The article presents a method for assessing the traffic demand on city streets and roads based on open data using a gravity model. The relevance of the research topic is due to the limited availability of reliable and comprehensive data on actual traffic congestion in Russian cities. The aim of the study is to develop an approach that can serve as an al-ternative or supplement to assessing and forecasting road congestion in conditions of limited data. The initial data used are the parameters of urban neighborhoods – population, density and diversity of services, as well as land use types – which allow calculating indicators of demand and attractiveness for travel between neighborhoods. Based on this data, a correspondence matrix is formed, reflecting the relative volume of traffic flows between nodes of the street and road network, presented in the form of a weighted directed graph. The method allows assessing the demand and potential congestion of city roads without using closed or expensive road traffic data, which is especially relevant when designing new sections of the street and road network and planning urban infrastructure. An experimental test was carried out on the example of Vasilyevsky Island in St. Petersburg using open data from OpenStreetMap. The proposed approach can be useful for improving the efficiency of urban planning and transport management.

A group has Property (NL) if it does not admit a loxodromic element in any hyperbolic action. In other words, a group with this property is inaccessible for study from the perspective of hyperbolic actions. This property was introduced by Balasubramanya, Fournier-Facio and Genevois, who initiated the study of this property. We expand on this research by studying Property (NL) in Coxeter groups, a class of groups that are defined by an underlying graph. One of our main results show that a right-angled Coxeter group (RACG) has Property (NL) if and only if its defining graph is complete. We then move beyond the right-angled case to show that if a defining graph is disconnected, its corresponding Coxeter group does not have Property (NL). Lastly, we classify which triangle groups (Coxeter groups with three generators) have Property (NL).

Linear compartmental models are a widely used tool for analyzing systems arising in biology, medicine, and more. In such settings, it is essential to know whether model parameters can be recovered from experimental data. This is the identifiability problem. For a class of linear compartmental models with one input and one output, namely, those for which the underlying graph is a bidirected tree, Bortner et al. completely characterized which such models are structurally identifiability, which means that every parameter is generically locally identifiable. Here, we delve deeper, by examining which individual parameters are locally versus globally identifiable. Specifically, we analyze mammillary models, which consist of one central compartment which is connected to all other (peripheral) compartments. For these models, which fall into five infinite families, we determine which individual parameters are locally versus globally identifiable, and we give formulas for some of the globally identifiable parameters in terms of the coefficients of input-output equations. Our proofs rely on a combinatorial formula due to Bortner et al. for these coefficients.

ABSTRACT This paper presents an event‐triggered distributed control protocol designed for scenarios involving Denial‐of‐Service (DoS) attacks within directed communication graphs. We address the consensus problem of uncertain systems by employing neural networks to approximate nonlinear components. Compared with traditional neural network observers, the proposed method incorporates damping terms to ensure the boundedness of neural network estimators. Initially, an auxiliary system was constructed to decouple the consensus problem under a directed communication graph framework. It is demonstrated that the uncertain nonlinear system can achieve consensus through the utilization of information exchanged among neighboring agents. Subsequently, to curtail the consumption of communication resources, we introduce an event‐triggered control protocol based on the aforementioned approach, incorporating an effective event‐triggering function. Building upon the proposed control protocol, we further develop a control strategy tailored for systems under DoS attacks. Furthermore, the event‐triggered mechanism without using global information in trigger condition not only curtails superfluous information exchange among agents but also precludes the occurrence of Zeno behavior (i.e., infinite triggering within a finite time interval). Finally, numerical simulations are carried out to validate the efficacy of the proposed control protocol.

Abstract Given a countable abelian group , we construct a row‐finite directed graph such that the ‐group of the graph ‐algebra is canonically isomorphic to . Moreover, under natural identification, each element of is a lift of an automorphism of the graph ‐algebra .

Precisely identifying cancer drivers helps us to understand the molecular mechanisms of cancer, offering critical targets for early diagnosis. Despite the increasing application of graph neural networks in predicting cancer driver genes, existing approaches do not fully leverage the information from gene networks, and are unable to effectively extract node features from directed graphs. To this end, we propose MDIGNN, a novel deep learning model designed to identify cancer driver genes by integrating directed gene networks with multi-omics data. First, we construct a directed graph through the integration of existing gene networks from diverse databases and multi-omics data. Then, to encode the edge directionality, we develop a graph neural network based on the magnetic Laplacian, which relies on a complex Hermitian matrix for representing the directed graph structure. Next, we apply the channel attention and spatial attention mechanisms to improve the model’s feature representation ability. Finally, MDIGNN uses a fully connected layer to compute the cancer driver probability for each gene. In a comparative evaluation, MDIGNN outperforms existing state-of-the-art methods in the field, and it is capable of detecting potential cancer driver genes.

ABSTRACT This paper investigates the leaderless consensus problem of high‐order multi‐agent systems (MASs) under a general directed graph via a fully distributed event‐triggered output feedback control strategy. First, a fully distributed event‐triggered state compensator with a static control gain is constructed, by which the information of the neighbors is asynchronously and intermittently obtained. Since only the output information can be used, an event‐triggered output feedback control strategy is designed without using any global information of MAS, with which leaderless consensus is guaranteed asymptotically, and the state of each agent is dynamically evolving instead of converging to some stationary point. The Zeno behavior is strictly ruled out in the event‐triggered communication. The effectiveness is finally verified by some simulation examples.

Purpose: to eliminate the methodological gap between the evolving needs of the labour market particularly in light of the digital transformation in transportation and the slow-moving processes associated with the development of major professional educational programmes (MPEP). Methods: various existing approaches to modelling MPEP have been systematically analyzed and classified. The structure of the programme has been formalized through graph theory, while intelligent data analysis techniques have been applied to assess and process the demands of employers. Results: the study reveals the limitations associated with both expert and ontological approaches when dealing with large arrays of labor market data. A novel mathematical model of the MPEP has been formulated as a weighted directed graph G = (V, E), where the vertices integrate various disciplines, competencies, and employer requirements, including professional standard and job vacancies. Furthermore, an innovative integral indicator for programme quality is introduced, derived from an additive convolution of criteria assessing the completeness of competency coverage and the graph connectivity. Practical significance: the proposed model and algorithms establish a foundation for an automated decision support system. This system aims to minimize the adaptation time of educational programmes to the demands of high-tech sectors, such as unmanned transportation and digital logistics, thereby facilitating a shift towards evidence-based management of education.

Today is the 21st advent the era of modern digital world, the digital world where internet and speed of internet is the main concern for individuals and organizations by using computer networks. Therefore, in this research we formalize and analyze the average usage of worldwide countries by using complex network and model the dataset of worldwide internet speed. Furthermore, using this data set we observe the complex network with global internet speed by average (Degree Distribution, Betweenness, and Closeness) by using weighted directed graph while the edge merge strategy is sum.

Over the past decade, a number of quantum processes have been proposed which are logically consistent, yet feature a cyclic causal structure. However, there is no general formal method to construct a process with an exotic causal structure in a way that ensures, and makes clear why, it is consistent. Here we provide such a method, given by an extended circuit formalism. This only requires directed graphs endowed with Boolean matrices, which encode basic constraints on operations. Our framework (a) defines a set of elementary rules for checking the validity of any such graph, (b) provides a way of constructing consistent processes as a circuit from valid graphs, and (c) yields an intuitive interpretation of the causal relations within a process and an explanation of why they do not lead to inconsistencies. We display how several standard examples of exotic processes, including ones that violate causal inequalities, are among the class of processes that can be generated in this way; we conjecture that this class in fact includes all unitarily extendible processes.

A small-gain approach for consensus of heterogeneous linear multi-agent systems.

FD-GCN: Feedback Directed Graph Convolutional Network for skeleton-based action recognition

Dynamic sparse directed graph convolutional network with attention mechanisms for EEG emotion recognition

Molecular self-assembly directed edge engineering of lignin-derived Fe-N-C single-atom catalysts for efficient oxygen reduction reaction

The present paper is devoted to the introduction and development of the notions of multivalued graphic contractions and multivalued GF-contractions in the setting of F-metric spaces. By extending the idea of contractions to multivalued mappings associated with an underlying graph structure, we aim to enrich the existing theory of fixed point results in generalized metric frameworks. The main contribution of this study is the establishment of new fixed point theorems for these classes of mappings in F-metric spaces, which provide a natural extension of classical fixed point principles. Furthermore, in order to demonstrate the validity and applicability of our theoretical findings, we construct a non-trivial illustrative example that highlights how the proposed conditions can be effectively utilized. These results not only advance the fixed point theory in abstract metric settings but also open potential avenues for applications in mathematical analysis and applied sciences.

Arithmetic circuits are a natural well-studied model for computing multivariate polynomials over a field. In this paper, we study planar arithmetic circuits . These are circuits whose underlying graph is planar. In particular, we prove an Ω ( n log n ) lower bound on the size of planar arithmetic circuits computing explicit bilinear forms on 2 n variables. As a consequence, we get an Ω ( n log n ) lower bound on the size of arithmetic formulas and planar algebraic branching programs computing explicit bilinear forms on 2 n variables. This is the first such lower bound on the formula complexity of an explicit bilinear form. In the case of read-once planar circuits, we show Ω ( n 2 ) size lower bounds for computing explicit bilinear forms on 2 n variables. Furthermore, we prove fine separations between the various planar models of computations mentioned above. In addition to this, we look at multi-output planar circuits and show Ω ( n 4/3 ) size lower bound for computing an explicit linear transformation on n -variables. For a suitable definition of multi-output formulas, we extend the above result to get an Ω ( n 2 /log n ) size lower bound. As a consequence, we demonstrate that there exists an n -variate polynomial computable by an n 1 + o (1) -sized formula such that any multi-output planar circuit (resp., multi-output formula) simultaneously computing all its first-order partial derivatives requires size Ω ( n 4/3 ) (resp., Ω ( n 2 /log n )). This shows that a statement analogous to that of Baur, Strassen [3] does not hold in the case of planar circuits and formulas.

This paper investigates the problem of practical prescribed-time trajectory tracking consensus for higher-order heterogeneous multi-agent systems (MASs) with unknown time-varying control gains and non-vanishing uncertainties, while also taking external disturbances into account. A directed graph is employed to characterize the communication topology. By introducing a time-varying scaling function and adopting an adaptive backstepping design, a distributed controller is developed that achieves practical prescribed-time trajectory tracking consensus of heterogeneous MASs, while avoiding unbounded control gains and preserving the continuity of control inputs. Furthermore, to optimize the use of communication resources, an event-triggered mechanism is incorporated to reduce the update frequency of controllers. Finally, numerical simulations are carried out to verify the effectiveness of the proposed method.

Abstract As the operational complexity of gas turbines increases due to grid fluctuation and renewable integration, reliable anomaly detection becomes vital for ensuring safety and efficiency. However, most existing methods require extensive labeled anomalies and face challenges from parameter coupling and data drift. This study proposes a normal behavior modeling (NBM) spatial-temporal feature-enhanced fusion network that requires only normal operational data to address these challenges. First, the relationships between variables are represented using a directed graph model based on the sensor monitoring scheme, facilitating the selection of relevant input parameters. Then, a temporal convolutional network, combined with channel attention mechanisms, is used to extract spatial features, while a Transformer encoder with multi-head attention captures temporal dependencies. A cross-attention mechanism is incorporated to integrate spatial and temporal information, and a normal behavior model for gas turbine operational parameters is established. Finally, a dynamic threshold calculation method is proposed for anomaly detection, which does not assume a normal distribution but analyzes the residual distribution. Comprehensive evaluations on real industrial operation data demonstrate that the proposed method achieves high prediction accuracy, with a mean absolute error of 0.65 and a root mean square error of 0.83 on the test set. Additional validation on the turbofan engine dataset confirms the method’s robustness in detecting anomalies early during degradation processes. This approach provides a reliable foundation for anomaly detection in gas turbine operational parameters.

Given a directed graph, the Minimum Feedback Arc Set (FAS) problem asks for a minimum (size) set of arcs in a directed graph, which, when removed, results in an acyclic graph. In a seminal paper, Berger and Shor [1], in 1990, developed initial upper bounds for the FAS problem in general directed graphs. Here we find asymptotic lower bounds for the FAS problem in a class of random, oriented, directed graphs derived from the Erdős-Rényi model \(G(n,M)\), with n vertices and M (undirected) edges, the latter randomly chosen. Each edge is then randomly given a direction to form our directed graph. We show that \[Pr\left(\textbf{Y}^* \le M \left( \frac{1}{2} -\sqrt{\frac{\log n}{\Delta_{av}}}\right)\right),\] approaches zero exponentially in \(n\), with \(\textbf{Y}^*\) the (random) size of the minimum feedback arc set and \(\Delta_{av}=2M/n\) the average vertex degree. Lower bounds for random tournaments, a special case, were obtained by Spencer [13] and de la Vega [3] and these are discussed. In comparing the bound above to averaged experimental FAS data on related random graphs developed by K. Hanauer [8] we find that the approximation \(\textbf{Y}^*_{av} \approx M\left( \frac{1}{2} -\frac{1}{2}\sqrt{\frac{\log n}{\Delta_{av}}}\right)\) lies remarkably close graphically to the algorithmically computed average size \(\textbf{Y}^*_{av}\) of minimum feedback arc sets.

Abstract The diameter of a directed graph is the maximum distance between any pair of vertices. We study a problem that generalizes Oriented Diameter : For a given directed graph and a positive integer d , what is the minimum number of arc reversals required to obtain a graph with diameter at most d ? We investigate variants of this problem, considering the number of arc reversals and the target diameter as parameters. We show hardness results under certain parameter restrictions, and give polynomial time algorithms for planar and cactus graphs. This work is partly motivated by the relation between oriented diameter and the volume of directed edge polytopes, which we show to be independent.