Edge Topology 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.

Unveiling nanoscale THz-STM imaging techniques on graphene nanoribbons with zigzag edge topology.

The development of near-field THz microscopes has transcended the diffraction limitation traditionally constraining THz super-resolution imaging, heralding a new era of precision. Notably, Terahertz combined scanning tunneling microscopy (THz-STM) has distinguished itself by achieving unparalleled spatial resolution alongside remarkable temporal precision. Despite the significant advancements in THz-STM imaging research, a thorough exploration of its unique imaging features remains elusive, particularly in resolving local electronic spectroscopy. This study methodically explores THz-STM imaging over atomically precise 6-zigzag-edged graphene nanoribbons (6-ZGNR) on Au(111), employing a constant-current mode. The investigation reveals that intense THz-driven electric fields can induce irreversible alterations to the occupied and unoccupied state densities of the 6-ZGNR. Utilizing these THz-modified nanoribbons, analyses of both THz-driven STM imaging and THz current imaging with an external lock-in amplifier are carried out, and experimental factors affecting their imaging qualities have been investigated. It is demonstrated that the imaging with an external lock-in amplified THz current signal accurately captures the local electronic spectroscopy variations at the nanoscale. What we believe is a novel imaging technique proficiently delineates the features on the Au(111) surface and the 6-ZGNR, showcasing superior performance over direct terahertz-driven STM imaging of the samples.

On-Surface Synthesis of Macrocycles, Non-Planar Carbon Ribbons and Heteroatom-Doped Nanographenes

On-surface synthesis via covalent coupling of adsorbed molecules on metal surfaces has attracted significant attention recently due to its potential to fabricate low-dimensional carbon materials with atomic precision. The bottom-up, atomically precise synthesis of carbon nanostructures enables the tailoring of their electronic properties at a molecular level. To understand and control the surface-chemistry-driven synthesis, many efforts have been made to design innovative precursors, explore novel reaction schemes, and utilize templating effects from the substrate.My presentation focuses on high-resolution scanning probe microscopy experiments combined with density functional theory to demonstrate recent highlights on the assembly of surface-supported low-dimensional carbon structures on metal surfaces. First, the assembly and electronic structure of planar π-extended cycloparaphenylene macrocycles, representing the first nanographene with an all-armchair edge topology, will be presented [1]. The second part will discuss the bottom-up synthesis of covalently-linked non-planar carbon ribbons and their electronic properties depending on their adsorption geometry. Finally, I will conclude with the on-surface cyclomerization of oxygen heterocycles to understand the on-surface synthesis of furan and pyran derivatives from ketone-functionalized precursors on metal surfaces.[1] Xiang, et al. Nature Chem., 2022 14, 871–876.

Non‐Volatile Reconfigurable p–n Junction Utilizing In‐Plane Ferroelectricity in 2D WSe2/α‐In2Se3 Asymmetric Heterostructures

AbstractIt is impossible to imagine modern electronic circuitry without a p–n junction—an essential building block for transistors, rectifiers, amplifiers, photovoltaics, etc. Conventional fabrication processes (ion implantation or chemical diffusion) result in an immutable potential configuration depriving reconfigurability. In contrast, the superior electrostatic tunability, dangling bonds‐ and reconstruction‐free interfaces are some of the key features of 2D based heterostructures, making them promising candidates for cutting‐edge optoelectronic and memory applications. Herein, the intercoupled 2D ferroelectricity of 𝛼‐In2Se3 is utilized to introduce micron‐scale, non‐volatile electrostatic doping in ambipolar WSe2, enabling reconfigurable p–n junction. The actuation mechanism is based on the strong polarization field along the edge topology of In2Se3. The fabricated device presents stable p–n to n–p switching, a superior rectification ratio of ≈106, and a low leakage current of ≈10−12 A. Furthermore, the switchable short‐circuit current response is utilized to demonstrate a novel self‐powered, non‐volatile memory based on photovoltaic reading. The ferroelectric non‐volatility coupled with the ability to control the device operation using optical and electrical signals paves the way for ultrathin energy‐efficient, multi‐level optoelectronic and in‐memory logic devices.

Constructing Highly Efficient Circularly Polarized Multiple Resonance Thermally Activated Delayed Fluorescence Materials with Intrinsically Helical Chirality.

Advanced circularly polarized multiple resonance thermally activated delayed fluorescence (CP-MR-TADF) materials synergize the advantages of circularly polarized luminescence (CPL), narrowband emission and TADF characteristic, which can be fabricated into highly efficient circularly polarized organic light-emitting diodes (CP-OLEDs) with high color purity, directly facing the urgent market strategic demand of ultra-high-definition and 3D displays. In this contribution, based on edge topology molecular engineering (ETME) strategy, a pair of high-performance CP-MR-TADF enantiomers, (P and M)-BN-Py, has been developed, which merges the intrinsically helical chirality into MR framework. The optimized CP-OLEDs with emitters (P and M)-BN-Py and the newly developed ambipolar transport host PhCbBCz exhibit pure green emission with sharp peaks of 532nm, full-width at half-maximums (FWHMs) of 37nm, and Commission Internationale de L'Eclairage (CIE) coordinates of (0.29, 0.68). Importantly, they achieve remarkable maximum external quantum efficiencies (EQEs) of 30.6% and 29.2%, and clear circularly polarized electroluminescence (CPEL) signals with electroluminescence dissymmetry factors (gEL s) of -4.37 × 10-4 and +4.35 × 10-4 for (P)-BN-Py and (M)-BN-Py, respectively. This article is protected by copyright. All rights reserved.

Higher-order topological phases emerging from Su-Schrieffer-Heeger stacking

In this work, we develop a systematic approach of constructing and classifying the model Hamiltonians for two-dimensional (2D) higher-order topological phase with corner zero-energy states (CZESs). Our approach is based on the direct construction of an analytical solution of the CZESs in a series of 2D systems stacking the 1D extended Su-Schrieffer-Heeger (SSH) model, two copies of the two-band SSH model, along with two orthogonal directions. Fascinatingly, our approach not only gives the celebrated Benalcazar-Bernevig-Hughes and 2D SSH models but also reveals a novel model and we name it 2D crossed SSH model. Although these three models exhibit completely different bulk topology, we find that the CZESs can be universally characterized by edge winding number for 1D edge states, attributing to their unified Hamiltonian construction form and edge topology. Remarkably, our principle of constructing CZESs can be readily generalized to 3D and superconducting systems. Our work sheds new light on the theoretical understanding of the higher-order topological phases and paves the way to looking for higher-order topological insulators and superconductors.

Multimodal Medical Image Fusion Using Two- Stage Decomposition Technique to Combine the Significant Features of Spatial Fuzzy Plane and Transformed Frequency Plane

Multimodal medical image fusion is becoming a powerful technique in various clinical applications such as disease diagnosis and treatment planning. In this work, a two-stage decomposition technique is proposed to capture the significant features from the spatial and spectral domains as well. The first stage decomposition method employs a multicluster fuzzy c-means (FCM) algorithm to produce gross- and fine-structural components. The fine-structural components containing the edge topology are again decomposed into amplitude and phase spectra in terms of the discrete cosine transformation-based discrete Fourier transform (DCT-DFT). Finally, all parts of decomposed images are integrated with three different fusion rules. A new window-based feature quality measuring (WFQM) filter is proposed for fusing the information of gross-structural components, while the singular value decomposition (SVD) method and gray-wolf optimization-based pulse-coupled neural network (GWO-PCNN) model are applied for fusing the amplitude and phase spectrum distributions of input images. As the WFQM filter and GWO-PCNN model are designed to fuse the significant information from the spatial fuzzy plane and transformed frequency plane respectively, relative contrast degradation and spectral distortion are less in the proposed fusion method. Experimental results are reported on Harvard University datasets and some qualitative as well as quantitative measures are presented for comparing the proposed method with other state-of-art-techniques. The quantitative evaluation used peak signal-to-noise ratio (PSNR), mutual information (MI), structural similarity index measurement (SSIM), visual information fidelity (VIF), and entropy (ENT) to study its superiority.

On-surface synthesis and characterization of teranthene and hexanthene: ultrashort graphene nanoribbons with mixed armchair and zigzag edges.

Graphene nanoribbons (GNRs) exhibit a broad range of physicochemical properties that critically depend on their width and edge topology. GNRs with armchair edges (AGNRs) are usually more stable than their counterparts with zigzag edges (ZGNRs) where the low-energy spin-polarized edge states render the ribbons prone to being altered by undesired chemical reactions. On the other hand, such edge-localized states make ZGNRs highly appealing for applications in spintronic and quantum technologies. For GNRs fabricated via on-surface synthesis under ultrahigh vacuum conditions on metal substrates, the expected reactivity of zigzag edges is a serious concern in view of substrate transfer and device integration under ambient conditions, but corresponding investigations are scarce. Using 10-bromo-9,9':10',9''-teranthracene as a precursor, we have thus synthesized hexanthene (HA) and teranthene (TA) as model compounds for ultrashort GNRs with mixed armchair and zigzag edges, characterized their chemical and electronic structure by means of scanning probe methods, and studied their chemical reactivity upon air exposure by Raman spectroscopy. We present a detailed identification of molecular orbitals and vibrational modes, assign their origin to armchair or zigzag edges, and discuss the chemical reactivity of these edges based on characteristic Raman spectral features.

Planar π-extended all-armchair edge topological cycloparaphenylenes.

It is important to reveal the optical properties and physical mechanisms of electron transitions within planar π-extended cycloparaphenylenes (CPPs) with full armchair edge topology in nanoscience and nanotechnology. The optical properties of the planar π-extended ring stripped from the Au(111) surface are theoretically studied, based on the latest experimental synthesis [Nat. Chem. 2022, 14, 871]. Our calculation results indicate that there is a blue-shift of absorption peaks in non-planar systems compared with planar systems. For non-planar systems, we proved that there is no fluorescence in the closed loop while the open loop exhibits fluorescence, using charge density differences and transition densities as evidence. And we realized the transition from the weak excited state to the strong excited state by the two photon absorption (TPA) method. The resonance Raman spectrum confirmed that the S1 excited state of the non-planar closed loop is a dark excited state. Moreover, there is a red-shift of absorption peaks in non-planar charged systems compared with non-planar uncharged systems. We also investigated the visualization of charge transfer using absorption and fluorescence spectroscopy. Our results can provide more insights into the optical properties and potential design of optical nanodevices.

Furan‐Extended Helical Rylenes with Fjord Edge Topology and Tunable Optoelectronic Properties

AbstractLateral furan‐expansion of polycyclic aromatics, which enables multipleO‐doping and peripheral edge evolution of rylenes, is developed for the first time. TetrafuranylperyleneTPF‐4CNand octafuranylquaterryleneOFQ‐8CNwere prepared as model compounds bearing unique fjord edge topology and helical conformations. Compared toTPF‐4CN, the higher congenerOFQ‐8CNdisplays a largely red‐shifted (≈333 nm) and intensified absorption band (λmax=829 nm) as well as a narrowed electrochemical band gap (≈1.08 eV) due to its pronounced π‐delocalization and emerging of open‐shell diradicaloid upon the increase of fjord edge length. Moreover, strong circular dichroism signals in a broad range until 900 nm are observed for open‐shell chiralOFQ‐8CN, owing to the excellent conformational stability of its central bis(tetraoxa[5]helicene) fragments. Our studies provide insights into the relationships between edge topologies and (chir)optoelectronic properties for this novel type ofO‐doped PAHs.

Furan-Extended Helical Rylenes with Fjord Edge Topology and Tunable Optoelectronic Properties.

Lateral furan-expansion of polycyclic aromatics, which enables multiple O-doping and peripheral edge evolution of rylenes, is developed for the first time. Tetrafuranylperylene TPF-4CN and octafuranylquaterrylene OFQ-8CN were prepared as model compounds bearing unique fjord edge topology and helical conformations. Compared to TPF-4CN, the higher congener OFQ-8CN displays a largely red-shifted (≈333 nm) and intensified absorption band (λmax =829 nm) as well as a narrowed electrochemical band gap (≈1.08 eV) due to its pronounced π-delocalization and emerging of open-shell diradicaloid upon the increase of fjord edge length. Moreover, strong circular dichroism signals in a broad range until 900 nm are observed for open-shell chiral OFQ-8CN, owing to the excellent conformational stability of its central bis(tetraoxa[5]helicene) fragments. Our studies provide insights into the relationships between edge topologies and (chir)optoelectronic properties for this novel type of O-doped PAHs.

G[formula omitted]DA: Geometry-guided dual-alignment learning for RGB-infrared person re-identification

RGB-Infrared (IR) person re-identification aims to retrieve person-of-interest from heterogeneous cameras, easily suffering from large image modality discrepancy caused by different sensing wavelength ranges. Existing works usually minimize such discrepancy by aligning modality distribution of global features, while neglecting deep semantics and high-order structural relations within each class. This might render the misalignment between heterogeneous samples. In this paper, we propose Geometry-Guided Dual-Alignment (G2DA) learning, which yields better sample-level modality alignment for RGB-IR ReID by solving a graph-enabled distribution matching task that maximizes agreement between multi-modality node representations considering edge topology. Specifically, we covert RGB/IR images into semantic-aligned graphs, in which whole-part features and their similarities are represented by nodes and associated edges, respectively. To simultaneously implement node- and edge-wise alignment (Dual Alignment), we introduce Optimal Transport (OT) as a metric to calculate cross-modality human body matching scores. By minimizing the displacement cost across RGB-IR graphs, G2DA could learn not just modality-invariant but structurally consistent cross-modality representations. Furthermore, we advance a Message Fusion Attention (MFA) mechanism to adaptively smooth the node representations within each RGB/IR graph, effectively alleviating occlusions caused by other individuals and/or objects. Extensive experiments on two standard benchmark datasets validate the superiority of G2DA, yielding competitive performance against previous state-of-the-arts.

The Independent Incompatible Edges Topology on Di-graphs

This sheet offers a novel topology for di-graphs termed independent incompatible edges topology, which creates the topology from the edges set \U0001d576 for whatever di-graph. On edges \U0001d576, a family of sub-basis is used for build the independent incompatible edges topology. After that, we look at assorted properties; explore the Independent Incompatible Edge Topology on some types of di-graphs. In addition, this topology’s some initial results were studied. Our objective is to understand several aspects of any di-graph using it is corresponding independent incompatible edges topology, the topology that is discussed in this paper.

SANA: cross-species prediction of Gene Ontology GO annotations via topological network alignment

Topological network alignment aims to align two networks node-wise in order to maximize the observed common connection (edge) topology between them. The topological alignment of two protein–protein interaction (PPI) networks should thus expose protein pairs with similar interaction partners allowing, for example, the prediction of common Gene Ontology (GO) terms. Unfortunately, no network alignment algorithm based on topology alone has been able to achieve this aim, though those that include sequence similarity have seen some success. We argue that this failure of topology alone is due to the sparsity and incompleteness of the PPI network data of almost all species, which provides the network topology with a small signal-to-noise ratio that is effectively swamped when sequence information is added to the mix. Here we show that the weak signal can be detected using multiple stochastic samples of “good” topological network alignments, which allows us to observe regions of the two networks that are robustly aligned across multiple samples. The resulting network alignment frequency (NAF) strongly correlates with GO-based Resnik semantic similarity and enables the first successful cross-species predictions of GO terms based on topology-only network alignments. Our best predictions have an AUPR of about 0.4, which is competitive with state-of-the-art algorithms, even when there is no observable sequence similarity and no known homology relationship. While our results provide only a “proof of concept” on existing network data, we hypothesize that predicting GO terms from topology-only network alignments will become increasingly practical as the volume and quality of PPI network data increase.

Planar π-extended cycloparaphenylenes featuring an all-armchair edge topology.

The [n]cycloparaphenylenes ([n]CPPs)-n para-linked phenylenes that form a closed-loop-have attracted substantial attention due to their unique cyclic structure and highly effective para-conjugation leading to a myriad of fascinating electronic and optoelectronic properties. However, their strained topology prevents the π-extension of CPPs to convert them either into armchair nanobelts or planarized CPP macrocycles. Here we successfully tackle this long-standing challenge and present the bottom-up synthesis and characterization of atomically precise in-plane π-extended [12]CPP on Au(111) by low-temperature scanning probe microscopy and spectroscopy combined with density functional theory. The planar π-extended CPP is a nanographene with an all-armchair edge topology. The exclusive para-conjugation at the periphery yields delocalized electronic states and the planarization maximizes the overlap of p orbitals, which both reduce the bandgap compared to conventional CPPs. Calculations predict ring currents and global aromaticity in the doubly charged system. The intriguing planar ring topology and unique electronic properties make planar π-extended CPPs promising quantum materials.

The independent compatible edges topology of directed graphs

A new topology is associated with the collection of edges in each digraph, we introduce a new topology for digraphs. The independent compatible edges topology is the name given to this topology. The independent compatible edges topology is constructed using a sub basis collection on the set of edges E. Then, we examine various properties and explain the independent compatible edge topology of a few key graph types. A few of the topology’s initial outcomes were examined. Our goal is to begin understanding some characteristics of directed graphs by examining the ability compatible edges topology, which is addressed in this article.

Photo/Electrochromic Dual Responsive Behavior of a Cage-like Zr(IV)-Viologen Metal-Organic Polyhedron (MOP).

Stable stimulus-responsive materials are highly desirable due to their widespread potential applications and growing demand in recent decades. Despite the fact that viologen derivatives have long been known as excellent photochromic and electrochromic materials, the development of stable viologen-based multifunctional smart materials with short coloration times remains an exciting topic. To obtain photochromic and electrochromic dual responsive materials, embedding the viologen ligand into a robust metal oxide cluster to increase its stability and sensitivity is an effective strategy. Herein, a viologen-based metal-organic polyhedron (MOP) {[Zr6L3(μ3-O)2(μ2-OH)6Cp6]·8Cl·CH3OH·DMF} [Zr-MOP-1; H2L·2Cl = 1,1'-bis(4-carboxyphenyl)-4,4'-bipyridinium dichloride, and Cp = η5-C5H5] was successfully prepared and characterized. It consists of trinuclear Zr-oxygen secondary building units and exhibits reversible photochromic and electrochromic dual responsive behaviors. As expected, the designed robust viologen-based nanocage with a V2E3 (V = vertex, and E = edge) topology can maintain its stability and rapid photo/electrochromic behaviors with an obvious reversible change in color from purple (brown) to green, mainly due to the enclosed cluster structure and the abundant free viologen radicals that originate from the effective Cl → N and O → N electron transfers. Spectroelectrochemistry and theoretical calculations of this Zr-MOP were also performed to verify the chromic mechanism.

Quantum Confinement in Aligned Zigzag “Pseudo‐Ribbons” Embedded in Graphene on Ni(100)

AbstractLateral quantum confinement is of great interest in tuning the electronic properties of graphene‐based nanostructures, making them suitable for technological applications. In principle, these properties might be controlled through the edge topology: for example, zigzag nanoribbons are predicted to have spin‐polarized edge states. The practical realization of these structures is of utmost importance in fully harnessing the electronic properties of graphene. Here, the formation of regular, 1.4 nm wide ribbon‐like graphene structures with zigzag edges are reported, showing 1D electronic states. It is found that these “pseudo‐ribbons” embedded in single‐layer graphene supported on Ni(100) can spontaneously form upon carbon segregation underneath 1D graphene moiré domains, extending hundreds of nanometers in length. On the basis of both microscopy/spectroscopy/diffraction experiments and theoretical simulations, it is shown that these structures, even though seamlessly incorporated in a matrix of strongly interacting graphene, exhibit electronic properties closely resembling those of zigzag nanoribbons.

PAPS: A Serverless Platform for Edge Computing Infrastructures

Edge computing infrastructures are often employed to run applications with low latency requirements. Users can exploits nodes that are close to their physical positions so that the delay of sending computations and data to the Cloud is mitigated. Since users frequently change their locations, and the resources available in the Edge are limited, the management of these infrastructures poses new, difficult challenges. This paper presents PAPS (Partitioning, Allocation, Placement, and Scaling), a framework for the efficient, automated and scalable management of large-scale Edge topologies. PAPS acts as a serveless platform for the Edge. Service providers can upload applications as compositions of lightweight and stateless functions along with latency constraints. At runtime, PAPS manages these applications by executing them in containers, it changes their placement in the Edge topology according to the geographical distribution of the workload, and efficiently allocates resources according to their needs. This paper also presents the architecture of a PAPS prototype built atop Kubernetes and OpenFaaS. The assessment shows both the feasibility of the approach and the ability of efficiently managing hundreds of serverless concurrent functions and of dealing with intense and unpredictable workload variations.

Versatile butt-joint regrowth for dense photonic integration

Butt-joint regrowth is widely used in photonic integration, but it has been challenging to break the density-quality tradeoff due to the edge growth rate enhancement (GRE) effect. In this work, we propose a scheme to circumvent this tradeoff by using large regrowth masks whose centers are exposed to epi-growth for neutralization of the excessive species. With the GRE under control, epi-stacks with arbitrarily large sizes supporting dense arrays can be butt-joint integrated with minimal compromise to their epitaxy quality. In our experiment, multi-quantum-well-based material of an exceptionally large area of 0.5 × 1.7 mm2 was epitaxially integrated with passive InP material on the same wafer. A more than 20 × reduction in edge topology compared to conventional methods was achieved.