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Magnetic skyrmions and bimerons, characterized by their topological properties and low current-induced motion, are promising magnetic textures for spintronic (skyrmionic) applications. In this work, through atomistic simulations and micromagnetic analysis, we investigate the field-driven manipulation and conversion of skyrmions into bimerons. By applying an in-plane magnetic field, we observe a smooth transition from skyrmions to bimerons, evidencing the persistence of the soliton topology over a wide range of external magnetic fields. Additionally, we obtain a state diagram elucidating the dependence of nucleated topological textures on material parameters and in-plane magnetic field strength. [ABSTRACT FROM AUTHOR]

We describe the impact of post-annealing on ferroelectric-domain structures in arrays of BiFeO3 (BFO) epitaxial nanoislands, which exhibit a domain evolution from an initial 71° stripe/vortex domains to center-convergent topological domains. These results suggest that the increase and redistribution of charged defects, e.g., oxygen vacancies, in BFO nanoislands play a crucial role in driving the formation of center-type domain structures. The observation of defect-driven domain evolution in BFO nanoislands provides a path for further exploring their formation mechanism, topological properties, novel functionalities, and potential applications. [ABSTRACT FROM AUTHOR]

With the in-depth study of open optical systems, the topological phases of non-Hermitian metasurfaces have attracted increasing attention due to their topological protection properties. Here, in this paper, a tunable non-Hermitian metasurface with bidirectional anisotropism is proposed. By incorporating the phase change material vanadium dioxide (VO2) into the metasurface, two topological exceptional points (EPs) appear in the system by adjusting the conductivity of VO2 and chiral responses appear at both EPs. This research shows that the conductivity significantly affects the reflection of the metasurface, and the zero-reflection points correspond to the EPs of the non-Hermitian system. Further results prove that circling around EPs leads to a 2π phase change, which is topologically protected and independent of the encirclement path. Therefore, this study employs an active control approach to realize two topological EPs. Through comprehensive investigations into the topological properties and chiral performance at EPs, we elucidate the mechanism for the chirality generation in non-Hermitian metasurfaces, which offers feasible solutions for the development of chiral topological devices and light transmission and modulation in future applications. [ABSTRACT FROM AUTHOR]

The body–boundary correspondence refers to the relationship between the body and boundary states of topological insulators (TIs). In TIs, the presence of boundary states is connected to the bulk topological properties of the material. The topology can be identified by studying the energy of the topological modes within the bulk bandgap. However, not all topological materials exhibit boundary states within the insulating energy gap. In many cases, the presence of boundary states can be hidden or masked by the bulk energy bands, making it difficult to measure TIs. Recent experiments have shown that defects, which are commonly found in crystalline materials, can be used as probes to explore higher-order topologies that have been recently realized on various platforms. These defects can generate fractional charges and stable bound states in the dispersion region, allowing us to observe the clear body–disclination correspondence. We have performed simulations using a coupled acoustic cavity system with C3 and C5 symmetries to investigate the body–disclination correspondence in topological crystal insulators (TCIs) in the field of acoustics. Simulation and theoretical results have demonstrated that defects such as disclinations can be used to probe higher-order topologies that were previously unobservable in three-dimensional structures. This approach allows us to detect fractional mode charges and stable bound states, which are crucial for understanding the topological nature of TCIs. Our work demonstrates the potential of using disclination defects to study the intricate relationship between the body and boundary states in topological materials, particularly in the context of acoustics. [ABSTRACT FROM AUTHOR]

Hybrid-order topological insulators combine first- and higher-order topological properties and host topological boundary states with codimension one and more than one in different bandgaps. A Weyl semimetal (WSM) can possess two types of Weyl points: one class of Weyl points terminates the Fermi arc surface states, while another class of Weyl points not only launch Fermi arc surface states but also hinge arc states, exhibiting the hybrid-order topology. Here, we propose a hybrid-order WSM by stacking two-dimensional rhomboid lattices based on chiral nearest-neighbor and double-helix next-nearest interlayer couplings. The first type of Weyl point that only truncates the Fermi arc surface states exists at the crossing of any two-fold degeneracy of two adjacent bands, and the second type of Weyl point that connects the hinge arc states only appears at the crossing of the two middle bands. Our findings enrich the classification of topological semimetals in condensed matter physics. [ABSTRACT FROM AUTHOR]

Higher‐order topological insulators (HOTIs) have attracted much attention in photonics partly because of the robust and highly confined corner modes they support. The growing availability of synthetic multi‐orbital platforms has recently stimulated research focus on the interplay between HOTIs and orbital degree of freedom. In this work, the topological properties of the two‐dimensional (2D) Su–Schrieffer–Heeger (SSH) model with p$p$‐orbital degree of freedom are explored and p$p$‐orbital topological corner states in a laser‐written photonic 2D SSH lattice are experimentally observed. It is shown that the p$p$‐band 2D SSH model is a HOTI, where zero‐energy orbital corner states appear either as in‐gap states or as bound states in the continuum (BICs). Chiral symmetry is sufficient for topological protection of the in‐gap p$p$‐orbital corner states, but not for their BIC counterparts because of the hybridization effect within the bulk continuum. The multipole chiral number is employed as an optimal topological invariant to characterize the p$p$‐orbital HOTIs. The flexibility of tuning the orbital couplings offers an extra degree of manipulation for the BICs, which may be useful for the development of novel photonic devices. [ABSTRACT FROM AUTHOR]

A topological index is a numerical representation of a chemical network in chemical graph theory. Similar to their chemical representation, a topological descriptor identifies specific the physical attributes of the underlying chemical compounds. We describe the third type of hex-derived networks rectangular hex-derived network R H D N 3 , chain hex-derived network C H D N 3 , in our work (r). In this paper, modified and efficient formulas based on multiplicative graph invariants will be constructed. Such as ordinary geometric-arithmetic (OGA), general version of harmonic index (GHI), sum connectivity indes (SI), general sum connectivity index (GSI), first and second Gourava and hyper- Gourava indices, Shegehalli and Kanabur indices, first generalised version of Zagreb index (GZI) and forgotten index (FI) for the subdivided hex -derived R H D N 3 (r) , C H D N 3 (r) networks. In order to develop some new formulas we the compute the multiplicative topological properties. This study found several types of edges for computing and also discussed the order and size.To properly appreciate the chemical compounds, physical and biological characteristics we can combine the study of the networks described above with the chemical compounds and their graphical structures. These observations have the potential to evaluate bio and physiological activities. [ABSTRACT FROM AUTHOR]

Investigation of chemical applicability and mathematical properties of topological indices is the contemporary research trend in chemical graph theory. The geometric arithmetic index (GA) stands out as an well nurtured index having strong correlation with properties and activities of molecules. Its exponential variant (EGA) is investigated here from chemical and mathematical point of view. The chemical connection of EGA is explored by assessing its structure–property modelling ability and isomer discrimination potential. Its mathematical features are demonstrated by finding bounds for numerous classes of graphs with characterizing extremal structures. Second maximum and minimum trees are characterized with respect to the EGA index. [ABSTRACT FROM AUTHOR]

The Tutte polynomial is a classical polynomial graph invariant that provides important information about the structure of a graph. In this study, we focus on the Tutte polynomials for typical silicate molecular networks and benzenoid systems, and derive exact formulas for the considered polycyclic chemical graphs. We also determine the explicit closed-form analytic expressions for the number of spanning trees, connected spanning subgraphs, spanning forests, and acyclic orientations of these chemical polycyclic graphs. Our approach employs a combinatorial decomposition technique, which is a general method that can be easily extended to other 2-connected chemical polycyclic networks. This research contributes to a better understanding of the topological properties of chemical structures and has potential applications in chemistry and materials science. [ABSTRACT FROM AUTHOR]

We consider the space of C 1 -diffeomorphims of a three dimensional closed manifold equipped with the C 1 -topology. It is known that there are open sets in which C 1 -generic diffeomorphisms display uncountably many chain recurrence classes, while only countably many of them may contain periodic orbits. The classes without periodic orbits, called aperiodic classes, are the main subject of this paper. The aim of the paper is to show that aperiodic classes of C 1 -generic diffeomorphisms can exhibit a variety of topological properties. More specifically, there are C 1 -generic diffeomorphisms with (1) minimal expansive aperiodic classes, (2) minimal but non-uniquely ergodic aperiodic classes, (3) transitive but non-minimal aperiodic classes, (4) non-transitive, uniquely ergodic aperiodic classes. [ABSTRACT FROM AUTHOR]

One-dimensional (1D) systems have received a lot of attention due to their exotic physical phenomena such as quantization of conductance, Peierls instability, and Luttinger liquid behavior. Here, we present the synthesis of self-assembled quasi-1D bismuth (Bi) chains on an Au(111) substrate, highlighting their topological properties. Scanning tunneling microscopy and spectroscopy measurements reveal that the high-quality large area array is composed of Bi atomic chains with a bandgap of 0.5 eV. Density functional theory (DFT) calculations confirm the experimental observation and reveal the topological properties of the system, providing evidence of the spin texture of the Bi atomic chains. Our DFT results predict that a single Bi chain hosts exotic topological properties. The atomically precise synthesis of Bi atomic chains overcomes the limitation of the top-down approach toward integration of devices. The work sheds light on the realization of 1D system, providing a platform for further investigation into the intriguing physics in 1D systems. [ABSTRACT FROM AUTHOR]

Firstly, a topology is constructed by nuclei and upsets in residuated lattices and it is shown that a residuated lattice endowed with this topology becomes a topological space. Furthermore, some properties of the topological space are investigated such as compactness and connectedness. Moreover, we study continuities of all the operations with respect to the topology in a residuated lattice. Finally, the relationships are revealed between the two topologies on quotient residuated lattices. [ABSTRACT FROM AUTHOR]

AbstractRecent theoretical studies have shown that heavy-tails can emerge in stochastic optimization due to ‘multiplicative noise’, even under surprisingly simple settings, such as linear regression with Gaussian data. While these studies have uncovered several interesting phenomena, they consider conventional stochastic optimization problems, which exclude decentralized settings that naturally arise in modern machine learning applications. In this paper, we study the emergence of heavy-tails in decentralized stochastic gradient descent (DE-SGD), and investigate the effect of decentralization on the tail behavior. We first show that, when the loss function at each computational node is twice continuously differentiable and strongly convex outside a compact region, the law of the DE-SGD iterates converges to a distribution with polynomially decaying (heavy) tails. To have a more explicit control on the tail exponent, we then consider the case where the loss at each node is a quadratic function, and show that the tail-index can be estimated as a function of the step-size, batch-size, and the topological properties of the network of the computational nodes. Then, we provide theoretical and empirical results showing that DE-SGD has heavier tails than centralized SGD. We also compare DE-SGD to disconnected SGD where nodes distribute the data but do not communicate. Our theory uncovers an interesting interplay between the tails and the network structure: we identify two regimes of parameters (stepsize and network size), where DE-SGD can have lighter or heavier tails than disconnected SGD depending on the regime. Finally, to support our theoretical results, we provide numerical experiments conducted on linear regression and neural networks that suggest the heavier tails is correlated with better generalization in the decentralized setting. [ABSTRACT FROM AUTHOR]

AbstractLet K be a compact subgroup of a locally compact group G. In this work, we initiate an investigation of the Lebesgue-Fourier algebra S1 A(G/K) on the coset space G/K with pointwise multiplication; after some general results on the Banach algebra S1 A(G/K), as our main result, we give some necessary conditions for that S1 A(G/K) be approximately amenable in terms of algebraic and topological properties of G and K . [ABSTRACT FROM AUTHOR]

In this paper, we study classes of meromorphic harmonic functions defined by Ruscheweyh derivatives. In addition to finding certain analytic criteria, we obtain radii of starlikeness and convexity, and some topological properties for the defined classes of functions. Some applications of these results are also given. [ABSTRACT FROM AUTHOR]

Motivation Intracellular organelle networks (IONs) such as the endoplasmic reticulum (ER) network and the mitochondrial (MITO) network serve crucial physiological functions. The morphology of these networks plays a critical role in mediating their functions. Accurate image segmentation is required for analyzing the morphology and topology of these networks for applications such as molecular mechanism analysis and drug target screening. So far, however, progress has been hindered by their structural complexity and density. Results In this study, we first establish a rigorous performance baseline for accurate segmentation of these organelle networks from fluorescence microscopy images by optimizing a baseline U-Net model. We then develop the multi-resolution encoder (MRE) and the hierarchical fusion loss (⁠ L h f ⁠) based on two inductive components, namely low-level features and topological self-similarity, to assist the model in better adapting to the task of segmenting IONs. Empowered by MRE and L h f ⁠ , both U-Net and Pyramid Vision Transformer (PVT) outperform competing state-of-the-art models such as U-Net++, HR-Net, nnU-Net, and TransUNet on custom datasets of the ER network and the MITO network, as well as on public datasets of another biological network, the retinal blood vessel network. In addition, integrating MRE and L h f with models such as HR-Net and TransUNet also enhances their segmentation performance. These experimental results confirm the generalization capability and potential of our approach. Furthermore, accurate segmentation of the ER network enables analysis that provides novel insights into its dynamic morphological and topological properties. Availability and implementation Code and data are openly accessible at https://github.com/cbmi-group/MRE. [ABSTRACT FROM AUTHOR]

This study presents two novel frameworks, termed a quasi-modular b-metric space and a non-Archimedean quasi-modular b-metric space, and various topological properties are provided. Using comparison and simulation functions, this paper rigorously proves several fixed point theorems in the non-Archimedean quasi-modular b-metric space. As a useful application, it also establishes Ulam–Hyers stability for the fixed point problem. Finally, this study concludes with a unique solution to a non-linear fractional differential equation, making a substantial contribution to the discipline. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Let R be a ring with unity. The upper ideal relation graph Γ U (R) of the ring R is a simple undirected graph whose vertex set is the set of all non-unit elements of R and two distinct vertices x, y are adjacent if and only if there exists a non-unit element z ∈ R such that the ideals (x) and (y) contained in the ideal (z). In this article, we classify all the non-local finite commutative rings whose upper ideal relation graphs are split graphs, threshold graphs and cographs, respectively. In order to study topological properties of Γ U (R) , we determine all the non-local finite commutative rings R whose upper ideal relation graph has genus at most 2. Further, we precisely characterize all the non-local finite commutative rings for which the crosscap of Γ U (R) is either 1 or 2. [ABSTRACT FROM AUTHOR]

The structural, electronic, and transport properties of CaAgAs, a recently predicted topological nodal line semimetal, are investigated using density‐functional theory with spin–orbit coupling (SOC) and Boltzmann transport theory. The material exhibits a topological phase transition from a nodal line semimetal to a topological insulator (TI) phase as a result of the SOC effect. The Voigt–Reuss–Hill approximation is used to compute various mechanical properties. The calculated Seebeck coefficient ≈153.19 μV K−1, power factor ≈5.9 × 1011 W m−1 K−2 s−1, and lattice thermal conductivity ≈6.20 W m−1 K−1 suggest that CaAgAs have superior thermoelectric performance compared to other well‐known predicted thermoelectric materials. The calculated value of figure of merit for without (NSOC) is 0.34, which increases to 0.43 with SOC at 500 K. In these findings, the potential of CaAgAs is reflected as a thermoelectric material, attributed to the topological phase transition induced by SOC. [ABSTRACT FROM AUTHOR]

Topological analysis is widely adopted in various research fields to unveil intricate features and structural relationships implied in geometrical objects. Especially, in the fields of data analysis, exploring the topological properties of various images offers rich insights into the intrinsic geometrical information within them. In this study, a novel approach is proposed to investigate the topological properties of arbitrary grayscale images by employing a straightforward procedure used in 2D magnetism studies to calculate topological numbers. This method utilizes machine learning techniques to transfer chiral magnetic textures onto the images. Then, the topological number is then computed directly from the converted images by integrating the solid angles formed by adjacent spin vectors. The method successfully identifies the topological numbers of various grayscale images, showing stable performances against small noises. Furthermore, two applications of the method: are demonstrated topological analysis of the Modified National Institute of Standards and Technology (MNIST) dataset and the counting of blood cells in microscopic images. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Let (Z , ω) be a Kähler manifold and let U be a compact connected Lie group with Lie algebra acting on Z and preserving ω. We assume that the U -action extends holomorphically to an action of the complexified group U ℂ and the U -action on Z is Hamiltonian. Then there exists a U -equivariant momentum map μ : Z → . If G ⊂ U ℂ is a closed subgroup such that the Cartan decomposition U ℂ = U exp (i) induces a Cartan decomposition G = K exp () , where K = U ∩ G , = ∩ i and = ⊕ is the Lie algebra of G , there is a corresponding gradient map μ : Z → . If X is a G -invariant compact and connected real submanifold of Z , we may consider μ as a mapping μ : X →. Given an Ad (K) -invariant scalar product on , we obtain a Morse like function f = 1 2 ∥ μ ∥ 2 on X. We point out that, without the assumption that X is a real analytic manifold, the Lojasiewicz gradient inequality holds for f. Therefore, the limit of the negative gradient flow of f exists and it is unique. Moreover, we prove that any G -orbit collapses to a single K -orbit and two critical points of f which are in the same G -orbit belong to the same K -orbit. We also investigate convexity properties of the gradient map μ in the Abelian case. In particular, we study two-orbit variety X and we investigate topological and cohomological properties of X. [ABSTRACT FROM AUTHOR]

One of the longstanding aims of network neuroscience is to link a connectome's topological properties--i.e., features defined from connectivity alone-with an organism's neurobiology. One approach for doing so is to compare connectome properties with annotational maps. This type of analysis is popular at the meso-/macroscale, but is less common at the nano-scale, owing to a paucity of neuron-level connectome data. However, recent methodological advances have made possible the reconstruction of whole-brain connectomes at single-neuron resolution for a select set of organisms. These include the fruit fly, Drosophila melanogaster, and its developing larvae. In addition to fine-scale descriptions of connectivity, these datasets are accompanied by rich annotations. Here, we use a variant of the stochastic blockmodel to detect multilevel communities in the larval Drosophila connectome. We find that communities partition neurons based on function and cell type and that most interact assortatively, reflecting the principle of functional segregation. However, a small number of communities interact nonassortatively, forming form a "rich-club" of interneurons that receive sensory/ascending inputs and deliver outputs along descending pathways. Next, we investigate the role of community structure in shaping communication patterns. We find that polysynaptic signaling follows specific trajectories across modular hierarchies, with interneurons playing a key role in mediating communication routes between modules and hierarchical scales. Our work suggests a relationship between systemlevel architecture and the biological function and classification of individual neurons. We envision our study as an important step toward bridging the gap between complex systems and neurobiological lines of investigation in brain sciences. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a strongly singular problem involving a non-local operator, a critical nonlinearity, and a subcritical perturbation. We apply techniques from non-smooth analysis to the energy functional, in combination with the study of the topological properties of the sublevels of its smooth part, to prove the existence of three weak solutions: two points of local minimum and a third one as a mountain pass critical point. [ABSTRACT FROM AUTHOR]

Recently, a concept of topological photonic alloy was proposed by mixing magnetized and non-magnetized gyromagnetic rods in a two-dimensional square photonic crystal that supports tunable Chern bandgaps and robust chiral edge states even at a low concentration of magnetized rods. However, whether such a notion can be extended to non-crystalline systems is still an open question. Here, we theoretically demonstrate that topological photonic quasicrystal alloys can also sustain nontrivial Chern bandgaps and nonreciprocal chiral edge states. More interestingly, compared with the conventional topological photonic alloy with a crystalline lattice, we find that the topological photonic quasicrystal alloy with a non-crystalline lattice needs a higher threshold concentration of magnetized rods to open the Chern bandgap. These results not only broaden our understanding of topological photonic alloy but also offer a platform for exploring the unique properties of topological photonic quasicrystals. [ABSTRACT FROM AUTHOR]

Magnetic Weyl semimetals are emerging as a new class of material systems for spintronics due to their intrinsic topological properties and the inherent interplay between topology and magnetism, giving rise to novel electronic states and spin‐orbital‐related effects. Here, ultrafast magnetization dynamics in the Weyl semimetal Heusler ferromagnet Co2MnGa is investigated, from femtosecond to nanosecond timescales, using time‐resolved magneto‐optical Kerr effect (TR‐MOKE) at room temperature. Ultrafast demagnetization and precessional dynamics corresponding to the Kittel and perpendicular standing spin‐wave (PSSW) modes of Co2MnGa, interfaced with Pt thin films of varying thickness, have been investigated. The exchange stiffness constant of Co2MnGa is determined, as well as detailed information about spin‐transport across the Co2MnGa/Pt interface. From the modulation of Gilbert damping of Co2MnGa with Pt thickness, a very high intrinsic spin‐mixing conductance, G↑↓ =  1.73  ×  1016 cm−2 is extracted of the interface and the spin diffusion length of Pt is determined to be 2.9 ± 0.2 nm. The interfacial spin transparency is found to reach a sizeable value of ≈83%, in the perfect spin‐sink regime, suggesting the great potential of this heterostructure for spin‐orbitronics and devices relying on ultrafast magnetization dynamics. [ABSTRACT FROM AUTHOR]

Theoretical and experimental results exploring a half‐Heusler compound TmPdSb with unusual band order and metallic surface states are presented. Typically, the half‐Heusler systems exhibit topological features in a semimetallic state, and trivial ones in an insulating state. Topological properties of the most of half‐Heusler systems are related to the band inversion around the Fermi level, similar to this observed in CdTe/HgTe systems. In the case of TmPdSb, the gapped electronic band structure with "band inversion" in the conductance band is observed, while the slab‐like system realized metallic surface states. The bulk insulating nature of the compound is corroborated by means of electrical transport measurements. The experimental data reveal several features due to the presence of metallic surface states, such as linear magnetoresistance and weak‐antilocalization effect, characterized by enhanced coherence length and a very large number of surface conductive channels. The findings reveal new features of the rare‐earth bearing half‐Heusler. [ABSTRACT FROM AUTHOR]

The intricate relationship between topology and disorder in non-equilibrium quantum systems presents a captivating avenue for exploring localization phenomenon. Here, we look for a suitable platform that enables an in-depth investigation of the topic. To this end, we delve into the nuanced analysis of the topological and localization characteristics exhibited by a one-dimensional dimerized Kitaev chain under periodic driving and perform detailed analyses of the Floquet Majorana modes. Such a non-equilibrium scenario is made further interesting by including a spatially varying quasiperiodic potential with a temporally modulated amplitude. Apriori, the motivation is to explore an interplay between dimerization and a quasiperiodic disorder in a topological setting which is also known to demonstrate unique (re-entrant) localization properties. While the topological properties of the driven system confirm the presence of zero and π Majorana modes, the phase diagram obtained by constructing a pair of topological invariants ( Z × Z ), also referred to as the real space winding numbers, at different driving frequencies reveal intriguing features that are distinct from the static scenario. In particular, at either low or intermediate frequency regimes, the phase diagram concerning the zero mode involves two distinct phase transitions, one from a topologically trivial to a non-trivial phase, and another from a topological phase to an Anderson localized phase. On the other hand, the study of the Majorana π mode unveils the emergence of a unique topological phase, characterized by complete localization of both the bulk and the edge modes, which may be called as the Floquet topological Anderson phase. Moreover, different frequency regimes showcase distinct localization features which can be examined via the localization toolbox, namely, the inverse and the normalized participation ratios. Specifically, the low and high-frequency regimes demonstrate the existence of completely extended and localized phases, respectively. While at intermediate frequencies, we observe the critical (multifractal) phase of the model which is further investigated via a finite-size scaling analysis of the fractal dimension. Finally, to add depth into our study, we have performed a mean level spacing analyses and computed the Hausdorff dimension which yields specific characteristics inherent to the critical phase, offering profound insights into its underlying properties. [ABSTRACT FROM AUTHOR]

This work studies a new topological property called C2-mild normality. A space X is called a C2-mildly normal space if there exist a Hausdorff mildly normal space Y and a bijective function f : X → Y such that the restriction function f|A : A → f(A) is a homeomorphism for each compact subspace A ⊆ X. We investigate this property and present some examples to illustrate the relationships between C2-mild normality and other kinds of topological properties. [ABSTRACT FROM AUTHOR]

Ionic liquids (ILs) have attracted considerable interest due to their unique properties and prospective uses in various industries. However, their potential toxicity, particularly regarding enzyme inhibition, has become a growing concern. In this study, a QSAR model was proposed to predict the enzyme inhibition toxicity of ILs. A dataset of diverse ILs with corresponding toxicity data against three enzymes was compiled. Molecular descriptors that capture the physicochemical, structural, and topological properties of the ILs were calculated. To optimize the selection of descriptors and develop a robust QSAR model, the chaotic spotted hyena optimization algorithm, a novel nature-inspired metaheuristic, was employed. The proposed algorithm efficiently searches for an optimal subset of descriptors and model parameters, enhancing the predictive performance and interpretability of the QSAR model. The developed model exhibits excellent predictive capability, with high classification accuracy and low computation time. Sensitivity analysis and molecular interpretation of the selected descriptors provide insights into the critical structural features influencing the toxicity of ILs. This study showcases the successful application of the chaotic spotted hyena optimization algorithm in QSAR modelling and contributes to a better understanding of the toxicity mechanisms of ILs, aiding in the design of safer alternatives for industrial applications. [ABSTRACT FROM AUTHOR]

Nonlinear phenomena are investigated in a topological photonic valley Hall insulator (VHI) using a Kagome system designed to have localized topological boundary state (TBS) at telecommunications wavelengths. Valley Hall topologically protected nonlinear phenomena are demonstrated. Similar transmission properties and parametric wavelength conversion of up to −12 dB are experimentally achieved using sub‐milliwatt average powers in a zigzag interface without back‐scattering, compared with a straight interface. Furthermore, a 7 dB slow light enhancement is observed in the conversion efficiency near the red edge in the transmission band of the boundary state, demonstrating how slow light‐induced backscattering may be circumvented by leveraging the topologically protected boundary state. A Kerr‐induced delocalization of the valley Hall topological state (VHTS) is further experimentally observed, which can be harnessed to control the properties of topological edge states. [ABSTRACT FROM AUTHOR]

A new mechanism of the generation of a random laser based on a random photonic network with dissipative tunneling of photons between microcavities that are placed at the nodes of such network and contain identical two-level quantum systems has been revealed. It has been shown that an additional source of photon losses in tunneling promotes the separation of individual modes of the random laser and the achievement of the lasing threshold even at a vanishingly small population inversion. In this case, the enhancement of laser modes has an interference nature and is due to the energy redistribution between the nodes of the photonic network that correspond to different signs of the frequency detuning of stationary modes of the random laser from the transition frequency of two-level systems. It has been shown that the traditional lasing mechanism, which demonstrates features of the spectrum of single microcavities, i.e., is almost independent of the topological properties of the network and the tunneling parameter, is present in the region of zero detuning. [ABSTRACT FROM AUTHOR]

Owing to their distinctive novel properties, topological metals hold significant promise for application in spintronics, quantum computing, and superconductivity. Using first-principle calculations, we have elucidated the unfolding band structure of 3d transition metal (3d-TM)-doped CrTe2. Notably, our investigation has revealed band crossings in Cu-doped CrTe2, forming a nodal ring near the Fermi level. Through analyzing Wannier charge centers, we have established the topological nontriviality of CrTe2 upon Cu doping. This study demonstrates a fresh platform for exploring their inherent topological properties and introduces a novel perspective on tectonic topological metals. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and rigorously define a novel class of difference sequence spaces, denoted by w I (M , ∆ v u , r) α β , w 0 I (M , ∆ v u , r) α β ,   w ∞ I (M , ∆ v u , r) α β , and w ∞ (M , ∆ v u , r) α β . These spaces are constructed through the application of the concept of I -convergence of sequences, combined with a Musielak–Orlicz function of order (α ,   β) . The primary focus of our work is to thoroughly investigate the algebraic and topological properties of these defined sequence spaces. We explore their linearity, examine their structure within the framework of paranormed spaces, and analyze various other algebraic characteristics pertinent to these spaces. In addition, we examine the topological nature of these sequence spaces, identifying the conditions under which they exhibit specific topological properties. A significant part of our study is dedicated to examining the inclusion relationships between these sequence spaces, thereby providing a comprehensive understanding of how these spaces are interrelated. Our analysis contributes to the broader field of functional analysis and sequence space theory, offering new insights and potential applications of these advanced mathematical constructs. [ABSTRACT FROM AUTHOR]

Herein, via first‐principle calculations and theoretical analysis, a new Dirac semimetal carbon system called C32, which is composed of pentagonal, hexagonal, heptagonal, and octagonal carbon rings is systematically investigated. The stability of C32 is verified by calculating the phonon dispersion, elastic constants, etc., and an appropriate pathway for experimental synthesis is proposed. Besides, it is discovered that the system holds the quadruple rotation and inversion symmetry, resulting in the emergence of eight twisted Dirac cones (D1 and D2) with a highly anisotropic Fermi velocity from 3.83 × 105 to 8.96 × 105 m s−1 along different k directions. To substantiate the semimetallic nature of C32, its nontrivial topological properties are confirmed through the presence of topologically protected edge states, and the nonzero ℤ2 topological invariant. More importantly, by introducing biaxial strain, it is uncovered that Dirac cones can gradually evolve into a nodal line, and the perfect nodal line can be obtained when the biaxial strain is 13.3%. Furthermore, by constructing the tight‐binding model, the appearance of the Dirac cone is perfectly repeated and its evolution into the nodal line under biaxial strain is explained. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the differential topological properties of a large class of singular spaces: subcarteisan space. First, a minor further result on the partition of unity for differential spaces is derived. Second, the tubular neighborhood theorem for subcartesian spaces with constant structural dimensions is established. Third, the concept of Morse functions on smooth manifolds is generalized to differential spaces. For subcartesian space with constant structural dimension, a class of examples of Morse functions is provided. With the assumption that the subcartesian space can be embedded as a bounded subset of an Euclidean space, it is proved that any smooth bounded function on this space can be approximated by Morse functions. The infinitesimal stability of Morse functions on subcartesian spaces is studied. Classical results on Morse functions on smooth manifolds can be treated directly as corollaries of our results here. [ABSTRACT FROM AUTHOR]

We introduce and motivate the definition of the virtual Rokhlin property for topological groups. We then classify the 2‐manifolds whose homeomorphism groups have the virtual Rokhlin property. We also establish the analogous result for mapping class groups of 2‐manifolds. [ABSTRACT FROM AUTHOR]

• Alterations in local cortical morphology and individual-based morphological brain networks were studied in Rolandic epilepsy (RE). • The RE group had disrupted morphological network organization beyond local morphology changes. • Abnormal morphological brain network alterations may provide new theoretical basis for exploring neuropathological mechanisms in RE. To investigate the local cortical morphology and individual-based morphological brain networks (MBNs) changes in children with Rolandic epilepsy (RE). Based on the structural MRI data of 56 children with RE and 56 healthy controls (HC), we constructed four types of individual-based MBNs using morphological indices (cortical thickness [CT], fractal dimension [FD], gyrification index [GI], and sulcal depth [SD]). The global and nodal properties of the brain networks were analyzed using graph theory. The between-group difference in local morphology and network topology was estimated, and partial correlation analysis was further analyzed. Compared with the HC, children with RE showed regional GI increases in the right posterior cingulate gyrus and SD increases in the right anterior cingulate gyrus and medial prefrontal cortex. Regarding the network level, RE exhibited increased characteristic path length in CT-based and FD-based networks, while decreased FD-based network node efficiency in the right inferior frontal gyrus. No significant correlation between altered morphological features and clinical variables was found in RE. These findings indicated that children with RE have disrupted morphological brain network organization beyond local morphology changes. The present study could provide more theoretical basis for exploring the neuropathological mechanisms in RE. [ABSTRACT FROM AUTHOR]

The Graph Minor Theorem of Robertson and Seymour implies a finite set of obstructions for any minor closed graph property. We show that there are only three obstructions to knotless embedding of size 23, which is far fewer than the 92 of size 22 and the hundreds known to exist at larger sizes. We describe several other topological properties whose obstruction set demonstrates a similar dip at small size. For order ten graphs, we classify the 35 obstructions to knotless embedding and the 49 maximal knotless graphs. [ABSTRACT FROM AUTHOR]

We study the evolution of band topology under external pressure in rare-earth gadolinium mono-antimonide (GdSb) using first-principles calculations. This material crystallizes in a rocksalt-type structure and shows a structural phase transition (SPT) to a CsCl-type structure at 26.1 GPa. The phonon dispersions are analyzed to ascertain the dynamical stability of this material. We use hybrid density functional theory with the inclusion of spin–orbit coupling to investigate the structural, electronic, and topological phase transitions (TPTs). At ambient pressure, GdSb shows a topologically trivial state which is in agreement with existing experimental reports. The first TPT is observed at 6 GPa of hydrostatic pressure (at the high symmetry X -point) which is verified with the help of single-band inversion and surface state analysis along the (001) plane. The non-zero value of the first Z2 topological invariant and the presence of the Dirac cone also confirm the topological phase of this material. A further increase in pressure to 12 GPa results in two band inversions at Γ - as well as X - points, which corresponds to the trivial nature of GdSb. The same is also verified with (0; 000) values of Z2 topological invariants and a pair of Dirac cones in surface states. It is noted that the crystal symmetries are preserved throughout the study and the TPT values are much lower than the SPT pressure, i.e. 26.1 GPa. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the concept of neutrosophic homotopic functions using topological properties. Also, we obtain some properties of neutrosophic homotopic functions and concept of neutrosophic homotopy. [ABSTRACT FROM AUTHOR]

The concept of g# α closed set in general topological spaces was first introduced by Muthukumaraswamy K et. al.,. Recently, kokilavani V, Tharani K et. al., introduced neutrosophic crisp g# α closed set in neutrosophic crisp topological space. Now, in this present paper, we introduced and study the neutrosophic crisp topological properties of neutrosophic crisp g# α interior, neutrosophic crisp g# α closure, neutrosophic crisp g# α frontier, neutrosophic crisp g# α border, neutrosophic crisp g# α exterior via the concept of neutrosophic crisp g# α open set. [ABSTRACT FROM AUTHOR]

The identification of psychopathological markers has been the focus of several scientific fields. The results were inconsistent due to lack of a clear nosology. Network analysis, focusing on the interactions between symptoms, provided important insights into the nosology of mental disorders. These interactions originate several topological properties that could constitute markers of psychopathology. One of these properties is network connectivity, which has been explored in recent years. However, the results have been inconsistent, and the topological properties of psychopathological networks remain largely unexplored and unknown. We compared several topological properties (i.e., connectivity, average path length, assortativity, average degree, modularity, global clustering) of psychopathological networks of healthy and disordered participants across depression (N = 2830), generalized anxiety (N = 13,463), social anxiety (N = 12,814), and obsessive-compulsive disorder (N = 16,426). Networks were estimated using Bayesian Gaussian Graphical Models. The Janson-Shannon measure of divergence was used to identify differences between the network properties. Network connectivity distinguished healthy and disordered participants' networks in all disorders. However, in depression and generalized anxiety, network connectivity was higher in healthy participants. The presence and number of motifs also distinguished the networks of healthy and disordered participants. Other topological properties (i.e., modularity, clustering, average path length and average degree) seem to be disorder-specific. The psychopathological significance of network connectivity must be clarified. Some topological properties of psychopathological networks are promising markers of psychopathology and may contribute to clarifying the nosology of mental disorders. • Network connectivity might not suffice has a marker of psychopathological networks. • Some topological properties seem to be disorder-specific. • Depression and anxiety healthy networks exhibit increased connectivity. [ABSTRACT FROM AUTHOR]

Topological insulators are insulators in the bulk but feature chiral energy propagation along the boundary. This property is topological in nature and therefore robust to disorder. Originally discovered in electronic materials, topologically protected boundary transport has since been observed in many other physical systems. Thus, it is natural to ask whether this phenomenon finds relevance in a broader context. We choreograph a dance in which a group of humans, arranged on a square grid, behave as a topological insulator. The dance features unidirectional flow of movement through dancers on the lattice edge. This effect persists when people are removed from the dance floor. Our work extends the applicability of wave physics to dance. [ABSTRACT FROM AUTHOR]

Ecological interactions between species can affect the performance of individuals, influence ecological and evolutionary dynamics of populations, and ultimately shape community structure. Therefore, documenting and studying interactions is necessary for a better comprehension of ecological patterns. Yet, sampling interactions in the field is challenging. Even with extensive sampling efforts we can hardly obtain a comprehensive picture of which species interact with each other. Such missing interactions can produce substantial gaps that affect how we perceive and interpret the network formed by species interactions and the roles of individual species within those networks. In this study we propose two methods that combine data on species interactions with information on species traits and phylogenies to estimate potentially missing interactions. We use one of the largest datasets on plant‐frugivore interactions, depicting thousands of interactions between birds and plants in the Atlantic Forest hotspot, to test those methods. Then, we analyze how adding newly estimated interactions change the network's overall structure and the topological importance of each species within the seed‐dispersal network. We show that estimated missing interactions more than tripled the number of interactions in the network and impact the general topological properties of the network increasing nestedness and reducing modularity. Both methods generated networks with a similar structure and were effective in estimating new interactions, accurately predicting known interactions without overestimating interactions in place of true absences. More importantly, added interactions changed our perception on the topological role of species, with several undersampled species earning novel interactions and becoming more central to network structure. This shows that estimating missing interactions can be helpful to get a more complete idea of how a network may look like, besides helping to inform which interactions should be the focus of further sampling efforts. [ABSTRACT FROM AUTHOR]

Two-dimensional topological semimetals are typically characterized by the vorticity of gapless points, and can be classified according to the band representations. However, the topological properties involving the distribution of the Berry curvature in the entire Brillouin zone are often overlooked. In this study, we investigate a two-band two-dimensional topological semimetal protected by C4zT magnetic symmetry, exhibiting a two-fold band degeneracy at the Γ(0, 0) and M(π, π) points. Due to the presence of C4zT symmetry, the Brillouin zone is divided into two patches characterized by half-quantized Berry curvature fluxes with opposite signs. In multi-band case, the half-quantization deviates, indicating the fragile nature. The semimetal presents counter-propagating half-edge channels, accompanied by power-law decaying and oscillating edge currents. The band topology leads to unconventional Landau levels featuring anisotropic edge modes. Each massless Dirac cone, associated with the half-quantized Berry curvature flux, exhibits an integer quantum Hall conductance. Additionally, we calculate the local orbital magnetization with open boundary conditions in both the x and y directions. This reveals isolated magnetization islands, highlighting an experimentally observable magnetic phenomenon in this topological semimetal. A two-dimensional semimetal is featured by its low energy physics near the degeneracy points, while the topology over the whole Brillouin zone is rarely studied. The authors find that the Brillouin zone of the C4zT symmetric semimetal is partitioned into two patches characterized by half quantized Berry curvature fluxes with opposite signs, accompanied by the topological transport phenomena. [ABSTRACT FROM AUTHOR]