Topological Type Research Articles

Fuzzy Topological Spaces Generated by Fuzzy Digraphs

In this paper, we defined various fuzzy topological spaces on fuzzy digraph and study interrelation between them. Using adjacency relation on fuzzy vertices and fuzzy edges of fuzzy digraph we defined, namely two types of fuzzy topologies, left(right) fuzzy vertex topology and left(right) fuzzy edge topology on fuzzy digraph, respectively. We have obtained results related to fuzzy topology on fuzzy subdigraph [Formula: see text] of fuzzy digraph [Formula: see text]. Separation axioms [Formula: see text], [Formula: see text] and [Formula: see text] for these fuzzy topological spaces are studied. Some characterization results for fuzzy topological spaces related to isomorphic fuzzy digraphs are given. Further, we have shown that two fuzzy digraphs are isomorphic if and only if their corresponding fuzzy topologies are homeomorphic, this relation on set of fuzzy digraphs forms an equivalence relation. We have also defined and studied fuzzy bitopological spaces on fuzzy digraphs.

Implementation of Parallel Applications on Linear Systolic and Star Topologies by Using Multistage Omega Network

Contemporary computer architecture comprises multicomputer settings. Multiple computers provide the facility of high performance to implement multiple threads that are faster and concurrently with different processors that can execute tasks simultaneously. The challenges are as follows: cost and high performance. Certain firms have to provide funding to establish data centers that need locations, hardware, and technicians. After the passage of a period of time, such equipment requires maintenance (updating and upgrading) to take place on it. This paper tackles these challenges by passing the drawbacks of data centers. It provides an algorithm that simulates a virtual machine, as one client is to be connected with eight servers to implement two applications namely convolution and mathematical operations. To represent different topologies, the algorithm simulates supercomputer systems by applying multistage omega network topology and parallel processing. Two types of topologies execute linear systolic and star, and is implemented on transmission control protocol (TCP) and user datagram protocol (UDP) protocols. The goal of this paper is to provide a kernel that draws near a cloud computing system by exploiting the JAVA programming language with its techniques (threading, socket, socket server, Datagram socket, and datagram packet). The results offer the connection between the client and servers to be successfully simulated by using multistage omega network. The linear systolic and star topologies are simulated in virtual parallel processing.

Corner and edge states in topological Sierpinski Carpet systems

Fractal lattices, with their self-similar and intricate structures, offer potential platforms for engineering physical properties on the nanoscale and also for realizing and manipulating high order topological insulator states in novel ways. Here we present a theoretical study on localized corner and edge states, emerging from topological phases in Sierpinski Carpet within a $\pi$-flux regime. A topological phase diagram is presented correlating the quadrupole moment with different hopping parameters. Particular localized states are identified following spatial signatures in distinct fractal generations. The specific geometry and scaling properties of the fractal systems can guide the supported topological states types and their associated functionalities. A conductive device is proposed by coupling identical Sierpinski Carpet units providing transport response through projected edge states which carry on the details of the system's topology. Our findings suggest that fractal lattices may also work as alternative routes to tune energy channels in different devices.

In-plane crushing behavior and energy absorption of CFRP honeycombs with different core topologies

The in-plane crushing behavior and energy absorption performance of carbon fiber reinforced polymer (CFRP) honeycombs with different core topologies were experimentally investigated under uniaxial loading conditions. Three types of CFRP honeycomb core topologies (i.e. circular, square and hexagonal) with different cell wall thicknesses and heights were considered in the designs. The honeycomb samples were fabricated by the molding and bonding process, which is widely used in the easy, fast and economical manufacturing of thin-walled honeycomb structures. A total of twenty-seven sample groups were experimentally tested for each loading condition, in which honeycomb samples with different core topologies were designed to have almost the same weights for a meaningful comparison. The experimental results revealed that all honeycomb designs have higher in-plane compression strength in the expansion direction, and hexagonal honeycombs showed the highest strength and energy absorption performance in both directions due to their stable load-carrying capacity and outstanding force efficiency. In particular, the experimental findings showed that the crushing strength and the specific energy absorption of CFRP honeycomb structures can be improved up to 6.1 and 4.2 times, respectively, by properly adjusting the cell wall thickness and height parameters. The results also revealed that the proposed lightweight CFRP honeycombs with the structural densities of 155–283 kg/m3 showed better in-plane crushing performance than many competing cellular topologies.

Synthesis, Structural Analysis and Bright Emission Performance of a New Family of 3D Lanthanide Coordination Polymers Based on 1,3‐phenylenediacetic acid

A novel series of isostructural lanthanide coordination polymers with the general formula [Ln2(PDA)3(DMF)2] (where Ln3+= La, Nd, Pr, Tb, Sm and Eu, DMF= N,N’‐dimethylformamide and PDA =1,3‐phenylenediacetate) were hydrothermally synthesized and further characterized by vibrational spectroscopy, thermal analysis, scanning electron microscopy (SEM), energy dispersive X‐ray (EDX) analysis, and powder and single‐crystal X‐ray diffraction techniques. In addition, from the crystallographic data, it was possible to determine the topology of the structure, finding that the network consists of 5‐connected nodes with topological type: nov; 5/4/o8 and point symbol (44.66). To study the luminescence properties regarding potential energy transfers among the building blocks, lanthanum‐based samples doped with Tb (III) and Eu (III) (1%, 2%, 5% and 10%) were analyzed in solid state. Upon ligand sensitization, 4f transitions could be observed confirming an "antenna effect" of the PDA ligand. These new compounds are potential materials for the construction of photoluminiscent devices.

Eigenmode and eigenpropagation of the electromagnetic waves in Möbius and Klein networks

To explore the distribution of characteristic frequencies and the propagation properties of eigenmodes in topological networks at the zero-energy level, we design optical waveguide networks with two typical topologies: Möbius network and Klein network, inspired by the Möbius strip and Klein bottle, respectively. We investigate the degeneracy at characteristic frequencies and the propagation properties of the eigenmodes of these networks, both theoretically and experimentally. We discovered an intriguing eigenpropagation in the Möbius network and multiple degenerate eigenmodes in the Klein network, analyzing the propagation characteristics and distribution patterns of electromagnetic waves within them. In our experiments, we utilize coaxial cables as one-dimensional waveguides to construct transmission line networks for the two networks. We observe the distinct transmission paths of the Möbius network’s eigenmode and the two degenerate eigenmodes of the Klein network. Our findings provide a theoretical foundation for new optical modal transmission devices and novel nanoarrays, with potential implications for theoretical and experimental research in other quantum systems and topological networks.

Static and stability analyses of multi-strut type aluminium alloy suspen-dome structure with large opening

By combining the advantages of the multi-strut concept in cable dome structures with aluminum alloy material, a new type of prestressed spatial structure—the multi-strut aluminum alloy suspen-dome with a large opening—has been developed by integrating a lower prestressed support system into an aluminum alloy reticulated shell. The optimal structural configuration was determined by comparing the static, stability, and economic performance of three types of upper chord mesh topologies for this structure. Subsequently, an analysis of the static performance and large-scale parameters affecting the structural stability of the optimal grid topology was conducted. The study explored the influence of structural prestressing, overall shape, and support stiffness—encompassing three categories and seven parameters—on structural stability and material consumption. Additionally, the effects of initial imperfections and load distribution forms on structural stiffness and stability were further examined. Finally, the static properties, stability, and economic indicators of the structure were compared with two other structural systems: the steel suspen-dome and the cable dome. The results indicate that the pentagonal grid topology provides the best structural performance and that the structure is sensitive to cooling effects. Optimal values for key design parameters, such as the rise-span ratio and thickness-span ratio, were identified. Moreover, the economic advantages of the aluminum alloy suspen-dome compensate for its mechanical performance shortcomings compared to the steel suspen-dome. These findings offer innovative solutions and a scientific basis for the selection and stability design of aluminum alloy suspen-dome structures.

Structural Features, Chemical Diversity, and Physical Properties of Microporous Sodalite-Type Materials: A Review

This review contains data on a wide class of microporous materials with frameworks belonging to the sodalite topological type. Various methods for the synthesis of these materials, their structural and crystal chemical features, as well as physical and chemical properties are discussed. Specific properties of sodalite-related materials make it possible to consider they as thermally stable ionic conductors, catalysts and catalyst carriers, sorbents, ion exchangers for water purification, matrices for the immobilization of radionuclides and heavy metals, hydrogen and methane storage, and stabilization of chromophores and phosphors. It has been shown that the diversity of properties of sodalite-type materials is associated with the chemical diversity of their frameworks and extra-framework components, as well as with the high elasticity of the framework.

RNAfcg: RNA Flexibility Prediction Based on Topological Centrality and Global Features.

The dynamics of RNAs are related intimately to their functions. Molecular flexibility, as a starting point for understanding their dynamics, has been utilized to predict many characteristics associated with their functions. Since the experimental measurement methods are time-consuming and labor-intensive, it is urgently needed to develop reliable theoretical methods to predict RNA flexibility. In this work, we develop an effective machine learning method, RNAfcg, to predict RNA flexibility, where the Random Forest (RF) is trained by features including the topological centralities, flexibility-rigidity index, and global characteristics first introduced by us, as well as some traditional sequence and structural features. The analyses show that the three types of features introduced first have significant contributions to RNA flexibility prediction, among which the topological type contributes the most, which indicates the importance of structural topology in determining RNA flexibility. The performance comparison indicates that RNAfcg outperforms the state-of-the-art machine learning methods and the commonly used Gaussian Network Model (GNM) models, achieving a much higher Pearson correlation coefficient (PCC) of 0.6619 on the test data set. This work is helpful for understanding RNA dynamics and can be used to predict RNA function information. The source code is available at https://github.com/ChunhuaLab/RNAfcg/.

Topology of Intermetallic Crystals: Classification, Uniformity, and Transitions.

We have analyzed the crystal structures of 7551 binary intermetallic compounds, which are deposited in the inorganic crystal structure database, using a combined geometrical-topological approach as implemented in our program package ToposPro. We represented each crystal structure with two models: (i) the topological model of periodic atomic net and (ii) the geometrical model of the Voronoi partition of crystal space. Within the former model, we have classified all intermetallics into 949 topological types, 20 of which cover 57% of the whole sample. Using our recently developed topological network model of reconstructive solid-state transformations, we have described possible mechanisms of displacive transitions between the most abundant topological types and revealed a key role of the body-centered lattice in these transitions. The Voronoi partition model enabled us to introduce the concept of uniformity of the overall structure and the environment of separate atoms; the uniformity is estimated by the second moment of inertia of atomic Voronoi polyhedra. We have shown that the structures with a low uniformity value either contain mistakes in the crystallographic data or have significantly directed interatomic bonds. The proposed uniformity criteria can serve for the estimation of the robustness of an intermetallic structure.

A highly stable, rapid and sensitive fluorescent probe for Al3+ and pefloxacin based on enhanced fluorescence of a Co(II) coordination polymer

Fabricating functional coordination polymer (CP) architectures and exploiting it as fluorescence sensors for detecting diverse metal ions and antibiotics, have attracted extensive attention. Based on a rarely-used benzimidazole-derived ligand 2,2′-bis-(2-pyridin-3-yl-vinyl)-3H,3′H-[5,5]bibenzoimidazole (L), a new CP {[Co(L)0.5(tbip)]·H2O}n (H2tbip =5‑tert-butylisophthalic acid) (1) was synthesized under solvothermal condition and characterized. Complex 1 reveals a two-dimensional network with the type of topology of 3,4,5L7. Complex 1 possesses excellent thermal and chemical stability. The fluorescence detection ability of complex 1 was explored and demonstrated that complex 1 can be used as the first fluorescent turn-on sensor to sense Al3+ and pefloxacin (PEF) with a low detection limit and fast response. The fluorescence enhancement mechanism was investigated in detail.

FDIA localization and classification detection in smart grids using multi-modal data and deep learning technique

False data injection attacks (FDIA) exploit the vulnerabilities of bad data detection in energy management systems to maliciously tamper with state estimation results, seriously jeopardizing the safe and reliable operation of power systems. In order to promptly detect FDIA, recent studies have used machine learning techniques to extract attack characteristics and detect FDIA based on changes in these characteristics. Current research predominantly focuses on detecting a single type of FDIA attack model and topology. However, the increasing diversification of FDIA construction methods and the variability of topological structures in power systems can reduce or even invalidate detection effectiveness. To cope with the abovementioned difficulties, this study introduces a multimodal deep learning detection model based on variational graph auto-encoders (VGAE), temporal convolutional networks (TCN), and gated recurrent units (GRU). The topological features of power systems are obtained through VGAE to adapt to the detection needs of various topological structures and performance enhancement. These features are then integrated with preprocessed measurement data via BDD to form multimodal data. Furthermore, this multimodal data is used to locate and classify FDIA with complete information, FDIA with incomplete information, and topology attack after applying a multi-label classification algorithm based on TCN-GRU for temporal feature extraction. Experiments carried out on the IEEE 14 and IEEE 118 bus systems show that the proposed method is robust and has high detection performance. The results indicate that the proposed detection method achieves AUC values that are, on average, 0.085, 0.145, and 0.04 higher than those of CNN, LSTM, and CNN-LSTM, respectively. Moreover, under various noise and attack intensities, recall, precision, F1 score, and RACC remain above 0.859, 0.877, 0.867, and 0.818, respectively, with a classification accuracy greater than 0.912. This study provides a unique perspective on detecting FDIA across various attack models and power system topologies.

Opinion dynamics analysis for stubborn individuals in cooperation–competition networks based on path-dependence framework

The opinion evolution problem is studied in this paper for stubborn individuals in cooperation–competition networks, where the individuals’ opinion dynamics is described by the Friedkin–Johnsen model and the competitive relationship between individuals is characterized by negative weights. Then the lifting approach is successfully applied to the Friedkin–Johnsen model to deal with the influence of the negative weights while the path-dependence theory is used to the transition of two arbitrarily adjacent topics. Starting from the weight topology, the relationship between the weight topology and the augmented topology is established, and some sufficient conditions about achieving neutrality, bipartite consensus and convergence for the individuals’ opinions in a sequence of topics are obtained. Interestingly, a necessary and sufficient condition is given to ensure bipartite consensus for the individuals’ opinions under the premise that the weight topology is structurally unbalanced. Furthermore, the Friedkin–Johnsen model with dynamic stubbornness is also considered, and the concept of common topic subsequence is introduced. It is proved that all elements of the topic transfer matrix are positive for the common topic subsequence, and neutrality and bipartite consensus for the individuals’ opinions can be achieved for different types of weight topologies, respectively. Finally, numerical examples are given to support the correctness of the theoretical results.

Distance synchrony in coupled systems

We investigate the phenomenon of distance synchrony in a system of coupled conservative axially symmetric chaotic oscillators using master–slave type coupling. Our study reveals that the variables of the coupled oscillators achieve synchronization at a constant difference that depends on the coupling strength. This distance synchrony is explored and confirmed with two coupled as well as different types of network topologies. Our findings provide insight into the dynamics of coupled chaotic systems and contribute to the understanding of synchronization patterns in axially symmetric chaotic systems. We also provide analytical support for the numerical findings, along with achieving the same with experiments. This research has potential applications in various fields, including secure communications, neural networks, and other complex systems exhibiting chaotic behavior.

Surrogate-Assisted Differential Evolution for the Design of Multimode Resonator Topology.

The microstrip devices based on multimode resonators represent a class of electromagnetic microwave devices, promising use in tropospheric communication, radar, and navigation systems. The design of wideband bandpass filters, diplexers, and multiplexers with required frequency-selective properties, i.e., bandpass filters, is a complex problem, as electrodynamic modeling is a time-consuming and computationally intensive process. Various planar microstrip resonator topologies can be developed, differing in their topology type, and the search for high-quality structures with unique frequency-selective properties is an important research direction. In this study, we propose an approach for performing an automated search for multimode resonators' conductor topology parameters using a combination of evolutionary computation approach and surrogate modeling. In particular, a variant of differential evolution optimizer is applied, and the model of the target function landscape is built using Gaussian processes. At every iteration of the algorithm, the model is used to search for new high-quality solutions. In addition, a general approach for target function formulation is presented and applied in the proposed approach. The experiments with two microwave filters have demonstrated that the proposed algorithm is capable of solving the problem of tuning two types of topologies, namely three-mode resonators and six-mode resonators, to the required parameters, and the application of surrogated-assisted algorithm has significantly improved overall performance.

Metal–organic frameworks and their composites: Design, synthesis, properties, and energy storage applications

Porous crystalline metal–organic frameworks (MOFs) are promising materials for supercapacitors (SCs) owing to their excellent pore structures, large surface areas, adjustable topological types, and multivalent active metal nodes, which endow them with ideal energy-storage performance. However, despite their successful application in many fields such as catalysis, gas adsorption and separation, and sensors, various intrinsic defects have hindered their practical application in SCs. In recent years, MOFs have demonstrated significant advancements in their electrochemical performance, and their applications in SCs have been gaining momentum. This review summarizes the design, classification, synthesis strategies, and properties of MOFs. The formation conditions and mechanisms of MOFs are discussed and the effects of the different types and synthesis strategies of MOFs on their properties are compared to improve their design and preparation. The research progress on pristine MOFs and their composites in SCs is reviewed, highlighting the solutions for the intrinsic defects in pristine MOFs in SC applications. The challenges of utilizing MOF-based materials in SC applications are summarized and potential solutions for their future development are suggested.

Topology-optimized lattice enhanced cementitious composites

In this work, the topology-optimized lattices structures were designed to serve as ductile nylon reinforcements in lattice-enhanced cementitious composites. The mechanical behavior of the prepared composites was examined via a flexural test where the strength and mid-span deflection were especially concerned. The digital image correlation (DIC) approach was employed to monitor and evaluate the failure pattern and strain distribution. Further investigation was conducted on the mechanical effects of two major optimization factors in the lattice design process, namely cell size and optimization volume fracture. Finally, the improved ductile performance of the suggested composites was compared to that of prior works. The results indicated that the proposed topology-optimized lattices significantly promote the mechanical performance of the prepared composites, i.e., strength and ductility. It may present a higher ductility enhancement efficiency than homogenous lattices under an identical volume. The cell size of lattices is inversely related to the enhancing effects, and more extensive optimization volume fracture enhances composite strength and ductility. Compared with previous works, this study gained advancement in terms of printing materials, unit topology, and cement types. The topology-optimized lattice generally provides a novel solution to the ductility enhancement effect, providing both superior performance and greater design flexibility.

Parametric investigation of aerodynamic performance degradation due to icing on a symmetrical airfoil

Ice accretion on lifting surfaces induces an aerodynamic penalty in lift and drag on an aircraft. This performance degradation depends on the geometric features, type, and surface characteristics of the accreted ice on the airfoil. In the present work, we propose a set of two-parameter, low-order models to represent some of the typical ice topologies: glaze, rime, and horn. The parametric space is swept for all types of ice to isolate the aerodynamic changes causing performance degradation on a canonical symmetrical airfoil, which is the representative airfoil used by the National Research Council of Canada's platform for ice accretion and coatings tests with ultrasonic readings platform for in-flight icing tests. The three ice topologies show a self-similar trend between the stall angle of attack and the ice thickness, with the horn-type of ice imparting the greatest drag and lift penalty due to strong boundary layer separation. The relative effect of ice roughness plays a secondary role in performance degradation, and in some cases, the roughness causes a thicker and more resilient boundary layer, which can, under very specific icing conditions, enhance the aerodynamic performance.

Multiple localized solutions of high topological type for semiclassical nonlinear Schrödinger-Poisson system

Multiple localized solutions of high topological type for semiclassical nonlinear Schrödinger-Poisson system

Topological Characterization and Typical Topologies of Disruption Aggregates in Asphalt Mixture

Topological Characterization and Typical Topologies of Disruption Aggregates in Asphalt Mixture