Topological Properties Research Articles

Optical Möbius strips in isotropic random non-paraxial light

Abstract The statistics of Möbius strips with various topologies, formed by the axes of polarization ellipses as they are traced along a closed circular contour of small size passing through the center of a solitary circular polarization singularity line (C-line), have been investigated both analytically and numerically in a random isotropic electromagnetic field. Found are the analytical expressions for the joint probability density function of the differential characteristics of the random isotropic electromagnetic field, which allow for the determination of the topological properties of diagrams of polarization ellipses and the normal vectors to them, as well as the optical strips that arise in the space around C-lines.

On Topologies Induced by Ideals, Primals, Filters and Grills

In this paper, one-to-one correspondences and equivalences between ideals, primals, filters and grills are introduced. It is shown that the local functions and the topological spaces induced by them are the same. From this point of view, the topological properties of one topology can be derived from the topological properties that are valid in the corresponding topology.

Braids and higher-order exceptional points from the interplay between lossy defects and topological boundary states

We show that the perturbation of the Su-Schrieffer-Heeger chain by a localized lossy defect leads to higher-order exceptional points (HOEP). Depending on the location of the defect, third- and fourth-order exceptional points (EP3 and EP4) appear in the space of Hamiltonian parameters. On the one hand, they arise due to the non-Abelian braiding properties of exceptional lines (EL) in parameter space. Namely, the HOEPs lie at intersections of mutually noncommuting ELs. On the other hand, we show that such special intersections happen due to the fact that the delocalization of edge states, induced by the non-Hermitian defect, hybridizes them with defect states. These can then coalesce together into an EP3. When the defect lies at the midpoint of the chain, a special symmetry of the full spectrum can lead to an EP4. In this way, our model illustrates the emergence of interesting non-Abelian topological properties in the multiband structure of non-Hermitian perturbations of topological phases. Published by the American Physical Society 2024

On Semi-?-Connected Subspace

In this paper, the concept of semi-?-open set will be used to define a new kind of strongly connectedness on a topological subspace namely "semi-?-connectedness". Moreover, we prove that semi-?-connectedness property is a topological property and give an example to show that semi-?-connectedness property is not a hereditary property. Also, we prove thate semi-?-irresolute image of a semi-?-connected space is a semi-?-connected space.

Electronic structure of zaykovite Rh3Se4, prediction, and analysis of physical properties of related materials: Pd3Se4, Ir3Se4, and Pt3Se4.

In this work, we explore the electronic properties and chemical bonding in the recently discovered mineral zaykovite, the first natural rhodium selenide Rh3Se4. We comprehensively studied the bulk electronic structure, hybridization of rhodium and selenium orbitals, and the influence of spin-orbit interaction on the electronic spectrum, as well as inspected its topological properties. In addition, we investigated the surface electronic structure of zaykovite and revealed the anisotropic Rashba-type spin splitting in the surface states. In addition, using calculations of the phonon spectra and enthalpy of formation, we predicted the family of similar selenides based on other 4d and 5d transition metals such as Ir, Pd, and Pt. The structural and electronic properties of these materials are discussed.

Schröder–Catalan Matrix and Compactness of Matrix Operators on Its Associated Sequence Spaces

In this article, the regular Schröder–Catalan matrix is constructed and acquired by benefiting Schröder and Catalan numbers. After that, two sequence spaces are introduced, described as the domain of Schröder–Catalan matrix. Additionally, some algebraic and topological properties of the spaces in question, such as completeness, inclusion relations, basis and duals, are examined. In the last two sections, the necessary and sufficient conditions of some matrix classes and compact operators related aforementioned spaces are presented.

Elastic spin angular momentum of zero-order flexural mode in thin rod system

The exploration of elastic wave behaviors in solid materials has revealed their intricate topological properties in recent years, particularly highlighting the significance of a previously underappreciated characteristic known as elastic spin angular momentum. This aspect plays a crucial role in the dynamics of elastic waves. Our research has focused on elucidating the theoretical aspects of elastic spin angular momentum, especially concerning the zero-order flexural mode in thin rod systems. Through meticulous theoretical analysis, we have deduced the nature of this angular momentum and successfully calculated the distribution of spin within these systems. The implications of our findings are substantial, as they contribute to an enhanced physical comprehension of the topological attributes associated with the flexural mode in thin rod structures, thereby offering new avenues for understanding material behaviors and their potential technological applications.

Cooperativity and halonium transfer in the ternary NCI···CH3I···-CN halogen-bonded complex: An ab initio gas phase study.

The strength and nature of the two halogen bonds in the NCI···CH3I···-CN halogen-bonded ternary complex are studied in the gas phase via ab initio calculations. Different indicators of halogen bond strength were employed to examine the interactions including geometries, complexation energies, Natural Bond Order (NBO) Wiberg bond indices, and Atoms in Molecules (AIM)-based charge density topological properties. The results show that the halogen bond is strong and partly covalent in nature when CH3I donates the halogen bond, but weak and noncovalent in nature when CH3I accepts the halogen bond. Significant halogen bond cooperativity emerges in the ternary complex relative to the corresponding heterodimer complexes, NCI···CH3I and CH3I···-CN, respectively. For example, the CCSD(T) complexation energy of the ternary complex (-18.27kcal/mol) is about twice the sum of the complexation energies of the component dimers (-9.54kcal/mol). The halonium transfer reaction that converts the ternary complex into an equivalent one was also investigated. The electronic barrier for the halonium transfer was calculated to be 6.70kcal/mol at the CCSD(T) level. Although the MP2 level underestimates and the MP3 overestimates the barrier, their calculated MP2.5 average barrier (6.44kcal/mol) is close to that of the more robust CCSD(T) level. Insights on the halonium ion transfer reaction was obtained by examining the reaction energy and force profiles along the intrinsic reaction coordinate, IRC. The corresponding evolution of other properties such as bond lengths, Wiberg bond indices, and Mulliken charges provides specific insight on the extent of structural rearrangements and electronic redistribution throughout the entire IRC space. The MP2 method was used for geometry optimizations. Energy calculations were performed using the CCSD(T) method. The aug-cc-pVTZ basis set was employed for all atoms other than iodine for which the aug-cc-pVTZ-PP basis set was used instead.

Double sequences of complex uncertain variables associated with multiplier sequences

Abstract In this article we introduce the notion of double sequences of complex uncertain variables associated with multiplier sequences. We study their different algebraic and topological properties like solidity, symmetricity, completeness etc.

Impact of charge density waves on superconductivity and topological properties in kagome superconductors

Impact of charge density waves on superconductivity and topological properties in kagome superconductors

Topological data analysis of monopole current networks in $U(1)$ lattice gauge theory

In 44-dimensional pure compact U(1)U(1) lattice gauge theory, we analyse topological aspects of the dynamics of monopoles across the deconfinement phase transition. We do this using tools from Topological Data Analysis (TDA). We demonstrate that observables constructed from the zeroth and first homology groups of monopole current networks may be used to quantitatively and robustly locate the critical inverse coupling \beta_{c}βc through finite-size scaling. Our method provides a mathematically robust framework for the characterisation of topological invariants related to monopole currents, putting on firmer ground earlier investigations. Moreover, our approach can be generalised to the study of Abelian monopoles in non-Abelian gauge theories.

Exploring the bioactive ingredients of three traditional Chinese medicine formulas against age-related hearing loss through network pharmacology and experimental validation.

Traditional Chinese medicine (TCM) formulas, including the Er-Long-Zuo-Ci pill, Tong-Qiao-Er-Long pill, and Er-Long pill, have long been utilized in China for managing age-related hearing loss (ARHL). However, the specific bioactive compounds, pharmacological targets, and underlying mechanisms remain elusive. This study aims to find the shared bioactive ingredients among these three formulas, uncover the molecular pathways they regulate, and identify potential therapeutic targets for ARHL. Furthermore, it seeks to validate the efficacy of these major components through both in vivo and in vitro experiments. Common bioactive ingredients were extracted from the TCMSP database, and their putative target proteins were predicted using the Swiss Target Prediction database. ARHL-related target proteins were collected from GeneCards and OMIM databases. Our approach involved constructing drug-target networks and drug-disease-specific protein-protein interaction networks and conducting clustering, topological property analyses, and functional annotation through GO and KEGG enrichment analysis. Molecular docking analysis was utilized to delineate interaction mechanisms between major bioactive ingredients and key target proteins. Finally, in vivo and in vitro experiments involving ABR recording, immunofluorescent staining, HE staining, and quantitative PCR were conducted to validate the treatment effects of flavonoids on the declining auditory function in DBA/2J mice. We identified 11 common chemical compounds across the three formulas and their associated 276 putative targets. Additionally, 3350 ARHL-related targets were compiled. As an intersection of the putative targets of the common compounds and ARHL-related proteins, 145 shared targets were determined. Functional enrichment analysis indicated that these compounds may modulate various biological processes, including cell proliferation, apoptosis, inflammatory response, and synaptic connections. Notably, potential targets such as TNFα, MAPK1, SRC, AKT, EGFR, ESR1, and AR were implicated. Flavonoids emerged as major bioactive components against ARHL based on target numbers, with molecular docking demonstrating diverse interaction models between these flavonoids and protein targets. Furthermore, baicalin could mitigate the age-related cochlear damage and hearing loss of DBA/2J mice through its multi-target and multi-pathway mechanism, involving anti-inflammation, modulation of sex hormone-related pathways, and activation of potassium channels. This study offers an integrated network pharmacology approach, validated by in vivo and in vitro experiments, shedding light on the potential mechanisms, major active components, and therapeutic targets of TCM formulas for treating ARHL.

Electric transport and topological properties of binary heterostructures in topological insulators

The design of devices with coupled hybrid structures offers an approach to creating synthetic topological materials. This work discusses the topological and transport properties of low-dimensional binary heterostructures of topological and trivial materials. By adjusting the parameters of each component, we control the global topological properties to enhance tunneling and optimize the transmission of the topological edge states (TES). Considering a one-dimensional tight-binding model, we build heterostructures of coupled chains employing Green’s functions (GF) formalism. We determine the topological characteristics of chains and couple them together, applying Dyson’s equation to generate the heterostructure. The intensity and decay length of the TES vary depending on the coupling parameters and the size of each chain. We investigate the topological diagrams phase using the energy bands of the periodic system and calculating the invariant from the Zak phase. Using cross-band condition, we derive analytical functions of the parameter space to get the phase topological diagram, which can be compared with the LDOS maps at zero energy. Finally, we calculate the differential conductance with the Keldysh GF technique to demonstrate the tunneling of the TES at the zero bias voltage and discuss potential design and experimental applications.

Graph Metrics Reveal Brain Network Topological Property in Neuropathic Pain Patients: A Systematic Review.

Neuropathic pain (NP) is a common and persistent disease that leads to immense suffering and serious social burden. Incomplete understanding of the underlying neural basis makes it difficult to achieve significant breakthroughs in the treatment of NP. We aimed to review the functional and structural brain topological properties in patients with NP and consider how graph measures reveal potential mechanisms and are applied to clinical practice. Related studies were searched in PubMed and Web of Science databases. Topological property changes in patients with NP, including small-worldness, functional separation, integration, and centrality metrics, were reviewed. The findings suggest that NP was characterized by retained but declined small-worldness, indicating an insidious imbalance between network integration and segregation. The global-level measures revealed decreased global and local efficiency in the NP, implying decreased information transfer efficiency for both long- and short-range connections. Altered nodal centrality measures involve various brain regions, mostly those associated with pain, cognition, and emotion. Graph theory is a powerful tool for identifying topological properties of patients with NP. These specific brain changes in patients with NP are very helpful in revealing the potential mechanisms of NP, developing new treatment strategies, and evaluating the efficacy and prognosis of NP.

Realization of a 2D Lieb Lattice in a Metal-Inorganic Framework with Partial Flat Bands and Topological Edge States.

Flat bands and Dirac cones in materials are the source of the exotic electronic and topological properties. The Lieb lattice is expected to host these electronic structures, arising from quantum destructive interference. Nevertheless, the experimental realization of a 2D Lieb lattice remained challenging to date due to its intrinsic structural instability. After computationally designing a Platinum-Phosphorus (Pt-P) Lieb lattice, it has successfully overcome its structural instability and synthesized on a gold substrate via molecular beam epitaxy. Low-temperature scanning tunneling microscopy and spectroscopy verify the Lieb lattice's morphology and electronic flat bands. Furthermore, topological Dirac edge states stemming from pronounced spin-orbit coupling induced by heavy Pt atoms are predicted. These findings convincingly open perspectives for creating metal-inorganic framework-based atomic lattices, offering prospects for strongly correlated phases interplayed with topology.

On the Gromov–Hausdorff limits of compact surfaces with boundary

In this work we investigate Gromov–Hausdorff limits of compact surfaces carrying length metrics. More precisely, we consider the case where all surfaces have the same Euler characteristic. We give a complete description of the limit spaces and study their topological properties. Our investigation builds on the results of a previous work which treats the case of closed surfaces.

Novel topological reverse indices and entropies of armchair versus zigzag polyhex carbon nanotubes with spectroscopic applications

The study of nanomaterials with different sizes and shapes is of considerable recent interest. Polyhex carbon nanotubes form an important class of nanomaterials that find several applications. Topological properties and entropies of two phases of carbon nanotubes, namely the zigzag and armchair configurations, have been juxtaposed through the reverse degree-based topological indices. The entropies and topologies of the two phases of the carbon nanotubes are also computed and compared which reveal that the zigzag nanotubes exhibit greater entropies compared to the armchair nanotubes. Applications of the developed techniques to various spectroscopies including NMR and ESR spectroscopies, are also pointed out. In future studies, detailed analysis and applications of reverse, reduced reverse topological indices and entropy of various other complex chemical structures will be considered.

Comment on the defamation in the paper by D. Panda et al. on SrMoO4

In the commented paper (“Investigation of structural, topological, and electrical properties of scheelite strontium molybdate for electronic devices”, Inorganic Chemistry Communications 158, 111501 (2023) [1]) there is a false and unacceptable statement on the conflict of interest.

Designing spongy-bone-like cellular materials: Matched topology and anisotropy

Bone is a natural material with properties such as high specific stiffness and strength. These exceptional mechanical properties are attributed to the meso-scale structure and elastic anisotropy of spongy bone. Replicating the topological traits and mechanical properties of spongy bone presents a novel opportunity to develop high-performance cellular materials. To achieve this, we propose an innovative framework for designing biomimetic cellular materials that match the trabecular structure and elastic anisotropy of spongy bone. This framework introduces a forward-flow design process that utilizes gradient-based feature tuning on a low-dimensional feature vector, transforming the complex inverse design problem into an efficient iterative process. A key innovation in our approach is the use of a pre-trained generative model, SliceGAN, to reconstruct 3D unit cells from 2D micro-CT images. This significantly reduces the cost and time associated with traditional layer-by-layer CT scans typically required for 3D training data. Numerical homogenization is then used to determine the effective elastic stiffness matrix, and a Fourier neural operator is trained to predict these matrices efficiently, greatly enhancing the computational efficiency of the design process. Using this framework, we successfully designed unit cells with topological traits and elastic anisotropy that closely approximate those of natural spongy bone. This opens new avenues for developing spongy-bone-mimetic cellular materials with exceptional mechanical properties. Moreover, the framework's versatility allows it to be extended to the design of other bio-inspired cellular materials.

Alterations in the mechanical properties of single dsDNA molecules, bare or cell-encapsulated, upon exposure to UVA-only radiation and sunlight

Exposure to ultraviolet radiation, which leads to the formation of mutagenic and cytotoxic DNA lesions such as cyclobutane pyrimidine dimers (CPDs) and 6–4 photoproducts (6–4 PPs), can be potentially fatal. The way UVA forms DNA lesions and alters DNA topology and mechanics is still unclear, unlike the cases of UVC and UVB. Herein, Atomic Force Microscopy (AFM) and AFM-based Force Spectroscopy (AFS) have been employed to investigate the topological and mechanical properties of single DNA molecules, bare or E. coli cell-encapsulated, with or without UVA (solar or from UV lamp) treatment. It is observed that both the dsDNA transitions, i.e., ‘B' to stretched ‘S' conformation and melting transition, are lost in UVA dose-dependent manner. Presumably, this is due to formation of the CPDs and 6–4 lesions that form inter-strand cross-links, causing dsDNA strand separation difficult. Gradual reduction in DNA extension length upon prolonged treatment with UVA-only radiation or sunlight (where, 95 % of solar UV is UVA) also indicates formation of the inter-strand cross-links, since such cross-links can reduce DNA flexibility and increase DNA stiffness. Although these observations are common for both bare and cell-encapsulated DNA, the UV dose at which the distinctive reversible BS and melting transition faded away varied widely from 240 kJ/m2 (bare DNA) to 900 kJ/m2 (cellular DNA). The UV-induced DNA damage was also evident in observation of increased number of open circular and linearized topologies, as formed due to single-strand and double-strand breaks, respectively, at damage sites, upon combined action of the apurinic/apyrimidinic site-specific endonucleases IV and V. The extent of DNA damage was further quantified by enzyme-linked immunosorbent assay, which is found to be correlated to the single molecule information.