma }\left(\mathbb{R}\right)$, which implies the ill-posedness for this system in $B_{p,\infty }^{\sigma -1}\left(\mathbb{R}\right)\times B_{p,\infty }^{\sigma }\left(\mathbb{R}\right)\times B_{p,\infty }^{\sigma }\left(\mathbb{R}\right)$. Full article

Indoor wireless positioning has long been a dynamic field of research due to its broad application range. While many commercial products have been developed, they often are not open source or require substantial and costly infrastructure. Academically, research has extensively explored Bluetooth Low Energy (BLE) for positioning, yet there are a noticeable lack of studies that comprehensively compare traditional algorithms under these conditions. This research aims to fill this gap by evaluating classical positioning algorithms such as K-Nearest Neighbor (KNN), Weighted K-Nearest Neighbor (WKNN), Naïve Bayes (NB), and a Received Signal Strength-based Neural Network (RSS-NN) using BLE technology. We also introduce a novel method using Convolutional Neural Networks (CNN), specifically tailored to process RSS data structured in an image-like format. This approach helps overcome the limitations of traditional RSS fingerprinting by effectively managing the environmental dynamics within indoor settings. In our tests, all algorithms performed well, consistently achieving an average accuracy of less than two meters. Remarkably, the CNN method outperformed others, achieving an accuracy of 1.22 m. These results establish a solid basis for future research, particularly towards enhancing the precision of indoor positioning systems using deep learning for cost-effective, easy to set up applications. Full article

Quantum Computing in the Noisy Intermediate-Scale Quantum (NISQ) era has shown promising applications in machine learning, optimization, and cryptography. Despite these progresses, challenges persist due to system noise, errors, and decoherence. These system noises complicate the simulation of quantum systems. The depolarization channel is a standard tool for simulating a quantum system’s noise. However, modeling such noise for practical applications is computationally expensive when we have limited hardware resources, as is the case in the NISQ era. This work proposes a modified representation for a single-qubit depolarization channel. Our modified channel uses two Kraus operators based only on X and Z Pauli matrices. Our approach reduces the computational complexity from six to four matrix multiplications per channel execution. Experiments on a Quantum Machine Learning (QML) model on the Iris dataset across various circuit depths and depolarization rates validate that our approach maintains the model’s accuracy while improving efficiency. This simplified noise model enables more scalable simulations of quantum circuits under depolarization, advancing capabilities in the NISQ era. Full article

The problem of finding the metric dimension of circulant graphs with t generators $1,2,\cdots ,t$ (and their inverses) has been extensively studied. The problem is solved for $t=2,3,4$, and some exact values and bounds are known also for $t=5$. We solve all the open cases for $t=5$. Full article

Wind turbines (WT) are a clean renewable energy source that have gained popularity in recent years. Gearboxes are complex, expensive, and critical components of WT, which are subject to high maintenance costs and several stresses, including high loads and harsh environments, that can lead to failure with significant downtime and financial losses. This paper focuses on the development of a digital twin-based approach for the modelling and simulation of WT gearboxes with the aim to improve their design, diagnosis, operation, and maintenance by providing insights into their behavior under different operating conditions. Powerful commercial computer-aided design tools (CAD) and computer-aided engineering (CAE) software are embedded into a computationally efficient multi-objective optimization framework (modeFrontier) with the purpose of maximizing the power density, compactness, performance, and reliability of the WT gearbox. High-fidelity models are used to minimize the WT weight, volume, and maximum stresses and strains achieved without compromising its efficiency. The 3D CAD model of the WT gearbox is carried out using SolidWorks (version 2023 SP5.0), the Finite Element Analysis (FEA) is used to obtain the stresses and strains, fields are modelled using Ansys Workbench (version 2024R1), while the multibody kinematic and dynamic system is analyzed using Adams Machinery (version 2023.3, Hexagon). The method has been successfully applied to different case studies to find the optimal design and analyze the performance of the WT gearboxes. The simulation results can be used to determine safety factors, predict fatigue life, identify potential failure modes, and extend service life and reliability, thereby ensuring proper operation over its lifetime and reducing maintenance costs. Full article

This article focuses on the analysis of dynamics emerging in a network of Hodgkin–Huxley reaction–diffusion equations. The network has three levels. The three neurons in level 1 receive a periodic input but do not receive inputs from other neurons. The three neurons in level 2 receive inputs from one specific neuron in level 1 and all neurons in level 3. The neurons in level 3 (all other neurons) receive inputs from all other neurons in levels 2 and 3. Furthermore, the right-hand side of pre-synaptic neurons is connected to the left-hand side of the post-synaptic neurons. The synchronization phenomenon is observed for neurons in level 3, even though the system is initiated with different functions. As far as we know, it is the first time that evidence of the synchronization phenomenon is provided for spatially extended Hodgkin–Huxley equations, which are periodically forced at three different sites and embedded in such a hierarchical network with space-dependent coupling interactions. Full article

Two summation theorems concerning the ${}_2{F}_1(1/2)$-series due to Gauss and Bailey will be examined by employing the “coefficient extraction method”. Forty infinite series concerning harmonic numbers and binomial/multinomial coefficients will be evaluated in closed form, including eight conjectured ones made by Z.-W. Sun. The presented comprehensive coverage for the harmonic series of convergence rate “$1/2$” may serve as a reference source for readers. Full article

Waddington envisioned stem cell differentiation as a marble rolling down a hill, passing through hierarchically branched valleys representing the cell’s temporal state. The terminal valleys at the bottom of the hill indicate the possible committed cells of the multicellular organism. Although originally proposed as a metaphor, Waddington’s hypothesis establishes the fundamental principles for characterizing the differentiation process as a dynamic system: the generated equilibrium points must exhibit hierarchical branching, robustness to perturbations (homeorhesis), and produce the appropriate number of cells for each cell type. This article aims to capture these characteristics using a mathematical model based on two fundamental hypotheses. First, it is assumed that the gene regulatory network consists of hierarchically coupled subnetworks of genes (modules), each modeled as a dynamical system exhibiting supercritical pitchfork or cusp bifurcation. Second, the gene modules are spatiotemporally regulated by feedback mechanisms originating from epigenetic factors. Analytical and numerical results show that the proposed model exhibits self-organized multistability with hierarchical branching. Moreover, these branches of equilibrium points are robust to perturbations, and the number of different cells produced can be determined by the system parameters. Full article

In this paper, we present sufficient conditions for Hyers–Ulam-Rassias stability of nonlinear implicit higher-order Volterra-type integrodifferential equations from above on unbounded time scales. These new sufficient conditions result by reducing Volterra-type integrodifferential equations to Volterra-type integral equations, using the Banach fixed point theorem, and by applying an appropriate Bielecki type norm, the Lipschitz type functions, where Lipschitz coefficient is replaced by unbounded rd-continuous function. Full article

This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the system are considered to be in the form of time-varying functions, which are more in line with the needs of real physical systems. The NN approximation technique is utilized to overcome the influence of the uncertainty term on controller design due to randomness. Based on the backstepping technique, a neural adaptive fixed-time tracking control strategy is designed. Under the designed control strategy, the tracking accuracy of the controlled system can reach the expectation in a fixed time. The multi-actuator constraints are converted into a generalized mathematical model to simplify the controller design process. Using the characteristics of the hyperbolic tangent function, a new function called practical virtual control signal is designed using the virtual control signal as the input. Due to the saturation constraint property of the hyperbolic tangent function, it is theoretically ensured that no state of the system exceeds the constraints through to the new form of the virtual controller. Using the adaptive controller constructed in this paper, the controlled system is semi-global fixed-time stabilized in probability (SGFSP). Finally, the effectiveness of the proposed control strategy is further verified by simulation examples. Full article

We explore the most probable phase portrait (MPPP) of a stochastic single-species model incorporating the Allee effect by utilizing the nonlocal Fokker–Planck equation (FPE). This stochastic model incorporates both non-Gaussian and Gaussian noise sources. It has three fixed points in the deterministic case. One is the unstable state, which lies between the two stable equilibria. Our primary focus is on elucidating the transition pathways from extinction to the upper stable state in this single-species model, particularly under the influence of jump-diffusion noise. This helps us to study the biological behavior of species. The identification of the most probable path relies on solving the nonlocal FPE tailored to the population dynamics of the single-species model. This enables us to pinpoint the corresponding maximum possible stable equilibrium state. Additionally, we derive the Onsager–Machlup function for the stochastic model and employ it to determine the corresponding most probable paths. Numerical simulations manifest three key insights: (i) when non-Gaussian noise is present in the system, the peak of the stationary density function aligns with the most probable stable equilibrium state; (ii) if the initial value rises from extinction to the upper stable state, then the most probable trajectory converges towards the maximally probable equilibrium state, situated approximately between 9 and 10; and (iii) the most probable paths exhibit a rapid ascent towards the stable state, then maintain a sustained near-constant level, gradually approaching the upper stable equilibrium as time goes on. These numerical findings pave the way for further experimental investigations aiming to deepen our comprehension of dynamical systems within the context of biological modeling. Full article

Unlike business process diagrams, where ISO/IEC 19510 (BPMN 2.0) prevails, high-level process landscape diagrams are being designed using a variety of standard- or semi-standard-based notations. Consequently, landscape diagrams differ among organizations, domains, and modeling tools. As (process landscape) diagrams need to be understandable in order to communicate effectively and thus form the basis for valid business decisions, this study aims to empirically validate the cognitive effectiveness of common landscape designs, including those BPMN-L-based, which represent a standardized extension of BPMN 2.0 specifically aimed at landscape modeling. Empirical research with 298 participants was conducted in which cognitive effectiveness was investigated by observing the speed, ease, accuracy, and efficiency of answering questions related to semantically equivalent process landscape diagrams modeled in three different notations: value chains, ArchiMate, and BPMN-L. The results demonstrate that BPMN-L-based diagrams performed better than value chain- and ArchiMate-based diagrams concerning speed, accuracy, and efficiency; however, subjects perceived BPMN-L-based diagrams as being less easy to use when compared to their counterparts. The results indicate that differences in cognitive effectiveness measures may result from the design principles of the underlying notations, specifically the complexity of the visual vocabulary and semiotic clarity, which states that modeling concepts should have unique visualizations. Full article