Search Results (40)

This paper investigates cylindrical sphere packings, that is, patterns of uniform spheres with mutually disjoint interiors which are all tangent to a common cylinder. The key unifying themes are the existence and uniqueness of hexagonal packings, in which each sphere is tangent to six others. Constructions are both intuitive and subtle, but result in the complete characterization in terms of integer parameter pairs $(m,n)$. Interesting questions in rigidity and density are encountered. Density questions arise because the packings, being of equal diameter, lie within the space between inner and outer cylinders. This density problem hovers between the 2D and 3D sphere packing cases, and though it is not solved here, it is conjectured that the hexagonal packings are densest for the countable number of cylinders which support them. Other geometric objects are along for the ride, including equilateral triangles and the packings’ dual graphs, which are associated with patterns of carbon atoms forming buckytubes. Interesting structural rigidity questions also arise. Full article

Natural gas pipeline networks are subject to supply instability due to random fluctuations. Current forecasting methodologies often suffer from limited accuracy, inadequate uncertainty quantification, and poor integration with dynamic network evaluation mechanisms. To address these challenges, this study presents an integrated framework that bridges short-term demand forecasting with supply assurance assessment. A deep learning model that combines a graph convolutional network and a bidirectional long short-term memory network is developed to produce accurate 72 h demand forecasts. Forecasting uncertainty is quantified using the cumulative distribution function. Based on the probabilistic forecasts, a supply assurance evaluation model is constructed that accounts for the dynamic regulation capability of line pack. The comprehensive indicator system incorporates key metrics such as user satisfaction and the line pack demand−storage ratio. A case study was conducted with the proposed method based on a regional real-world pipeline network. The results demonstrate that the proposed model outperforms conventional baselines, achieving a mean absolute percentage error of less than 1%. The uncertainty quantification captures the risk probability associated with demand fluctuations. The proposed evaluation method identifies vulnerable sections and assesses supply margins under various scenarios, thus providing effective decision support for operational scheduling and supply assurance. Full article

This paper addresses the question of how many autonomous aerial vehicles (UAVs or drones) can safely operate within a bounded three-dimensional airspace. First, we derive the absolute mathematical limits on drone density using geometric arguments from sphere packing and covering theory. Then, we verify these limits empirically by simulating a swarm controlled via model predictive control. We incrementally increase the number of drones until motion becomes impossible. Each drone is modeled as a double-integrator system with a bounded speed and acceleration and is surrounded by a radius spherical safety zone $r>0$. The drones are controlled via model predictive control with hard separation constraints. We formalize complete blockage as the loss of any feasible non-trivial trajectory set, either due to geometric crowding or dynamic limitations. Using tools from discrete geometry, we establish absolute upper bounds on a safe population via sphere-packing results and sufficient conditions for total immobilization via sphere-covering arguments. We extend these static bounds by incorporating dynamics through stopping-distance analysis, leading to an inflated exclusion radius that captures the effect of finite control authority. In addition, we prove min-cut style flow-capacity bounds that limit feasible throughput across bottlenecks and derive horizon-dependent conflict-graph conditions that capture MPC infeasibility at high densities. These results provide a rigorous theoretical framework for determining the transition from feasible multi-drone operation to inevitable gridlock, offering explicit quantitative thresholds that can inform airspace design, drone density regulation, and the tuning of predictive controllers. We evaluate our theoretical findings with a simulation environment. Full article

This paper presents a novel edge-computing-based architecture for optimal inverse time overcurrent relays installed to protect mesh microgrids (MGs) with distributed generation. The procedure employs graph theory to automate the detection of network changes, fault locations, and relay pairs in an MG. In addition, an automated process obtains the initial protection settings based on the operating conditions of the MG. Furthermore, the Continuous Genetic Algorithm (CGA), Salp Swarm Algorithm (SSA), and Particle Swarm Optimization (PSO) were implemented to determine the optimal protection settings to obtain better coordination between primary and backup protection relays. These processes were implemented using PowerFactory 2024 Service Pack 5A and Python 3.13.1. The proposal was validated in 68 operating scenarios that considered the islanded and connected operation modes of the MG, charging and discharging cycles of electric vehicle stations, and the presence or absence of photovoltaic generation. The overcurrent protection relays were organized into 100 primary–backup relay pairs to ensure proper coordination and selectivity. The total miscoordination time (TMT) index was used to measure when all pairs of relays were coordinated, with a minimum time close to zero. The results of the graph theory show that all the meshes, fault locations, and relay pairs were identified in the MG. The approach successfully coordinated 100 relay pairs across 68 scenarios, demonstrating its scalability in complex real-world MGs. The automation process obtained an average TMT of 12.2%, while the optimization obtained a TMS of 91.6% with the CGA, and a TMT of 99% was obtained with the SSA and PSO, demonstrating the effectiveness of the optimization process in ensuring selectivity and appropriate fault clearing times. Full article

Graph representation learning (GRL) has emerged as a unifying paradigm for modeling the relational and heterogeneous nature of battery energy storage systems (BESS), yet a systematic synthesis focused on data-scarce (few-shot) battery scenarios is still lacking. Graph representation learning offers a natural way to describe the structure and interaction of battery cells, modules and packs. At the same time, battery applications often suffer from very limited labeled data, especially for new chemistries, extreme operating conditions and second-life use. This review analyzes how graph representation learning can be combined with few-shot learning to support key battery management tasks under such data-scarce conditions. We first introduce the basic ideas of graph representation learning, including models based on neighborhood aggregation, contrastive learning, autoencoders and transfer learning, and discuss typical data, model and algorithm challenges in few-shot scenarios. We then connect these methods to battery state estimation problems, covering state of charge, state of health, remaining useful life and capacity. Particular attention is given to approaches that use graph neural models, meta-learning, semi-supervised and self-supervised learning, Bayesian deep networks, and federated learning to extract transferable features from early-cycle data, partial charge–discharge curves and large unlabeled field datasets. Reported studies show that, with only a small fraction of labeled samples or a few initial cycles, these methods can achieve state and life prediction errors that are comparable to or better than conventional models trained on full datasets, while also improving robustness and, in some cases, providing uncertainty estimates. Based on this evidence, we summarize the main technical routes for few-shot battery scenarios and identify open problems in data preparation, cross-domain generalization, uncertainty quantification and deployment on real battery management systems. The review concludes with a research outlook, highlighting the need for pack-level graph models, physics-guided and probabilistic learning, and unified benchmarks to advance reliable graph-based few-shot methods for next-generation intelligent battery management. Full article

Despite the value of molecular packing (MP) calculations in modeling the properties of organic crystals, its widespread adoption is hindered by the absence of a simple tool broadly accessible to non-specialists, and by the lack of reliability inherent to transferable force fields. To fill these gaps, we describe a versatile workflow, leveraging recent progress in the application of machine learning to the parameterization of interatomic potentials. It is provided as a Python script based only on free academic software running on any Linux system. A key ingredient to this workflow is a recent neural network pretrained to predict bespoke force field parameters for any organic compound on the basis of its molecular diagram. The resulting graph-based force field (GB-FF) is fed into the Tinker simulation engine and applied to crystal structures generated using the USPEX crystal structure prediction package. This low-cost workflow is found to outperform current state-of-the-art procedures based on heavily parameterized force fields, thus demonstrating the value of machine-learned bespoke potential parameters. Full article

The proliferation of wireless sensor networks in remote and inaccessible areas demands efficient data collection approaches that minimize energy consumption while ensuring comprehensive coverage. Traditional data retrieval methods face significant challenges when sensors are sparsely distributed across extensive areas, particularly in scenarios where direct sensor access is impractical due to terrain constraints or operational limitations. This research addresses these challenges through a novel hybrid optimization framework that combines integer linear programming (ILP) with multiple traveling salesperson problem (mTSP) algorithms for drone-based data collection in wireless sensor networks (WSNs). The methodology employs a two-phase approach, where ILP optimally determines strategic access point locations for sensor clustering based on communication capabilities, followed by mTSP optimization to generate efficient inter-AP flight trajectories rather than individual sensor visits. Comprehensive simulations across diverse network configurations and drone quantities demonstrate consistent performance improvements, with travel distance reductions reaching 32% compared to conventional mTSP implementations. Comparative evaluation against established clustering algorithms including Voronoi, DBSCAN, Constrained K-Means, Graph-Based clustering, and Greedy Circle Packing confirms that ILP consistently achieves optimal access point allocation while maintaining superior routing efficiency. Additionally, a novel quality assessment metric quantifies sensor grouping effectiveness, revealing that ILP-based clustering advantages become increasingly pronounced with higher sensor densities, providing substantial operational benefits for large-scale wireless sensor network deployments. Full article

We consider mixed Hamming packings, addressing the maximal cardinality of codes with a minimum codeword Hamming distance. We do not rely on any algebraic structure of the alphabets. We extend known-integer linear programming models of the problem to be efficiently tractable using standard ILP solvers. This is achieved by adopting the concept of contact graphs from classical continuous sphere packing problems to the present discrete context, resulting in a reduction technique for the models which enables their efficient solution as well as their decomposition to smaller subproblems. Based on our calculations, we provide a systematic summary of all lower and upper bounds for packings in the smallest Hamming spaces. The known results are reproduced, with some bounds found to be sharp, and the upper bounds improved in some cases. Full article

A new type of solid bismuth microelectrode array characterized by eco-friendly properties and the simplicity of its construction is presented for the first time. The proposed array of microelectrodes consists of exactly forty-three single capillaries of an inner diameter of about 10 µm filled with metallic bismuth and packed in one casing. The proposed sensor is reusable thanks to its distinctive design. The microelectrode properties of the proposed working electrodes were confirmed by comparing the analytical signals of cadmium and lead recorded from stirred and unstirred solutions during the deposition step. The practical application of the solid bismuth microelectrode array is presented by detailing the procedure for the simultaneous determination of Pb and Cd by anodic stripping voltammetry. The calibration graphs were linear from 5 × 10⁻⁹ to 2 × 10⁻⁷ mol L⁻¹ and 2 × 10⁻⁹ to 2 × 10⁻⁷ mol L⁻¹ for Cd(II) and Pb(II), respectively (deposition time of 60 s). The detection limits for Cd(II) and Pb(II) were equal to 2.3 × 10⁻⁹ mol L⁻¹ and 8.9 × 10⁻¹⁰ mol L⁻¹, respectively. Potential interferences were investigated. The developed procedure was successfully used for the analysis of certified water reference material and environmental water samples. Full article

Three novel multicomponent crystals of trimethylglycine with 2-cyanoguanidine, guanidinium and aminoguanidinium chlorides are synthesized and structurally characterized. All three crystal packings are based on the supramolecular synthon formed by two N–H groups of the guanidine species and carboxylate group of trimethylglycine (graph set notation R²₂(8)). Its enthalpy is about 50 kJ/mol. The three-dimensional structure of crystals is stabilized by intermolecular interactions of various types. The energy of C–H∙∙∙X⁻ interactions, where X = O, Cl, reaches 16 kJ/mol due to the acidic nature of methyl hydrogens. The possible structure of the trimethylglycine–urea–2H₂O complex is discussed. Its theoretical metric and spectroscopic parameters are in reasonable agreement with the available literature data on the deep eutectic solvent trimethylglycine–urea. Full article

Surfactants are among the most versatile molecules in the chemical industry because they can self-assemble in bulk solutions and at interfaces. Predicting the properties of surfactant solutions, such as their critical micelle concentration (CMC), limiting surface tension (${\gamma }_{cmc}$), and maximal packing density (${\Gamma }_{max}$) at water–air interfaces, is essential to their rational design. However, the relationship between surfactant structure and these properties is complex and difficult to predict theoretically. Here, we develop a graph neural network (GNN)-based quantitative structure–property relationship (QSPR) model to predict the CMC, ${\gamma }_{cmc}$, and ${\Gamma }_{max}$. Ninety-two surfactant data points, encompassing all types of surfactants—anionic, cationic, zwitterionic, and nonionic—are fed into the model, covering a temperature range of [20–30 °C], which contributes to its generalization across all surfactant types. We show that our models have high accuracy (R² = 0.87 on average in tests) in predicting the three parameters across all types of surfactants. The effectiveness of the QSPR model in capturing the variation of CMC, ${\gamma }_{cmc}$, and ${\Gamma }_{max}$ with molecular design parameters are carefully assessed. The curated dataset, developed model, and critical assessment of the developed model will contribute to the development of improved surfactants QSPR models and facilitate their rational design for diverse applications. Full article

A mixed graph has both edges and directed edges (or “arcs”). A complete mixed graph on v vertices, denoted $M_v$, has, for every pair of vertices u and v, an edge $\{u,v\}$, an arc $(u,v)$, and an arc $(v,u)$. A decomposition of the complete mixed graph on v vertices into a partial orientation of a three-cycle with one edge and two arcs (of which there are three types) is a mixed triple system of order v. Necessary and sufficient conditions for the existence of a mixed triple system of order v are well known. In this work packings and coverings of the complete mixed graph with mixed triples are considered. Necessary conditions are given for each of the three relevant mixed triples, and these conditions are shown to be sufficient for two of the relevant mixed triples. For the third mixed triple, a conjecture is given concerning the sufficient conditions. Applications of triple systems in general are discussed, as well as possible applications of mixed graphs, mixed triple systems, and packings and coverings with mixed triples. Full article

The growing popularity of microservices architectures generated the need for tools that orchestrate their deployment in containerized infrastructures, such as Kubernetes. Microservices running in separate containers are packed in pods and placed in virtual machines (nodes). For applications with multiple communicating microservices, the decision of which services should be placed in the same node has a certain impact on both the running time and the operation cost of an application. The default Kubernetes scheduler is not optimal in that case. In this work, the service placement problem is treated as graph clustering. An application is modeled using a graph with nodes and edges representing communicating microservices. Graph clustering partitions the graph into clusters of microservices with high-affinity rates. Then, the microservices of each cluster are placed in the same Kubernetes node. A class of methods resorts to hard clustering (i.e., each microservice is placed in exactly one node). We advocate that graph clustering should be fuzzy to allow high-utilized microservices to run in more than one instance (i.e., pods) in different nodes. ModSoft-HP Scheduler is a custom Kubernetes scheduler that takes scheduling decisions based on the results of the ModSoft fuzzy clustering method followed by heuristic packing (HP). For proof of concept, the workloads of two applications (i.e., an e-commerce application, eShop, and an IoT architecture) are given as input to the default Kubernetes Scheduler, the Bisecting K-means, and the Heuristic First Fit (hard) clustering schedulers and to the ModSoft-HP fuzzy clustering method. The experimental results demonstrate that ModSoft-HP can achieve up to 90% reduction of egress traffic, up to 20% savings in response time, and up to 25% less hosting costs compared to service placement with the default Kubernetes Scheduler in the Google Kubernetes Engine. Full article

The synthesis and characterization of the multicomponent crystals formed by 2,2′-thiodiacetic acid (H₂tda) and 2,6-diaminopurine (Hdap) or N9-(2-hydroxyethyl)adenine (9heade) are detailed in this report. These crystals exist in a salt rather than a co-crystal form, as confirmed by single crystal X-ray diffractometry, which reflects their ionic nature. This analysis confirmed proton transfer from the 2,2′-thiodiacetic acid to the basic groups of the coformers. The new multicomponent crystals have molecular formulas [(H9heade⁺)(Htda⁻)] 1 and [(H₂dap⁺)₂(tda²⁻)]·2H₂O 2. These were also characterized using FTIR, ¹H and ¹³C NMR and mass spectroscopies, elemental analysis, and thermogravimetric/differential scanning calorimetry (TG/DSC) analyses. In the crystal packing the ions interact with each other via O–H⋯N, O–H⋯O, N–H⋯O, and N–H⋯N hydrogen bonds, generating cyclic hydrogen-bonded motifs with graph-set notation of $R_2^2$(16), $R_2^2$(10), $R_3^2$(10), $R_3^3$(10), $R_2^2$(9), $R_3^2$(8), and $R_4^2$(8), to form different supramolecular homo- and hetero-synthons. In addition, in the crystal packing of 2, pairs of diaminopurinium ions display a strong anti-parallel π,π-stacking interaction, characterized by short inter-centroids and interplanar distances (3.39 and 3.24 Å, respectively) and a fairly tight angle (17.5°). These assemblies were further analyzed energetically using DFT calculations, MEP surface analysis, and QTAIM characterization. Full article

Urban transport systems play a major role in the development of today’s societies, but they require technological changes to reduce their environmental impact. The problem lies in their level of autonomy, which is why electrical energy production systems are proposed for self-consumption, efficiently feeding their accumulators. As the energy provided by photovoltaic installations has lower recharge speeds, conventional systems with high transfer amperage and higher voltage are required. For this reason, solar installations are used for additional services and to support their autonomy. The present work tries to find the best solution for both constant voltage and peak current systems. Once found, these solutions will be applied in real time for the dynamic recharging of battery packs, trying to achieve vehicles that are progressively more energetically autonomous. To solve these situations, a new computational method for calculating voltage and amperage has been developed in this work, based on Dijkstra’s minimum path search algorithm on graph theory, adapted to electrical circuits. Once this algorithm has been established, the panel performance analysis sensors, developed at the University of Malaga, are combined with different electronic solutions described in this article (Wi-Fi relay devices using esp8266 chips or feeding these relays through panels and establishing the voltage drop to switch the connection), achieving precise and sufficiently fast solutions at very low cost. Both series and parallel transitions are possible, depending on the type of energy generation required. The theoretical solutions using Minkowski paths, analyzed in the past, have been simulated and subsequently constructed in this paper, indicating the diagrams necessary for their realization. Full article