Topological Framework Research Articles

Fully π-conjugated dense topological salphen organic frameworks with atomic dispersed tetradentate cobalt sites for high‐efficiency electrocatalytic oxygen reduction

Highly effective electrocatalysts are of vital importance for advanced applications. Here we show that fully π-conjugated dense topological salophen organic frameworks with atomic dispersed tetradentate cobalt sites in-situ growth on Kejtenblack are high-efficiency and durable electrocatalyst for the oxygen reduction, with a remarkable half-wave potential of 0.959 V which surpassing that of benchmark Pt/C catalyst, and is among the highest of reported single atom electrocatalysts. The electron transfer number was 3.92–3.99 and the yield of peroxide remains below 4% in 0.40–0.95 V. When employed as a cathode electrocatalyst for zinc-air batteries, it showed a high open-circuit voltage (1.5558 V) and maximum power density (178 mWcm−2) and high specific capacity (804 mAhgzn−1). The work reported here revealed that tailoring the active centers, conjugated structures, building blocks and topologies at atomic level could synergistically enhance the ORR activity which are highly valuable for zinc–air batteries and fuel cells.

Geometrically nonlinear design of compliant mechanisms: Topology and shape optimization with stress and curvature constraints

In this work, we exploit a sequential topology and shape optimization framework to design compliant mechanisms. We pay particular attention to a refined and exact design of flexure hinges via shape optimization in a geometrically nonlinear setting. We propose improved adaptive shape and domain refinement strategies for the embedding domain discretization method (EDD) to achieve numerically and geometrically accurate designs of the flexure hinges. Furthermore, to account for durability and manufacturability of the flexure hinges, we employed local stress constraints and a curvature constraint. The local stress constraints are integrated into an augmented Lagrange functional together with the output displacement to form a combined objective response. The design update is realized by employing and adapting the traction method for the specifics of the embedded boundary. Hence, the curvature constraint does not appear in a standard response form, but is rather introduced into the auxiliary boundary value problem (BVP) of the traction method via a penalty functional. The novelties of this work include: (1) enhanced adaptive shape and domain refinement strategies for EDD; (2) geometrically nonlinear shape optimization using EDD; (3) adapted traction method with curvature constraint.

Sequential topology and shape optimization framework to design compliant mechanisms with boundary stress constraints

We present a sequential topology and shape optimization framework to design compliant mechanisms with boundary stress constraints. In our approach, a density-based topology optimization method is used to generate the configuration of the mechanisms. Afterwards, a node-based shape optimization is invoked to obtain an exact boundary representation. A specialized, optimality criteria-based design update is formulated for the shape optimization. To avoid impractical hinges with point connections, stress constraints are imposed. The stress constraints are imposed using two strategies: Local stress constraints on the nodes of the boundary or global P-norm stress constraints in the domain. Further, an adaptive shape refinement strategy is adopted to increase the design space of shape optimization and to capture the fine-scale details of the geometry. Finally, numerical experiments are presented, showing that the proposed approach can be effectively applied to the design of compliant mechanisms with stress constraints.

Topology of Robotic Mechanisms: Framework and Mathematics Methods – In Conjunction with a Review of Four Original Theories

In this work, a new basic framework of robotic mechanism topology is proposed, which includes: ① two important concepts (i.e., topological structure and kinematic characteristics), ② three basic formulas (i.e., POC equation of serial mechanisms, POC equation of parallel mechanisms (PMs), and DOF formula) and ③ topological structure synthesis methods of PMs. Based upon this framework, literature review and comparative study of four original theories for topological structure synthesis of PMs (i.e., screw theory, velocity space, subgroup and POC set) are carried out. Moreover, it is found that these four theories and their computable methods (linear operation, nonlinear symbolic operation and linear symbolic operation) originate from different definitions and their mathematical representations of the two concepts. These basic formulas accounting for mechanism topology are derived based on the two concepts, which reveal the mapping relationship among topological structures, POCs and DOF of mechanisms. Further, these four theories are grouped into two categories: ① the algebraic methods related to the fixed coordinate system for screw theory, velocity space and subgroup; ② the intrinsic geometry method independent of the fixed coordinate system for POC set.

A topology framework for macromolecular complexes and condensates

Macromolecular assemblies such as protein complexes and protein/RNA condensates are involved in most fundamental cellular processes. The arrangement of subunits within these nano-assemblies is critical for their biological function and is determined by the topology of physical contacts within and between the subunits forming the complex. Describing the spatial arrangement of these interactions is of central importance to understand their functional and stability consequences. In this concept article, we propose a circuit topology-based formalism to define the topology of a complex consisting of linear polymeric chains with inter- and intrachain interactions. We apply our method to a system of model polymer chains as well as protein assemblies. We show that circuit topology can categorize different forms of chain assemblies. Our multi-chain circuit topology should aid analysis and predictions of mechanistic and evolutionary principles in the design of macromolecular assemblies.

A topological framework for real-time 3D weather radar data processing

ABSTRACT Real-time 3D weather radar data processing makes it possible to efficiently simulate meteorological processes in digital Earth and support the assessment of meteorological disasters. The current real-time meteorological operation system can only deal with radar data within 2D space as a flat map and lacks supporting 3D characteristics. Thus, valuable 3D information imbedded in radar data cannot be completely presented to meteorological experts. Due to the large amount of data and high complexity of radar data 3D operation, regular methods are not competent for supporting real-time 3D radar data processing and representation. This study aims to perform radar data 3D operations with high efficiency and instant speed to provide real-time 3D support for the meteorological field. In this paper, a topological framework composed of basic inner topological objects is proposed along with the quadtree structure and LOD architecture, based on which 3D operations on radar data can be conducted in a split second and 3D information can be presented in real time. As the applications of the proposed topological framework, two widely used 3D algorithms in the meteorological field are also implemented in this paper. Finally, a case study verifies the applicability and validity of the proposed topological framework.

On symplectomorphisms and Hamiltonian flows

We propose the construction of a sequence of time one flows of autonomous Hamiltonian vector fields, converging to a fixed near the identity C^1 symplectic diffeomorphism psi . This convergence is proved to be uniformly exponentially fast, in a non analytic symplectic topology framework.

Transient sensitivity analysis and topology optimization of particle suspended in transient laminar fluid

This study develops a new topology optimization scheme using coupled forward and coupled sensitivity analyses to manipulate and control time-varying particle trajectories in transient laminar flow, that is transient fluid–particle assemblies. It is an important scientific and engineering subject to manipulate or control the trajectories of particles by the drag force in steady-state or transient fluids. The drag force varies with the material properties of fluid, and the velocity differences between fluid and particles cause the particles to move. Despite some research regarding the shape and topological optimization frameworks for particles in steady-state flow, the optimization of transient particle motion in transient laminar flow is still a difficult subject. Thus, this study presents a new topology optimization scheme that considers the transient motion of particles in transient laminar flow. Owing to the time variation in the direction and magnitude of the fluid, the optimization of particle motion requires a new development of the transient sensitivity analysis. For efficient optimization, a two-scale time integration scheme for the fluid and particle was developed. The developed coupled analysis and optimization framework were applied to determine optimal layouts for transient fluids and particles. Several optimization problems were formulated and solved to validate the present scheme.

Triangular Topological 2D Covalent Organic Frameworks Constructed via Symmetric or Asymmetric "Two-in-One" Type Monomers.

Most of the reported covalent organic frameworks (COFs) so far are prepared from highly symmetric building blocks, which to some extent limits the expansion of COF diversity and complexity. Low‐symmetric building blocks can be designed through a desymmetrized vertex strategy, which might be used to construct new topological COFs. But reports of COFs constructed by asymmetric building blocks are thus far very rare. Here, a feasible strategy to design asymmetric building blocks for COF synthesis is introduced, by simply varying the positions of functional groups in the monomer. As a proof of concept, two isomeric hexaphenylbenzene‐based “two‐in‐one” type monomers (1,2,4‐HPB‐NH2 and 1,3,5‐HPB‐NH2) are designed and synthesized. To the authors’ surprise, self‐polycondensation of the asymmetric 1,2,4‐HPB‐NH2 (i.e., the isomer of common C3 ‐symmetric 1,3,5‐HPB‐NH2) also affords highly crystalline COF (1,2,4‐HPB‐COF) similar to the symmetric 1,3,5‐HPB‐NH2 counterpart with identical topological structure. The triangular porous structures of both HPB‐based COFs are well resolved by powder X‐ray diffraction (PXRD), theoretical simulations, nitrogen sorption, and morphologies analysis. This work demonstrates the “two‐in‐one” type asymmetric building blocks can also produce highly crystalline frameworks and thus provides a new structural design strategy for reticular chemistry.

First look at the topology of reionisation redshifts in models of the epoch of reionisation

Context. During the epoch of reionisation (EoR), the first stars and galaxies appeared while creating ionised bubbles that eventually percolated near z ∼ 6. These ionised bubbles and percolation process are closely scrutinised today because observations of neutral hydrogen will be carried on in the next decade with the Square Kilometre Array radio telescope, for instance. In the meantime, EoR studies are performed in semi-analytical and fully numerical cosmological simulations to investigate the topology of the process, for instance. Aims. We analyse the topology of EoR models by studying regions that are under the radiative influence of ionisation sources. These regions are associated with peak patches of the reionisation redshift field, for which we measure the general properties such as their number, size, shape, and orientation. We aim to gain insights into the geometry of the reionisation process and its relation to the matter distribution, for example. We also assess how these measurements can be used to quantify the effect of physical parameters on the EoR models or the differences between fully numerical simulations and semi-analytical models. Methods. We used the framework of Morse theory and persistent homology in the context of the EoR, which was investigated via the DisPerSE algorithm on gas density and redshift of reionisation maps. We analysed different EoR scenarios with semi-analytical 21cmFAST and fully numerical EMMA simulations. Results. We can distinguish between EoR models with different sources using simple analyses of the number, shape, and size distributions of the reionisation redshift patches. For every model (of the semi-analytical and fully numerical simulations), we statistically show that these bubbles are rather prolate and aligned with the underlying gas filaments. Moreover, we briefly highlight that the percolation process of HII bubbles during the EoR can be followed by studying the reionisation redshift fields with different persistence thresholds. Finally, we show that fully numerical EMMA simulations can be made consistent with 21cmFAST models in this topological framework as long as the source distribution is diffuse enough.

A novel topology framework for simultaneous topology, size and shape optimization of trusses under static, free vibration and transient behavior

A novel topology framework for simultaneous topology, size and shape optimization of trusses under static, free vibration and transient behavior

ProteinCT: An implementation of the protein circuit topology framework

The ability to describe the topology of a folded protein conformation is critically important for functional analysis, protein engineering, and drug design. Circuit topology is a unique topological framework which is widely applicable to protein analysis, yet a state-of-the art implementation of this concept is lacking. Here, we present an open-source Python-implemented circuit topology tool called ProteinCT. The platform provides a method for acquiring, visualizing, analyzing, and quantifying circuit topology data from proteins of interest. We mapped the universe of human proteins to a circuit topology space using conventional hardware within a few hours, demonstrating the performance of ProteinCT. In brief,•A Python-implemented circuit topology tool is developed to extract global and local topological information from a protein structure file.•Modules are developed to combine topological information with geometric and energetic information.•It is demonstrated that the method can be efficiently applied to a large set of proteins, opening a wide range of possibilities for structural proteomics research.

Online Semantic-Assisted Topological Map Building With LiDAR in Large-Scale Outdoor Environments: Toward Robust Place Recognition

The building of map model is crucial to the efficiency of unmanned ground vehicles’ (UGVs) navigation and robust place recognition. This paper presents an online semantic-assisted topological map building approach using 3-D LiDAR point clouds in large-scale outdoor environments. To achieve global consistency while switching between global navigation satellite system (GNSS)-denied and GNSS-fixed scenes, a pose estimation module composed of semantic-assisted LiDAR-simultaneous localization and mapping (SLAM) and the GNSS positioning is designed and integrated seamlessly, which can supply both the UGV’s global 6-degrees of freedom (DoF) poses and the local semantic-metric map. On the basis of semantic-metric map output, an online topological map building framework is implemented aiming to construct the topological map with robust place recognition performance, in which a novel local node density adjustment (LoNDA) algorithm is proposed to online adjust the distance between adjacent nodes based on both the targeted node density and appearance similarity. Field experiments are conducted on both self-collected datasets and public datasets. Experimental results demonstrate that the proposed approach can perform the online LiDAR-based topological map building with high accuracy, and the proposed LoNDA algorithm can achieve superior place recognition performance than the density-based scheme.

Synthesis, structure and highly selective C3H8/CH4 and C2H6/CH4 adsorption of a (4,8)-c ternary flu-metal–organic framework based upon both [Sc4O2(COO)8] and [Cu4OCl6] clusters

A new ternary flu-MOF based upon both the torsional cubic 8-c [Sc4O2(COO)8] cluster and the tetrahedral 4-c [Cu4OCl6] cluster has been successfully synthesized and exhibits highly selective C3H8/CH4 and C2H6/CH4 adsorption.

BEAM: A Network Topology Framework to Detect Weak Signals

In these days, strategic decision making and im-mediate action are becoming a complex task for companies and policymakers, since the environment is subject to emerging changes that might include unknown factors. When facing these challenges, companies are exposed to opportunities for growth, but also to threats. Therefore, they seek to explore and analyze large amounts of data to detect emerging changes, or so-called weak signals, that can help maintaining their competitive advantages and shaping up their future operational environments. But due to the increasing volume of daily produced data, scalable and automated computer-aided systems are needed to explore and extract these weak signals. To overcome the automation and scalability challenges, and capture early signs of change in a big data environment, we propose a framework for weak signals detection relying on the network topology. It is implemented under the Cocktail project framework whose goal is to create a real-time observatory of trends, innovations and weak signals circulating in the discourses of the food and health sectors on Twitter. This method analyses quantitatively the network local structure using the graphlets (particular type of motifs) to find weak signals. It provides accordingly qualitative elements that contextualise the identified signals, which will allow business experts to interpret and evaluate their dynamics to determine which ones may have a relevant future. After testing this method on different types of networks (we present two of them in this paper), we proved that it is able to detect weak signals and provides a quantifiable signature that allows better decision making.

Electrostatic-Elastic MEMS with Fringing Field: A Problem of Global Existence

In this paper, we prove the existence and uniqueness of solutions for a nonlocal, fourth-order integro-differential equation that models electrostatic MEMS with parallel metallic plates by exploiting a well-known implicit function theorem on the topological space framework. As the diameter of the domain is fairly small (similar to the length of the device wafer, which is comparable to the distance between the plates), the fringing field phenomenon can arise. Therefore, based on the Pelesko–Driscoll theory, a term for the fringing field has been considered. The nonlocal model obtained admits solutions, making these devices attractive for industrial applications whose intended uses require reduced external voltages.

CTCF-mediated chromatin looping provides a topological framework for the formation of phase-separated transcriptional condensates.

CTCF is crucial to the organization of mammalian genomes into loop structures. According to recent studies, the transcription apparatus is compartmentalized and concentrated at super-enhancers to form phase-separated condensates and drive the expression of cell-identity genes. However, it remains unclear whether and how transcriptional condensates are coupled to higher-order chromatin organization. Here, we show that CTCF is essential for RNA polymerase II (Pol II)-mediated chromatin interactions, which occur as hyperconnected spatial clusters at super-enhancers. We also demonstrate that CTCF clustering, unlike Pol II clustering, is independent of liquid-liquid phase-separation and resistant to perturbation of transcription. Interestingly, clusters of Pol II, BRD4, and MED1 were found to dissolve upon CTCF depletion, but were reinstated upon restoration of CTCF, suggesting a potent instructive function for CTCF in the formation of transcriptional condensates. Overall, we provide evidence suggesting that CTCF-mediated chromatin looping acts as an architectural prerequisite for the assembly of phase-separated transcriptional condensates.

Two stable cadmium(II) coordination polymers for fluorimetric detection of tetracycline and Fe3+ ions

Two stable Cd(II) coordination polymers [Cd(L)(chdc)·(H2O)]n (1) and [Cd(L)(SA)]n (2) (L ​= ​1,6-bis(benzimidazol-1-yl)hexane, H2chdc ​= ​cis-1,2-cyclohexanedicarboxylic acid, H2SA ​= ​suberic acid), were successfully constructed under hydrothermal condition. 1 shows that the 2D structure can be defined as a 63-hcb layer. 2 displays a rare mog topological framework with the point symbol {4·64·8}2{42·62·82}. 1 and 2 exhibit the high sensing capability through luminescence quenching effects. The limits of detection (LOD) of 1 and 2 for Fe3+ are 8.8 × 10−7 ​mol·L−1 and 1.2 × 10−6 ​mol·L−1, respectively. The LOD toward tetracycline (TC) for 1 is 7.6 × 10−8 ​mol·L−1, for 2 is 3.3 × 10−8 ​mol·L−1. 1 and 2 are firstly promising dual-functional fluorescent sensors based MOFs for detection of Fe3+ and TC with high sensitivity and selectivity. In addition, 1 and 2 exhibit excellent thermal and chemical stability.

A Comprehensive Experimental and Theoretical Study on the [{(η5-C5H5)2Zr[P(µ-PNEt2)2P(NEt2)2P]}]2O Crystalline System.

The structure of tetraphosphetane zirconium complex C52H100N8OP10Zr2 1 was determined by single crystal X-ray diffraction analysis. The crystal belongs to the monoclinic system, space group P21/c, with a = 19.6452(14), b = 17.8701(12), c = 20.7963(14)Å, α = γ = 90°, β = 112.953(7)°, V = 6722.7(8)Å3, Z = 4. The electronic structure of the organometallic complex has been characterized within the framework of Quantum Chemical Topology. The topology of the Electron Localization Function (ELF) and the electron density according to the Quantum Theory of Atoms in Molecules (QTAIM) show no covalent bonds involving the Zr atom, but rather dative, coordinate interactions between the metal and the ligands. This is the first reported case of a Zr complex stabilized by an oxide anion, anionic cyclopentadienyl ligands and rare tetraphosphetane anions.

Big data directed acyclic graph model for real-time COVID-19 twitter stream detection

Every day, large-scale data are continuously generated on social media as streams, such as Twitter, which inform us about all events around the world in real-time. Notably, Twitter is one of the effective platforms to update countries leaders and scientists during the coronavirus (COVID-19) pandemic. Other people have also used this platform to post their concerns about the spread of this virus and a rapid increase of death cases globally. The aim of this work is to detect anomalous events associated with COVID-19 from Twitter. To this end, we propose a distributed Directed Acyclic Graph topology framework to aggregate and process large-scale real-time tweets related to COVID-19. The core of our system is a novel lightweight algorithm that can automatically detect anomaly events. In addition, our system can also identify, cluster, and visualize important keywords in tweets. On 18 August 2020, our model detected the highest anomaly since many tweets mentioned the casualties’ updates and the debates on the pandemic that day. We obtained the three most commonly listed terms on Twitter: “covid”, “death”, and “Trump” (21,566, 11,779, and 4761 occurrences, respectively), with the highest TF-IDF score for these terms: “people” (0.63637), “school” (0.5921407) and “virus” (0.57385). From our clustering result, the word “death”, “corona”, and “case” are grouped into one cluster, where the word “pandemic”, “school”, and “president” are grouped as another cluster. These terms were located near each other on vector space so that they were clustered, indicating people’s most concerned topics on Twitter.