Search Results (45)

Over the last decade, numerical simulations and experiments have confirmed the existence of a novel class of vibrationally excited solid-particle attractors in cubic cavities containing a fluid in non-isothermal conditions. The diversity of emerging particle structures, in both morphology and multiplicity, depends strongly on the uni- or multi-directional nature of the imposed temperature gradients. The present study seeks to broaden this theoretical framework by further increasing the complexity of the thermal “information” coded along the external boundary of the fluid container. In particular, in place of the thermal inhomogeneities located in the center of otherwise uniformly cooled or heated walls, here, a cubic cavity with temperature boundary conditions satisfying the D₂h (in Schoenflies notation) or “mmm” (in Hermann–Mauguin notation) symmetry is considered. This configuration, equivalent to a bipartite vertex coloring of a cube leading to a total of 24 thermally controlled planar surfaces, possesses three mutually perpendicular twofold rotation axes and inversion symmetry through the cube’s center. To reduce the problem complexity by suppressing potential asymmetries due to fluid-dynamic instabilities of inertial nature, the numerical analysis is carried out under the assumption of dilute particle suspension and one-way solid–liquid phase coupling. The results show that a kaleidoscope of new particle structures is enabled, whose main distinguishing mark is the essentially one-dimensional (filamentary) nature. These show up as physically disjoint or intertwined particle circuits in striking contrast to the single-curvature or double-curvature spatially extended accumulation surfaces reported in earlier investigations. Full article

Fixed-time coordination is critical for networked unmanned aerial vehicle (UAV) systems to accomplish time-sensitive missions such as rapid target encirclement, cooperative search, and emergency response. However, dynamic topology variations, caused by mission reassignment, obstacle avoidance, or communication disruptions, along with model uncertainties and external disturbances, present significant challenges to robust and timely coordination. To address these issues, this paper investigates the fixed-time bipartite containment tracking control problem of uncertain multi-UAV systems under switching communication topologies. A neuroadaptive robust containment tracking controller is developed to guarantee that all follower UAVs converge within a fixed time to the region spanned by multiple dynamic leaders, regardless of initial conditions. To handle unknown nonlinear dynamics, a neuroadaptive estimator is constructed using online parameter adaptation. A topology-dependent multiple Lyapunov function framework is employed to rigorously establish fixed-time convergence under switching topologies. Moreover, an explicit upper bound on the convergence time is analytically derived as a function of system parameters and dwell time constraints. Comparative analysis demonstrates that the proposed method reduces conservativeness in convergence time estimation and enhances robustness against frequent topology changes. Simulation results are provided to validate the effectiveness and advantages of the proposed control scheme. Full article

Signed networks, which incorporate both cooperative and antagonistic interactions, naturally give rise to symmetric behaviors in multi-agent systems. One such behavior is bipartite containment tracking, where follower agents converge to a symmetric configuration determined by multiple groups of leaders with opposing influence. Moreover, a timely response is critical to ensuring high performance in containment tracking tasks, particularly for high-order multi-agent systems operating in dynamic and uncertain environments. To this end, this paper investigates the predefined-time bipartite containment tracking problem for high-order multi-agent systems affected by external disturbances. A robust tracking control scheme is developed based on the backstepping method to ensure that the tracking errors converge to a predefined residual set within a user-specified time. The convergence time is explicitly adjustable through a design parameter, and the proposed scheme effectively avoids the singularities often encountered in conventional predefined-time control approaches. The stability and robustness of the proposed scheme are rigorously established through Lyapunov-based analysis, and extensive simulation results are provided to validate our theoretical findings. Full article

With the increasing deployment of Unmanned Aerial Vehicle (UAV) swarms in uncertain and dynamically changing environments, optimal cooperative control has become essential for ensuring robust and efficient system coordination. To this end, this paper designs a data-driven optimal bipartite containment tracking control scheme for multi-UAV systems under compound uncertainties. A novel Dynamic Iteration Regulation Strategy (DIRS) is proposed, which enables real-time adjustment of the learning iteration step according to the task-specific demands. Compared with conventional fixed-step data-driven algorithms, the DIRS provides greater flexibility and computational efficiency, allowing for better trade-offs between the performance and cost. First, the optimal bipartite containment tracking control problem is formulated, and the associated coupled Hamilton–Jacobi–Bellman (HJB) equations are established. Then, a data-driven iterative policy learning algorithm equipped with the DIRS is developed to solve the optimal control law online. The stability and convergence of the proposed control scheme are rigorously analyzed. Furthermore, the control law is approximated via the neural network framework without requiring full knowledge of the model. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of the proposed DIRS-based optimal containment tracking scheme for multi-UAV systems, which can reduce the number of iterations by 88.27% compared to that for the conventional algorithm. Full article

The Maximum Colored Cut problem aims to seek a bipartition of the vertex set of a graph, maximizing the number of colors in the crossing edges. It is a classical Max-Cut problem if the host graph is rainbow. Let $mcc\left(G\right)$ denote the maximum number of colors in a cut of an edge-colored graph G. Let $C_k$ be a cycle of length k; we say G is PC-$C_k$-free if G contains no properly colored $C_k$. We say G is a p-edge-colored graph if there exist p colors in G. In this paper, we first show that if G is a PC-$C_3$-free p-edge-colored complete 4-partite graph, then $mcc\left(G\right)=p$. Let $k\ge 3$ be an integer. Then, we show that if G is a PC-$C_4$-free p-edge-colored complete k-partite graph, then $mcc\left(G\right)\ge min\{p-1,15p/16\}$. Finally, for a p-edge-colored complete graph G, we prove that $mcc\left(G\right)\ge p-1$ if G is PC-$C_4$-free, and $mcc\left(G\right)\ge min\{p-6,7p/8\}$ if G is PC-$C_5$-free and $p\ge 7$. Full article

The n-dimensional folded hypercube, denoted as ${FQ}_n$, is an extended version of the n-dimensional hypercube $Q_n$, constructed by adding edges between opposite vertices in $Q_n$, i.e., vertices with complementary addresses. Folded hypercubes outperform traditional hypercubes in various metrics such as the fault diameter, connectivity, and path length. It is known that ${FQ}_n$ has bipartite characteristics in odd $n\ge 3$ and non-bipartite in even $n\ge 2$. In this paper, let ${FF}_v$ represent the set of faulty vertices in ${FQ}_n$ and suppose that each vertex is adjacent to at least four fault-free vertices in ${FQ}_n-{FF}_v$. Then, we consider the following path embedding properties: (1) For every odd $n\ge 3$, ${FQ}_n-{FF}_v$ contains a fault-free path with a length of at least $2^n-2\left|{FF}_v\right|-1$ (respectively, $2^n-2\left|{FF}_v\right|-2$) between any two fault-free vertices of odd (respectively, even) distance if $\left|{FF}_v\right|\le 2n-5$; (2) For every even $n\ge 4$, ${FQ}_n-{FF}_v$ contains a fault-free path with a length of at least $2^n-2\left|{FF}_v\right|-1$ between any two fault-free vertices if $\left|{FF}_v\right|\le 2n-6$. Full article

This paper addresses the event-triggered neuroadaptive bipartite containment tracking problem for networked unmanned aerial vehicles (UAVs) subject to resource constraints and actuator failures. A fully distributed event-triggered mechanism is innovatively developed to eliminate dependency on global information while rigorously excluding the Zeno phenomenon through nonperiodic threshold verification. The proposed mechanism enables neighboring UAVs to exchange information and update control signals exclusively at triggering instants, significantly reducing communication burdens and energy consumption. To handle unknown nonlinear dynamics under resource-limited scenarios, a novel event-triggered neural network (NN) approximation scheme is established where weight updating occurs only during event triggers, effectively decreasing computational resource occupation. Simultaneously, an adaptive robust compensation mechanism is constructed to counteract composite disturbances induced by actuator failures and approximation residuals. Based on the Lyapunov stability analysis, we theoretically prove that all closed-loop signals remain uniformly ultimately bounded while achieving prescribed bipartite containment objectives, where follower UAVs ultimately converge to the dynamic convex hull formed by multiple leaders with cooperative-competitive interactions. Finally, numerical simulations are conducted to validate the effectiveness of the theoretical results. Comparative simulation results show that the proposed event-triggered control scheme reduces the utilization of resources by $95\%$ and $67\%$ compared with the traditional time-triggered and static-triggered mechanisms, respectively. Full article

Cross-Site Scripting (XSS) attacks are a common source of vulnerability for web applications, necessitating scalable mechanisms for detection. In this work, a new method based on bipartite graph-based feature extraction and an ensemble learning classifier containing CNN, LSTM, and GRU is introduced. Our proposed bipartite graph model is novel as the payloads constitute the first set, while the words constructing the payloads comprise the second set. This representation allows structural and contextual dependencies to be extracted so the model can recognize complex and obfuscated XSS payloads. Our method surpasses state-of-the-art methods by having 99.97% detection accuracy. It has a significantly increased ability to detect complicated payload variations by utilizing co-occurrence patterns and interdependence between smaller payload parts through the adoption of these bipartite features. In addition to improving the F1-score, recall, and precision associated with such methods, it also demonstrates the adaptability of graph-based representation in cybersecurity applications. Our findings highlight the possibility of integrating ensemble classifiers and refined feature engineering into a scalable, precise XSS detection system. Full article

The threshold protocol game is a graphical game that models the adoption of an idea or product through a population. There are two states players may take in the game, and the goal of the game is to motivate the state that begins in the minority to spread to every player. Here, the threshold protocol game is defined, and existence results are studied on infinite graphs. Many generalizations are proposed and applied. This work explores the impact of graph topology on the outcome of the threshold protocol game and consequently considers finite graphs. By exploiting the well-known topologies of complete and complete bipartite graphs, the outcome of the threshold protocol game can be fully characterized on these graphs. These characterizations are ideal, as they are given in terms of the game parameters. More generally, initial conditions in terms of game parameters that cause the preferred game outcome to occur are identified. It is shown that the necessary conditions differ between non-bipartite and bipartite graphs because non-bipartite graphs contain odd cycles while bipartite graphs do not. These results motivate the primary result of this work, which is an exhaustive list of achievable game outcomes on bipartite graphs. While possible outcomes are identified, it is noted that a complete characterization of when game outcomes occur is not possible on general bipartite graphs. Full article

This paper presents research in the field of optimization in maritime passenger traffic that can ensure the long-term sustainability of coastal maritime passenger lines system. For the purpose of the research contained in this paper, it has been hypothesized that the optimal arrangement of boats within a coastal maritime passenger lines system will reduce the consumption of propulsion energy, the emission of harmful gasses and operating costs. The aim of this paper is to present an efficient algorithm for a reduction in propulsion energy consumption in coastal maritime passenger lines systems by reassigning boats to lines that they service. The problem is modeled using a bipartite graph and the solution is obtained by searching for optimal matching using Edmonds’ algorithm. The authors apply, for the first time, Edmonds’ algorithm to the problems of the optimization of assignments of boats to lines. The research results were confirmed by tests on a representative example. The optimization results on only 10 ships in the given example show yearly savings of 91,097.30 L of fuel (lowering costs by EUR 69,233.95) and reducing CO₂ by 243.59 tons, which proves that this algorithm found a much more efficient arrangement that could result in a significant reduction in propulsion energy consumption, thus providing economic and ecological benefits. Full article

This paper introduces an advanced observer-based control strategy designed for fractional multi-agent systems operating in hostile environments. We take into account the dynamic nature of the agents with nonlinear delayed dynamics and consider external disturbances affecting the system. The manuscript presents an improved observation-based control approach tailored for fractional-order multi-agent systems functioning in challenging conditions. We also establish various applicable conditions governing the creation of observers and disturbance compensation controllers using the fractional Razmikhin technique, signed graph theory, and matrix transformation. Furthermore, our investigation includes observation-based control on switching networks by employing a typical Lyapunov function approach. Finally, the effectiveness of the proposed strategy is demonstrated through the analysis of two simulation examples. Full article

This study investigated the stability of bipartite nonlinear fractional-order multi-agent systems (FOMASs) in the presence of false data injection attacks (FDIAs) in a hostile environment. To tackle this problem we used signed graph theory, the Razumikhin methodology, and the Lyapunov function method. The main focus of our proposed work is to provide a method of stability for FOMASs against FDIAs. The technique of Razumikhin improves the Lyapunov-based stability analysis by supporting the handling of the intricacies of fractional-order dynamics. Moreover, utilizing signed graph theory, we analyzed both hostile and cooperative interactions between agents within the MASs. We determined the system stability requirements to ensure robustness against erroneous data injections through comprehensive theoretical investigation. We present numerical examples to illustrate the robustness and efficiency of our proposed technique. Full article

Anticipating the demand for professional job market skills needs to consider trends such as automation, offshoring, and the emerging Gig economy, as they significantly impact the future readiness of skills. This article draws on the scientific literature, expert assessments, and deep learning to estimate two indicators of high relevance for a skill’s future readiness: its automatability and offshorability. Based on gold standard data, we evaluate the performance of Support Vector Machines (SVMs), Transformers, Large Language Models (LLMs), and a deep learning ensemble classifier for propagating expert and literature assessments on these indicators of yet unseen skills. The presented approach uses short bipartite skill labels that contain a skill topic (e.g., “Java”) and a corresponding verb (e.g., “programming”) to describe the skill. Classifiers thus need to base their judgments solely on these two input terms. Comprehensive experiments on skewed and balanced datasets show that, in this low-token setting, classifiers benefit from pre-training and fine-tuning and that increased classifier complexity does not yield further improvements. Full article

The vertex quadrangulation $QG$ of a 4-regular graph G visually looks like a graph whose vertices are depicted as empty squares, and the connecting edges are attached to the corners of the squares. In a previous work [JOMC 59, 1551–1569 (2021)], the question was posed: does the spectrum of an arbitrary unweighted graph $QG$ include the full spectrum $\{3,{(-1)}^3\}$ of the tetrahedron graph (complete graph $K_4$)? Previously, many bipartite and nonbipartite graphs $QG$ with such a subspectrum have been found; for example, a nonbipartite variant of the graph $Q{K}_5$. Here, we present one of the variants of the nonbipartite vertex quadrangulation $QO$ of the octahedron graph O, which has eigenvalue $(-1)$ of multiplicity 2 in the spectrum, while the spectrum of the bipartite variant $QO$ contains eigenvalue $(-1)$ of multiplicity 3. Thus, in the case of nonbipartite graphs, the answer to the question posed depends on the particular graph $QG$. Here, we continue to explore the spectrum of graphs $QG$. Some possible connections of the mathematical theme to chemistry are also noted. Full article

The trimming of fast-evolving sites, often known as “slow–fast” analysis, is broadly used in microbial phylogenetic reconstruction under the assumption that fast-evolving sites do not retain an accurate phylogenetic signal due to substitution saturation. Therefore, removing sites that have experienced multiple substitutions would improve the signal-to-noise ratio in phylogenetic analyses, with the remaining slower-evolving sites preserving a more reliable record of evolutionary relationships. Here, we show that, contrary to this assumption, even the fastest-evolving sites present in the conserved proteins often used in Tree of Life studies contain reliable and valuable phylogenetic information, and that the trimming of such sites can negatively impact the accuracy of phylogenetic reconstruction. Simulated alignments modeled after ribosomal protein datasets used in Tree of Life studies consistently show that slow-evolving sites are less likely to recover true bipartitions than even the fastest-evolving sites. Furthermore, site-specific substitution rates are positively correlated with the frequency of accurately recovered short-branched bipartitions, as slowly evolving sites are less likely to have experienced substitutions along these intervals. Using published Tree of Life sequence alignment datasets, we also show that both slow- and fast-evolving sites contain similarly inconsistent phylogenetic signals, and that, for fast-evolving sites, this inconsistency can be attributed to poor alignment quality. Furthermore, trimming fast sites, slow sites, or both is shown to have a substantial impact on phylogenetic reconstruction across multiple evolutionary models. This is perhaps most evident in the resulting placements of the Eukarya and Asgardarchaeota groups, which are especially sensitive to the implementation of different trimming schemes. Full article