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This paper addresses the Hilbert–Schmidt frame (HS-frame) theory. We introduce the concept of generalized dual HS-frame (g-dual HS-frame) which generalizes that of g-dual frame. We prove that two equivalent HS-frames form a g-dual HS-frame pair, characterize operators on ℓ 2 that transform a pair of HS-Riesz bases into a g-dual HS-frame pair, and present a parametric expression of all g-dual HS-frames of an arbitrarily given HS-frame. Also the perturbation-stability and topological properties of g-dual HS-frames are investigated. Finally, applying our results, we not only recover some known results but also derive some new results in the classical Hilbert space frame setting. [ABSTRACT FROM AUTHOR]

Our purpose in this work is to present a new generalized soft open set in supra soft topological spaces, named supra soft sd-sets. With deep discussion, we found out that they contain almost all kinds of weaker supra soft open sets which have been discussed in earlier studies, as shown in the following figure. So, directly we can notice the value of the introduced results. Also, the notion of a supra soft sc-set is presented, and many of its basic properties are explored. Furthermore, we show that the new family fails to form soft topology or supra soft topology. In addition, the definitions of the supra soft sd-closure operator, supra soft sd-cluster operator, and supra soft sd- interior operator are introduced, and many of their interesting properties are explored. Finally, we prove that the property of being a supra soft sd-set is a supra soft topological property. [ABSTRACT FROM AUTHOR]

Two-dimensional materials, such as transition metal dichalcogenides, have generated much interest due to their strain-sensitive electronic, optical, magnetic, superconducting, or topological properties. Harnessing control over their strain state may enable new technologies that operate by controlling these materials' properties in devices such as straintronic transistors. Piezoelectric oxides have been proposed as one method to control such strain states on the device scale. However, there are few studies of how conformal 2D materials remain on oxide materials with respect to dynamic applications of the strain. Non-conformality may lead to non-optimal strain transfer. In this work, we explore this aspect of oxide-2D adhesion in the nanoscale switching of the substrate structural phase in thin 1T′-MoTe2 attached to a mixed-phase thin-film BiFeO3 (BFO), a multiferroic oxide with an electric-field induced structural phase transition that can generate mechanical strains of up to 2%. We observe that flake thickness impacts the conformality of 1T′-MoTe2 to structural changes in BFO, but below four layers, 1T′-MoTe2 fully conforms to the nanoscale BFO structural changes. The conformality of few-layer 1T′-MoTe2 suggests that BFO is an excellent candidate for deterministic, nanoscale strain control for 2D materials. [ABSTRACT FROM AUTHOR]

We report the experimental observation of second-order corner states in a two-dimensional breathing honeycomb topolectrical circuit with sixfold rotational symmetry C 6 through voltage measurements. The topological corner states originate from the nontrivial bulk topology, which can be characterized by the topological invariant associated with the rotation eigenspectrum. We confirm two types of corner states, both originate from the C 6 symmetry, while one of them is specially pinned to zero admittance because of the emerging chiral symmetry protection. We then examine the robustness of zero modes in the presence of next-nearest-neighbor hopping terms that destroy chiral symmetry but still preserve C 6 symmetry. Our work provides a paradigm in circuit systems to study the exotic topological physics. [ABSTRACT FROM AUTHOR]

We report here on the properties of topological crystalline insulator Pb0.5Sn0.5Te epitaxial films doped with bismuth at levels from 0% (undoped) to 0.15%. The undoped film exhibits a p-type character due to metal vacancies. As the doping level rises, the hole concentration reduces. At a level of 0.06%, the electrical character inverts to n-type and the electron density continues to increase for rising doping level up to 0.15%. This result demonstrates an effective extrinsic n-type doping of Pb0.5Sn0.5Te crystal with bismuth due to substitutional Bi atoms in metal sites. High-resolution x-ray diffraction and reciprocal space mapping show that fully relaxed high-quality films are obtained. A pristine (111) film surface is revealed after removal of the Te cover layer using a method combining Ar+ sputtering and thermal desorption. Angle-resolved photoemission spectroscopy (ARPES) data acquired at 30 K near the Γ ¯ point of the undoped film surface show a parabolic-like dispersion of the bulk valence band close to the Fermi level. Now, the ARPES data for a sample doped with 0.1% of Bi reveal that the chemical potential is shifted by 40 meV upwards in the direction of the conduction band. The ARPES results also indicate that there might be a discrepancy between surface and bulk chemical potential in the doped sample. This divergence suggests that Te atoms diffuse into the surface during the thermal process to desorb the protective layer, inverting the surface to p-type. [ABSTRACT FROM AUTHOR]

In this study, building on the 1D topological Su–Schrieffer–Heeger (SSH) model, we propose a model of quantum dot arrays with odd and even parity and variable on-site local potentials to examine topological edge states and a possible quantum information encoding, using these states. We first investigate the SSH model with alternating tunneling amplitudes t 1 and t 2. We study the model in a ring-like structure and then proceed to minimal open-end chains with even (N = 4) and odd (N = 5) number of dots. Furthermore, we depart from the basic SSH model by introducing local potentials μ i , which offer additional control at the cost of breaking the chiral symmetry of the Hamiltonian and study the implications. Then, we propose an idealized "static" charge qubit design, based on encoding the topological invariant ν as qubit states, that exploits the topological nature of the edge states and their collective character. We introduce perturbing noise δ t i j (t) into the system and demonstrate the robustness of the states for some range of the ratio ξ = t 1 / t 2. Moreover, we show a possible way to detect the presence of topological order in the system using equilibrium dynamics for both even and odd chains. We utilize the quantum informatic measure of bipartite mutual information I { b : e } (2) (t) as a measure of bulk-edge quantum correlations and a quantitative indicator for the manifestation of bulk-edge correspondence; here, we also propose a dynamical qubit encoding with ν for specific quantum chain parity. Finally, we offer a few remarks on potential future explorations. [ABSTRACT FROM AUTHOR]

Agreeing on a common value among a set of agents is a fundamental problem in distributed computing, which occurs in several variants: In contrast to exact consensus, approximate variants are studied in systems where exact agreement is not possible or required, e.g., in human-made distributed control systems and in the analysis of natural distributed systems, such as bird flocking and opinion dynamics. We study the time complexity of two classical agreement problems: non-terminating asymptotic consensus and terminating approximate consensus. Asymptotic consensus, requires agents to repeatedly set their out- puts such that the outputs converge to a common value within the convex hull of initial values; approximate consensus requires agents to eventually stop setting their outputs, which must then lie within a predefined distance of each other. We prove tight lower bounds on the contraction ratios of asymptotic consensus algorithms subject to oblivious message adversaries, from which we deduce bounds on the time complexity of approximate consensus algorithms. In particular, the obtained bounds show optimality of asymptotic and approximate consensus algorithms presented by Charron-Bost et al. (ICALP’16) for certain systems, including the strongest oblivious message adversary in which asymptotic and approximate consensus are solvable. As a corollary we also obtain asymptotically tight bounds for asymptotic consensus in the classical asynchronous model with crashes. Central to the lower-bound proofs is an extended notion of valency, the set of reachable limits of an asymptotic consensus algorithm starting from a given configuration. We further relate topological properties of valencies to the solvability of exact consensus, shedding some light on the relation of these three fundamental problems in dynamic networks. [ABSTRACT FROM AUTHOR]

Approximately 36% of patients with neuromyelitis optica spectrum disorders (NMOSD) suffer from severe visual and motor disability (blindness or light perception or unable to walk) with abnormalities of whole-brain functional networks. However, it remains unclear how whole-brain functional networks and their dynamic properties are related to clinical disability in patients with NMOSD. Our study recruited 30 NMOSD patients (37.70 ± 11.99 years) and 45 healthy controls (HC, 41.84 ± 11.23 years). The independent component analysis, sliding-window approach and graph theory analysis were used to explore the static strength, time-varying and topological properties of large-scale functional networks and their associations with disability in NMOSD. Compared to HC, NMOSD patients showed significant alterations in dynamic networks rather than static networks. Specifically, NMOSD patients showed increased occurrence (fractional occupancy; P < 0.001) and more dwell times of the low-connectivity state (P < 0.001) with fewer transitions (P = 0.028) between states than HC, and higher fractional occupancy, increased dwell times of the low-connectivity state and lower transitions were related to more severe disability. Moreover, NMOSD patients exhibited altered small-worldness, decreased degree centrality and reduced clustering coefficients of hub nodes in dynamic networks, related to clinical disability. NMOSD patients exhibited higher occurrence and more dwell time in low-connectivity states, along with fewer transitions between states and decreased topological organizations, revealing the disrupted communication and coordination among brain networks over time. Our findings could provide new perspective to help us better understand the neuropathological mechanism of the clinical disability in NMOSD. [ABSTRACT FROM AUTHOR]

Objective: To assess the alteration of individual brain morphological and functional network topological properties and their clinical significance in patients with neuromyelitis optica spectrum disorder (NMOSD). Materials and methods: Eighteen patients with NMOSD and twenty-two healthy controls (HCs) were included. The clinical assessment of NMOSD patients involved evaluations of disability status, cognitive function, and fatigue impact. For each participant, brain images, including high-resolution T1-weighted images for individual morphological brain networks (MBNs) and resting-state functional MR images for functional brain networks (FBNs) were obtained. Topological properties were calculated and compared for both MBNs and FBNs. Then, partial correlation analysis was performed to investigate the relationships between the altered network properties and clinical variables. Finally, the altered network topological properties were used to classify NMOSD patients from HCs and to analyses time- to-progression of the patients. Results: The average Expanded Disability Status Scale score of NMOSD patients was 1.05 (range from 0 to 2), indicating mild disability. Compared to HCs, NMOSD patients exhibited a higher normalized characteristic path length (λ) in their MBNs (P = 0.0118, FDR corrected) but showed no significant differences in the global properties of FBNs (p: 0.405-0.488). Network-based statistical analysis revealed that MBNs had more significantly altered connections (P< 0.01, NBS corrected) than FBNs. Altered nodal properties of MBNs were correlated with disease duration or fatigue scores (P< 0.05/6 with Bonferroni correction). Using the altered nodal properties of MBNs, the accuracy of classification of NMOSD patients versus HCs was 96.4%, with a sensitivity of 93.3% and a specificity of 100%. This accuracy was better than that achieved using the altered nodal properties of FBNs. Nodal properties of MBN significantly predicted Expanded Disability Status Scale worsening in patients with NMOSD. Conclusion: The results indicated that patients with mild disability NMOSD exhibited compensatory increases in local network properties to maintain overall stability. Furthermore, the alterations in the morphological network nodal properties of NMOSD patients not only had better relevance for clinical assessments compared with functional network nodal properties, but also exhibited predictive values of EDSS worsening. [ABSTRACT FROM AUTHOR]

In this Letter, we report on the realization of higher-order topology in electric circuit systems by generalizing the two-dimensional asymmetric Su–Schrieffer–Heeger (SSH) model to a bilayer model, which consists of two monolayer models that are directly coupled. Such a system inherits the topological properties of its monolayer counterparts and exhibits the existence of split edge states and corner states in a finite size. As well, the number of topological states is doubled due to the mirror-stacking operation. This work substantiates the existence of rich topological states in bilayer asymmetric SSH electric circuits and may inspire further research into higher-order topological insulators in artificial topological systems. [ABSTRACT FROM AUTHOR]

The kagome ferromagnet, Co-based shandite Co3Sn2S2, shows a large anomalous Hall effect (AHE) associated with the Weyl nodes. A thin film with a Co kagome monolayer was predicted to exhibit the quantum AHE, which awaits the experimental realisation. However, it is challenging to precisely predict how the Weyl nodes reside in thin films where the lattice and electronic structures are in general different from the bulk. Here we report comprehensive ab initio results for thin films of Co3Sn2S2 with one, two and three Co layers with Sn or S surface terminations. We find that all the Sn-end films stabilise a ferromagnetic state similar to the bulk, and retain the large AHE down to the monolayer limit where the AHE is quantised, while the magnetic and topological properties drastically change with the number of Co layers in the S-end films. Our results would stimulate further experimental exploration of thin Weyl materials. The Weyl semimetal represents a distinctive topological state of matter, yet understanding its behaviour in thin films remains challenging, despite its significance for device applications. The authors reveal the layer number dependence of the band topology and transport properties in atomically thin films of a ferromagnetic Weyl semimetal, Co shandite. [ABSTRACT FROM AUTHOR]

Community structure, a critical topological property of complex networks, has recently received extensive and in-depth attention from researchers. Recognizing the non-uniform degree distribution of nodes within network subgraphs, this paper presents a novel algorithm called MD-RWR (Maximum Degree-based Random Walk with Restart) for community detection in complex networks. The proposed algorithm not only excels at identifying overlapping communities but also enhances the objectivity and accuracy of the results. To evaluate its performance, the algorithm is tested on five real-world networks. The experimental results demonstrate its effectiveness in detecting communities, particularly when dealing with overlapping ones. Furthermore, the algorithm surpasses Walktrap, Infomap, LPA, and LPA-S algorithms in terms of modularity and NMI scores, while exhibiting faster execution time compared to these algorithms. [ABSTRACT FROM AUTHOR]

In this article, we compute the irregularity measures of generalized Sierpiński graphs and obtain some bounds on these irregularities. Moreover, we discuss some bounds on connectivity indices for generalized Sierpiński graphs of any arbitrary graph H along with classification of the extremal graphs used to attain them. [ABSTRACT FROM AUTHOR]

The rationale of this work is to introduce the notion of graphical symmetric spaces and some fixed-point results are proved for H - (ϑ , φ) -contractions in this setting. The idea of graphical symmetric spaces generalizes various spaces equipped with a function which characterizes the distance between two points of the space. Some topological properties of graphical symmetric spaces are discussed. Some fixed-point results for the mappings defined on graphical symmetric spaces are proved. The fixed-point results of this paper generalize and extend several fixed-point results in this new setting. The main results of this paper are applied to obtain the positive solutions of fractional periodic boundary value problems. [ABSTRACT FROM AUTHOR]

Human whole-brain functional connectivity networks have been shown to exhibit both local/quasilocal (e.g., a set of functional sub-circuits induced by node or edge attributes) and non-local (e.g., higher-order functional coordination patterns) properties. Nonetheless, the non-local properties of topological strata induced by local/quasilocal functional sub-circuits have yet to be addressed. To that end, we proposed a homological formalism that enables the quantification of higher-order characteristics of human brain functional sub-circuits. Our results indicate that each homological order uniquely unravels diverse, complementary properties of human brain functional sub-circuits. Noticeably, the H 1 homological distance between rest and motor task was observed at both the whole-brain and sub-circuit consolidated levels, which suggested the self-similarity property of human brain functional connectivity unraveled by a homological kernel. Furthermore, at the whole-brain level, the rest–task differentiation was found to be most prominent between rest and different tasks at different homological orders: (i) Emotion task ( H 0 ), (ii) Motor task ( H 1 ), and (iii) Working memory task ( H 2 ). At the functional sub-circuit level, the rest–task functional dichotomy of the default mode network is found to be mostly prominent at the first and second homological scaffolds. Also at such scale, we found that the limbic network plays a significant role in homological reconfiguration across both the task and subject domains, which paves the way for subsequent investigations on the complex neuro-physiological role of such network. From a wider perspective, our formalism can be applied, beyond brain connectomics, to study the non-localized coordination patterns of localized structures stretching across complex network fibers. [ABSTRACT FROM AUTHOR]

Designing a cost-effective, energy-efficient and highly scalable network for data centers that can deliver sufficient bandwidth has drawn tremendous attentions recently. The data center networks constructed by using multi-port servers can provide sufficient bandwidth, such as BCube, DCell and GBC3. As the volume of data keeps growing rapidly, more and more servers are continuously added into data centers. In order to reduce the cost and energy consumption, data center networks can be expanded gradually by adding a small number of servers from time to time instead of adding a huge number of servers at a time. This paper proposes a new type of data center network structure called GHB, which is constructed by using commercial switches and multi-port servers. Two types of incomplete GHB structures are also proposed. A small number of servers can be gradually added into the incomplete structures without changing their topological properties. As shown in the experimental results, the throughput of GHB is comparable to that of BCube, and is larger than that of GBC3 and DCell. The analysis results indicate that GHB strikes a good balance among diameter, bisection width, incremental scalability, cost, and energy consumption in contrast to BCube, DCell and GBC3. Compared with the BCube and GBC3, GHB reduces the cost and energy consumption by about 6% and 18%, respectively. The highest throughput of GHB is higher than that of DCell and GBC3 by about 3.4% and 8.35%, respectively. [ABSTRACT FROM AUTHOR]

Although the spin‐controlled vortex generation and photonic spin‐Hall effect of spin‐flipped abnormal mode have been widely studied recently, the traditional method based on the metasurface is difficult to fabricate, and the efficiency of the spin‐flipped abnormal mode is rather low due to process errors and intrinsic material loss. Here, a new method is proposed based on the insights into the topological singularity and special Bragger reflections resonant (BRR) mode of one‐dimensional (1D) finite photonic crystals (PhCs) with anisotropic material to realize nearly perfect (100%) spin‐conversion efficiency. For a finite 1D PhC with cell number N, there are 3N complete spin‐conversion (CSC) and complete spin‐maintained (CSM) channels. Two mechanisms of these CSC and CSM channels are revealed. The working bandwidths and the angular ranges of these CSC and CSM are also studied. Based on these theoretical findings, multi‐angles and multi‐frequencies perfect spin‐conversion (‐maintained) devices can be designed. At last, these theoretical results are confirmed by the numerical experiments based on finite‐difference time‐domain (FDTD) methods. This work paves the way to exploring the topological properties and polarization control of PhCs made of anisotropic dielectrics and provides a prospective method for the design of multi‐channels spin optical devices. [ABSTRACT FROM AUTHOR]

Mathematical chemistry plays a vital role in investigating the metal-insulator transition Superlattice (GST-SL) of strongly correlated $ 3D $ 3 D electrons due to quantum confinement. The development of epitaxial GST-SL thin films with the design of heterogenous openings is of extraordinary interest due to their applications. The thin-film declaration and the construction of exceptionally arranged amalgam accumulates are crucial for phase transformation application in non-erratic retentiveness. Softening and crystalline elements of the multi-part GST composite have been explored. This paper determines some topological properties, such as degree-based topological descriptors and their entropy measures. More precisely, we analyzed the entropy and the heat of the formation of single crystals, monolayers, and various layers of Ge–Sb–Te. [ABSTRACT FROM AUTHOR]

The morphological brain connectome (MBC) can be mapped at an individual level from a single structural MRI scan. Individualized MBCs can be modeled using both low-order and high-order methods, each of which has its own advantages and disadvantages. Individualized MBCs exhibit nontrivial topological properties such as small-worldness, modular organization, and hubs with high robustness, reproducibility, and reliability. Future work is needed to elucidate the cellular and molecular basis of individualized MBCs and to establish normative benchmarks to better understand individual variations in healthy and diseased conditions. The morphological brain connectome (MBC) delineates the coordinated patterns of local morphological features (such as cortical thickness) across brain regions. While classically constructed using population-based approaches, there is a growing trend toward individualized modeling. Currently, the methods for individualized MBCs are varied, posing challenges for method selection and cross-study comparisons. Here, we summarize how individualized MBCs are modeled through low-order methods (correlation-, divergence-, distance-, and deviation-based methods) describing relations in brain morphology, as well as high-order methods capturing similarities in these low-order relations. We discuss the merits and limitations of different methods, examining them in the context of robustness, reproducibility, and reliability. We highlight the importance of elucidating the cellular and molecular mechanisms underlying the individualized connectome, and establishing normative benchmarks to assess individual variation in development, aging, and neuropsychiatric disorders. [ABSTRACT FROM AUTHOR]

In this manuscript, the potential utility of 6CF macrocyclic oligofuran is theoretically investigated to create novel nanotubes. The energetic, electronic, structural and topological properties of π-stacked systems are examined at B3LYP/6-31 + G(d), wB97XD/6-31 + G(d) and M06-2X/6-31 + G(d) levels of theory. The findings indicate that the self-assembly of 6CF macrocyclic oligofurans can be considered to create organic nanotubes through π–π stacking. The strength and nature of π-π interactions are examined using the atoms in molecules (AIM) approach. Meaningful relationships are obtained between stability, electronic properties and the number of stacked π-conjugated macrocyclic oligofurans. The stability and polarisability of π-stacked systems are amplified by increasing number of macrocycles. Reverse behaviours are found for the values of band gap, electronic chemical potential and first ionisation energy. [ABSTRACT FROM AUTHOR]

Analyzing and characterizing the differences between networks is a fundamental and challenging problem in network science. Most previous network comparison methods that rely on topological properties have been restricted to measuring differences between two undirected networks. However, many networks, such as biological networks, social networks, and transportation networks, exhibit inherent directionality and higher-order attributes that should not be ignored when comparing networks. Therefore, we propose a motif-based directed network comparison method that captures local, global, and higher-order differences between two directed networks. Specifically, we first construct a motif distribution vector for each node, which captures the information of a node's involvement in different directed motifs. Then, the dissimilarity between two directed networks is defined on the basis of a matrix, which is composed of the motif distribution vector of every node and the Jensen–Shannon divergence. The performance of our method is evaluated via the comparison of six real directed networks with their null models, as well as their perturbed networks based on edge perturbation. Our method is superior to the state-of-the-art baselines and is robust with different parameter settings. [ABSTRACT FROM AUTHOR]

The spectral properties of a non‐Hermitian quasi‐1D lattice in two of the possible dimerization configurations are investigated. Specifically, it focuses on a non‐Hermitian diamond chain that presents a zero‐energy flat band. The flat band originates from wave interference and results in eigenstates with a finite contribution only on two sites of the unit cell. To achieve the non‐Hermitian characteristics, the system under study presents non‐reciprocal hopping terms in the chain. This leads to the accumulation of eigenstates on the boundary of the system, known as the non‐Hermitian skin effect. Despite this accumulation of eigenstates, for one of the two considered configurations, it is possible to characterize the presence of non‐trivial edge states at zero energy by a real‐space topological invariant known as the biorthogonal polarization. This work shows that this invariant, evaluated using the destructive interference method, characterizes the non‐trivial phase of the non‐Hermitian diamond chain. For the second non‐Hermitian configuration, there is a finite quantum metric associated with the flat band. Additionally, the system presents the skin effect despite the system having a purely real or imaginary spectrum. The two non‐Hermitian diamond chains can be mapped into two models of the Su‐Schrieffer‐Heeger chains, either non‐Hermitian, and Hermitian, both in the presence of a flat band. This mapping allows to draw valuable insights into the behavior and properties of these systems. [ABSTRACT FROM AUTHOR]

Modal logic enjoys topological semantics that may be traced back to McKinsey and Tarski, and the classification of topological spaces via modal axioms is a lively area of research. In the past two decades, there has been interest in extending topological modal logic to the language of the mu-calculus, but previously no class of topological spaces was known to be mu-calculus definable that was not already modally definable. In this paper, we show that the full mu-calculus is indeed more expressive than standard modal logic, in the sense that there are classes of topological spaces (and weakly transitive Kripke frames), which are mu-definable but not modally definable. The classes we exhibit satisfy a modally definable property outside of their perfect core, and thus we dub them imperfect spaces. We show that the mu-calculus is sound and complete for these classes. Our examples are minimal in the sense that they use a single instance of a greatest fixed point, and we show that least fixed points alone do not suffice to define any class of spaces that is not already modally definable. [ABSTRACT FROM AUTHOR]

This paper presents the spectral gap-based topology control algorithm (SGTC) for wireless backhaul networks, a novel approach that employs the Laplacian Spectral Gap (LSG) to find expander-like graphs that optimize the topology of the network in terms of robustness, diameter, energy cost, and network entropy. The latter measures the network's ability to promote seamless traffic offloading from the Macro Base Stations to smaller cells by providing a high diversity of shortest paths connecting all the stations. Given the practical constraints imposed by cellular technologies, the proposed algorithm uses simulated annealing to search for feasible network topologies with a large LSG. Then, it computes the Pareto front of the set of feasible solutions found during the annealing process when considering robustness, diameter, and entropy as objective functions. The algorithm's result is the Pareto efficient solution that minimizes energy cost. A set of experimental results shows that by optimizing the LSG, the proposed algorithm simultaneously optimizes the set of desirable topological properties mentioned above. The results also revealed that generating networks with good spectral expansion is possible even under the restrictions imposed by current wireless technologies. This is a desirable feature because these networks have strong connectivity properties even if they do not have a large number of links. [ABSTRACT FROM AUTHOR]

We show how machine learning techniques can be applied for the classification of topological phases in finite leaky photonic lattices using limited measurement data. We propose an approach based solely on a single real-space bulk intensity image, thus exempt from complicated phase retrieval procedures. In particular, we design a fully connected neural network that accurately determines topological properties from the output intensity distribution in dimerized waveguide arrays with leaky channels, after propagation of a spatially localized initial excitation at a finite distance, in a setting that closely emulates realistic experimental conditions. [ABSTRACT FROM AUTHOR]

The effects of age and gender on large-scale resting-state networks (RSNs) reflecting within- and between-network connectivity in the healthy brain remain unclear. This study investigated how age and gender influence the brain network roles and topological properties underlying the ageing process. Ten RSNs were constructed based on 998 participants from the REST-meta-MDD cohort. Multivariate linear regression analysis was used to examine the independent and interactive influences of age and gender on large-scale RSNs and their topological properties. A support vector regression model integrating whole-brain network features was used to predict brain age across the lifespan and cognitive decline in an Alzheimer's disease spectrum (ADS) sample. Differential effects of age and gender on brain network roles were demonstrated across the lifespan. Specifically, cingulo-opercular, auditory, and visual (VIS) networks showed more incohesive features reflected by decreased intra-network connectivity with ageing. Further, females displayed distinctive brain network trajectory patterns in middle-early age, showing enhanced network connectivity within the fronto-parietal network (FPN) and salience network (SAN) and weakened network connectivity between the FPN-somatomotor, FPN-VIS, and SAN-VIS networks. Age — but not gender — induced widespread decrease in topological properties of brain networks. Importantly, these differential network features predicted brain age and cognitive impairment in the ADS sample. By showing that age and gender exert specific dispersion of dynamic network roles and trajectories across the lifespan, this study has expanded our understanding of age- and gender-related brain changes with ageing. Moreover, the findings may be useful for detecting early-stage dementia. [ABSTRACT FROM AUTHOR]

When semi-infinite phononic crystals (PCs) are in contact, localized modes may exist at their boundary. The central question is generally to predict their existence and to determine their stability. With the rapid expansion of the field of topological insulators, powerful tools have been developed to address these questions. In particular, when applied to one-dimensional systems with mirror symmetry, the bulk-boundary correspondence claims that the existence of interface modes is given by a topological invariant computed from the bulk properties of the PC, which ensures strong stability properties. This one-dimensional bulk-boundary correspondence has been proven in various works. Recent attempts have exploited the notion of surface impedance, relying on analytical calculations of the transfer matrix. In the present work, the monotonic evolution of surface impedance with frequency is proven for all one-dimensional PCs with mirror symmetry. This result allows us to establish a stronger version of the bulk-boundary correspondence that guarantees not only the existence but also the uniqueness of a topologically protected interface state. This correspondence is extended to a larger class of one-dimensional models that include imperfect interfaces, array of resonators, or dispersive media. Numerical simulations are proposed to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

Street classification is fundamental to transportation planning and design. Urban transportation planning is mostly based on function-based classification schemes (FCS), which classifies streets according to their respective requirements in the pre-defined hierarchy of the urban street network (USN). This study proposes a computational approach for a network-based categorization of street segments (NSC). The main objectives are, first, to identify and describe NSC categories, second, to examine the spatial distribution of street segments from FCS and NSC within a city, and third, to compare FCS and NSC to identify similarities and differences between the two. Centrality measures derived from network science are computed for each street segment and then clustered based on their topological importance. The adaption of clustering, which is a numerical categorization technique, potentially facilitates the integration with other analytical processes in planning and design. The quantitative description of street characteristics obtained by this method is suitable for development of new knowledge-based planning approaches. When extensive data or knowledge of the real performance of streets are not available or costly, this method provides an objective categorization from those data sets that are readily available. The method can also assign the segments that are categorized as "unclassified" in FCS to the categories in the NSC scheme. Since centrality metrics are associated with the functioning of USNs, the comparison between FCS and NSC not only contributes to the understanding and description of the fine variations in topological properties of the segments within each FCS class but also supports the identification of the mismatched segments, where reassessment and adjustment is required, for example, in terms of planning and design. [ABSTRACT FROM AUTHOR]

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- (T -) invariant (helical) 3D TCIs—termed higher-order TCIs (HOTIs)—the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), "spin-Weyl" semimetals, and T -doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that β-MoTe2 realizes a spin-Weyl state and that α-BiBr hosts both 3D QSHI and T-DAXI regimes. 3D higher-order topological insulators (HOTIs) exhibit 1D hinge states depending on extrinsic sample details, while intrinsic features of HOTIs remain unknown. Here, K.S. Lin et al. introduce the framework of spin-resolved topology to show that helical HOTIs can realize a doubled axion insulator phase with nontrivial partial axion angles. [ABSTRACT FROM AUTHOR]

The main results of the theory of separable algorithmic representations of classical algebraic systems are presented. The most important classes of such systems and their representations in the lower classes of the arithmetic hierarchy — positive and negative — are described. Special attention is paid to the algorithmic, structural and topological properties of separable representations of groups, rings and bodies, as well as to effective analogs of the Maltsev theorem on embedding rings into bodies. The possibilities of using the studied concepts in the framework of theoretical informatics are considered. [ABSTRACT FROM AUTHOR]

Temporal networks are essential for modeling and understanding time-dependent systems, from social interactions to biological systems. However, real-world data to construct meaningful temporal networks are expensive to collect or unshareable due to privacy concerns. Generating arbitrarily large and anonymized synthetic graphs with the properties of real-world networks, namely surrogate networks, is a potential way to bypass the problem. However, it is not easy to build surrogate temporal networks which do not lack information on the temporal and/or topological properties of the input network and their correlations. Here, we propose a simple and efficient method that decomposes the input network into star-like structures evolving in time, used in turn to generate a surrogate temporal network. The model is compared with state-of-the-art models in terms of similarity of the generated networks with the original ones, showing its effectiveness and its efficiency in terms of execution time. The simplicity of the algorithm makes it interpretable, extendable and scalable. Surrogate networks are synthetic alternatives to real world networks that avoid expensive data collection and privacy issues, but they often lack information on the temporal or topological properties of the input network. The authors propose a method to construct realistic surrogate network, outperforming the existing ones in accuracy and execution time. [ABSTRACT FROM AUTHOR]

Kagome lattice magnets are an interesting class of materials as they can host topological properties in their magnetic and electronic structures. YMn6Sn6 is one such compound in which various exotic magnetic and electronic topological properties have been realized. Here, by means of a partial substitution of Sn with an isovalent and slightly smaller atom Ge, we demonstrate the sensitivity of such chemical substitution on the magnetic structure and its influence in the electronic properties. Magnetic structure of YMn6Sn4Ge2 determined by neutron diffraction reveals an incommensurate staggered magnetic spiral with a slightly larger spiral pitch than in YMn6Sn6. This change in magnetic structure influences the Fermi surface enhancing the out-of-plane conductivity. Such a sensitivity to the partial chemical substitution provides a great potential for engineering the magnetic phases and associated electronic properties not only in YMn6Sn6, but also in the large family of 166 rare-earth kagome magnet. [ABSTRACT FROM AUTHOR]

In this paper, we introduced the hull-kernel topology τ on the set P of prime ideals in a partially ordered ternary semigroup T and investigated various topological properties of the structure space (P, τ). We also obtained some useful results about compactness and connectedness of the set of all prime full ideals of T. [ABSTRACT FROM AUTHOR]

Connectivity is one of the most essential notions in general topology. Convex structures are topological-like structures. Many properties in topological spaces have been generalized to convex structures, such as separation. However, connectivity has not been studied in convex structures yet. In this paper, firstly, based on the consideration to hull operators, separatedness is defined in classical convex structures, and then we provide the concept of connectivity. Secondly, some equivalent characterizations of connectivity are discussed, and we investigate the related properties of connectivity. In additional, through (L, M)-fuzzy convex hull operators, we propose the separatedness degrees of (L, M)-fuzzy convex structures. Furthermore, the notion of connectedness degrees of (L, M)-fuzzy convex structures is introduced. Finally, many properties of connectivity in general convex structures can be generalized to (L, M)-fuzzy convex structures. [ABSTRACT FROM AUTHOR]

In this work, we will define a new type metric with degree m and m+1 points which is called m-hemi metric as a generalization of 2-metric spaces. We will give and prove some topological properties. Also, Banach contraction mapping principle was proved and an application to Fredholm integral equation were gived in hemi metric spaces. [ABSTRACT FROM AUTHOR]

The concept of a Q operation on a new class of δPs-open subsets was defined. The comparisons were made with all other existing open sets with this new open set. Here for the same topological space two different operations Q and Q'are defined and a new concept of bioperation was introduced. The concepts of [Q, Q']-open sets and [Q, Q']-regular spaces along with some topological properties were analysed. Two types of [Q, Q']-closures were studied with their properties, and the submaximal spaces were analyzed. [ABSTRACT FROM AUTHOR]

In this work, we introduce a generalization of the Sν$S^\nu$ spaces underlying a multifractal formalism for non‐concave spectra. We prove among other things that the essential topological properties of the Sν$S^\nu$ spaces can be transposed in this context; in particular, these new spaces are metric. [ABSTRACT FROM AUTHOR]

It is known that a 2D‐dimerized Su–Schrieffer–Heeger model can produce a nontrivial topological phase. It is a simple nearest‐neighbor model with four lattice sites in 2D. The Su–Schrieffer–Heeger model is easy to analyze but neglects important interaction in physical systems. Herein, an extended version of this model is proposed which includes all possible second‐nearest‐neighbor interactions in order to grant more flexibility when describing realistic systems. The addition of these interactions changes the symmetry of the model and as a result affects the topological properties. In order to characterize the topological changes to the model, a polarization invariant is used. It is further shown that these symmetry breaking interactions can be used to evoke a topological phase transition as well. [ABSTRACT FROM AUTHOR]

The residual finite-dimensionality of a |${\textrm{C}}^{\ast }$| -algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this paradigm to general (possibly non-self-adjoint) operator algebras. While numerous subtleties emerge in this greater generality, we exhibit novel tools for constructing finite-dimensional approximations. One such tool is a notion of a residually finite-dimensional coaction of a semigroup on an operator algebra, which allows us to construct finite-dimensional approximations for operator algebras of functions and operator algebras of semigroups. Our investigation is intimately related to the question of when residual finite-dimensionality of an operator algebra is inherited by its maximal |${\textrm{C}}^{\ast }$| -cover, which we establish in many cases of interest. [ABSTRACT FROM AUTHOR]

The closedness of certain sets plays an important role in mathematics, especially in convex and functional analysis. In this short note, we give some connections between closedness of Minkowski sum of sets, closedness of the convex hull of sets, and other properties of the topological vector space. [ABSTRACT FROM AUTHOR]

The formulations of polynomials over a topological simplex combine the elements of topology and algebraic geometry. This paper proposes the formulation of simplicial polynomials and the properties of resulting topological manifolds in two classes, non-degenerate forms and degenerate forms, without imposing the conditions of affine topological spaces. The non-degenerate class maintains the degree preservation principle of the atoms of the polynomials of a topological simplex, which is relaxed in the degenerate class. The concept of hybrid decomposition of a simplicial polynomial in the non-degenerate class is introduced. The decompositions of simplicial polynomial for a large set of simplex vertices generate ideal components from the radical, and the components preserve the topologically isolated origin in all cases within the topological manifolds. Interestingly, the topological manifolds generated by a non-degenerate class of simplicial polynomials do not retain the homeomorphism property under polynomial extension by atom addition if the simplicial condition is violated. However, the topological manifolds generated by the degenerate class always preserve isomorphism with varying rotational orientations. The hybrid decompositions of the non-degenerate class of simplicial polynomials give rise to the formation of simplicial chains. The proposed formulations do not impose strict positivity on simplicial polynomials as a precondition. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give an interesting connection between two mathematical approaches to vagueness: binary bipolar soft sets and binary bipolar soft topology. The binary bipolar soft points are defined using binary bipolar soft sets. The binary bipolar soft set will be the binary bipolar soft union of its binary bipolar soft points. Moreover, the notion of binary bipolar soft topological spaces over two universal sets and a parameter set is proposed. Some topological properties of binary bipolar soft sets, such as binary bipolar soft open, binary bipolar soft closed, binary bipolar soft closure, binary bipolar soft interior, and binary bipolar soft boundary, are introduced. Some important properties of these classes of binary bipolar soft sets are investigated. Furthermore, the symmetry relation is compared between binary bipolar soft topology and binary soft topology on a common universe set. Finally, some results and counterexamples are demonstrated to explain this work. [ABSTRACT FROM AUTHOR]

Spatial objects in a geographical information system are often vague. Fuzzy topology-based intersection methods were introduced to obtain the topological relation between such vague objects by considering the objects as fuzzy sets. The elements of the intersection matrices express the nature of the intersections between topological parts of the objects. In reality, it may only be possible to calculate some of the required intersections due to the unavailability of data. This paper introduces a method to construct a fuzzy 9-intersection matrix under incomplete observations. Further, it computes the possible fuzzy topological relation using a quantitative fuzzy 9-intersection method based on fuzzy similarity measure. Some special cases of the incomplete observations and fuzzy topological relation under such situations are discussed. Finally, few applications are presented, where the proposed method is used to obtain relation between two uncertain objects under the condition that the topological properties of the objects are partially known. [ABSTRACT FROM AUTHOR]

We prove that every mapping with finite distortion on a Carnot group is open and discrete provided that it is quasilight and the distortion coefficient is integrable. Also, we estimate the Hausdorff dimension of the preimages of points for mappings on a Carnot group with a bounded multiplicity function and summable distortion coefficient. Furthermore, we give some example showing that the obtained estimates cannot be improved. [ABSTRACT FROM AUTHOR]

Let E be a Hausdorff locally convex space. We investigate the space Λ φ [ E ] of weakly Köthe–Orlicz summable sequences in E with respect to an Orlicz function φ and a perfect sequence space Λ . We endow Λ φ [ E ] with a Hausdorff locally convex topology and determine the continuous dual of the so-obtained space in terms of strongly Köthe–Orlicz summable sequences from the dual space E ′ of E . Next, we give necessary and sufficient conditions for Λ φ [ E ] to be barrelled or quasi-barrelled. This contributes to the understanding of different spaces of vector-valued sequences and their topological properties. [ABSTRACT FROM AUTHOR]

Higher‐order topological insulators hosting topological modes at hinges and corners provide a new avenue for disorder‐immune light transport, which prospects great potential in applications of integrated photonics devices. However, the active control of topological modes in 3D higher‐order topological insulators is not realized yet, and its construction is too complicated and huge to analyze. Here, a method is proposed to construct effective Hamiltonians for higher‐order topological insulators, which provides a correct physical picture of the states and the corresponding energies at the domain walls. A non‐Hermitian 3D honeycomb lattice is constructed, which can generate arbitrary‐located, arbitrary‐shaped, and robust topological hinge states propagating at gain‐loss domain walls. The 3D honeycomb lattice can also appear as non‐Hermitian third‐order TIs exhibiting corner states, which can be dynamically controlled and show new topologically protected confinement rules. This work expands the understanding of the topological properties in non‐Hermitian systems and enables the dynamic control of topological states of different dimensions. [ABSTRACT FROM AUTHOR]

In this work we present a new local to global criterion for proving a form of high dimensional expansion, which we term cosystolic expansion. Applying this criterion on Ramanujan complexes yields for every dimension an infinite family of bounded degree complexes with the topological overlap property. This answers an open question raised by Gromov. [ABSTRACT FROM AUTHOR]

Background: Diffusion tensor imaging (DTI) studies have demonstrated white matter (WM) abnormalities in patients with temporal lobe epilepsy (TLE). However, alterations in the topological properties of the WM structural network in patients with TLE remain unclear. Graph theoretical analysis provides a new perspective for evaluating the connectivity of WM structural networks. Methods: DTI was used to map the structural networks of 18 patients with TLE (10 males and 8 females) and 29 (17 males and 12 females) age‐ and gender‐matched normal controls (NC). Graph theory was used to analyze the whole‐brain networks and their topological properties between the two groups. Finally, partial correlation analyses were performed on the weighted network properties and clinical characteristics, namely, duration of epilepsy, verbal intelligence quotient (IQ), and performance IQ. Results: Patients with TLE exhibited reduced global efficiency and increased characteristic path length. A total of 31 regions with nodal efficiency alterations were detected in the fractional anisotropy_ weighted network of the patients. Communication hubs, such as the middle temporal gyrus, right inferior temporal gyrus, left calcarine, and right superior parietal gyrus, were also differently distributed in the patients compared with the NC. Several node regions showed close relationships with duration of epilepsy, verbal IQ, and performance IQ. Conclusions: Our results demonstrate the disruption of the WM structural network in TLE patients. This study may contribute to the further understanding of the pathological mechanism of TLE. [ABSTRACT FROM AUTHOR]

In this paper, we define and discuss the Orlicz sequence spaces ΓM(∆n u, q, s) and ΓM(p, ∆n u, q, s) of entire sequences, where (X, q) is a seminormed space and s is any real number such that s ≥ 0. Furthermore, we study some topological properties of these spaces. We discuss some inclusion relations between them and related results. [ABSTRACT FROM AUTHOR]

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]