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Non-Hermitian topology is a recent hot topic in condensed matters. In this paper, we propose a novel platform drawing interdisciplinary attention: rock–paper–scissors (RPS) cycles described by the evolutionary game theory. Specifically, we demonstrate the emergence of an exceptional point and a skin effect by analyzing topological properties of their payoff matrix. Furthermore, we discover striking dynamical properties in an RPS chain: the directive propagation of the population density in the bulk and the enhancement of the population density only around the right edge. Our results open new avenues of the non-Hermitian topology and the evolutionary game theory. [ABSTRACT FROM AUTHOR]

The article looks into the structures of directed graphs through the Borromean rings and the game rock-paper-scissors. Topics discussed include the graph representations for the two-player game rock-paper-scissors (RPS(3)), in which in mathematics is referred to as a balanced tournament, for the five-weapon game (RPS(5)), and for the hexagonal pyramid. The isomorphism and automorphisms of graph are also mentioned.

With the continuous development of new energy power generation and smart grid, Power Electronic Transformer (PET) has a good prospect for development because of its remarkable advantages. Based on the topology of AC/DC/AC, the modulation strategy with dual-PWM (Pulse Width Modulation) is adopted to control the operation of power electronic transformers in this paper. The PET structure consists of three units: importation portion, isolation portion and output portion. Model building and analyzing both at the input and output terminals are achieved step by step. And the simulation of the whole PET system with dual-PWM is accomplished with MATLAB/ Simulink. The simulation results show the control system stability and output voltage regulation precision are improved with feed-forward voltage decoupling vector control system. The correctness and effectiveness of the control strategy are demonstrated through the simulation. PETs play an important role in enhancing power supply reliability for Power Grid and promoting the new energy power generation development. [ABSTRACT FROM AUTHOR]

Problem $$1$$ of (Bulman-Fleming et al. Commun Algebra 34:1291-1317, ) asks: what conditions on a pomonoid $$S$$ and a convex, proper right ideal $$K$$ , guarantee that $$S/K$$ has property $$(P_w)$$ ? This question was first answered in Proposition 3.2 of (Qiao and Li Semigroup Forum 77:306-315, ) and later in Lemma $$5$$ of (Kilp Semigroup Forum 86:592-602, ). In this note we first show, by counterexample, that the result of Qiao and Li is incorrect, and then demonstrate a condition equivalent to that of Kilp. [ABSTRACT FROM AUTHOR]

It is shown that an approach earlier used by the author for classification of closed simply connected 6-manifolds (reduction to the problem of calculating certain bordism groups) can also be applied for easily obtaining the results by Barden (1965) on classification of closed simply connected 5-manifolds. Bibliography: 11 titles. [ABSTRACT FROM AUTHOR]

In recent years, factorization combined with attribute information has played an important role in attribute community detection. However, previous studies focused more on connecting the original shallow topological and attribute data. They ignored the potential representation structure of the network. To solve the problem that shallow information cannot fully represent the network structure, this paper proposes an attribute node classification method based on Attribute Edges weights Fusion and graph Embedding Factorization, called AEFEF. First, AEFEF converts topological information and attribute information into corresponding matrices representing node associations. Then, AEFEF constructs a new adjacency matrix by increasing the weights of shared edges between the topology structure and attribute structure. This operation can strengthen the tightness between nodes. Second, to explore the potential community structure, feature embedding is obtained by factorizing the attribute similarity matrix. Meanwhile, the new adjacency matrix is designed as a weight matrix to make the feature embedding between related nodes more similar. Finally, semi Non-negative Matrix Factorization (NMF) is introduced to modify the feature embedding by converting the negative values into positive values. Then the embedding is factorized to generate the membership matrix. At the same time, the network with a rich structure is decomposed with topological data as the main component. Otherwise, attribute information is the main component of NMF used to increase the accuracy of node classification. AEFEF is compared with 10 state-of-the-art algorithms on 7 real network datasets. The results reveal that AEFEF can improve the precision of attribute community detection. [ABSTRACT FROM AUTHOR]

The paper proposes a new multilevel inverter (MLI) topology that is designed to overcome the challenges posed by conventional MLIs, which can have high costs and complexity due to the large number of power components. The proposed MLI is designed to work with both symmetric and asymmetric DC sources, and uses fewer power semiconductor switches compared to recently propose reduced components MLIs. The paper presents the ratio of voltage levels generated per power semiconductor switch, and the gate pulses for the inverter are generated using a DSPACE1103 controller. A prototype of the 7-level inverter is developed, and experimental outcomes are provided to evaluate the simulated results. The paper highlights the importance of reducing the number of power components in MLIs to reduce costs and improve reliability. The proposed MLI offers a promising solution to this challenge, while also maintaining the advantages of MLIs such as reduced harmonic distortion and electromagnetic interference. Overall, the research offers valuable insights into the design and performance of multilevel inverters, and the proposed topology has the potential to be a useful tool for researchers and engineers working in the field of power electronics. [ABSTRACT FROM AUTHOR]

We consider standard T-interval dynamic networks, under the synchronous timing model and the broadcast CONGEST model. In a T-interval dynamic network, the set of nodes is always fixed and there are no node failures. The edges in the network are always undirected, but the set of edges in the topology may change arbitrarily from round to round, as determined by some adversary and subject to the following constraint: For every T consecutive rounds, the topologies in those rounds must contain a common connected spanning subgraph. Let H r to be the maximum (in terms of number of edges) such subgraph for round r through r + T - 1 . We define the backbone diameterd of a T-interval dynamic network to be the maximum diameter of all such H r 's, for r ≥ 1 . We use n to denote the number of nodes in the network. Within such a context, we consider a range of fundamental distributed computing problems including Count/Max/Median/Sum/LeaderElect/Consensus/ConfirmedFlood. Existing algorithms for these problems all have time complexity of Ω (n) rounds, even for T = ∞ and even when d is as small as O(1). This paper presents a novel approach/framework, based on the idea of massively parallel aggregation. Following this approach, we develop a novel deterministic Count algorithm with O (d 3 log 2 n) complexity, for T-interval dynamic networks with T ≥ c · d 2 log 2 n . Here c is a (sufficiently large) constant independent of d, n, and T. To our knowledge, our algorithm is the very first such algorithm whose complexity does not contain a Θ (n) term. This paper further develops novel algorithms for solving Max/Median/Sum/LeaderElect/Consensus/ConfirmedFlood, while incurring O (d 3 polylog (n)) complexity. Again, for all these problems, our algorithms are the first ones whose time complexity does not contain a Θ (n) term. [ABSTRACT FROM AUTHOR]

Abstract  In this paper exact, analytical solutions are derived for another highly popular benchmark problem, namely, L-shaped domains having a horizontal line support and one or several point loads. The optimal topologies are obtained in the context of Michell structures, i.e., least-weight, stress, or compliance-controlled trusses with a single load condition. [ABSTRACT FROM AUTHOR]

In the last decade, the Poincaré conjecture has probably been the most famous statement among all the contributions of Poincaré to the mathematics community. There have been many papers and books that describe various attempts and the final works of Perelman leading to a positive solution to the conjecture, but the evolution of Poincaré's works leading to this conjecture has not been carefully discussed or described, and some other historical aspects about it have not been addressed either. For example, one question is how it fits into the overall work of Poincaré in topology, and what are some other related questions that he had raised. Since Poincaré did not state the Poincaré conjecture as a conjecture but rather raised it as a question, one natural question is why he did this. In order to address these issues, in this paper, we examine Poincaré's works in topology in the framework of classifying manifolds through numerical and algebraic invariants. Consequently, we also provide a full history of the formulation of the Poincaré conjecture which is richer than what is usually described and accepted and hence gain a better understanding of overall works of Poincaré in topology. In addition, this analysis clarifies a puzzling question on the relation between Poincaré's stated motivations for topology and the Poincaré conjecture. [ABSTRACT FROM AUTHOR]

Disjoint paths are defined as paths between the source and destination nodes where the intermediate nodes in any two paths are disjoint. They are helpful in fault-tolerance routing and securing message distribution in the network. Several research papers were proposed to solve the problem of finding disjoint paths for a variety of interconnection networks such as Hypercube, Generalized Hypercube, Mesh, Torus, Gaussian, Eisenstein–Jacobi, and many other topologies. In this research, we have developed a general algorithm that constructs maximal node-to-node disjoint paths for symmetric networks where all paths are shortest. The algorithm presented in this paper outperforms other algorithms in finding not only the disjoint paths but shortest and maximal disjoint paths with a complexity of O (n 2) . In addition, we have simulated the proposed algorithm on different networks. The solution of unsolved problem in Cube-Connected-Cycles is given in the simulation results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the well-posedness and asymptotic behavior of solutions for the following extensible beam equation with non-local energy damping u tt + Δ 2 u - κ ϕ (‖ ∇ u ‖ 2 ) Δ u - φ (‖ Δ u ‖ 2 + ‖ u t ‖ 2) Δ u t + f (u) = h. More specifically, this is a complementary work to the paper by Sun and Yang (Discrete Contin Dyn Syst Ser B 27(6):3101–3129, 2022), where the authors consider this model assuming the hypothesis that φ ∈ C 1 (R +) with non-degenerate condition φ (s) > 0 , s ∈ R + . They prove the existence of strong global and exponential attractors and their robustness on the perturbed extensibility parameter κ . In this paper assuming φ (s) ⪆ γ s q which contemplates the degenerate condition φ (0) = 0 , we prove the existence of weak and regular solutions to the problem proposed and employing the method given in Temam (Springer-Verlag, New York, 1998) we show that the dynamic system (X , S t) given by the weak solutions of the problem has a compact global attractor in the weak topology of the phase space X. This class of nonlinear beams arising in connection with models for flight structures with non-local energy damping is proposed by Balakrishnan and Taylor (Proceedings Damping 89, Flight Dynamics Lab and Air Force Wright Aeronautical Labs, WPAFB, 1989). [ABSTRACT FROM AUTHOR]

Topology and Orchestration Specification for Cloud Applications (TOSCA) is an OASIS standard for specifying the topology of cloud applications, their deployment on physical or virtual cloud resources, and their orchestration. In recent years, the cloud research community has shown significant interest in TOSCA, leading to an increasing number of related publications. Such publications address a wide-ranging set of topics around TOSCA, e.g., devise sophisticated cloud orchestration methodologies using TOSCA, extend the language of TOSCA, or present tools for manipulating TOSCA models. To help researchers and practitioners overview this multifaceted area of research, this paper presents the results of a systematic survey of the relevant literature. We have processed over 120 papers and categorized them, leading to a taxonomy with 6 categories and 19 subcategories. The analysis of the results reveals several notable tendencies, as well as areas requiring future research. [ABSTRACT FROM AUTHOR]

Topological properties of the co-authorship graph are considered as applied to the physical studies in Russia for 2012–2018. Objects of the study are two various weighted graphs; in the first one, edge weights correspond to the number of joint papers of two researchers; in the second one, weights are calculated by the technique accounting for the quality of journals in which joint papers are published. Based on an analysis of the PageRank centrality vector, it was shown that ranking of authors in the data of two graphs differs significantly. However, preferentially regularly published researchers annually become leaders in both graphs. [ABSTRACT FROM AUTHOR]

Deep learning has been recently used to extract the relevant features for representing input data also in the unsupervised setting. However, state-of-the-art techniques focus mostly on algorithmic efficiency and accuracy rather than mimicking the input manifold. On the contrary, competitive learning is a powerful tool for replicating the input distribution topology. It is cognitive/biologically inspired as it is founded on Hebbian learning, a neuropsychological theory claiming that neurons can increase their specialization by competing for the right to respond to/represent a subset of the input data. This paper introduces a novel perspective by combining these two techniques: unsupervised gradient-based and competitive learning. The theory is based on the intuition that neural networks can learn topological structures by working directly on the transpose of the input matrix. At this purpose, the vanilla competitive layer and its dual are presented. The former is representative of a standard competitive layer for deep clustering, while the latter is trained on the transposed matrix. The equivalence of the layers is extensively proven both theoretically and experimentally. The dual competitive layer has better properties. Unlike the vanilla layer, it directly outputs the prototypes of the data inputs, while still allowing learning by backpropagation. More importantly, this paper proves theoretically that the dual layer is better suited for handling high-dimensional data (e.g., for biological applications), because the estimation of the weights is driven by a constraining subspace which does not depend on the input dimensionality, but only on the dataset cardinality. This paper has introduced a novel approach for unsupervised gradient-based competitive learning. This approach is very promising both in the case of small datasets of high-dimensional data and for better exploiting the advantages of a deep architecture: the dual layer perfectly integrates with the deep layers. A theoretical justification is also given by using the analysis of the gradient flow for both vanilla and dual layers. [ABSTRACT FROM AUTHOR]

An ideal I of Q [ x 1 , ⋯ , x n ] is said to be m-absorbing if any monomial of total degree p > m belongs to I and if there is a monomial M of total degree m such that M ∉ I. Inspired by the fundamental work of Lechuga and Murillo (Topology 39:89–94, 2000) who established a connection between graph theory and rational homotopy theory, these paper aims to characterise the m-absorbing ideals of Q [ x 1 , ⋯ , x n ] generated by a family of complete homogeneous symmetric polynomials of the form P rs (k) = ∑ t = 1 k x r k - t x s t - 1 , where k ≥ 3. [ABSTRACT FROM AUTHOR]

Clones of operations of arity ω (referred to as ω -operations) have been employed by Neumann to represent varieties of infinitary algebras defined by operations of at most arity ω . More recently, clone algebras have been introduced to study clones of functions, including ω -operations, within the framework of one-sorted universal algebra. Additionally, polymorphisms of arity ω , which are ω -operations preserving the relations of a given first-order structure, have recently been used to establish model theory results with applications in the field of complexity of CSP problems. In this paper, we undertake a topological and algebraic study of polymorphisms of arity ω and their corresponding invariant relations. Given a Boolean ideal X on the set A ω , we endow the set of ω -operations on A with a topology, which we refer to as X-topology. Notably, the topology of pointwise convergence can be retrieved as a special case of this approach. Polymorphisms and invariant relations are then defined parametrically with respect to the X-topology. We characterise the X-closed clones of ω -operations in terms of Pol ω - Inv ω and present a method to relate Inv ω - Pol ω to the classical (finitary) Inv - Pol . [ABSTRACT FROM AUTHOR]

The fundamental principle of satellite/node-based positioning involves triangulating the receiver's coordinates through the intersection of spatial distances. Advancements in hybrid wireless networks have yielded high-precision positioning at decimeter-level (wavelength-level), approaching the resolution limits in free space. Here we present a 3D super-resolution positioning paradigm in free space by utilizing a kind of topologically structured pulses, toroidal electromagnetic pulses. We demonstrate that the space-time nonseparability and skyrmion topology inherent in toroidal pulses can be harnessed to achieve freespace microwave 3D positioning with super-resolution accuracy, reaching the centimeter level, using a single emitting antenna. This work opens up avenues for exploring the potential applications of topological electromagnetic pulses including but not limited to positioning, imaging and sensing technologies. This paper presents a positioning paradigm in free space by utilizing toroidal electromagnetic pulses. The space-time nonseparability and skyrmion topology inherent in toroidal pulses are harnessed to achieve freespace microwave 3D positioning with super-resolution accuracy, reaching the centimeter level, using a single emitting antenna. [ABSTRACT FROM AUTHOR]

Wind power DC collection system, as a crucial component of wind farms, plays a vital role in ensuring the safe and stable operation of the entire wind farm. This paper proposes a reliability assessment method for wind power DC collection systems based on MLFTA-SMC. Firstly, it analyzes the topology and key equipment of wind power DC collection systems. Secondly, based on the topology of different wind power DC collection systems, it constructs multi-level fault tree models to calculate the comprehensive importance of different events, thus providing data support for subsequent reliability assessment. Then, it utilizes the MLFTA-SMC method to assess and analyze the reliability of different wind power DC collection system topologies. Finally, taking a 100 MW wind farm in Northwest China as an example, the proposed reliability assessment method is verified through simulation. The results indicate that this method exhibits good effectiveness and superiority. [ABSTRACT FROM AUTHOR]

Modern computing infrastructures are evolving due to virtualisation, especially with the advent of 5G and future technologies. While this transition offers numerous benefits, it also presents challenges. Consequently, understanding these complex systems, including networks, services, and their interconnections, is crucial. This paper introduces ServiceNet, a groundbreaking architecture that accurately performs the important task of providing understanding of a multi-tenant architecture by discovering the complete topology, crucial in the realm of high-performance distributed computing. Experimental results have been carried out in different scenarios in order to validate our approach, demonstrating the effectiveness of our approach in comprehensive multi-tenant topology discovery. The experiments, involving up to forty tenant, highlight the adaptability of ServiceNet as a valuable tool for real-time monitoring in topology discovery purposes, even in challenging scenarios. [ABSTRACT FROM AUTHOR]

In skeleton-based action recognition, graph convolution networks have been widely applied and very successful. However, because graph convolution is a local operation with a small field of perception, it cannot investigate well for the connections between joints that are far apart in the skeleton graph. In addition, graph convolution makes all channels share the same adjacency matrix, which causes the topology learned to be the same among different channels, which limits the ability of graph convolution to learn topological information. In this paper, we propose an enhanced decoupling graph convolution network that effectively expands the perceptual field of the graph convolution by adding additional graphs, and the decoupled feature fusion mechanism increases its expressive power. In addition, we introduce an attention mechanism in the model to obtain the important elements in the whole feature map from both spatial and temporal dimensions simultaneously, so that the graph convolution can focus on the important elements more precisely and efficiently and suppress the influence of irrelevant elements on the model performance. To validate the effectiveness and advancedness of the proposed model, we conducted extensive experiments on three large datasets: NTU RGB+D 60, NTU RGB+D120 and Northwestern-UCLA. On the NTU RGB+D 60 dataset, the accuracy of our model archieves 91.6% and 96.5% on the two protocols. [ABSTRACT FROM AUTHOR]

Community detection is a crucial aspect in network analysis. Real-world networks are often enriched with attributes providing extensive information for nodes beyond mere topology. Integrating these nodal attributes into community detection for attributed networks poses notable challenges and remains an active research field. In this paper, we propose a novel method that incorporates structural information into fused attributes. This is achieved by defining a fusion similarity between nodes, which is a convex combination of topology similarity, pairwise attribute similarity, and attribute similarity with their immediate neighbors. One advantage of the proposed method is its flexibility in identifying communities in disassortative networks, where nodes exhibit more connections between different groups than within their own group. We employ an iterative spectral clustering technique to discover communities and assess the influence of various attributes within these communities. Our experimental results validate the effectiveness of this approach, demonstrating its utility in leveraging node attributes in diverse simulated and real-world network datasets. [ABSTRACT FROM AUTHOR]

There is a well-known variety of contact paradoxes which are significantly linked to topology. The aim of this paper is to present a new paradox concerning contact with bodies composed of a denumerable infinity of parts. This paradox establishes the logical necessity, in a Newtonian context, of contact forces (herein called "phantom forces") that violate what is probably our most basic causal intuition, embodied in what I call the Principle of Influence: any force exerted on a body B induces (causes) change of movement of B or (inclusive disjunction) the emergence of internal forces in B. However, the above paradox can be made strictly compatible with a Newtonian framework by introducing phantom forces as ideal elements in the Hilbert sense, though it will be seen that this does not solve all the problems. [ABSTRACT FROM AUTHOR]

Sokół and Lewiñski (Struct Multidisc Optim 42:835-853, Sokół and Lewiñski ) published a paper on Michell trusses for three forces in the plane, with an application to a class of symmetric trusses. Vazquez Espi and Cervera Bravo () have written a Discussion on the above paper, which was replied by Sokół and Lewiñski (). In the current Discussion, some comments on the above exchange are offered, because it involves some fundamental issues of topology optimization. [ABSTRACT FROM AUTHOR]

Sigmund's 2001 educational paper with a self-contained 99-line MATLAB code had far-reaching impact to teaching and research of topology optimization. This brief note aims to close the gaps on self-contained content desirable for classroom teaching. The goal is to add clarity to the theoretical foundation, and to enable students' learning of the complete iterative optimization solution with minimum additional effort. [ABSTRACT FROM AUTHOR]

Single-phase converters are commonly used in small and medium power supply systems, but their inherent 2ω-ripple power has a significant impact on system performance, including maximum power point fluctuations in photovoltaic systems, low-frequency light flicker in light-emitting diode lighting systems, and the efficiency and lifetime of fuel cell systems. In this paper, we review the single-phase converter topologies with 2ω-ripple suppress and provide a comprehensive summary and comparison of power decoupling topologies. Power decoupling topology can be divided into passive power decoupling topology (PPDT) and active power decoupling topology (APDT). Among them, the PPDT does not need to add switching devices and has simple structure and convenient control. However, due to the volume and life of the energy storage element, the application place is also limited. The APDT needs to add an active power buffer to suppress the 2ω-ripple power. According to the different working modes of the active power buffer switch, the APDT can be divided into independent APDT and dependent APDT. The former operates independently in the original converter, while the latter needs to share switching devices or energy storage elements with the original converter. This paper systematically summarizes the existing single-phase converter circuit topologies for suppressing 2ω-ripple and their development process, aiming to provide classification and comparison for researchers and engineers to select the circuit topologies suitable for their specific applications. [ABSTRACT FROM AUTHOR]

A procedure for simultaneous topology, shape, and sizing optimization of tall pinned guyed masts is presented in the paper, seeking the minimal total mass of the mast structure including guys. The typical schemes of tall telecommunication masts of four different heights with different antenna areas distributed in the top 15% of the mast height that is triangular in plan and supported by two to four guys' clusters are examined. The mast structure is optimized for self-weight and wind loading evaluated according to Eurocodes. Since the non-gradient stochastic optimization algorithm requiring thousands of problem solutions is used, the non-linear behaviour of the guyed mast is mimicked by a suggested approximate linear analysis procedure. The optimization constraints involve all strength, local, and global stability requirements. Analysis of the optimization results leads to the following most important findings: at equal conditions of the mast scheme, a higher number of guys' clusters always reduces the mast mass; in case of four guys' clusters levels the anchoring points of the top and the next-to-last level guys should be superposed. Also, the optimal ranges of pre-stresses in guys of different levels, their inclination angles, and the ratios of spans between guys' levels are provided. [ABSTRACT FROM AUTHOR]

The escalating demand for heat dissipation has prompted considerable interest in the manifold micro-pin–fin heat sink (MMPFHS) as a promising solution for high heat flux cooling applications. The two-dimensional topology of this multi-layered heat sink plays a pivotal role in organizing the three-dimensional spatial flow, consequently influencing both hydraulic and thermal performance. This study proposes and comparatively analyzes the only three rhombus-based tiling topologies applicable to MMPFHS, specifically the rhombus topology (RT), triangle hexies topology (THT), and firecracker topology (FT), all of which adhere to the principles of gapless, non-overlapping, and spatially expandable tiling topology. The relations of topological geometry and the hydraulic and thermal performances are explored and compared. And figure of merit (FOM) is also introduced to assess their overall performance. The results indicate that the overall performance of THT is predominant. When DPF = 100 μm, a = 200 μm, Din = 50, Re = 64.87, the temperature non-uniformity on the heating surface of THT is only 0.022 K, the thermal resistance is 9.4 × 10–6 km2 W−1, and the FOM of THT is about 1.14 times of that of RT. RT and FT have a similar performance, and the maximum deviation of FOM for both of them within the conditions studied in this paper is only 0.04. The paper provides a reference for selecting topologies in MMPFHS design. [ABSTRACT FROM AUTHOR]

This paper presents a unique five-level inverter consisting of one DC voltage source and one capacitor. Here the capacitor acts like another source and is fed to the inverter along with the DC voltage source. The DC voltage source is also used to charge the capacitor with the help of an additional switch used inside the converter circuit. An inductor is used in the charging path to reduce the peak of the charging current. The in-phase disposition sinusoidal pulse-width modulation technique is used to generate the gate pulse for the devices of the presented converter. The proposed topology operates in two modes. One is energy stored mode and another is energy release mode. By using both modes of operation, the additional switch is triggered to charge the capacitor. The capacitor's charging and discharging mode and inverter power loss have been described thoroughly in this paper. The proposed five-level inverter topology has been developed and verified inside the laboratory. The controller of the converter has been implemented in the FPGA platform. The experimental results are obtained to evaluate the efficacy of the proposed inverter. [ABSTRACT FROM AUTHOR]

In this paper, considering L being a GL-quantale, we further develop the theory of L-valued rough sets with an L-set as the basic universe of defining L-valued rough approximation operators. Choosing an L-set as the universe can break the rules of adopting Zadeh's fuzzy sets as the universe. We first introduce three types of L-valued relations on L-sets, namely, inverse serial, mediate, Euclidean, and then characterize them by L-valued rough sets. Adopting the idea of single axiomatic characterizations of L-valued rough sets, we present the axiomatical characterizations of L-valued upper and lower rough approximation operators on an L-set concerning these new L-valued relations by fuzzy unions and fuzzy intersections. Moreover, in the framework of category, we introduce the concepts of L-valued Alexander co-topological spaces and L-valued closure spaces on L-sets by fuzzy unions and fuzzy intersections, then prove they are category isomorphic. By fuzzy unions, we obtain a simplified axiomatic system of the L-valued closure spaces, which highlights the advantages of fuzzy unions. Finally, we obtain the category of L-valued Alexander co-topological spaces and their continuous mappings is isomorphic to the category of L-valued preordered approximation spaces and their order-preserving mappings. [ABSTRACT FROM AUTHOR]

One of the most simple facts of combinatorial topology is that the subposet P n , k m = { A ⊆ [ m ] : 1 ≤ k ≤ card (A) ≤ n < m } of B m is homotopy equivalent to a wedge of spheres. In this paper, we determine the homotopy type of an other subposet C m , n of B m induced by 'tight' n-subset of [m]. As we will see, this complex is precisely the neighborhood complex of the circular complete graphs K p q for the right choice of parameters. Finally, we investigate the power of Lovász's lower bound for the chromatic number of the graph K p q using this result. [ABSTRACT FROM AUTHOR]

With the development of the economy, the demand for heavy-duty transportation vehicles is increasing. Due to the limitations of national standards and regulations, and the market's requirements for the reliability and economy of the whole vehicle, it is urgent to optimize the structure of each part of the heavy-duty transportation vehicle. In this paper, the sub-frame of a certain type of cement mixer truck is taken as an example. Firstly, the finite element analysis method is used to find the structural defects of the existing products through static analysis and modal analysis of the existing products under full-load condition. Then, the density method is used to carry out topology optimization design of the existing sub-frame structure, and the optimized frame is checked. The conclusion is expected to provide a theoretical basis for the lightweight design of heavy transport vehicles. [ABSTRACT FROM AUTHOR]

In this review paper we summarize a recent progress on the problem of describing range of dynamics supported by a network. We show that there is natural connection between network models consisting of collections of multivalued monotone boolean functions and ordinary differential equations models. We show how to construct such collections and use them to answer questions about prevalence of cellular phenotypes that correspond to equilibria of network models. [ABSTRACT FROM AUTHOR]

A tunable active-noise-control (ANC) circuit topology for headsets used in different applications is presented in this article. In the current consumer headset market, ANC is a mature technology that is commonly applied to wireless headsets connected to smartphones for listening to music and making phone calls. The development of ANC headsets has resulted in low-cost and simple devices due to the built-in ANC registers in the digital circuit. Digital circuit implementation is important to provide ultra-low latency processing for different algorithms compared with using digital signal processors (DSPs). However, a limitation associated with these built-in ANC filters is that the ANC digital circuit has been designed only for the wireless headset consumer market. Consequently, ANC headsets can only be used for designated features. ANC tuned for planes by eliminating low-frequency engine noise has been commonly used in the past twenty years. Pass-through (PT) amplification is also commonly tuned to allow users to hear external sounds and have conversations without having to remove their headset. In addition, ANC and PT amplification are also not allowed to operate simultaneously on the existing chipsets. In this paper, an ANC circuit topology with ultra-low latency processing is presented, where the ANC response of the headset can be tuned without any restriction imposed by the built-in ANC filters. The proposed ANC circuit topology consists of a commercial ANC chipset with an external audio codec to provide tunable characteristics. It is achieved by fixed maximum noise cancellation of ANC chipset being modified by summing with the signal from audio-codec path via an audio mixer. Acoustic performance for several headset applications implemented using the proposed circuit is validated. This simple circuit topology can be easily developed and adapted to the current headset consumer market for consumer-selective ANC in different environments. [ABSTRACT FROM AUTHOR]

This paper proposes a normalized compensation method for voltage nonlinearity of the three-level active neutral point clamped (3L ANPC) inverter. The operation of the 3L ANPC inverter includes the voltage nonlinearity caused by voltage errors, which are induced by the nonlinear components of switching devices and their operations. Since this voltage nonlinearity seriously distorts the phase current, it must be compensated to improve the quality of power conversion. For the 3L ANPC inverter, however, the voltage nonlinearity varies depending on the topology and modulation scheme, as well as the power factor of the system. Although many conventional methods have been proposed, these methods do not fully deal with the factors affecting the voltage nonlinearity. In this paper, a normalized compensation method for the voltage nonlinearity considering the characteristics of the 3L ANPC inverter and the power factor of the system is proposed. Two general topologies and modulation schemes of the 3L ANPC inverter are discussed in this paper, and the voltage nonlinearity is analyzed to derive the compensation components. By executing the compensation based on these analyses, the proposed method ensures its performance remains consistent across operating conditions, and is simply implemented. The effectiveness of the proposed method is verified by experimental results. [ABSTRACT FROM AUTHOR]

In this paper, new purely topological approaches are furnished in order to characterize self-majorizing elements in an Archimedean vector lattice A. More precisely, it is shown that an element 0 < f ∈ A is a self-majorizing element if and only if every f-maximal order ideal of A is relatively uniformly closed. In addition, it is proved that self-majorizing elements are characterized via the hull–kernel topology on both the set of all proper prime order ideals P and on the set of all g-maximal order ideals Q of A, for all g ∈ A +. In fact, the set of all prime order ideals of A not containing f (respectively, the set of all g-maximal order ideals of A not containing f, for all g ∈ A +) is a closed with respect to the hull–kernel topology on P (respectively, on Q) if and only if f is a self-majorizing element in A. [ABSTRACT FROM AUTHOR]

This paper presents a novel topology for Z-source inverters (ZSI). The new Z-Source network is based on the coupled-inductors and active switched boost. Features of the topology include high voltage boost ability, single magnetic-core, low voltage stress on the active switch, and capacitors. The principles of operation, analysis, voltage and current equations of each component, and the converter voltage gain in the steady-state are presented. A comparison with other topologies has also been performed to determine the advantages and disadvantages of the proposed ZSI. Finally, experimental results of the laboratory prototype are presented to confirm the performance of the proposed topology. [ABSTRACT FROM AUTHOR]

The Delaunay triangulation of a set of points P on a hyperbolic surface is the projection of the Delaunay triangulation of the set P ~ of lifted points in the hyperbolic plane. Since P ~ is infinite, the algorithms to compute Delaunay triangulations in the plane do not generalize naturally. Using a Dirichlet domain, we exhibit a finite set of points that captures the full triangulation. We prove that an edge of a Delaunay triangulation has a combinatorial length (a notion we define in the paper) smaller than 12 g - 6 with respect to a Dirichlet domain. To achieve this, we introduce new tools, of intrinsic interest, that capture the properties of length-minimizing curves in the context of closed curves. We then use these to derive structural results on Delaunay triangulations and exhibit certain distance minimizing properties of both the edges of a Delaunay triangulation and of a Dirichlet domain. The bounds produced in this paper depend only on the topology of the surface. They provide mathematical foundations for hyperbolic analogs of the algorithms to compute periodic Delaunay triangulations in Euclidean space. [ABSTRACT FROM AUTHOR]

Two-dimensional materials with unique properties have received much attention in recent years. Current research is exploring their potential applications in various fields. Acoustic topological insulators have been an emerging branch in the field of acoustic metamaterials in recent years. Its strong unidirectional transmission capability has potential applications in acoustic sensors, filters, and beamwaves. However, to realize a wide range of applications of acoustic topological materials, it is necessary to solve the problems of multi-band and wide bandgap. To this end, this paper proposes a jointly resonant acoustic topological insulator structure. The structure achieves multi-band filtering, and three filterable bandgaps can be obtained below 6200 Hz. Meanwhile, the total width of the three filterable bandgaps accounts for 65.5% at 6200 Hz and below. In this paper, the band structure is obtained by using the method of finite element simulation. The generation of topological phase transition induced by the rotation angle of the scatterer is analyzed. The pseudo-spin case of the valley hall effect is also analyzed from the point of view of acoustic energy flow, and the existence of edge states is verified. Finally, the unidirectional transport properties possessing backward scattering immunity are verified. The multi-band structure with a great bandwidth means that this work will have great potential for applications in filters. Also, since acoustic topologies based on the Valley hall effect do not possess strong defect immunity, this work proposes to utilize defect states as acoustic switches. [ABSTRACT FROM AUTHOR]

This paper highlights the incentives of individuals to add or sever links in shaping stable and efficient networks when the society is partitioned into groups. In terms of the group partitioning, the players may unequally pay for the link connecting them. To be precise, the cost a player pays for her direct connection is determined by the composition of her neighborhood. In particular, the more members of a group the player has in her neighborhood, the less the average cost of a link is within this group. The main contributions of our paper lie in a detailed analysis of conditions under which particular network configurations—complete network, majority complete network, and complete bipartite network—achieve stability and unique efficiency. The paper examines the impact of the distribution of players across different groups on the stability and efficiency of these networks. We prove that majority complete networks can never be uniquely efficient when there is an equal number of players between two groups, but if they are efficient, the other two types of structures also attain efficiency. Moreover, under certain distributions of players, the unique stability of majority complete networks implies their unique efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we prove the multiplicity and concentration behavior of complex-valued solutions for the following Kirchhoff–Schrödinger equation with magnetic field - (a ε 2 + b ε [ u ] A / ε 2) Δ A / ε u + V (x) u = f (| u | 2) u , x ∈ R 2 , where ε > 0 is a small parameter, the nonlinearity f is involved in critical exponential growth in the sense of Trudinger–Moser inequality and both V : R 2 → R and A : R 2 → R 2 are continuous potential and magnetic potential, respectively. Imposing a local constraint of potential V(x) first introduced from del Pino and Felmer, we get the multiplicity of solutions by way of the relationship between the number of the solutions and the topology of the set with V attaining the minimum. Our strategy of main proof is based on the variational methods combined with the penalization technique, the Trudinger–Moser inequality and Ljusternik–Schnirelmann theory, and our result is still new even without magnetic effect. [ABSTRACT FROM AUTHOR]

The paper presents a fault region identification method for the active distribution network (ADN) with limited PMU. First, PMU configuration and region division strategies are proposed based on the network topology. Next, the difference in three-phase current variations between the normal and fault regions of the ADN is analyzed. A multi-dimensional state monitoring matrix is built using the measured current data. The spectral norm ratio coefficient is constructed based on the 2-norm to lower the complexity of the multi-dimensional state monitoring matrix and quantify the difference in state changes before and after the fault occurs in each region. Then, the fault region is identified by combining each region's spectral norm ratio coefficient and the change of the current phase. Finally, an IEEE 33-node simulation model is created to simulate faults under different working conditions. According to the simulation results, the suggested approach is less impacted by fault type, neutral point grounding mode, and transition resistance. Furthermore, even if the communication does not match the rigorous synchronization requirements, the proposed method can still complete the fault identification of the distribution network correctly and has high robustness. [ABSTRACT FROM AUTHOR]

Topological properties of the coauthorship graph are considered as applied to studies on physical sciences in Russia for 2012—2018. It was shown that key global properties of the coauthorship graph are formed by publications with a relatively small number of authors. Based on the analysis of characteristics of the distributions of degrees and weighted vertex degrees, it was shown that the weighted graph with edge weights equal to the fractional number most accurately describes the main features of the interaction of researchers in this field. [ABSTRACT FROM AUTHOR]

In real path selection decisions, besides the cost of the path which is the major decision factor, the chance of the path connection is also significant. A path which has low weight but low chance of existence is not a good choice for decision-making. In order to make network optimization more in line with the actual situation, this paper studies one model of it on a network whose existence and weight of edges are both indeterminate. The aim of this paper is to obtain a spanning tree which satisfies the connectivity constraint and minimizes the total weight as well. The study uses conditional uncertain variable to describe the relationship between these two aspects of uncertain variables. On this basis, three different models of the UMST problem are suggested, and the equivalence relation between the MST model of uncertain networks with uncertain edge existence and weight and the MST of related deterministic networks is found. Examples of experiments with specific numerical values are provided to verify the variation in the network when two variables are considered simultaneously. [ABSTRACT FROM AUTHOR]

This paper investigates the structural, elastic, radiation, and optical properties of Orthosilicate-based crystals (OSMs). Through comprehensive analyses of molar volumes, densities, band gap values and effective atomic numbers, it offers insights into the intricate relationship between these parameters and the physical behavior of OSMs. The structural and elastic properties were found to depend on the space group and crystal system while correlate well with the interatomic interactions gained for the analysis of Hirshfeld surfaces (HSs) and voids. Also, the study encompassing a broad energy spectrum from 0.015–15 MeV, the focus centers on mass and linear attenuation coefficients (MAC and LAC). Results elucidate the unique shielding behavior of various OSMs against γ-rays. At an intermediate energy of E = 0.05 MeV, SiO4 exhibits a MAC value of 0.282. On the other hand, OSMs materials, including CoSiO4 (1.01), K4SiO4 (0.651), CuSiO4 (1.234), MgSiO4 (0.292), MnSiO4 (0.817), and Eu2SiO4 (14.26) g/cm2, displays distinct MAC values. Effective atomic numbers (Zeff) range from 13.96 to 59.15, surpassing those of SiO4 and underscoring the superior γ-ray attenuation capabilities of OSMs. The study pinned out the elastic constant modeled by bulk (48.13 < B < 164.68 GPa) and shear (29.33 < S < 71.96 GPa) moduli depending on the crystal's density (1.982 to 6.79 g/cm3) and its crystal system and space group. The least bulk modulus found for K4SiO4, while the maximum attained by Eu2SiO4 crystal with monoclinic and P121/c1 symmetry. The study delves into the optical features, revealing the intricate interplay of density, band gap energy, and refractive index. As density increases, band gap energy decreases (0.216 eV to 3.630 eV), and refractive index varies (2.24539 to 5.18338). Additionally, the investigation explores Hirshfeld topological surfaces, and their voids unveiling distinct electron density distribution characteristics in OSM materials. The study also probes the impact of charge density within Hirshfeld voids on structural, elastic, optical and radiation shielding values, showing that increased O...A (A = Co, K4, Cu, Mg, Mn, Eu2) interactions align with higher charge density, potentially tuning these physical values. The fine-tuning of topological volumes, surface and the interatomic interaction via HSs distributions within crystal voids emerges as a promising avenue to optimize these materials for enhanced radiation properties. In summary, this research enhances our understanding of OSM's potential in structural, elastic, radiation shielding and optical applications, emphasizing the interplay of crystal structure, composition, and Hirshfeld topological constraints as pivotal factors shaping their crystal capabilities. [ABSTRACT FROM AUTHOR]

The main goal of this paper is the study of the Boolean algebra of all characteristic elements in a unital ℓ -group and we investigate some topological properties of it in the case that the unital ℓ -group equipped with a link or positive filter topology. We also introduce the concept of Boolean region as a subset of a unital ℓ -group. [ABSTRACT FROM AUTHOR]

Current low-light enhancement algorithms fail to suppress noise when enhancing brightness, and may introduces structural distortion and color distortion caused by halos or artifacts. This paper proposes a content-illumination coupling guided low-light image enhancement network (CICGNet), it develops a truss topology based on Retinex as backbone to decompose low-light image component in an end-to-end way. The preservation of content features and the enhancement of illumination features are carried out along with depth and width direction of the truss topology. Each submodule uses the same resolution input and output to avoid the introduction of noise. Illumination component prevents misestimation of global and local illumination by using pre- and post-activation features at different depth levels, this way could avoid possible halos and artifacts. The network progressively enhances the illumination component and maintains the content component stage-by-stage. The proposed algorithm demonstrates better performance compared with advanced attention-based low-light enhancement algorithms and state-of-the-art image restoration algorithms. We also perform extensive ablation studies and demonstrate the impact of low-light enhancement algorithm on the downstream task of computer vision. Code is available at: https://github.com/Ruini94/CICGNet. [ABSTRACT FROM AUTHOR]

A well-known open problem on the behavior of optimal paths in random graphs in the strong disorder regime, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade (Braunstein et al. in Phys Rev Lett 91(16):168701, 2003; Braunstein et al. in Int J Bifurc Chaos 17(07):2215–2255, 2007; Chen et al. in Phys Rev Lett 96(6):068702, 2006; Wu et al. in Phys Rev Lett 96(14):148702, 2006) is as follows: for a large class of random graph models with degree exponent τ ∈ (3 , 4) , distances in the minimal spanning tree (MST) on the giant component in the supercritical regime scale like n (τ - 3) / (τ - 1) . The aim of this paper is to make progress towards a proof of this conjecture. We consider a supercritical inhomogeneous random graph model with degree exponent τ ∈ (3 , 4) that is closely related to Aldous's multiplicative coalescent, and show that the MST constructed by assigning i.i.d. continuous weights to the edges in its giant component, endowed with the tree distance scaled by n - (τ - 3) / (τ - 1) , converges in distribution with respect to the Gromov–Hausdorff topology to a random compact real tree. Further, almost surely, every point in this limiting space either has degree one (leaf), or two, or infinity (hub), both the set of leaves and the set of hubs are dense in this space, and the Minkowski dimension of this space equals (τ - 1) / (τ - 3) . The multiplicative coalescent, in an asymptotic sense, describes the evolution of the component sizes of various near-critical random graph processes. We expect the limiting spaces in this paper to be the candidates for the scaling limit of the MST constructed for a wide array of other heavy-tailed random graph models. [ABSTRACT FROM AUTHOR]

The optimal selection of pinning nodes for multi-agent flocking is a challenging NP-hard problem. Current pinning node selection strategies mainly rely on centrality measures of complex networks, which lack rigorous mathematical proof for effective flocking control. This paper proposes a pinning node selection strategy based on matrix eigenvalue theory. First, the effect of the pinning node on the eigenvalue of the Laplacian matrix is analyzed. Then, a synchronization index representing the topology uniformity of the multi-agent system is proposed to exert maximum influence on the system synchronizability. A practical optimal pinning node selection method based on the synchronization index is proposed and analyzed using the eigenvalue perturbation method. Finally, simulations demonstrate that the convergence rate of the system obtained using the optimal synchronizability pinning node selection method is better than that achieved with the maximum degree centrality node selection strategy. [ABSTRACT FROM AUTHOR]