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In this paper, a new approach for fuzzy gyronorms on gyrogroups is presented. The relations between fuzzy metrics(in the sense of Morsi), fuzzy gyronorms, gyronorms on gyrogroups are studied. Also, some sufficient conditions, which can make a fuzzy normed gyrogroup to be a topological gyrogroup and a fuzzy topological gyrogroup, are found. Meanwhile, the relations between topological gyrogroups, fuzzy topological gyrogroups and stratified fuzzy topological gyrogroups are studied. Finally, the properties of fuzzifying topological gyrogroups are studied. [ABSTRACT FROM AUTHOR]

An empirical investigation was held regarding whether topological properties associated with point clouds formed by cryptocurrencies' prices could contain information on (locally) explosive dynamics of the processes involved. Those dynamics are associated with financial bubbles. The Phillips, Shi and Yu [33, 34] (PSY) timestamping method as well as notions associated with the Topological Data Analysis (TDA) like persistent simplicial homology and landscapes were employed on a dataset consisting of the time series of daily closing prices of the Bitcoin, Ethereum, Ripple and Litecoin. The note provides some empirical evidence that TDA could be useful in detecting and timestamping financial bubbles. If robust, such an empirical conclusion opens some interesting paths of further research. [ABSTRACT FROM AUTHOR]

We say that a C*-algebra is nowhere scattered if none of its quotients contains a minimal open projection. We characterize this property in various ways, by topological properties of the spectrum, by divisibility properties in the Cuntz semigroup, by the existence of Haar unitaries for states, and by the absence of nonzero ideal-quotients that are elementary, scattered or type I. Under the additional assumption of real rank zero or stable rank one, we show that nowhere scatteredness implies even stronger divisibility properties of the Cuntz semigroup. [ABSTRACT FROM AUTHOR]

One of the most famous quantum systems with topological properties, the spin S = 1 antiferromagnetic Heisenberg chain, is well-known to display exotic S = 1 / 2 edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons – the two-orbital Hubbard model—with increasing repulsion strength U and Hund interaction JH. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed. At the microscopic level, the localized spins arise due to the electron-electron interactions. Here, the authors show how a topological phase of the Haldane spin chain emerges in a two-orbital Hubbard model with increasing interaction strength. [ABSTRACT FROM AUTHOR]

Objective: The study aimed to find the difference in functional network topology on interictal electroencephalographic (EEG) between patients with drug-resistant epilepsy (DRE) and healthy people. Methods: We retrospectively analyzed the medical records as well as EEG data of ten patients with DRE and recruited five sex-age-matched healthy controls (HC group). Each participant remained awake while undergoing videoelectroencephalography (vEEG) monitoring. After excluding data that contained abnormal discharges, we screened EEG segments that were free of artifacts and put them together into 20-min segments. The screened data was bandpass filtered to different frequency bands (delta, theta, alpha, beta, and gamma). The weighted phase lag index (wPLI) and the network properties were calculated to evaluate changes in the topology of the functional network. Finally, the results were statistically analyzed, and the false discovery rate (FDR) was used to correct for differences after multiple comparisons. Results: In the full frequency band (0.5-45 Hz), the functional connectivity in the DRE group during the interictal period was significantly lower than that in the HC group (p < 0.05). Compared to the HC group, in the full frequency band, the DRE group exhibited significantly decreased clustering coefficient (CC), node degree (D), and global efficiency (GE), while the characteristic path length (CPL) significantly increased (p < 0.05). In the sub-frequency bands, the functional connectivity of the DRE group was significantly lower than that of the HC group in the delta band but higher in the alpha, beta, and gamma bands (p < 0.05). The statistical results of network properties revealed that in the delta band, the DRE group had significantly decreased values for D, CC, and GE, but in the alpha, beta, and gamma bands, these values were significantly increased (p < 0.05). Additionally, the CPL of the DRE group significantly increased in the delta and theta bands but significantly decreased in the alpha, beta, and gamma bands (p < 0.05). Conclusion: The topology structure of the functional network in DRE patients was significantly changed compared with healthy people, which was reflected in different frequency bands. It provided a theoretical basis for understanding the pathological network alterations of DRE. [ABSTRACT FROM AUTHOR]

Delay discounting (DD), a parameter derived from the intertemporal choice task, is a representative behavioral indicator of choice impulsivity. Previous research reported not only an association between DD and impulsive control disorders and negative health outcomes but also the neural correlates of DD. However, to date, there are few studies investigating the structural brain network topologies associated with individual differences in DD and whether self-reported measures (BIS-11) of impulsivity associated with DD share the same or distinct neural mechanisms is still unclear. To address these issues, here, we combined graph theoretical analysis with diffusion tensor imaging to investigate the associations between DD and the topological properties of the structural connectivity network and BIS-11 scores. Results revealed that people with a steep DD (greater impatience) had decreased small-worldness (a shift toward weaker small-worldnization) and increased degree centrality in the medial superior prefrontal cortex, associated with subjective value in the task. Though DD was associated with the BIS-11 motor impulsiveness subscale, this subscale was linked to topological properties different from DD; that is, high motor impulsiveness was associated with decreased local efficiency (less segregation) and decreased degree centrality in the precentral gyrus, involved in motor control. These findings provide insights into the systemic brain characteristics underlying individual differences in impulsivity and potential neural markers which could predict susceptibility to impulsive behaviors. [ABSTRACT FROM AUTHOR]

The paper describes results of the band structure measurements of SnAs single crystals by the ARPES technique. We performed detailed analysis of isoenergetic surfaces in the vicinity and below the Fermi energy. The ARPES experimental data are consistent with theoretically predicted shape of the SnAs Fermi surface. The determined type of the Fermi surface provides the basis for estimating the Ginzburg–Landau parameter, from which it follows that SnAs is a type-I superconductor. In addition, our results of ARPES measurements confirm the presence of band splitting in the energy spectrum at the point at electron binding energies in the range of 0.6–1.2 eV associated with spin–orbit interaction. [ABSTRACT FROM AUTHOR]

Systematic studies of magneto-transport properties of the whole (MnBi2Te4)(Bi2Te3)m family of magnetic topological insulators ( have been carried out. Temperature dependences of the resistivity, magnetoresistance and the Hall effect at low temperatures have been studied. When m increases, i.e., when the separation between 2D MnBi2Te4 magnetic layers becomes larger, the transition from antiferromagnetic to ferromagnetic state takes place. We have found that ferromagnetic state survives even in the samples with , when 2D magnets are separated by six non-magnetic Bi2Te3 blocks. [ABSTRACT FROM AUTHOR]

Neural stem/progenitor cells live in an intricate cellular environment, the neurogenic niche, which supports their function and enables neurogenesis. The niche is made of a diversity of cell types, including neurons, glia and the vasculature, which are able to signal to and are structurally organised around neural stem/progenitor cells. While the focus has been on how individual cell types signal to and influence the behaviour of neural stem/progenitor cells, very little is actually known on how the niche is assembled during development from multiple cellular origins, and on the role of the resulting topology on these cells. This review proposes to draw a state-of-the art picture of this emerging field of research, with the aim to expose our knowledge on niche architecture and formation from different animal models (mouse, zebrafish and fruit fly). We will span its multiple aspects, from the existence and importance of local, adhesive interactions to the potential emergence of larger-scale topological properties through the careful assembly of diverse cellular and acellular components. [ABSTRACT FROM AUTHOR]

SmB6, a topological Kondo insulator, possesses topologically protected surface states, in which carrier mobility is supposed to be high but is significantly varied in orders of magnitude dependent upon characterization methods. Herein, we performed magnetoresistance measurements on a Hall-bar device constructed on a highly uniform SmB6 nanoribbon with (001) surface grown by chemical vapor deposition. Unusual non-linear Hall resistance was observed at low temperature and explained with a two-carrier model. The two types of carriers were attributed to two types of Fermi pockets on the Brillouin zone of the SmB6 (001) surface. The Fermi pocket on Γ point provided high hole mobility up to 1.4 × 10 3 cm2/V s but low hole density at a temperature of 2.2 K. On the other hand, the Fermi pockets on X points supplied low electron mobility down to 1.8 cm2/V s but high electron density. The identification of the two types of pockets laid the foundation for the understanding of the transport via the topological surface states of the SmB6 (001) surface. [ABSTRACT FROM AUTHOR]

The unique features of spinless time-reversal symmetry and tunable ℤ 2 gauge fields in artificial systems facilitate the emergence of topological properties in the landscape, such as the recently explored Möbius-twisted phase and real second-order nodal-loop semimetals. However, these properties have predominantly been proposed only in theoretical frameworks. In this study, we present a cunningly designed blueprint for realizing an acoustic real second-order nodal-loop semimetal through the incorporation of projective translation symmetry into a three-dimensional stacked acoustic graphitic lattice. Additionally, we introduce non-Hermitian modulation to the topologically protected propagation of degenerate drumhead surface and hinge states, which depend on the specific on-site gain and loss textures. It should be emphasized that this demonstration can be extended to other classical wave systems, thereby potentially opening up opportunities for the design of functional topological devices. [ABSTRACT FROM AUTHOR]

This document provides an overview of the design and applications of metamaterials, which are composites with engineered architectures that have unique properties. The article discusses different design strategies for metamaterials, including nonlinear properties and bio-inspired approaches. It also explores the expansion of metamaterial functionalities, such as tunable architectures and topological properties. The article highlights recent breakthroughs in metamaterial functionalities, including plasmon-mediated optical transmission and negative refraction. It discusses various applications of metamaterials, such as photolithography, sensors, and wave control devices. The authors acknowledge the contributions of the authors and editors involved in the Special Topic. [Extracted from the article]

Recently, higher-order topological insulators (HOTIs) have been introduced, and were shown to host topological corner states under the theoretical framework of Benalcazar-Bernevig-Hughes. Here we unveil some topological effects in HOTIs by studying the three-dimensional (3D) non-Abelian Bloch oscillations (BOs). In HOTIs, BOs with a multiplied period occur when a force with a special direction is applied due to the effect of the non-Abelian Berry curvature. Along the direction of the oscillations we find a higher-order topological state that goes beyond the theoretical framework of multipole moments. The emergence of such a higher-order topological state coincides with the appearance of the 3D non-Abelian BOs. That is, the 3D non-Abelian BOs can be used as a tool to probe higher-order topological states. These phenomena are observed experimentally with designed electric circuit networks. Our work opens up a way to detect topological phases theoretically and experimentally. Bloch oscillations (BOs) are developed to be a powerful tool for the detection of topological properties in lattice systems. Here, the authors propose topological BOs in a three-dimensional higher-order topological insulator model and demonstrate the dynamics of the wave-packet and certain higher-order edge states in this model using electronic circuits. [ABSTRACT FROM AUTHOR]

Objective: Although intracranial electrical stimulation has emerged as a treatment option for various diseases, its impact on the properties of brain networks remains challenging due to its invasive nature. The combination of intracranial electrical stimulation and whole-brain functional magnetic resonance imaging (fMRI) in patients with refractory epilepsy (RE) makes it possible to study the network properties associated with electrical stimulation. Thus, our study aimed to investigate the brain network characteristics of RE patients with concurrent electrical stimulation and obtain possible clinical biomarkers. Methods: Our study used the GRETNA toolbox, a graph theoretical network analysis toolbox for imaging connectomics, to calculate and analyze the network topological attributes including global measures (small-world parameters and network efficiency) and nodal characteristics. The resting-state fMRI (rs-fMRI) and the fMRI concurrent electrical stimulation (es-fMRI) of RE patients were utilized to make group comparisons with healthy controls to identify the differences in network topology properties. Network properties comparisons before and after electrode implantation in the same patient were used to further analyze stimulus-related changes in network properties. Modular analysis was used to examine connectivity and distribution characteristics in the brain networks of all participants in study. Results: Compared to healthy controls, the rs-fMRI and the es-fMRI of RE patients exhibited impaired small-world property and reduced network efficiency. Nodal properties, such as nodal clustering coefficient (NCp), betweenness centrality (Bc), and degree centrality (Dc), exhibited differences between RE patients (including rs-fMRI and es-fMRI) and healthy controls. The network connectivity of RE patients (including rs-fMRI and es-fMRI) showed reduced intra-modular connections in subcortical areas and the occipital lobe, as well as decreased inter-modular connections between frontal and subcortical regions, and parietooccipital regions compared to healthy controls. The brain networks of es-fMRI showed a relatively weaker small-world structure compared to rs-fMRI. Conclusion: The brain networks of RE patients exhibited a reduced small-world property, with a tendency toward random networks. The network connectivity patterns in RE patients exhibited reduced connections between cortical and subcortical regions and enhanced connections among parieto-occipital regions. Electrical stimulation can modulate brain network activity, leading to changes in network connectivity patterns and properties. [ABSTRACT FROM AUTHOR]

We investigate compact ultrametric measure spaces which form a subset U w of the collection of all metric measure spaces M w . In analogy with the notion of the ultrametric Gromov–Hausdorff distance on the collection of ultrametric spaces U , we define ultrametric versions of two metrics on U w , namely of Sturm's Gromov–Wasserstein distance of order p and of the Gromov–Wasserstein distance of order p. We study the basic topological and geometric properties of these distances as well as their relation and derive for p = ∞ a polynomial time algorithm for their calculation. Further, several lower bounds for both distances are derived and some of our results are generalized to the case of finite ultra-dissimilarity spaces. Finally, we study the relation between the Gromov–Wasserstein distance and its ultrametric version (as well as the relation between the corresponding lower bounds) in simulations and apply our findings for phylogenetic tree shape comparisons. [ABSTRACT FROM AUTHOR]

In this theoretical study, we examine the topological properties of the recently discovered A2Cr3As3 (A = K, Rb, Cs) superconductors. In the superconducting state, characterized by a typical -wave pairing symmetry, a line nodal exists in the plane, confirming the system as a topological nodal-line superconductor. When considering an open boundary along the -direction, flat surface bands emerge. In contrast, when an s-wave pairing symmetry is considered, the system becomes fully gapped and topologically trivial. Additionally, we investigate the spectral function and the local density of states, which may be employed to experimentally detect the topological features. [ABSTRACT FROM AUTHOR]

We have utilized the density functional theory (DFT) in conjunction with graph‐theoretical techniques to compute the vibrational, electronic and topological properties of porous nanographenes starting with the building blocks of kekulene, septulene, extended kekulenes, and circumkekulene. Furthermore, graph theoretically based spectral polynomials and other topological properties including Kekulé counts, delocalization energies, and resonance energies are computed for such structures and larger tessellations of kekulenes which are precursors to nanographene belts with multiple pores. The success of the DFT methods is demonstrated with the computed vibrational modes and infrared and Raman spectra of several of these structures. The computed spectral polynomials and the spectra reveal the underlying patterns of the energy levels and structural features and hence suggest the possibility of integration of graph theory with quantum chemical techniques for the computations of properties of large porous graphenes including the possibility of the Pariser–Parr–Pople (PPP) method with parameters extracted from machine learning of the DFT computations on a combinatorial library of precursors. Finally, the computations reveal that the porous structures can be tailored for sequestration of various ions including heavy metal ions for environmental remediation. [ABSTRACT FROM AUTHOR]

In this article, we introduce and study sequence spaces of Cesàro–Nörlund operators of order n associated with a sequence of Orlicz functions. We obtain some topological properties and Schauder basis of these sequence spaces. Moreover, we compute the α-, β- and γ-duals and the matrix transformations of these newly formed sequence spaces. Finally, we prove that these sequence spaces are of Banach–Saks type p and have a weak fixed-point property. [ABSTRACT FROM AUTHOR]

We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma's martingale inequality and provides a method for establishing extreme amenability. Building on this technique, we exhibit new examples of extremely amenable groups arising from von Neumann's continuous geometries. Along the way, we also answer a question by Pestov on dynamical concentration in direct products of amenable topological groups. [ABSTRACT FROM AUTHOR]

In this paper, we study the properties of topological spaces preserved by quasihomeomorphisms. Particularly, we show that quasihomeomorphisms preserve Whyburn, weakly Whyburn, submaximal and door properties. Moreover, we offer necessary conditions on continuous map q : X → Y where Y is Whyburn (resp., weakly Whyburn) in order to render X Whyburn (resp., weakly Whyburn). Also, we prove that if q : X → Y is a one-to-one continuous map and Y is submaximal (resp., door), then X is submaximal (resp., door). Finally, we close this paper by studying the relation between quasihomeomorphisms and k-primal spaces. [ABSTRACT FROM AUTHOR]

For over two decades, Turing machines (TMs) have been studied as dynamical systems. Several results related to topological properties were established, such as equicontinuity, periodicity, mortality, and entropy. There are two main topological models for TMs, and these properties strongly depend on the considered model. Here, we focus on transitivity, minimality and other related properties. In the context of TMs, transitivity refers to the existence of a configuration whose evolution contains every possible pattern over any finite window. Minimality means that every configuration fulfills the aforementioned statement, which strongly restricts TM behaviour. This paper establishes relations between the following properties: transitivity, minimality, the existence of blocking words, aperiodicity and reversibility. It also explores some properties of the embedding technique, which combines two TMs to produce a third. This technique has been used in previous works to prove the undecidability of several dynamical properties. Here, we demonstrate its power and versatility and how the produced machine, under a few particular conditions, will inherit the properties of one of the original machines. [ABSTRACT FROM AUTHOR]

In this article we have introduced some new sequence spaces cI 0(Rb n ), cI(Rb n), ℓI ∞(Rb n) and ℓ∞(Rb n) as a domain of triangular Riesz matrix, and study some of their algebraic and topological properties. Further, our work will devote to argue some inclosions regarding those fore-said sequence spaces. [ABSTRACT FROM AUTHOR]

Getting precise aspects of road through segmentation from remote sensing imagery is useful for many real-world applications such as autonomous vehicles, urban development and planning, and achieving sustainable development goals (SDGs). 1 1 https://sdgs.un.org/goals. Roads are only a small part of the image, and their appearance, type, width, elevation, directions, etc. exhibit large variations across geographical areas. Furthermore, due to differences in urbanization styles, planning, and the natural environments; regions along the roads vary significantly. Due to these variations among the train and test domains (domain shift), the road segmentation algorithms fail to generalize to new geographical locations. Unlike the generic domain alignment scenarios, road segmentation has no scene structure and generic domain adaptive segmentation methods are unable to enforce topological properties like continuity, connectivity, smoothness, etc., thus resulting in degraded domain alignment. In this work, we propose a topology-aware unsupervised domain adaptation approach for road segmentation in remote sensing imagery. During domain adaptation for road segmentation, we predict road skeleton, an auxiliary task to enforce the topological constraints. To enforce consistent predictions of road and skeleton, especially in the unlabeled target domain, the conformity loss is defined across the skeleton prediction head and the road-segmentation head. Furthermore, for self-training, we filter out the noisy pseudo-labels by using a connectivity-based pseudo-labels refinement strategy, on both road and skeleton segmentation heads, thus avoiding holes and discontinuities. Extensive experiments on the benchmark datasets show the effectiveness of the proposed approach compared to existing state-of-the-art methods. Specifically, for SpaceNet to DeepGlobe adaptation, the proposed approach outperforms the competing methods by a minimum margin of 6.6%, 6.7%, and 9.8% in IoU, F1-score, and APLS, respectively. (The source code is available on Github). [ABSTRACT FROM AUTHOR]

A topological space X is monotonically star countable if for every open cover u of X we can assign a subspace s(u) ⊆ X, called the kernel, such that s(u) is a countable subset of X, and st(s(u), u) = X, and if V refines u, then s(u) ⊆ s(V), where st(s(u), u) = S {u ∈ u : u ∩ s(u) ≠ ∅}. In this paper we study the relation between monotonically star countable spaces and related spaces, and we also study topological properties of monotonically star countable spaces. [ABSTRACT FROM AUTHOR]

In this paper a two-dimensional Brownian motion (modeling the endowment of two companies), absorbed at the boundary of the positive quadrant, with controlled drift, is considered. The volatilities of the Brownian motions are different. We control the drifts of these processes and allow that both drifts add up to the maximal value of one. Our target is to choose the strategy in a way, s.t. the probability that both companies survive is maximized. It turns out that the state space of the problem is divided into two sets. In one set the first company gets the full drift, and in the other set the second one. We describe some topological properties of these sets and their separating curve. [ABSTRACT FROM AUTHOR]

Functional connectivity has been used as a framework to investigate widespread brain interactions underlying cognitive deficits in mild cognitive impairment (MCI). However, many functional connectivity metrics focus on the average of the periodic activities, disregarding the aperiodic bursts of activity (i.e., the neuronal avalanches) characterizing the large-scale dynamic activities of the brain. Here, we apply the recently described avalanche transition matrix framework to source-reconstructed magnetoencephalography signals in a cohort of 32 MCI patients and 32 healthy controls to describe the spatio-temporal features of neuronal avalanches and explore their topological properties. Our results showed that MCI patients showed a more centralized network (as assessed by higher values of the degree divergence and leaf fraction) as compared to healthy controls. Furthermore, we found that the degree divergence (in the theta band) was predictive of hippocampal memory impairment. These findings highlight the role of the changes of aperiodic bursts in clinical conditions and may contribute to a more thorough phenotypical assessment of patients. [ABSTRACT FROM AUTHOR]

Metric learning aims to learn a distance metric to properly measure the similarities between pairwise examples. Most existing learning algorithms are designed to reduce intra-class distances and meanwhile enlarge inter-class distances by critically introducing a margin between intra-class and inter-class distances. However, such learning objectives may yield boundless (distance) metric space, because their enlargements on inter-class distances are usually unconstrained. In this case, excessively enlarged inter-class distances would relatively reduce the ratio of margin to the whole distance range (i.e., the margin-range-ratio), and thus being against the initial large-margin purpose for discriminating the similarities of data pairs. To address this issue, we propose a new boundary-restricted metric (BRM), which confines the metric space by a restriction function. Such a restriction function is monotonous and gradually converges to an upper bound, which suppresses excessively large distances of data pairs and concurrently maintains the reliable discriminability. After that, the learned metric can be successfully restricted in a finite region, and thereby avoiding the reduction of margin-range-ratio. Theoretically, we prove that BRM tightens the generalization error bound of the traditional learning model without sacrificing the fitting capability or destroying the topological property of the learned metric, which implies that BRM makes a good bias-variance tradeoff for the metric learning task. Extensive experiments on toy data and real-world datasets validate the superiority of our approach over the state-of-the-art metric learning methods. [ABSTRACT FROM AUTHOR]

The Neumann–Zagier matrices of an ideal triangulation are integer matrices with symplectic properties whose entries encode the number of tetrahedra that wind around each edge of the triangulation. They can be used as input data for the construction of a number of quantum invariants that include the loop invariants, the 3D-index and state-integrals. We define a twisted version of Neumann–Zagier matrices, describe their symplectic properties, and show how to compute them from the combinatorics of an ideal triangulation. As a sample application, we use them to define a twisted version of the 1-loop invariant (a topological invariant) which determines the 1-loop invariant of the cyclic covers of a hyperbolic knot complement, and conjecturally is equal to the adjoint twisted Alexander polynomial. [ABSTRACT FROM AUTHOR]

Optical vortices (OVs), as eigenmodes of optical orbital angular momentum, have been widely used in particle micro-manipulation. Recently, perfect optical vortices (POVs), a subclass of OVs, are gaining increasing interest and becoming an indispensable tool in optical trapping due to their unique property of topological charge-independent vortex radius. Here, we expand the concept of POVs by proposing concentric ring optical traps (CROTs) and apply them to trapping and rotating particles. A CROT consists of a series of concentric rings, each being a vortex whose radius and topological charge can be controlled independently with respect to the other rings. Quantitative results show that the generated CROTs have weak sidelobes, good uniformity, and relatively high diffraction efficiency. In experiments, CROTs are observed to trap multiple dielectric particles simultaneously on different rings and rotate these particles with the direction and speed of rotation depending on the topological charge sign and value of each individual ring. In addition, gold particles are observed to be trapped and rotate in the dark region between two bright rings. As a novel tool, CROTs may find potential applications in fields like optical manipulation and microfluidic viscosity measurements. [ABSTRACT FROM AUTHOR]

Rough sets, as a tool for handling uncertain data, have been successfully applied to solve practical problems. Many scholars have conducted various studies on rough sets, especially on various rough set models and upper and lower approximation operators. Recently, these studies have gradually begun to expand on lattice values. The other side of the shield, overlap and grouping functions, come as two distinct from the ordinary binary aggregation functions, due to their not necessarily associative property, have become two new mathematical models for processing information and have been successfully applied in practice. As a result, in this study, (G O , O) - fuzzy rough sets based on the overlap and grouping functions on the complete lattices are introduced and their topological properties are evaluated, further promoting the concept of rough sets. First, the G O - lower L - fuzzy rough approximation operator is defined the lower approximation operator in the (G O , O) - fuzzy rough set on complete lattices utilizing Q L - implications, as well as, the upper approximation operator in (G O , O) - fuzzy rough set on complete lattices is filled by the O - upper L - fuzzy rough approximation operator which is formulated by Jiang and Hu in (G , O) - fuzzy rough set. Second, we talk about some basic properties of the (G O , O) - fuzzy rough set on complete lattices; moreover, the discussion of these basic properties mainly focus on G O - lower L - fuzzy approximation operator. Third, it is considered the characterization of the (G O , O) - fuzzy approximation operator by making use of various classes of L - fuzzy relations. Finally, we study the topological properties of (G O , O) - fuzzy rough set. [ABSTRACT FROM AUTHOR]

Abstract Background Electroacupuncture (EA) has been shown to facilitate brain plasticity‐related functional recovery following ischemic stroke. The functional magnetic resonance imaging technique can be used to determine the range and mode of brain activation. After stroke, EA has been shown to alter brain connectivity, whereas EA's effect on brain network topology properties remains unclear. An evaluation of EA's effects on global and nodal topological properties in rats with ischemia reperfusion was conducted in this study. Methods and results There were three groups of adult male Sprague‐Dawley rats: sham‐operated group (sham group), middle cerebral artery occlusion/reperfusion (MCAO/R) group, and MCAO/R plus EA (MCAO/R + EA) group. The differences in global and nodal topological properties, including shortest path length, global efficiency, local efficiency, small‐worldness index, betweenness centrality (BC), and degree centrality (DC) were estimated. Graphical network analyses revealed that, as compared with the sham group, the MCAO/R group demonstrated a decrease in BC value in the right ventral hippocampus and increased BC in the right substantia nigra, accompanied by increased DC in the left nucleus accumbens shell (AcbSh). The BC was increased in the right hippocampus ventral and decreased in the right substantia nigra after EA intervention, and MCAO/R + EA resulted in a decreased DC in left AcbSh compared to MCAO/R. Conclusion The results of this study provide a potential basis for EA to promote cognitive and motor function recovery after ischemic stroke.

Most of the photonic valley-Hall edge states were constructed by changing structures to break the spatial inversion symmetry, restricting the practical application potential. In this paper, we construct a tunable topological valley-Hall edge state based on the large optical Kerr effect. It is demonstrated that topological phase transition happens by engineering the intensity of the injected pump and that a valley-Hall edge state can be generated at the interface between two regions with different topological properties. In addition, eigenfrequency and transmission characteristics of the edge state as a function of applied pump intensity are investigated. The topological protected valley-dependent transmission is studied under non-uniform distributed pump intensity. This work may open a new path toward designing reconfigurable all-optical metadevices. [ABSTRACT FROM AUTHOR]

The field of topological photonics has made great strides in the past decade with many new designs based on bandgap and band inversion structures that provide robust, unidirectional, and reflection-free propagation of energy. The topological invariant or Chern number of a metamaterial guarantees the existence of topologically protected edge modes. However, its mathematical application to real systems is not always straightforward and can be greatly simplified by reducing the dimensional complexity of the problem by the calculation of a Zak phase that determines the topological phase in just one dimension. This work explores two methods of creating interface modes with finite height dielectric slabs: (1) transverse resonance through variable edge truncation of a photonic crystal (PhC) or cell sliding and (2) a uni-axial topological phase by means of scaling the internal features of a unit cell. The proposed metamaterial devices use the same C 4 v symmetric unit cell structure on both sides of the interface and are finite in all three dimensions, allowing for easy fabrication, excitation, and implementation in real-world applications. The all-dielectric design also enables an easy transition to and from conventional PhC waveguides and lends itself well to operation in frequencies spanning across the microwave and optical spectrum without concerns of additional metallic losses in the THz region. [ABSTRACT FROM AUTHOR]

Acoustic transport through topological edge states in phononic crystals improves the suppression of backscattering, which gives these systems significant potential for controlling sound waves. Recent research shows that only one acoustic edge state caused by topological valley phases can transmit in phononic crystals. This paper proposes a genre of valley phases with one, two, and three topological edge states created by transforming the structure of unit cells. The bulk-edge correspondence indicates that these edge states are topological based on the topological invariant number (i.e., the valley Chern number of one, two, and three) of this system coinciding with the number of topological edge states. Different types of defects are introduced into the phononic crystals, whose transmission spectra show that they can withstand bending defects. These results indicate that these systems have significant potential for application in noise control, acoustic communication, and acoustic-electrical integration. [ABSTRACT FROM AUTHOR]

Non-Hermiticity extends the topological phase beyond the given Hermitian structure. Whereas the phases of non-Hermitian topological systems derived from Hermitian components have been extensively explored, the topological properties of an acoustic crystal that occur purely due to non-Hermiticity require further investigation. In this letter, we describe the development of an acoustic crystal with an adjustable loss that is composed of a chain of one-dimensional, coupled acoustic resonators. Each unit cell can contain three or six resonators, which are equivalent to 3 × 3 or 6 × 6 non-Hermitian Hamiltonian matrices, respectively. The topological properties of the crystal were verified by calculating the defined topological invariant, and the states of the edge and interface of the acoustic crystal were obtained by using a practical model. We obtained the states of the edges and the interface for both odd and even numbers of resonators in each unit cell and found that the location of the inductive loss had an important effect on the topological properties. This results here can guide research on advanced wave control for sensing and communication applications. [ABSTRACT FROM AUTHOR]

Higher-order topological phases featured by hierarchical topological states (HTSs) have spawned a paradigm for developing robust multidimensional wave manipulation. While non-Hermitian skin effects (NHSEs) entail that bulk states collapse to open boundaries as local skin modes, the topological transport properties at the interplay between HTS and NHSE are still at early stage of exploration. Here, we report the non-Hermitian reconstruction of HTSs by incorporating the interplay of NHSEs and HTSs, which manifests robust and controllable topological transport properties. By a feasible design in coupled resonant optical waveguides, we demonstrate that zero-dimensional topological states of HTSs only undergo non-Hermitian reconstruction at finitely small system sizes, while nonzero-dimensional topological states of HTSs undergo non-Hermitian reconstruction independent of bulk states. We link the behaviour of zero-dimensional topological states to the restriction of their spatially non-negligible couplings under a macroscopic non-reciprocal framework. Our study unveils the interplay mechanism between NHSEs and HTSs, and underpins topological applications in various wave systems. Higher-order topological phase appears as a pioneering topic, and together with the non-Hermiticity, brings broad attentions recently. The authors explore the interplay between the non-Hermiticity and hierarchical topological states in a non-reciprocal framework and show the flexible reconstruction of non-Hermitian higher-order topological states. [ABSTRACT FROM AUTHOR]

Recently, deep generative models using machine intelligence are widely utilized to investigate scientific systems by generating scientific data. In this study, we experiment with a hybrid model of a variational autoencoder (VAE) and a generative adversarial network (GAN) to generate a variety of plausible two-dimensional magnetic topological structure data. Due to the topological properties in the system, numerous and diverse metastable magnetic structures exist, and energy and topological barriers separate them. Thus, generating a variety of plausible spin structures avoiding those barrier states is a challenging problem. The VAE-GAN hybrid model can present an effective approach to this problem because it brings the advantages of both VAE's diversity and GAN's fidelity. It allows one to perform various applications including searching a desired sample from a variety of valid samples. Additionally, we perform a discriminator-driven latent sampling (DDLS) using our hybrid model to improve the quality of generated samples. We confirm that DDLS generates various plausible data with large coverage, following the topological rules of the target system. [ABSTRACT FROM AUTHOR]

Link prediction in complex networks has recently attracted a great deal of attraction in diverse scientific domains, including social and biological sciences. Given a snapshot of a network, the goal is to predict links that are missing in the network or that are likely to occur in the near future. This problem has both theoretical and practical significance; it not only helps us to identify missing links in a network more efficiently by avoiding the expensive and time consuming experimental processes, but also allows us to study the evolution of a network with time. To address the problem of link prediction, numerous attempts have been made over the recent years that exploit the local and the global topological properties of the network to predict missing links in the network. In this paper, we use parametrised matrix forest index (PMFI) to predict missing links in a network. We show that, for small parameter values, this index is linked to a heat diffusion process on a graph and therefore encodes geometric properties of the network. We then develop a framework that combines the PMFI with a local similarity index to predict missing links in the network. The framework is applied to numerous networks obtained from diverse domains such as social network, biological network, and transport network. The results show that the proposed method can predict missing links with higher accuracy when compared to other state-of-the-art link prediction methods. [ABSTRACT FROM AUTHOR]

Studying the edge states of a topological system and extracting their topological properties is of great importance in understanding and characterizing these systems. In this paper, we present a novel analytical approach for obtaining explicit expressions for the edge states in the Kane-Mele model within a ribbon geometry featuring armchair boundaries. Our approach involves a mapping procedure that transforms the system into an extended Su–Schrieffer–Heeger model, specifically a two-leg ladder, in momentum space. Through rigorous derivation, we determine various analytical properties of the edge states, including their wave functions and energy dispersion. Additionally, we investigate the condition for topological transition by solely analyzing the edge states, and we elucidate the underlying reasons for the violation of the bulk-edge correspondence in relatively narrow ribbons. Our findings shed light on the unique characteristics of the edge states in the quantum spin Hall phase of the Kane–Mele model and provide valuable insights into the topological properties of such systems. [ABSTRACT FROM AUTHOR]

Complex networks capture the structure, dynamics, and relationships among entities in real-world networked systems, encompassing domains like communications, society, chemistry, biology, ecology, politics, etc. Analysis of complex networks lends insight into the critical nodes, key pathways, and potential points of failure that may impact the connectivity and operational integrity of the underlying system. In this work, we investigate the topological properties or indicators, such as shortest path length, modularity, efficiency, graph density, diameter, assortativity, and clustering coefficient, that determine the vulnerability to (or robustness against) diverse attack scenarios. Specifically, we examine how node- and link-based network growth or depletion based on specific attack criteria affect their robustness gauged in terms of the largest connected component (LCC) size and diameter. We employ partial least squares discriminant analysis to quantify the individual contribution of the indicators on LCC preservation while accounting for the collinearity stemming from the possible correlation between indicators. Our analysis of 14 complex network datasets and 5 attack models invariably reveals high modularity and disassortativity to be prime indicators of vulnerability, corroborating prior works that report disassortative modular networks to be particularly susceptible to targeted attacks. We conclude with a discussion as well as an illustrative example of the application of this work in fending off strategic attacks on critical infrastructures through models that adaptively and distributively achieve network robustness. [ABSTRACT FROM AUTHOR]

Seasonal variations have long been observed in various aspects of human life. While there is an abundance of research that has characterized seasonality effects in, for example, cognition, mood, and behavior, including studies of underlying biophysical mechanisms, direct measurements of seasonal variations of brain functional activities have not gained wide attention. We have quantified seasonal effects on functional connectivity as derived from MRI scans. A cohort of healthy human subjects was divided into four groups based on the seasons of their scanning dates as documented in the image database of the Human Connectome Project. Sinusoidal functions were used as regressors to determine whether there were significant seasonal variations in measures of brain activities. We began with the analysis of seasonal variations of the fractional amplitudes of low frequency fluctuations of regional functional signals, followed by the seasonal variations of functional connectivity in both global- and network-level. Furthermore, relevant environmental factors, including average temperature and daylength, were found to be significantly associated with brain functional activities, which may explain how the observed seasonal fluctuations arise. Finally, topological properties of the brain functional network also showed significant variations across seasons. All the observations accumulated revealed seasonality effects of human brain activities in a resting-state, which may have important practical implications for neuroimaging research. [ABSTRACT FROM AUTHOR]

We investigate the photonic topological phases in chiral metamaterials characterized by the magnetoelectric tensors with diagonal chirality components. The underlying medium is considered a photonic analogue of the topological semimetal featured with a Weyl cone and a cylindrical surface in the frequency-wave vector space. As the 'spin'-degenerate condition is satisfied, the photonic system can be rearranged as two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in the form of spin-orbit Hamiltonians of spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between vacuum and the chiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes form a pair of spiral surface sheets wrapping around the Weyl cone, resembling the helicoid surface states that occur in topological semimetals. At the Weyl frequency, the surface modes contain two Fermi arc-like states that concatenate to yield a straight line segment. [ABSTRACT FROM AUTHOR]

Three series of functionalized ion pairs composed of ethyl phenyl imidazolium [PhIM(C2H5)]+, (vinyl) ethenyl phenyl imidazolium [PhIM(C2H3)]+ and ethynyl phenyl imidazolium [PhIM(C2H)]+ cations and acetate ([Y1]−), nitrate ([Y2]−), tetrafluoroborate ([Y3]−) and perchlorate ([Y4]−) anions were designed and their physical and chemical properties were analyzed at M06‐2X‐GD3/AUG‐cc‐pVDZ level of theory. The effect of alkyl chain unsaturation on structural characteristics, energetic parameters, electronic and topological properties, and the global reactivity parameters and also on some physical and chemical properties such as dipole moment, melting point, and electrochemical window of the introduced IPs was discussed. Based on electrochemical window values, the studied IPs including alkyl chain unsaturation in the cation and [Y1‐2]− anions have no suitable electrochemical stability for use in electrochemical devices. [ABSTRACT FROM AUTHOR]

In an article published in 2015, Hussain et al. introduced a notion of a fuzzy b-metric space and obtained some fixed point theorems for this kind of space. Shortly thereafter, Nădăban presented a notion of a fuzzy b-metric space that is slightly different from the one given by Hussain et al., and explored some of its topological properties. Related to Nădăban's study, Sedghi and Shobe, Saadati, and Šostak independently conducted investigations in articles published in 2012, 2015, and 2018, respectively, about another class of spaces that Sedgi and Shobe called b-fuzzy metric spaces, Saadati, fuzzy metric type spaces, and Šostak, fuzzy k-metric spaces. The main contributions of our paper are the following: First, we propose a notion of fuzzy b-metric space that encompasses and unifies the aforementioned types of spaces. Our approach, which is based on Gabriec's notion of a fuzzy metric space, allows us to simultaneously cover two interesting classes of spaces, namely, the 01-fuzzy b-metric spaces and the K-stationary fuzzy b-metric spaces. Second, we show that each fuzzy b-metric space, in our sense, admits uniformity with a countable base. From this fact, we derive, among other consequences, that the topology induced by means of its "open" balls is metrizable. Finally, we obtain a characterization of complete fuzzy b-metric spaces with the help of a fixed point result which is also proved here. In support of our approach, several examples, including an application to a type of difference equations, are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we study the space of G-permutation degree of some classes of topological spaces and the properties of the functor SP G n of G-permutation degree. In particular, we prove: (a) If a topological space X is developable, then so is SP G n X ; (b) If X is a Moore space, then so is SP G n X ; (c) If a topological space X is an M 1 -space, then so is SP G n X ; (d) If a topological space X is an M 2 -space, then so is SP G n X . [ABSTRACT FROM AUTHOR]