Symmetry, Volume 16, Issue 6 (June 2024) – 105 articles

The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend the principal dynamical ideas of the founder. Specifically, the research delves into the phenomena of unpredictability and Poisson stability, which have been examined in previous studies relating to models of continuous and discontinuous neural networks with constant components. We extend the analysis to discontinuous models characterized by variable impulsive actions and structural ingredients. The method of included intervals based on the B-topology is employed to investigate the networks. It is a novel approach that addresses the unique challenges posed by the sophisticated recurrence. Full article

This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness of fixed points and fulfill the Suzuki-type nonlinear hybrid contractions on various generalized metrics. Full article

Picard iteration is on the basis of a great number of numerical methods and applications of mathematics. However, it has been known since the 1950s that this method of fixed-point approximation may not converge in the case of nonexpansive mappings. In this paper, an extension of the concept of nonexpansiveness is presented in the first place. Unlike the classical case, the new maps may be discontinuous, adding an element of generality to the model. Some properties of the set of fixed points of the new maps are studied. Afterwards, two iterative methods of fixed-point approximation are analyzed, in the frameworks of b-metric and Hilbert spaces. In the latter case, it is proved that the symmetrically averaged iterative procedures perform well in the sense of convergence with the least number of operations at each step. As an application, the second part of the article is devoted to the study of fractal mappings on Hilbert spaces defined by means of nonexpansive operators. The paper considers fractal mappings coming from $\phi$-contractions as well. In particular, the new operators are useful for the definition of an extension of the concept of $\alpha$-fractal function, enlarging its scope to more abstract spaces and procedures. The fractal maps studied here have quasi-symmetry, in the sense that their graphs are composed of transformed copies of itself. Full article

In this contribution, we first present a new recursion relation fulfilled by the linearization coefficients of Bessel polynomials (LCBPs), which is different than the one presented by Berg and Vignat in 2008. We will explain why this new recursion formula is as important as Berg and Vignat’s. We introduce the matrix linearization coefficients of Bessel polynomials (MLCBPs), and we present some new results and some conjectures on these matrices. Second, we present the inverse of the connection coefficients with an application involving the modified Bessel function of the second kind. Finally, we introduce the inverse of the matrix of the linearization coefficients of the Bessel polynomials (IMLCBPs), and we present some open problems related to these IMLCBPs. Full article

When studying an unfamiliar system, we first look for the symmetry that the system has so that we can make many predictions about the possible properties of the system. The symmetry in transport network security needs to maintain a stable state and maintain a constant state of transport network security. With the development of China–Europe freight trains, the transport between Asia and Europe has gradually formed the Belt and Road (B&R) land–sea transport network. In order to analyze the cascading failure mechanism of the B&R land–sea transport network, a network cascading failure model is constructed. Then, the quantitative analysis of the connectivity indicators of the land–sea transport network is conducted from the node attack strategy, and it is compared with the Maritime Silk Road (MSR) shipping network. Finally, the robustness of the land–sea transport network under emergencies is analyzed. From the results of deliberate attacks, the attack threshold of the B&R land–sea transport network is the same as that of the MSR shipping network, and the maximum number of attacks is slightly less than that of the MSR shipping network. The Russia–Ukraine conflict has a minimal impact on the robustness of cascading failure in the land–sea transport network. The Red Sea crisis may have a significant impact on the robustness of cascading failure in the land–sea transport network. The research results can provide suggestions for improving the robustness of the B&R land–sea transport network. Full article

Let $D\left(R_{m,n}\left(q\right)\right)$ be the Drinfeld double of Radford Hopf algebra $R_{m,n}\left(q\right)$ and $D\left(H_{s,t}\right)$ be the Drinfeld double of generalized Taft algebra $H_{s,t}$. Both $D\left(R_{m,n}\left(q\right)\right)$ and $D\left(H_{s,t}\right)$ have very symmetric structures. We calculate all Hopf automorphisms of $D\left(R_{m,n}\left(q\right)\right)$ and $D\left(H_{s,t}\right)$, respectively. Furthermore, we prove that the Hopf automorphism group $Au{t}_{Hopf}\left(D\left(R_{m,n}\left(q\right)\right)\right)$ is isomorphic to the direct sum ${\mathbb{Z}}_n⨁{\mathbb{Z}}_m$ of cyclic groups ${\mathbb{Z}}_m$ and ${\mathbb{Z}}_n$, the Hopf automorphism group $Au{t}_{Hopf}\left(D\left(H_{s,t}\right)\right)$ is isomorphic to the semi-direct products ${\mathbb{k}}^{*}⋊{\mathbb{Z}}_d$ of multiplicative group ${\mathbb{k}}^{*}$ and cyclic group ${\mathbb{Z}}_d$, where $s=td,{\mathbb{k}}^{*}=\mathbb{k}\setminus \left\{0\right\}$, and $\mathbb{k}$ is an algebraically closed field with char$\left(\mathbb{k}\right)\nmid t$. Full article

Alternative mathematical explorations in quantum computing can be of great scientific interest, especially if they come with penetrating physical insights. In this paper, we present a critical revisitation of our application of geometric (Clifford) algebras (GAs) in quantum computing as originally presented in [C. Cafaro and S. Mancini, Adv. Appl. Clifford Algebras 21, 493 (2011)]. Our focus is on testing the usefulness of geometric algebras (GAs) techniques in two quantum computing applications. First, making use of the geometric algebra of a relativistic configuration space (namely multiparticle spacetime algebra or MSTA), we offer an explicit algebraic characterization of one- and two-qubit quantum states together with a MSTA description of one- and two-qubit quantum computational gates. In this first application, we devote special attention to the concept of entanglement, focusing on entangled quantum states and two-qubit entangling quantum gates. Second, exploiting the previously mentioned MSTA characterization together with the GA depiction of the Lie algebras $\mathrm{SO}\left(3;\mathbb{R}\right)$ and $\mathrm{SU}\left(2;\mathbb{C}\right)$ depending on the rotor group ${\mathrm{Spin}}^{+}\left(3,0\right)$ formalism, we focus our attention to the concept of universality in quantum computing by reevaluating Boykin’s proof on the identification of a suitable set of universal quantum gates. At the end of our mathematical exploration, we arrive at two main conclusions. Firstly, the MSTA perspective leads to a powerful conceptual unification between quantum states and quantum operators. More specifically, the complex qubit space and the complex space of unitary operators acting on them merge in a single multivectorial real space. Secondly, the GA viewpoint on rotations based on the rotor group ${\mathrm{Spin}}^{+}\left(3,0\right)$ carries both conceptual and computational advantages compared to conventional vectorial and matricial methods. Full article

With the continuously growing requirement for encryption in network environments, web browsers are increasingly employing hypertext transfer protocol security. Despite the increase in encrypted malicious network traffic, the encryption itself limits the data accessible for analyzing such behavior. To mitigate this, several studies have examined encrypted network traffic by analyzing metadata and payload bytes. Recent studies have furthered this approach, utilizing graph neural networks to analyze the structural data patterns within malicious encrypted traffic. This study proposed an enhanced encrypted traffic analysis leveraging graph neural networks which can model the symmetric or asymmetric spatial relations between nodes in the traffic network and optimized feature dimensionality reduction. It classified malicious network traffic by leveraging key features, including the IP address, port, CipherSuite, MessageLen, and JA3 features within the transport-layer-security session data, and then analyzed the correlation between normal and malicious network traffic data. The proposed approach outperformed previous models in terms of efficiency, using fewer features while maintaining a high accuracy rate of 99.5%. This demonstrates its research value as it can classify malicious network traffic with a high accuracy based on fewer features. Full article

A curve on a surface is a geodesic curve if its principal normal vector is anywhere aligned with the surface normal. Using the Serret–Frenet frame, a timelike surface couple ($\mathcal{TLSC})$ with the symmetry of a Bertrand couple ($\mathcal{BC}$) can be specified in terms of linear combinations of the components of the local frames in Minkowski 3-space ${\mathcal{E}}_1^3$. With these parametric representations, the necessary and sufficient conditions for the specified $\mathcal{BC}$ are derived to be the geodesic curves defining these surfaces. Afterward, the definition of a $\mathcal{TL}$ ruled surface ($\mathcal{RS}$) is also provided. Furthermore, the application of the method to some significant models is given. Full article

Concrete expanding-plate piles (CEP piles) represent a novel type of variable cross-section concrete cast-in-place pile, wherein one or more bearing plates are added to the pile body to enhance its load-bearing capacity. Compared to traditional uniform-diameter uplift piles, the bearing plates of CEP uplift piles provide additional resistance against uplift, substantially increasing the pile’s uplift bearing capacity. CEP piles exhibit a wide range of application potential in structures such as high-rise buildings, cable-stayed bridges, and offshore platforms. However, due to changes in the load-bearing mechanism, the pile–soil interaction of CEP piles significantly differs from that of straight-shaft piles. Theories applicable to the group effect of straight-shaft piles cannot be directly applied to CEP piles, which has led to imperfections in the theoretical framework for designing CEP piles in practical engineering applications, hindering their broader adoption. Therefore, this paper employs a finite element simulation analysis to study the failure modes of three groups of symmetrically arranged CEP pile groups. The effects of pile spacing on the uplift bearing capacity of CEP pile groups are investigated, leading to a revision of the formula for calculating the uplift bearing capacity of CEP pile groups. This study enhances the theoretical understanding of the load-bearing behavior of CEP pile groups, providing a theoretical basis for their practical engineering applications. Full article

In recent years, frequent chemical production safety incidents in China have been primarily attributed to dangerous behaviors by workers. Current monitoring methods predominantly rely on manual supervision, which is not only inefficient but also prone to errors in complex environments and with varying target scales, leading to missed or incorrect detections. To address this issue, we propose a deep learning-based object detection model, YOLO-GP. First, we utilize a grouped pointwise convolutional (GPConv) module of symmetric structure to facilitate information exchange and feature fusion in the channel dimension, thereby extracting more accurate feature representations. Building upon the YOLOv8n model, we integrate the symmetric structure convolutional GPConv module and design the dual-branch aggregation module (DAM) and Efficient Spatial Pyramid Pooling (ESPP) module to enhance the richness of gradient flow information and the capture of multi-scale features, respectively. Finally, we develop a channel feature enhancement network (CFE-Net) to strengthen inter-channel interactions, improving the model’s performance in complex scenarios. Experimental results demonstrate that YOLO-GP achieves a 1.56% and 11.46% improvement in the [email protected]:.95 metric on a custom dangerous behavior dataset and a public Construction Site Safety Image Dataset, respectively, compared to the baseline model. This highlights its superiority in dangerous behavior object detection tasks. Furthermore, the enhancement in model performance provides an effective solution for improving accuracy and robustness, promising significant practical applications. Full article

A cyclic antipodal pair of a circle is a pair of points that are the intersection of the circle with the diameter of the circle. In this article, a recent proof of Ptolemy’s Theorem—simultaneously in both (i) Euclidean geometry and (ii) the relativistic model of hyperbolic geometry (also known as the Klein model)—motivates the study of four cyclic antipodal pairs of a circle, ordered arbitrarily counterclockwise. The translation of results from Euclidean geometry into hyperbolic geometry is obtained by means of hyperbolic trigonometry, called gyrotrigonometry, to which Einstein addition gives rise. Identities that extend the Pythagorean identity in both Euclidean and hyperbolic geometry are obtained. Full article

In this paper, we have provided a mathematical analysis of an empirical result, namely, the Fahraeus–Lindqvist effect, a phenomenon that occurs in capillary tubes with a diameter lower than 0.3 mm. According to this effect, in capillary tubes under 0.3 mm in diameter, the apparent viscosity of blood decreases as the diameter of the tube decreases, making flow possible in these vessels. A two-phase blood flow mathematical model for human capillaries has been presented here. According to Haynes’ theory, blood is separated into two layers when it flows from the capillary. It is assumed that the first layer is plasma, and the second layer is the core layer. The plasma layer flows near the wall of the capillary, and the core layer flows along the axis of the capillary. Further, the core layer is assumed to be a mixture of two phases: one is the plasma, and the other is that of RBCs. For mathematical modeling purposes, a curvilinear coordinate system has been adopted, with physical quantities used in tensorial form. Derived equations are solved to find the effective viscosity, which depends upon the radius of the capillary; that is, it reduces viscosity to make blood flow possible. A comparative study was conducted with the experimental result of this effect, and it was observed that the proposed two-phase blood flow model is much closer to the experimental data than the single-phase blood flow model, and both have the same trends. After validation of the model with the experimental result, this model was applied to human capillaries (diameter lower than 10 $\mathsf{\mu }\mathrm{m}$) to show the F-L effect, and the impact of various physiological quantities that are relevant to the flow of blood into human capillaries are also discussed here. The impact of hematocrit on various parameters has been demonstrated explicitly. Full article

This work presents a study on the modeling, analysis, and control of asymmetric source structures, which focuses on a multi-directional active mounting system that aims to consider the location and orientation of an actual automotive powertrain mount. An active mount was created by connecting a PZT (piezo-stack) actuator with a rubber grommet. Additional force necessary for every mount was determined by using forces caused by harmonic stimulation and the control input has the capability to reduce vibrations by engaging in detrimental opposition against the input. In addition, the vibration in the horizontal direction can be reduced with the adjustment of variables that can be modified via the dynamic interconnection of the source frame. This study especially evaluated the effectiveness of vibration reduction without a horizontal active component and determined the feasibility of control. Through sequences of simulated outcomes, it was demonstrated that the implementation of this asymmetric, bi-directional (both horizontally and vertically) active mount may effectively reduce stimulation oscillations. Additionally, a numerical validation was performed to reduce the vibrations generated by the modulation. It was accomplished by observing the system’s response utilizing a digital filter with a normalized least mean square method. The simulations of adaptive digital filters demonstrated that the efficacy of control diminishes when faced with intricate noise and signals, while the attenuation trend stays unaltered. Full article

Currently, Internet of Things (IoT)-based cloud systems face several problems such as privacy leakage, failure in centralized operation, managing IoT devices, and malicious attacks. The data transmission between the cloud and healthcare IoT needs trust and secure transmission of Electronic Health Records (EHRs). IoT-enabled healthcare equipment is seen in hospitals that have been implementing the technology for many years. Nonetheless, medical agencies fail to consider the security risk associated with healthcare IoT devices, which are readily compromised and cause potential threats to authentication and encryption procedures. Existing cloud computing methods like homomorphic encryption and the elliptic curve cryptography are unable to meet the security, identity, authentication, and security needs of healthcare IoT devices. The majority of conventional healthcare IoT algorithms lack secure data transmission. Therefore, fog computing is introduced to overcome the problems of IoT device verification, authentication, and identification for scalable and secure transmission of data. In this research manuscript, fog computing includes a hybrid mathematical model: Elliptic Curve Cryptography (ECC) and Proxy Re-encryption (PR) with Enhanced Salp Swarm Algorithm (ESSA) for IoT device verification, identification, and authentication of EHRs. ESSA is incorporated into the PR algorithm to determine the optimal key size and parameters of the PR algorithm. Specifically, in the ESSA, a Whale Optimization Algorithm (WOA) is integrated with the conventional Salp Swarm Algorithm (SSA) to enhance its global and local search processes. The primary objective of the proposed mathematical model is to further secure data sharing in the real time services. The extensive experimental analysis shows that the proposed model approximately reduced 60 Milliseconds (ms) to 18 milliseconds of processing time and improved 25% to 3% of reliability, compared to the traditional cryptographic algorithms. Additionally, the proposed model obtains a communication cost of 4260 bits with a memory usage of 680 bytes in the context of security analysis. Full article

We examine the heap of linear connections on anchored vector bundles and Lie algebroids. Naturally, this covers the example of affine connections on a manifold. We present some new interpretations of classical results via this ternary structure of connections. Endomorphisms of linear connections are studied, and their ternary structure, in particular the endomorphism truss, is explicitly presented. We remark that the use of ternary structures in differential geometry is novel and that the endomorphism truss of linear connections provides a concrete geometric example of a truss. Full article

Mainstream semi-supervised learning (SSL) techniques, such as pseudo-labeling and contrastive learning, exhibit strong generalization abilities but lack theoretical understanding. Furthermore, pseudo-labeling lacks the label enhancement from high-quality neighbors, while contrastive learning ignores the supervisory guidance provided by genuine labels. To this end, we first introduce a generalized bias-variance decomposition framework to investigate them. Then, this research inspires us to propose two new techniques to refine them: neighbor-enhanced pseudo-labeling, which enhances confidence-based pseudo-labels by incorporating aggregated predictions from high-quality neighbors; label-enhanced contrastive learning, which enhances feature representation by combining enhanced pseudo-labels and ground-truth labels to construct a reliable and complete symmetric adjacency graph. Finally, we combine these two new techniques to develop an excellent SSL method called GBVSSL. GBVSSL significantly surpasses previous state-of-the-art SSL approaches in standard benchmarks, such as CIFAR-10/100, SVHN, and STL-10. On CIFAR-100 with 400, 2500, and 10,000 labeled samples, GBVSSL outperforms FlexMatch by 3.46%, 2.72%, and 2.89%, respectively. On the real-world dataset Semi-iNat 2021, GBVSSL improves the Top-1 accuracy over CCSSL by 4.38%. Moreover, GBVSSL exhibits faster convergence and enhances unbalanced SSL. Extensive ablation and qualitative studies demonstrate the effectiveness and impact of each component of GBVSSL. Full article

Target detection algorithms can greatly improve the efficiency of tomato leaf disease detection and play an important technical role in intelligent tomato cultivation. However, there are some challenges in the detection process, such as the diversity of complex backgrounds and the loss of leaf symmetry due to leaf shadowing, and existing disease detection methods have some disadvantages in terms of deteriorating generalization ability and insufficient accuracy. Aiming at the above issues, a target detection model for tomato leaf disease based on deep learning with a global attention mechanism, TDGA, is proposed in this paper. The main idea of TDGA includes three aspects. Firstly, TDGA adds a global attention mechanism (GAM) after up-sampling and down-sampling, as well as in the SPPF module, to improve the feature extraction ability of the target object, effectively reducing the interference of invalid targets. Secondly, TDGA uses a switchable atrous convolution (SAConv) in the C3 module to improve the model’s ability to detect. Thirdly, TDGA adopts the efficient IoU loss (EIoU) instead of complete IoU loss (CIoU) to solve the ambiguous definition of aspect ratio and sample imbalance. In addition, the influences of different environmental factors such as single leaf, multiple leaves, and shadows on the performance of tomato disease detection are extensively experimented with and analyzed in this paper, which also verified the robustness of TDGA. The experimental results show that the average accuracy of TDGA reaches 91.40%, which is 2.93% higher than that of the original YOLOv5 network, which is higher than YOLOv5, YOLOv7, YOLOHC, YOLOv8, SSD, Faster R-CNN, RetinaNet and other target detection networks, so that TDGA can be utilized for the detection of tomato leaf disease more efficiently and accurately, even in complex environments. Full article

This paper explores a historical innovation created by Henry Muncaster: a stationary steam engine featuring a single-cylinder horizontal design with a crosshead trunk guide. Through the application of engineering graphics techniques, we have elucidated the functioning of this invention by developing a 3D CAD model based on the original drawings published in Model Engineer magazine in 1957. However, the geometric modeling process faced challenges due to missing and erroneous dimensions for several components. Consequently, dimensional, geometric, and movement constraints were applied to ensure the coherence and functionality of the 3D CAD model, alongside conducting an interference analysis. Ultimately, the proper alignment of the cylinder and crosshead was ascertained, which is crucial for maintaining uniform forces and motions within the steam engine. This alignment is pivotal for achieving balanced operation, minimizing vibrations, and enhancing the overall efficiency of the invention. Full article

Fractional order differential equations often possess inherent symmetries that play a crucial role in governing their dynamics in a variety of scientific fields. In this work, we consider numerical solutions for fractional-order linear delay differential equations. The numerical solution is obtained via the Laplace transform technique. The quadrature approximation of the Bromwich integral provides the foundation for several commonly employed strategies for inverting the Laplace transform. The key factor for quadrature approximation is the contour deformation, and numerous contours have been proposed. However, the highly convergent trapezoidal rule has always been the most common quadrature rule. In this work, the Gauss–Hermite quadrature rule is used as a substitute for the trapezoidal rule. Plotting figures of absolute error and comparing results to other methods from the literature illustrate how effectively the suggested approach works. Functional analysis was used to examine the existence of the solution and the Ulam–Hyers (UH) stability of the considered equation. Full article

A soft fault in an analog circuit is a symptom where the parameter range of a component exists symmetrically to the left and right of its nominal value and exceeds a specific range. The proposed method uses the Grey Wolf Optimization (GWO) optimized tunable Q-factor wavelet transform (TQWT) algorithm for feature refinement, the Inception model for feature extraction, and an SVM for fault diagnosis. First, the Q-factor is optimized to make it more compatible with the signal. Second, the signal is decomposed, and a single-branch reconstruction is performed using the TQWT to extract features adequately. Then, fault feature extraction is conducted using the Inception model to obtain multiscale features. Finally, a Support Vector Machine (SVM) is used to complete the entire fault diagnosis process. The proposed method is comprehensively evaluated using the Sallen–Key bandpass filter circuit and the four-op-amp biquad high-pass filter circuit widely used in electronic systems. The experimental results prove that the proposed method outperforms the existing methods in terms of diagnosis accuracy and reliability. Full article

In this paper, we conduct a thorough study of CR-warped product submanifolds in a Kaehler manifold, utilizing a semi-symmetric metric connection within the framework of warped product geometry. Our analysis yields fundamental and noteworthy results that illuminate the characteristics of these submanifolds. Additionally, we investigate the implications of our findings on the homology of these submanifolds, offering insights into their topological properties. Notably, we present a compelling proof demonstrating that, under a specific condition, stable currents cannot exist for these warped product submanifolds. Our research outcomes contribute significant knowledge concerning the stability and behavior of CR-warped product submanifolds equipped with a semi-symmetric metric connection. Furthermore, this work establishes a robust groundwork for future explorations and advancements in this particular field of study. Full article

Inspired by the fact that both the dilaton potential encoding the trace anomalies of QCD and the Polyakov loop potential measuring the deconfinement phase transition can be expressed in the logarithmic forms, as well as the fact that the scale symmetry is expected to be restoring and colors are deconfined in extreme conditions such as high temperatures and/or densities, we conjecture a relation between the dilaton potential and the Polyakov loop potential. Explicitly, we start from the Coleman–Weinberg type potential of a real scalar field—a dilaton or conformal compensator—and make an ansatz of the relation between this scalar field and the Polyakov loop to obtain the Polyakov loop potential, which can be parameterized in Lattice QCD (LQCD) in the pure glue sector. We find that the coefficients of Polyakov potential fitted from Lattice data are automatically satisfied in this ansatz, the locations of deconfinement and scale restoration are locked to each other, and the first-order phase transition can be realized. Extensions to the low-energy effective quark models are also discussed. The conjectured relation may deepen our understanding of the evolution of the universe, the mechanism of electroweak symmetry breaking, the phase diagram of QCD matter, and the properties of neutron stars. Full article

This study examines the behavior of single-walled carbon nanotubes (SWCNTs) suspended in a water-based ionic solution, driven by the combined mechanisms of electroosmosis and peristalsis through ciliated media. The inclusion of nanoparticles in ionic fluid expands the range of potential applications and allows for the tailoring of properties to suit specific needs. This interaction between ionic fluids and nanomaterials results in advancements in various fields, including energy storage, electronics, biomedical engineering, and environmental remediation. The analysis investigates the influence of a transverse magnetic field, thermal radiation, and mixed convection acting on the channel walls. The novel physical outcomes include enhanced propulsion efficiency due to SWCNTs, understanding the influence of thermal radiation on fluid behavior and heat exchange, elucidation of the interactions between SWCNTs and the nanofluid, and recognizing implications for microfluidics and biomedical engineering. The Poisson–Boltzmann ionic distribution is linearized using the modified Debye–Hückel approximation. By employing real-world approximations, the governing equations are simplified using long-wavelength and low-Reynolds-number approximation. Conducting sensitivity analyses or exploring the impact of higher-order corrections on the model’s predictions in recent literature might alter the results significantly. This acknowledges the complexities of the modeling process and sets the groundwork for further enhancement and investigation. The resulting nonlinear system of equations is solved through regular perturbation techniques, and graphical representations showcase the variation in significant physical parameters. This study also discusses pumping and trapping phenomena in the context of relevant parameters. Full article

In dense scenes, pedestrians often exhibit a variety of symmetrical features, such as symmetry in body contour, posture, clothing, and appearance. However, pedestrian detection poses challenges due to the mutual occlusion of pedestrians and the small scale of distant pedestrians in the image. To address these challenges, we propose a pedestrian detection algorithm tailored for dense scenarios called YOLO-RAD. In this algorithm, we integrate the concept of receiving field attention (RFA) into the Conv and C2f modules to enhance the feature extraction capability of the network. A self-designed four-layer adaptive spatial feature fusion (ASFF) module is introduced, and shallow pedestrian feature information is added to enhance the multi-scale feature fusion capability. Finally, we introduce a small-target dynamic head structure (DyHead-S) to enhance the capability of detecting small-scale pedestrians. Experimental results on WiderPerson and CrowdHuman, two challenging dense pedestrian datasets, show that compared with YOLOv8n, our YOLO-RAD algorithm has achieved significant improvement in detection performance, and the detection performance of [email protected] has increased by 2.5% and 6%, respectively. The detection performance of [email protected]:0.95 was improved by 2.7% and 6.8%, respectively. Therefore, the algorithm can effectively improve the performance of pedestrian detection in dense scenes. Full article

In today’s TEST interconnected world, the security of 5G Medical IoT networks is of paramount concern. The increasing number of connected devices and the transmission of vast amounts of data necessitate robust measures to protect information integrity and confidentiality. However, securing Medical IoT edge nodes poses unique challenges due to their limited resources, making the implementation of cryptographic protocols a complex task. Within these protocols, modular multiplication assumes a crucial role. Therefore, careful consideration must be given to its implementation. This study focuses on developing a resource-efficient hardware implementation of the Montgomery modular multiplication algorithm over GF($2^l$), which is a critical operation in cryptographic algorithms. The proposed solution introduces a bit-serial systolic array layout with a modular structure and local connectivity between processing elements. This design, inspired by the principles of symmetry, allows for efficient utilization of resources and optimization of area and delay management. This makes it well-suited for deployment in compact Medical IoT edge nodes with limited resources. The suggested bit-serial processor structure was evaluated through ASIC implementation, which demonstrated substantial improvements over competing designs. The results showcase an average area reduction of 24.5% and significant savings in the area–time product of 26.2%. Full article

Abstract: The modular robotic arms can achieve desired performances in different scenarios through the combination of various modules, and concurrently hold the potential to exhibit geometric symmetry and uniform mass symmetry. Therefore, selecting the appropriate combination of modules is crucial for realizing the functions of the robotic arm and ensuring the elegance of the system. To this end, this paper proposes a double deep Q-network (DDQN)-based configuration design algorithm for modular robotic arms, which aims to find the optimal configuration under different tasks. First, a library of small modules of collaborative robotic arms consisting of multiple tandem robotic arms is constructed. These modules are described in a standard format that can be directly imported into the software for simulation, providing greater convenience and flexibility in the development of modular robotic arms. Subsequently, the DDQN design framework for module selection is established to obtain the optimal robotic arm configuration. The proposed method could deal with the overestimation problem in the traditional deep Q-network (DQN) method and improve the estimation accuracy of the value function for each module. In addition, the experience replay mechanism is improved based on the SumTree technique, which enables the algorithm to make effective use of historical experience and prevents the algorithm from falling into local optimal solutions. Finally, comparative experiments are carried out on the PyBullet simulation platform to verify the effectiveness and superiority of the configuration design method developed in the paper. The simulation results show that the proposed DDQN-based method with experience replay mechanism has higher search efficiency and accuracy compared to the traditional DQN scheme. Full article

In the present paper, we consider an effective computational method to analyze a coupled dynamical system with Caputo–Fabrizio fractional derivative. The method is based on expanding the approximate solution into a symmetry Haar wavelet basis. The Haar wavelet coefficients are obtained by using the collocation points to solve an algebraic system of equations in mathematical physics. The error analysis of this method is characterized by a good convergence rate. Finally, some numerical examples are presented to prove the accuracy and effectiveness of this method. Full article

Many studies have shown successful applications of the Dirichlet process mixture model (DPMM) for clustering continuous data. Beyond continuous data, in practice, one can expect to see different data types, including ordinal and nominal data. Existing DPMMs for clustering mixed-type data assume a strict covariance matrix structure, resulting in an overfit model. This article explores a DPMM for mixed-type data that allows the covariance matrix to differ from one cluster to another. We assume an underlying latent variable framework for ordinal and nominal data, which is then modeled jointly with the continuous data. The identifiability issue on the covariance matrix poses computational challenges, thus requiring a nonstandard inferential algorithm. The applicability and flexibility of the proposed model are illustrated through simulation examples and real data applications. Full article

In this paper, we present a new class of linear fractional differential operators that are based on classical Gaussian hypergeometric functions. Then, we utilize the new operators and the concept of differential subordination to construct a convex set of analytic functions. Moreover, through an examination of a certain operator, we establish several notable results related to differential subordination. In addition, we derive inclusion relation results by employing Briot–Bouquet differential subordinations. We also introduce a perspective study for developing subordination results using Gaussian hypergeometric functions and provide certain properties for further research in complex dynamical systems. Full article