Topological Conditions Research Articles

AFM-IR study of interfacial nanostructures in high-temperature dilute nanocomposites

The dilute nanocomposite strategy facilitates a promising route for high-temperature polymer dielectrics to achieve high dielectric constant and energy density, robust breakdown strength, and low loss. The dielectric enhancement of the dilute nanocomposites strongly ties to the topological conditions of the nanofiller–polymer interface. Here, atomic force microscopy-based infrared spectroscopy was employed to observe the interfacial region of a high-temperature poly(arylene ether urea) (PEEU) dilute nanocomposite directly. The experimental results showed that the nanoparticles induce morphological changes in PEEU, and the interface region extends over 150 nm away from the nanofiller surfaces. Such nano-morphology changes are highly indicative of generating a large enhancement of the dielectric performance in the PEEU dilute nanocomposite.

Big Mapping Class Groups and the Co-Hopfian Property

We study injective homomorphisms between big mapping class groups of infinite-type surfaces. First, we construct (uncountably many) examples of surfaces without boundary whose (pure) mapping class groups are not co-Hopfian; these are first such examples of injective endomorphisms of mapping class groups that fail to be surjective. We then prove that, subject to some topological conditions on the domain surface, any continuous injective homomorphism between (arbitrary) big mapping class groups that sends Dehn twists to Dehn twists is induced by a subsurface embedding. Finally, we explore the extent to which, in stark contrast to the finite-type case, superinjective maps between curve graphs impose no topological restrictions on the underlying surfaces.

Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds

If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. We present formulas for eigenmodes in orientable Euclidean manifolds with the topologies E 1–E 6, E 11, E 12, E 16, and E 18 that encompass the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the observed CMB sky. We find that topologies where the distance to our nearest clone is less than about 1.2 times the diameter of the last scattering surface of the CMB give a correlation signal that is larger than cosmic variance noise in the CMB. This implies that if cosmic topology is the explanation of large-angle anomalies in the CMB, then the distance to our nearest clone is not much larger than the diameter of the last scattering surface. We argue that the topological information is likely to be better preserved in three-dimensional data, such as will eventually be available from large-scale structure surveys.

Discord in the voter model for complex networks.

Online social networks have become primary means of communication. As they often exhibit undesirable effects such as hostility, polarization, or echo chambers, it is crucial to develop analytical tools that help us better understand them. In this paper we are interested in the evolution of discord in social networks. Formally, we introduce a method to calculate the probability of discord between any two agents in the multistate voter model with and without zealots. Our work applies to any directed, weighted graph with any finite number of possible opinions, allows for various update rates across agents, and does not imply any approximation. Under certain topological conditions, the opinions are independent and the joint distribution can be decoupled. Otherwise, the evolution of discord probabilities is described by a linear system of ordinary differential equations. We prove the existence of a unique equilibrium solution, which can be computed via an iterative algorithm. The classical definition of active links density is generalized to take into account long-range, weighted interactions. We illustrate our findings on real-life and synthetic networks. In particular, we investigate the impact of clustering on discord and uncover a rich landscape of varied behaviors in polarized networks. This sheds lights on the evolution of discord between, and within, antagonistic communities.

Some results regarding the ideal structure of C∗$C^*$‐algebras of étale groupoids

AbstractWe prove a sandwiching lemma for inner‐exact locally compact Hausdorff étale groupoids. Our lemma says that every ideal of the reduced ‐algebra of such a groupoid is sandwiched between the ideals associated to two uniquely defined open invariant subsets of the unit space. We obtain a bijection between ideals of the reduced ‐algebra, and triples consisting of two nested open invariant sets and an ideal in the ‐algebra of the subquotient they determine that has trivial intersection with the diagonal subalgebra and full support. We then introduce a generalisation to groupoids of Ara and Lolk's relative strong topological freeness condition for partial actions, and prove that the reduced ‐algebras of inner‐exact locally compact Hausdorff étale groupoids satisfying this condition admit an obstruction ideal in Ara and Lolk's sense.

Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems

We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topological quantum order condition. In contrast with earlier results, we do not require a positive lower bound for finite-system spectral gaps uniform in the system size. To obtain this result, we extend the Bravyi–Hastings–Michalakis strategy so it can be applied to perturbations of the GNS Hamiltonian of the infinite-system ground state.

Generalized essential spectra involving the class of g-g-Riesz operators

Abstract In this paper, we explore the spectral properties of unbounded generalized Fredholm operators acting on a non-reflexive Banach space X. The results are formulated in terms of some topological conditions made on X or on its dual X * {X^{*}} . In addition, we introduce the concept of the so-called g-g-Riesz linear operators as an extension of Riesz operators. The obtained results are used to discuss the incidence of the behavior of generalized essential spectra. Furthermore, a relation between the generalized essential spectrum and the left (resp. the right) essential spectrum by means of g-Riesz perturbation is provided.

Incomplete preferences or incomplete information? On Rationalizability in games with private values

I propose a notion of Rationalizability, called Incomplete Preference Rationalizability, for games with incomplete preferences. Under an appropriate topological condition, the incomplete preference rationalizable set is non-empty and compact. I argue that incomplete orderings can be used to model incomplete information in strategic settings. Drawing on this connection, I show that in games with private values the sets of incomplete preference rationalizable actions, of belief-free rationalizable actions (Battigalli et al., 2011; Bergemann and Morris, 2017), and of interim correlated rationalizable actions (Dekel et al., 2007) of the universal type space coincide.

Cross-Layer Methods for Ad Hoc Networks—Review and Classification

The OSI model used to be a common network model for years. In the case of ad hoc networks with dynamic topology and difficult radio communications conditions, gradual departure is happening from the classical kind of OSI network model with a clear delineation of layers (physical, channel, network, transport, application) to the cross-layer approach. The layers of the network model in ad hoc networks strongly influence each other. Thus, the cross-layer approach can improve the performance of an ad hoc network by jointly developing protocols using interaction and collaborative optimization of multiple layers. The existing cross-layer methods classification is too complicated because it is based on the whole manifold of network model layer combinations, regardless of their importance. In this work, we review ad hoc network cross-layer methods, propose a new useful classification of cross-layer methods, and show future research directions in the development of ad hoc network cross-layer methods. The proposed classification can help to simplify the goal-oriented cross-layer protocol development.

Deformations of Calabi–Yau varieties with k-liminal singularities

Abstract The goal of this paper is to describe certain nonlinear topological obstructions for the existence of first-order smoothings of mildly singular Calabi–Yau varieties of dimension at least $4$ . For nodal Calabi–Yau threefolds, a necessary and sufficient linear topological condition for the existence of a first-order smoothing was first given in [Fri86]. Subsequently, Rollenske–Thomas [RT09] generalized this picture to nodal Calabi–Yau varieties of odd dimension by finding a necessary nonlinear topological condition for the existence of a first-order smoothing. In a complementary direction, in [FL22a], the linear necessary and sufficient conditions of [Fri86] were extended to Calabi–Yau varieties in every dimension with $1$ -liminal singularities (which are exactly the ordinary double points in dimension $3$ but not in higher dimensions). In this paper, we give a common formulation of all of these previous results by establishing analogues of the nonlinear topological conditions of [RT09] for Calabi–Yau varieties with weighted homogeneous k-liminal hypersurface singularities, a broad class of singularities that includes ordinary double points in odd dimensions.

Supra v-open set and some of its properties

The idea of supra v-open set is introduced, and several different properties of supra v-open set are proven. Furthermore, the notion of supra v-space has been presented and which is satisfying the conditions of supra topology. In addition, the relations between v-open set and supra v-open set have been shown. Finally, the concept supra v-base and some of its properties were studied.

Distributed GNE Seeking Strategy for Second-Integrator Multiplayer Systems Over Directed Topologies.

This article studies the generalized Nash equilibrium (GNE) seeking problem of second-integrator multiplayer systems. In particular, each player is endowed with an individual payoff function with respect to collective decision variables, and simultaneously, a coupling inequality constraint and a set constraint are imposed to each player. The players communicate with their local neighbors over a directed topology. To begin with, a distributed-observer-based seeking strategy is synthesized by leveraging a proper composite variable. It is first demonstrated using nonsmooth analysis that the established distributed observer enables each player to accurately estimate the decision variables of others in terms of a strongly connected topology condition. Upon this basis, all the decision variables are then shown to converge to the expected GNE asymptotically borrowing from convex theory. In addition, three extension results are also given under the built GNE seeking framework. First, under the postulation that the velocity information is unavailable, a velocity-free distributed GNE seeking strategy is synthesized for second-integrator systems by implementing a proper auxiliary dynamics. Second, we consider nonlinear Euler-Lagrange systems with unknown inertia parameters and synthesize an improved distributed GNE seeking strategy resorting to an adaptation technique. Third, we focus on integrator chain systems and synthesize a modified distributed GNE seeking strategy using a new composite variable based on a proper coordinate transformation. For three extension cases, we all show in detail the achievement of the GNE seeking objective. Finally, a practical example is simulated to confirm the built GNE seeking results.

Persistent homology for functionals

We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in particular, implies that they satisfy generalized Morse inequalities. We illustrate the applicability of these results by recasting the original proof of the Unstable Minimal Surface Theorem given by Morse and Tompkins in a modern and rigorous framework.

Some rigidity results for compact initial data sets

In this paper, we prove several rigidity results for compact initial data sets, in both the boundary and no boundary cases. In particular, under natural energy, boundary, and topological conditions, we obtain a global version of the main result by Galloway and Mendes [Comm. Anal. Geom. 26 (2018), pp. 63–83]. We also obtain some extensions of results by Eichmair, Galloway, and Mendes [Comm. Math. Phys. 386 (2021), pp. 253–268]. A number of examples are given in order to illustrate some of the results presented in this paper.

A Passenger Flow Prediction Method Using SAE-GCN-BiLSTM for Urban Rail Transit

To address the problems of existing passenger flow prediction methods such as low accuracy, inadequate learning of spatial features of station topology, and inability to apply to large networks, a SAE-GCN-BiLSTM-based passenger flow forecasting method for urban rail transit is proposed. First, the external features are extracted layer by layer using stacked autoencoder (SAE). Then, graph convolutional network (GCN) is used to capture the spatial features of station topology, and bi-directional long and short-term memory network (BiLSTM) is used to extract the bi-directional temporal features, realizing the extraction of the spatio-temporal features. Finally, external features and spatio-temporal features are fused for accurate prediction of urban rail transit passenger flow. The experimental results show that the proposed method is higher than several other advanced models in the evaluation indexes under different granularities, indicating that the model effectively develops the accuracy and robustness of urban rail transit passenger flow prediction.

A Basic Design Tool for Grid-Connected AC–DC Converters Using Silcon Carbide MOSFETs

The design and optimization of power converters is a key factor in the growth and development of the power electronics field. However, the process of designing a power converter is not straightforward, and engineers often rely on experience and intuition, sometimes requiring time-consuming computer simulations. This paper presents a tool for the basic design of grid-connected AC–DC converters. The design tool takes specifications and operating conditions for two-level and three-level NPC converter topologies and derives a draft design. The tool calculates the input filter’s electrical parameters, the converter’s losses, the temperature rise of the power semiconductor devices, and the ripple current and voltage of the DC-link capacitor. In order to validate the proposed design tool, four AC–DC converters using SiC MOSFETs were designed. Based on the design results, simulation models and prototypes were fabricated to verify the performance and confirm that the proposed design tool can be used in the basic design process of converters.

DNA superhelicity.

Closing each strand of a DNA duplex upon itself fixes its linking number L. This topological condition couples together the secondary and tertiary structures of the resulting ccDNA topoisomer, a constraint that is not present in otherwise identical nicked or linear DNAs. Fixing L has a range of structural, energetic and functional consequences. Here we consider how L having different integer values (that is, different superhelicities) affects ccDNA molecules. The approaches used are primarily theoretical, and are developed from a historical perspective. In brief, processes that either relax or increase superhelicity, or repartition what is there, may either release or require free energy. The energies involved can be substantial, sufficient to influence many events, directly or indirectly. Here two examples are developed. The changes of unconstrained superhelicity that occur during nucleosome attachment and release are examined. And a simple theoretical model of superhelically driven DNA structural transitions is described that calculates equilibrium distributions for populations of identical topoisomers. This model is used to examine how these distributions change with superhelicity and other factors, and applied to analyze several situations of biological interest.

Rigidity and Non-Rigidity of $\mathbb{H}^n/\mathbb{Z}^{n-2}$ with Scalar Curvature Bounded from Below

We show that the hyperbolic manifold $\mathbb{H}^n/\mathbb{Z}^{n-2}$ is not rigid under all compactly supported deformations that preserve the scalar curvature lower bound $-n(n-1)$, and that it is rigid under deformations that are further constrained by certain topological conditions. In addition, we prove two related splitting results.

Centralized Protection of Networked Microgrids with Multi-Technology DERs

The structure and connections in networked microgrids consisting of two or more interconnected microgrids is influenced by the dynamic behaviors of power markets, the demand and supply interactions between market participants, and the possibility of operating in the grid-connected or islanded modes. Protection zones in the above-mentioned scenarios are dynamic and should not be determined a priori. Also, fault currents will vary depending on the operating modes, online or offline status of Distributed Energy Resources (DERs), variation of solar irradiation or wind speed, etc. This paper proposes a Centralized Intelligent Station-Level Protection (CISP) approach for the protection of various electric power equipment technologies in networked (interconnected) microgrids using adaptive protective relaying algorithms and a network theory-based zone selection algorithm. The proposed CISP approach utilizes wide area IEC 61869-9 Sampled Values (SVs) measurements and IEC 61850 Generic Object-Oriented Substation Events (GOOSE) messages, intelligently determines the protection zones, and automatically selects the protection algorithms to use in each of the protection zones based on the prevailing system topology and operating conditions. The effectiveness of the proposed CISP approach is demonstrated through real-time simulations using the RTDS®. The results obtained were promising for the various system configurations, operating conditions, and fault conditions considered.

A defense strategy for false data injection attacks in multi-agent systems

The issue of defense strategy for cooperative control in multi-agent systems under false data injection attacks is investigated in this paper. False data injection attacks are typical cyber-attacks, some of which can evade detection and result in system instability. A communication strategy is proposed to ensure the security of multi-agent systems. In the proposed defense strategy, each agent is assigned to transmit its state to its neighbours and extra communication edges are stochastically triggered by the designed trigger signals. Furthermore, the communication topology condition is derived to ensure the security of multi-agent systems under the defense strategy. The theoretical results are verified through numerical simulation.