Search Results (95)

Monitoring traffic flow across large-scale transportation networks is essential for effective traffic management, yet comprehensive sensor deployment is often infeasible due to financial and practical constraints. The traffic sensor location problem (TSLP) aims to determine the minimal set of sensor placements needed to achieve full link flow observability. Existing solutions primarily rely on algebraic or optimization-based approaches, but often neglect the impact of sensor measurement errors and struggle with scalability in large, complex networks. This study proposes a new scalable and robust methodology for solving the TSLP under uncertainty, incorporating a formulation that explicitly models the propagation of measurement errors in sensor data. Two nonlinear integer optimization models, Min-Max and Min-Sum, are developed to minimize the inference error across the network. To solve these models efficiently, we introduce the BBA Algorithm (BBA) as an adaptive metaheuristic optimizer, not as a subject of comparative study, but as an enabler of scalability within the proposed framework. The methodology integrates LU decomposition for efficient matrix inversion and employs a node-based flow inference technique that ensures observability without requiring full path enumeration. Tested on benchmark and real-world networks (e.g., fishbone, Sioux Falls, Barcelona), the proposed framework demonstrates strong performance in minimizing error and maintaining scalability, highlighting its practical applicability for resilient traffic monitoring system design. Full article

Interpretable decision-making algorithms are important when used in the context of production optimization. While concepts like Petri nets are inherently interpretable, they are not straightforwardly learnable. This paper presents a novel approach to transform the Petri net model into a learnable entity. This is accomplished by establishing a relationship between the Petri net description in the event domain, its representation in the max-plus algebra, and a one-layer perceptron neural network. This allows us to apply standard supervised learning methods adapted to the max-plus domain to infer the parameters of the Petri net. To this end, the feed-forward and back-propagation paths are modified to accommodate the differing mathematical operations in the context of max-plus algebra. We apply our approach to a multi-robot handling system with potentially varying processing and operation times. The results show that essential timing parameters can be inferred from data with high precision. Full article

The growing importance of social networks has led to increased research into trust estimation and interpretation among network entities. It is important to predict the trust score between users in order to minimize the risks in user interactions. This article enables the identification of the most reliable and least reliable entities in a network by expressing trust scores numerically. In this paper, the social network is modeled as a graph, and trust scores are calculated by taking the powers of the ratio matrix between entities and summing them. Taking the power of the proportion matrix based on the number of entities in the network requires a lot of arithmetic load. After taking the powers of the eigenvalues of the ratio matrix, these are multiplied by the eigenvector matrix to obtain the power of the ratio matrix. In this way, the arithmetic cost required for calculating trust between entities is reduced. This paper calculates the trust score between entities using linear algebra techniques to reduce the arithmetic load. Trust detection algorithms use shortest paths and similar methods to eliminate paths that are deemed unimportant, which makes the result questionable because of the loss of data. The novelty of this method is that it calculates the trust score without the need for explicit path numbering and without any data loss. Full article

This study investigates the relationship between sovereign credit rating transitions and domestic equity market performance, focusing on Greece from 2004 to 2024. Although credit ratings are central to sovereign risk assessment, their immediate influence on financial markets remains contested. This research adopts a multi-method analytical framework combining algebraic combinatorics and time-series econometrics. The methodology incorporates the construction of a directed credit rating transition graph, the partially ordered set representation of rating hierarchies, rolling-window correlation analysis, Granger causality testing, event study evaluation, and the formulation of a reward matrix with optimal rating path optimization. Empirical results indicate that credit rating announcements in Greece exert only modest short-term effects on the Athens Stock Exchange General Index, implying that markets often anticipate these changes. In contrast, sequential downgrade trajectories elicit more pronounced and persistent market responses. The reward matrix and path optimization approach reveal structured investor behavior that is sensitive to the cumulative pattern of rating changes. These findings offer a more nuanced interpretation of how sovereign credit risk is processed and priced in transparent and fiscally disciplined environments. By bridging network-based algebraic structures and economic data science, the study contributes a novel methodology for understanding systemic financial signals within sovereign credit systems. Full article

This paper introduces a framework of hypercompositional algebra on fuzzy graphs by defining and analyzing fuzzy path-based hyperoperations. Building on the notion of strongest strong paths (paths that are both strength-optimal and composed exclusively of strong edges, where each edge achieves maximum connection strength between its endpoints), we define two operations: a vertex-based fuzzy path hyperoperation and an edge-based variant. These operations generalize classical graph hyperoperations to the fuzzy setting while maintaining compatibility with the underlying topology. We prove that the vertex fuzzy path hyperoperation is associative, forming a fuzzy hypersemigroup, and establish additional properties such as reflexivity and monotonicity with respect to $\alpha$-cuts. Structural features such as fuzzy strong cut vertices and edges are examined, and a fuzzy distance function is introduced to quantify directional connectivity strength. We define an equivalence relation based on mutual full-strength reachability and construct a quotient fuzzy graph that reflects maximal closed substructures under the vertex fuzzy path hyperoperation. Applications are discussed in domains such as trust networks, biological systems, and uncertainty-aware communications. This work aims to lay the algebraic foundations for further exploration of fuzzy hyperstructures that support modeling, analysis, and decision-making in systems governed by partial and asymmetric relationships. Full article

As optical networks operate using light-based transmission, assigning wavelengths to the paths taken by traffic demands is a key aspect of their design. This paper revisits the wavelength assignment problem in optical backbone networks, focusing on survivability via 1 + 1 Optical Chanel (OCh) protection, which ensures fault tolerance by duplicating data over two disjoint optical paths. The analysis gives great emphasis to studying the influence of topological parameters on wavelength requirements, with algebraic connectivity being identified as the most significant parameter. The results show that, across a set of 27 real-world networks, the wavelength increment factor, defined as the ratio between the number of wavelengths required with protection and without protection, ranges from 1.49 to 3.07, with a mean value of 2.26. Using synthetic data, formulas were derived to estimate this factor from network parameters, resulting in a mean relative error of 12.7% and errors below 15% in 70% of the real-world cases studied. Full article

A food pasteurization or sterilization process was treated as a system comprising a target microorganism, a food medium, and applied lethal agents (both thermal and nonthermal). So, the state of such a system was defined by the target microorganism’s concentration, the food medium parameters (food composition, pH, and water activity), and the magnitudes of temperature and nonthermal lethal agents. Further, a path was defined as a series of profiles that describe the changes in state factors over time when a food process system changes from its initial state to any momentary state. Using the Weibull model as an example, results showed that, if the microbial inactivation rate depends on path, then there exists an infinite number of rate equations that can result in the same algebraic primary model under constant conditions but, theoretically, only one of them is true. Considering the infinite possibilities, there is no way to find the most suitable or true rate equation. However, the inactivation rate equation can be uniquely derived from the algebraic primary model if the inactivation rate does not depend on path, which was demonstrated to be true by most microbial survival data reported in previous studies. Full article

A new multi-robot path planning (MRPP) algorithm for 2D static environments was developed and evaluated. It combines a roadmap method, utilising the visibility graph (VG), with the algebraic connectivity (second smallest eigenvalue (λ₂)) of the graph’s Laplacian and Dijkstra’s algorithm. The paths depend on the planning order, i.e., they are in sequence path-by-path, based on the measured values of algebraic connectivity of the graph’s Laplacian and the determined weight functions. Algebraic connectivity maintains robust communication between the robots during their navigation while avoiding collisions. The algorithm efficiently balances connectivity maintenance and path length minimisation, thus improving the performance of path finding. It produced solutions with optimal paths, i.e., the shortest and safest route. The devised MRPP algorithm significantly improved path length efficiency across different configurations. The results demonstrated highly efficient and robust solutions for multi-robot systems requiring both optimal path planning and reliable connectivity, making it well-suited in scenarios where communication between robots is necessary. Simulation results demonstrated the performance of the proposed algorithm in balancing the path optimality and network connectivity across multiple static environments with varying complexities. The algorithm is suitable for identifying optimal and complete collision-free paths. The results illustrate the algorithm’s effectiveness, computational efficiency, and adaptability. Full article

Existing studies on ontology evolution lack automated mechanisms to balance semantic coherence and adaptability under real-time uncertainties, particularly in resolving spatiotemporal asymmetry and multidimensional coupling imbalances in dam-break scenarios. Traditional methods such as WordNet’s tree symmetry and FrameNet’s frame symmetry fail to formalize dynamic adjustments through quantitative metrics, leading to path dependency and delayed responses. This study addresses this gap by introducing a novel symmetry-entropy-constrained matrix fusion algorithm, which integrates algebraic direct sum operations and Hadamard product with entropy-driven adaptive weighting. The original contribution lies in the symmetry entropy metric, which quantifies structural deviations during fusion to systematically balance semantic stability and adaptability. This work formalizes ontology evolution as a symmetry-driven optimization process. Experimental results demonstrate that shared concepts between ontologies (s = 3) reduce structural asymmetry by 25% compared to ontologies (s = 1), while case studies validate the algorithm’s ability to reconcile discrepancies between theoretical models and practical challenges in evacuation efficiency and crowd dynamics. This advancement promotes the evolution of traditional emergency management systems towards an adaptive intelligent form. Full article

Intelligent driving technology can effectively improve transportation efficiency and vehicle safety and has become a development trend in automotive technology. As one of the core technologies of autonomous driving, path tracking control is directly related to the driving safety and comfort of vehicles and therefore has become a key research area of autonomous driving technology. In order to improve the reliability and control accuracy of path tracking algorithms, this paper proposed a path tracking control method based on the Gaussian pseudospectral method. Firstly, a vehicle motion model was constructed, and then an optimal trajectory solving method based on the hp adaptive pseudospectral method was proposed. The optimal trajectory control problem with differential constraints was transformed into an algebraic constrained nonlinear programming problem and solved using the sequential quadratic programming and compared with traditional control methods. The simulation results show that the tracking error of the lateral distance under the condition of $\mu =0.8$ is smaller than that of $\mu =0.4$. At the same time, the tracking error of the lateral distance under the condition of u = 30 km/h is smaller than that of u = 90 km/h. The optimal path tracking control using the improved hp adaptive pseudospectral method has higher accuracy and better control effect compared to traditional control algorithms. Finally, virtual and real vehicle tests were conducted to verify the effectiveness and accuracy of the improved hp adaptive trajectory control algorithm. Full article

Dynamic post-buckling behavior of microscale cylindrical shells reinforced with functionally graded carbon nanotubes (FG-CNTs) and conveying microfluid is discussed for the first time. The microshell is embedded in a Kerr foundation and subjected to an axial compressive load and a two-dimensional magnetic field effect. CNTs dispersion across the shell thickness follows a power law, with five distribution types developed. The modified couple stress theory is applied to incorporate the small-size effect using a single material parameter. Furthermore, the Knudsen number is used to address the small-size effect on the microfluid. The external force between the magnetic fluid and microshell is modeled by applying the Navier–Stokes equation depending on the fluid velocity. Nonlinear motion equations of the present model are derived using Hamilton’s principle, containing the Lorentz magnetic force. According to the Galerkin method, the equations of motion are transformed into an algebraic system to be solved, determining the post-buckling paths. Numerical results indicate that the presence of the magnetic field, CNT reinforcement, and fluid flow improves the load-bearing performance of the cylindrical microshells. Also, many new parametric effects on the post-buckling curves of the FG-CNT microshells have been discovered, including the shell geometry, magnetic field direction, length scale parameter, Knudsen number, and CNT distribution types. Full article

We propose a vertiport location-allocation methodology for urban air mobility (UAM) from the perspective of transportation network topology. The location allocation of vertiports within a transportation network is a crucial factor in determining the unique characteristics of UAM compared to existing transportation modes. However, as UAM is still in the pre-commercialization phase, with significant uncertainties, there are limitations in applying location-allocation models that optimize objective functions such as maximizing service coverage or minimizing travel distance. Instead, vertiport location allocation should be approached from a strategic perspective, taking into account public capital investments aimed at improving the transportation network by leveraging UAM’s distinct characteristics compared to existing urban transportation modes. Therefore, we present a methodology for evaluating the impact of vertiport location-allocation strategies on changes in transportation network topology. To analyze network topology, we use the Seoul Metropolitan railway network as the base network and construct scenarios where vertiports are allocated based on highly connected nodes and those prioritizing structurally vulnerable nodes. We then compare and analyze global network efficiency, algebraic connectivity, average shortest path length, local clustering coefficient, transitivity, degree assortativity and modularity. We confirm that while allocating vertiports based on network centrality improves connectivity compared to vulnerability-based allocation, the latter approach is superior in terms of network efficiency. Additionally, as the proportion of vertiports increases, the small-world property of the network rapidly increases, indicating that the vertiport network can fundamentally alter the structure of multimodal transportation systems. Regardless of whether centrality or vulnerability is prioritized, we observe that connectivity increase exponentially, while network efficiency changes linearly with the increase in vertiport proportion. Our findings highlight the necessity of a network-based approach to vertiport location allocation in the early stages of UAM commercialization, and we expect our results to inform future research directions on vertiport allocation in multimodal transportation networks. Full article

The study of algebraic invariants associated with Brauer configuration algebras induced by appropriate multisets is said to be a Brauer analysis of the data that define the multisets. In general, giving an explicit description of such invariants as the dimension of the algebras or the dimension of their centers is a hard problem. This paper performs a Brauer analysis on some generators of Thompson’s group F. It proves that such generators and some appropriate Christoffel words induce Brauer configuration algebras whose dimensions are given by the number of edges and vertices of the binary trees defining them. The Brauer analysis includes studying the covering graph induced by a corresponding quiver; this paper proves that these graphs allow for finding set-theoretical solutions of the Yang–Baxter equation. Full article

The implementation of quantum gates by means of microwave cryo-RFICs controlling qubits is a promising path toward scalable quantum processors. Quantum gate fidelity quantifies how well an actual quantum gate produces a quantum state close to the desired ideal one. Regrettably, the literature usually reports on quantum gate fidelity in a highly theoretical way, making it hard for RFIC designers to understand. This paper explains quantum gate fidelity by moving from Shannon’s concept of fidelity and proposing a detailed mathematical proof of a valuable integral formulation of quantum gate fidelity. Shannon’s information theory and the simple mathematics adopted for the proof are both expected to be in the background of electronics engineers. By using Shannon’s fidelity, this paper rationalizes the integral formulation of quantum gate fidelity. Because of the simple mathematics adopted, this paper also demystifies to electronics engineers how this integral formulation can be reduced to a more practical algebraic product matrix. This paper makes evident the practical utility of this matrix formulation by applying it to the specific examples of one- and two-qubit quantum gates. Moreover, this paper also compares mixed states, entanglement fidelity, and the error rate’s upper bound. Full article

The Riordan group of Riordan arrays was first described in 1991, and since then, it has provided useful tools for the study of areas such as combinatorial identities, polynomial sequences (including families of orthogonal polynomials), lattice path enumeration, and linear recurrences. Useful extensions of the idea of a Riordan array have included almost Riordan arrays, double Riordan arrays, and their generalizations. After giving a brief overview of the Riordan group, we define two further extensions of the notion of Riordan arrays, and we give a number of applications for these extensions. The relevance of these applications indicates that these new extensions are worthy of study. The first extension is that of the reverse symmetrization of a Riordan array, for which we give two applications. The first application of this symmetrization is to the study of a family of Riordan arrays whose symmetrizations lead to the famous Robbins numbers as well as to numbers associated with the 20 vertex model of mathematical physics. We provide closed-form expressions for the elements of these arrays, and we also give a canonical Catalan factorization for them. We also describe an alternative family of Riordan arrays whose symmetrizations lead to the same integer sequences. The second application of this symmetrization process is to the area of the enumeration of lattice paths. We remain with the applications to lattice paths for the second extension of Riordan arrays that we introduce, which is the interleaved Riordan array. The methods used include generating functions, linear algebra, weighted compositions, and linear recurrences. In the case of the symmetrization process applied to Riordan arrays, we focus on the principal minor sequences of the resulting square matrices in the context of integrable lattice models. Full article