Topological Characterization Research Articles

Anisotropic Elasticity, Spin-Orbit Coupling, and Topological Properties of ZrTe2 and NiTe2: A Comparative Study for Spintronic and Nanoscale Applications.

The present work investigates the interfacial and atomic layer-dependent mechanical properties, SOC-entailing phonon band structure, and comprehensive electron-topological-elastic integration of ZrTe2 and NiTe2. The anisotropy of Young's modulus, Poisson's ratio, and shear modulus are analyzed using density functional theory with the TB-mBJ approximation. NiTe2 has higher mechanical property values and greater anisotropy than ZrTe2. Phonon dispersion analysis with SOC effects predicts the dynamic stability of both compounds. Thus, the current research unifies electronic band structure analysis, topological characterization, and elastic property calculation to reveal how these transition metal dichalcogenides are influenced by their structural, electronic, and mechanical properties. The results obtained in this work can be used in the further development of spintronic and nanoelectronic devices.

On topological characterizations and computational analysis of benzenoid networks for drug discovery and development.

Topological indices are numerical invariants that provide key insights into the structural properties of molecular graphs and are crucial in predicting physio-chemical and biological activities. This paper applies established computational methodologies for analyzing benzenoid networks and their application to polycyclic aromatic hydrocarbons (PAHs) through degree-based topological indices computed via M-polynomial and NM-polynomial approaches. By examining tessellations, including linear chain, hexagonal, rhomboidal, and triangular configurations alongside their line graphs, this work highlights the influence of molecular topology on biological activity. Notably, the line graph of hexagonal tessellations resembling Kagome structures exhibits the highest potential bioactivity, revealing additional connectivity patterns that offer a structured framework for early-stage drug discovery and potentially enhance the understanding of molecular interactions. These findings underscore the value of topological indices in identifying key structural features, reducing attrition rates in drug development, and improving screening technologies, contributing to efficient drug design.

The topology of a chaotic attractor in the Kuramoto-Sivashinsky equation.

The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal dimension of a chaotic attractor in a partial differential equation (PDE) is less than three, even though that attractor is embedded within an infinite-dimensional space. Here, we study the Kuramoto-Sivashinsky PDE at the onset of chaos. We use two different dimensionality-reduction techniques-proper orthogonal decomposition and an autoencoder neural network-to find two different mappings of the chaotic attractor into three dimensions. By finding the image of the attractor's UPOs in these reduced spaces and examining their linking numbers, we construct templates for the branched manifold, which encodes the topological properties of the attractor. The templates obtained using two different dimensionality reduction methods are equivalent. The organization of the periodic orbits is identical and consistent symbolic sequences for low-period UPOs are derived. While this is not a formal mathematical proof, this agreement is strong evidence that the dimensional reduction is robust, in this case, and that an accurate topological characterization of the chaotic attractor of the chaotic PDE has been achieved.

Local and energy-resolved topological invariants for Floquet systems

Periodically driven systems offer a perfect breeding ground for out-of-equilibrium engineering of topological boundary states at zero energy (0 mode), as well as finite energy (π mode), with the latter having no static analog. The Floquet operator and the effective Floquet Hamiltonian, which encapsulate the stroboscopic features of the driven system, capture both spectral and localization properties of the 0 and π modes but sometimes fail to provide complete topological characterization, especially when 0 and π modes coexist. In this work, we utilize the spectral localizer, a powerful local probe that can provide numerically efficient, spatially local, and energy-resolved topological characterization. In particular, we apply the spectral localizer to the effective Floquet Hamiltonian for driven one- and two-dimensional topological systems with no or limited symmetries and are able to assign topological invariants, or local markers, that characterize the 0- and the π-boundary modes individually and unambiguously. Due to the spatial resolution, we also demonstrate that the extracted topological invariants are suitable for studying driven disordered systems and can even capture disorder-induced phase transitions. Published by the American Physical Society 2024

Topological characterization of [n]-triangulenes through degree-based molecular descriptors with the prediction to π-electron energy

Abstract Triangulene and its π-extended homologues are a family of polycyclic aromatic hydrocarbons
with a peculiar chemical structure. They are recognized for their intricate structural configurations
and electrical properties, which make them a promising material for potential uses in spintronics.
They are built of benzenoid rings fused in a triangular manner. Topological indices are widely
utilized as graph theoretical measures for evaluating the physicochemical properties of polycyclic
aromatic hydrocarbons by analyzing their molecular structures, makes them hold a significant position
in the domain of mathematical and computational chemistry. In this study, a mathematical
exploration of topological indices of [n]-triangulenes has been done to establish a comprehensive
understanding of their applications and significance. Generalized expressions for topological indices
have been computed, and their predictive power for various physicochemical properties has been
studied using statistical methods. Also, a quantitative structure-property relationship analysis of
[n]-triangulene’s energetic characteristics has been performed. Moreover, a generalized algebraic
expression to predict the π-electron energy of [n]-triangulene structure has been derived.

Topology and monoid representations I: Foundations

This paper aims to use topological methods to compute Ext between an irreducible representation of a finite monoid inflated from its group completion and one inflated from its group of units, or more generally coinduced from a maximal subgroup, via a spectral sequence that collapses on the E2-page over fields of good characteristic. As an application, we determine the global dimension of the algebra of the monoid of all affine transformations of a vector space over a finite field. We provide a topological characterization of when a monoid homomorphism induces a homological epimorphism of monoid algebras and apply it to semidirect products. Topology is used to construct projective resolutions of modules inflated from the group completion for sufficiently nice monoids. A sequel paper will use these results to study the representation theory Hsiao's monoid of ordered G-partitions (connected to the Mantaci-Reutenauer descent algebra for the wreath product G≀Sn).

3d topological characterisation of aggregates contact network in asphalt mixture

Aggregates contact each other to form a complex network. 3D topological models are established to characterise the mesostructue of asphalt mixtures. Upon analysing the distribution of algebraic connectivity ( La ), it’s observed that topologies are dominated by the topologies corresponding to La = 1.000 and La = 2.000 . And 10 representative topologies are identified. Furthermore, Upon analysing the relationship between coordination number( K n ), clustering coefficient( C i ) and the maximum size, it’s observed that with the increase of the maximum size, the AC asphalt mixture skeleton is more compact, the compactness of the SMA asphalt mixture is not significantly affected and the fine-grained OGFC asphalt mixture has a more compact skeleton than medium-grained OGFC mixture. Moreover, the AC asphalt mixture skeleton is relatively loose, the SMA asphalt mixture skeleton is more compact and the OGFC asphalt mixture skeleton exhibits the highest degree of compactness.

Remediation of crude oil contaminated oily wastewater using nanostructured ZnO-decorated ceramic membrane: Membrane fouling and their mitigation using photo-catalytic self-cleaning process

In membrane-based oil water separation, the fouling of oil on the membrane pores due to the adsorption of oily feed components (crude oil) is a major disadvantage. In order to address the problem of membrane fouling, in this work, the filtration membrane itself was coated with a photoactive semiconducting material to self-clean the fouled membrane by photo-catalytic degradation. In addition to the self-cleaning, the other major functionality of the coating is to render a favorable surface wettability, conducive for water passing oil water separation. The basic membrane is porous alumina (Al2O3) substrate, on which a layer of crystalline Zinc Oxide (ZnO) thin film was coated by single step RF magnetron sputtering. The fabricated membrane is super-hydrophilic in the air and super-oleophobic underwater, and this contrasting wettability is crucial for the water passing oil water separation. The advantage of preferentially water passing membrane is that the oil clogging on the membrane surface is less than that of the oil passing membrane. However, after prolonged use with crude oil-contaminated feed, the accumulation of organic pollutants on the membrane surface hinders the smooth permeation of water through the membrane. The oil water filtration system involves cross flow through the ZnO-deposited Al2O3 membrane with the application of trans-membrane pressure. The membrane achieved an excellent separation efficiency (99.66 %) of oil and water from the oil emulsified water, and high permeates flux (908.4 L/m2.h.bar) for 200 ppm crude oil contaminated oily feed (surfactant stabilized crude oil-in-water emulsion). After a prolonged use of 540 min, the permeate flux declined due to the accumulation of organic pollutants present in the oily water. The original flux was restored by initiating photocatalytic degradation of organic pollutants by the exposure of UV radiation on the used membrane surface. The ZnO-deposited Al2O3 membrane shows an excellent light induced photocatalytic self-cleaning and antifouling with flux recovery ratio of around 88 %. In addition to this application, this manuscript also presents the morphological, elemental, structural, and topological characterizations of coated membrane.

Emerging topological characterization in nonequilibrium states of quenched Kitaev chains

Emerging topological characterization in nonequilibrium states of quenched Kitaev chains

Topological characterization, entropy measures and prediction of properties of Iridium cored dendrimer

This study presents a comprehensive structural analysis of Iridium-cored dendrimers, denoted by Inmlr;n≥1, with an emphasis on degree and distance based metrics to elucidate their structure-property relationships. Dendrimers, known for their highly branched architectures, are versatile macromolecules with applications across various scientific fields. In this work, molecular descriptors serve as essential numerical indicators, capturing bonding characteristics and aiding in the prediction of material properties. Leveraging a novel quotient graph approach, we compute a range of distance based indices, including the Wiener (W), Szeged (Sz and Sze), Mostar (Mo and Moe), and Padmakar-Ivan (PI) indices. We further derive generalized expressions for entropy measures associated with degree based indices, such as Shannon's entropy, providing a robust framework for assessing the structural complexity of these compounds. Additionally, we examine various degree based descriptors with entropy measures—including the Zagreb (M1, M2, and HM), Harmonic (H), Forgotten (F), Randic (R and RR), ABC, GA, SC, σ, and Irregularity indices (irr). A linear regression analysis is conducted to model dendrimer properties and forecast attributes for subsequent generations, potentially minimizing the need for extensive laboratory experimentation. Our findings provide valuable insights into the molecular intricacies of Iridium-cored dendrimers, bridging theoretical chemistry with practical applications and contributing to future advancements in materials science and engineering.

Topological Characterization of Consensus in Distributed Systems

We provide a complete characterization of both uniform and non-uniform deterministic consensus solvability in distributed systems with benign process and communication faults using point-set topology. More specifically, we non-trivially extend the approach introduced by Alpern and Schneider in 1985, by introducing novel fault-aware topologies on the space of infinite executions: the process-view topology, induced by a distance function that relies on the local view of a given process in an execution, and the minimum topology, which is induced by a distance function that focuses on the local view of the process that is the last to distinguish two executions. Consensus is solvable in a given model if and only if the sets of admissible executions leading to different decision values is disconnected in these topologies. By applying our approach to a wide range of different applications, we provide a topological explanation of a number of existing algorithms and impossibility results and develop several new ones, including a general equivalence of the strong and weak validity conditions.

Distance based topological characterization, graph energy prediction, and NMR patterns of benzene ring embedded in P-type surface in 2D network

Nanostructures are tiny objects at the molecular and microscopic scale, with carbon nanotubes being the most notable among them. The elements possess exceptional microelectronic properties and other unique characteristics. Researchers have recently focused on the mathematical features of these materials. Molecular descriptors are crucial in mathematical chemistry, particularly in QSAR and QSPR modeling. Topological indices hold a significant position among them. This study presents the precise formulation of the ten most crucial topological indices for a benzene ring positioned on a P-type surface within the highly symmetric 2D lattice BCZ48\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {BCZ}_{48}$$\\end{document}. We have incorporated the computed indices to develop a predictive model for the graph energy of the 2D lattice and, in addition, provided the NMR patterns and the HOMO-LUMO gap.

Topological Characterization of Coronoid Structures via Valency Based Topological Indices.

The number of atoms producing a bond with an atom a in a molecular structure (graph) is regarded as the valency of a. A number of molecular structures have been topologically characterized via a large number of valency-based topological indices, which correlate certain physio-chemical properties like boiling point, stability, strain energy, and many more chemical compounds. Our intention is to perform the topological characterization of primitive coronoid structures initially on the base of seven different valency-based topological indices. Fundamentally, our purpose is to provide the universal formula by using the topological characterization of any primitive coronoid structures with any valency-based topological index. The technique of atom-bonds partitions according to the valency of atoms besides counting principals are used to find the results. Exact values of valency-based topological index, namely the Randic index, sum connectivity index, harmonic index, atom bond connectivity index, geometric arithmetic index, forgotten index, and symmetric division index are calculated coronoid structures initially constructed with at most three benzene lyres. All these indices are valency-dependent structural invariants that have been used to elaborate several chemical properties of compounds of the structure. Moreover, we provide the general formula to compute any valency-based topological index for any type of coronoid structure constructed with any number of benzene lyres.

Computational Characterization of Lymphocyte Topology in FSGS/Minimal Change Disease

Computational Characterization of Lymphocyte Topology in FSGS/Minimal Change Disease

Synthetic, Electrochemical, DFT, and Synchrotron X-ray Charge-Density Studies on Oxo-centered Triruthenium Clusters Supported by Electron-Withdrawing Carboxylates.

We herein report the synthesis, characterizations, and synchrotron X-ray charge-density studies of oxo-centered triruthenium(II,III,III) clusters [Ru3O(CHCl2COO)6(py)3] (1) and [Ru3O(CHCl2COO)6(CO)(py)2] (2) (py = pyridine). Dichloroacetate was chosen for its large scattering factor of the Cl atom, and its electron-withdrawing nature results in significant stabilization of the targeted lower-valent Ru3II,III,III state in the cluster framework. Multipole analysis revealed that the difference in electron populations between two crystallographically independent Ru centers is small for 1 (Δ = 0.30 e) but large for 2 (Δ = 1.46 e). Remarkable differences between 1 and 2 are also found in their static deformation density maps; substantial local charge depletion was found around the central μ3O atom for 1, which is less pronounced for 2. According to the topological characterization of Ru-μ3O bonds associated with the bond critical point, bcp, the electron density, ρbcp, is in the range of 0.79-0.89 e Å-3, and the total energy density, Hbcp, is in the range of -0.21 to -0.05 hartree Å-3. These findings represent the first charge-density distribution analysis of mixed-valence multinuclear Ru complexes including comparison between 3d and 4d transition-metal systems.

Modified reverse degree descriptors for combined topological and entropy characterizations of 2D metal organic frameworks: applications in graph energy prediction.

Topological descriptors are widely utilized as graph theoretical measures for evaluating the physicochemical properties of organic frameworks by examining their molecular structures. Our current research validates the usage of topological descriptors in studying frameworks such as metal-butylated hydroxytoluene, NH-substituted coronene transition metal, transition metal-phthalocyanine, and conductive metal-octa amino phthalocyanine. These metal organic frameworks are crucial in nanoscale research for their porosity, adaptability, and conductivity, making them essential for advanced materials and modern technology. In this study, we provide the topological and entropy characterizations of these frameworks by employing robust reverse degree based descriptors, which offer insightful information on structural complexities. This structural information is applied to predict the graph energy of the considered metal organic frameworks using statistical regression models.

Topology and functional characterization of major outer membrane proteins of Treponema maltophilum and Treponema lecithinolyticum.

Numerous Treponema species are prevalent in the dysbiotic subgingival microbial community during periodontitis. The major outer sheath protein is a highly expressed virulence factor of the well-characterized species Treponema denticola. Msp forms an oligomeric membrane protein complex with adhesin and porin properties and contributes to host-microbial interaction. Treponema maltophilum and Treponema lecithinolyticum species are also prominent during periodontitis but are relatively understudied. Msp-like membrane surface proteins exist in T. maltophilum (MspA) and T. lecithinolyticum (MspTL), but limited information exists regarding their structural features or functionality. Protein profiling reveals numerous differences between these species, but minimal differences between strains of the same species. Using protein modeling tools, we predict MspA and MspTL monomeric forms to be large β-barrel structures composed of 20 all-next-neighbor antiparallel β strands which most likely adopt a homotrimer formation. Using cell fractionation, Triton X-114 phase partitioning, heat modifiability, and chemical and detergent release assays, we found evidence of amphiphilic integral membrane-associated oligomerization for both native MspA and MspTL in intact spirochetes. Proteinase K accessibility and immunofluorescence assays demonstrate surface exposure of MspA and MspTL. Functionally, purified recombinant MspA or MspTL monomer proteins can impair neutrophil chemotaxis. Expressions of MspA or MspTL with a PelB leader sequence in Escherichia coli also demonstrate surface exposure and can impair neutrophil chemotaxis in an in vivo air pouch model of inflammation. Collectively, our data demonstrate that MspA and MspTL membrane proteins can contribute to pathogenesis of these understudied oral spirochete species.

Protein Complex Heterogeneity and Topology Revealed by Electron Capture Charge Reduction and Surface Induced Dissociation.

We illustrate the utility of native mass spectrometry (nMS) combined with a fast, tunable gas-phase charge reduction, electron capture charge reduction (ECCR), for the characterization of protein complex topology and glycoprotein heterogeneity. ECCR efficiently reduces the charge states of tetradecameric GroEL, illustrating Orbitrap m/z measurements to greater than 100,000 m/z. For pentameric C-reactive protein and tetradecameric GroEL, our novel device combining ECCR with surface induced dissociation (SID) reduces the charge states and yields more topologically informative fragmentation. This is the first demonstration that ECCR yields more native-like SID fragmentation. ECCR also significantly improved mass and glycan heterogeneity measurements of heavily glycosylated SARS-CoV-2 spike protein trimer and thyroglobulin dimer. Protein glycosylation is important for structural and functional properties and plays essential roles in many biological processes. The immense heterogeneity in glycosylation sites and glycan structure poses significant analytical challenges that hinder a mechanistic understanding of the biological role of glycosylation. Without ECCR, average mass determination of glycoprotein complexes is available only through charge detection mass spectrometry or mass photometry. With narrow m/z selection windows followed by ECCR, multiple glycoform m/z values are apparent, providing quick global glycoform profiling and providing a future path for glycan localization on individual intact glycoforms.

Computational insights into zinc silicate MOF structures: topological modeling, structural characterization and chemical predictions

Metal-organic frameworks (MOFs) play a pivotal role in modern material science, offering unique properties such as flexibility, substantial pore space, distinctive structure, and large surface area. Recently, zinc-based MOFs have attracted significant attention, particularly in the biomedical arena, owing to their versatile applications in drug delivery, biosensing, and cancer imaging. However, there remains a crucial need to explore and understand the structural properties of zinc silicate-based MOFs to fully exploit their potential in various applications. The objective of this study is to address this need by employing topological modeling techniques to characterize zinc silicate networks. Utilizing connection number concept of chemical graph theory and novel AL molecular descriptors, we aim to investigate the structural intricacies of these MOFs. More precisely, zinc silicate-based MOF networks are topologically modeled via novel AL topological indices, and derived mathematical closed form formulae for them. By comparing experimental and calculated values and constructing linear regression models, the predictive capabilities of the proposed descriptors are evaluated. Specifically, the performance of derived topological indices against the physico-chemical properties of octane isomers is assessed, which provide valuable insights into their predictive potential. The findings of this study demonstrated the potential of novel AL indices in predicting a wide range of important physico-chemical properties, further enhancing their practicality in materials science and beyond.

Interacting crystalline topological insulators in two-dimensions with time-reversal symmetry

Topology is routinely used to understand the physics of electronic insulators. However, for strongly interacting electronic matter, such as Mott insulators, a comprehensive topological characterization is still lacking. When their ground state only contains short-range entanglement and does not break symmetries spontaneously, they generically realize crystalline fermionic symmetry-protected topological phases (cFSPTs), supporting gapless modes at the boundaries or at the lattice defects. Here, we provide an exhaustive classification of cFSPTs in two dimensions with U(1) charge-conservation and spinful time-reversal symmetries, namely, those generically present in spin-orbit coupled insulators, for any of the 17 wallpaper groups. It has been shown that the classification of cFSPTs can be understood from appropriate real-space decorations of lower-dimensional subspaces, and we expose how these relate to the Wyckoff positions of the lattice. We find that all nontrivial one-dimensional decorations require electronic interactions. Furthermore, we provide model Hamiltonians for various decorations, and discuss the signatures of cFSPTs. This classification paves the way to further explore topological interacting insulators, providing the backbone information in generic model systems and ultimately in experiments. Published by the American Physical Society 2024