Performance Of Topology Research Articles

A concrete construction of a topological operator in factorization algebras

Abstract Factorization algebras play a central role in the formulation of quantum field theories given by Kevin Costello and Owen Gwilliam. In this paper, we propose a concrete construction of a topological operator in their formulation. We focus on a shift symmetry of a one-dimensional massless scalar theory. And we give some discussions of $\mathbb {Z}$-gauging of it, i.e., compact scalar theory and its θ-vacuum.

Earthward‐Tailward Asymmetry of Plasma Temperature in Reconnection Outflow in Earth's Magnetotail

AbstractTo explore the asymmetry in ion and electron heating at Earth's magnetotail at mid‐tail distances ( −30 ), we analyze near‐simultaneous observations of reconnection outflows from two opposite sides of reconnection sites at those distances using Magnetospheric Multiscale (MMS) and Acceleration, Reconnection, Turbulence and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) data. We report a pronounced temperature asymmetry between the earthward and tailward reconnection outflows. The asymmetry is more significant for electrons than for ions: Earthward moving ions are only three times hotter than tailward ones, but earthward moving electrons are 5–20 times hotter than tailward ones. The closed field‐line topology on the earthward side of the reconnection region, as opposed to the open topology on the tailward side, is likely a critical contributor to this asymmetry. These findings cast light on the underlying mechanisms of particle heating and energization in magnetotail reconnection, highlighting the significant role of Earth's dipolar magnetic field. This study offers insights for refining magnetic reconnection models, emphasizing the importance of incorporating realistic magnetic field topologies to accurately simulate the heating and energization processes observed in space plasma environments.

Employing a Generalization of Open Sets Defined by Ideals to Initiate Novel Rough Approximation Spaces with a Chemical Application

A close similarity and analogy between rough set theory and topology is attributed to the corresponding behavior of lower and upper rough approximations with interior and closure topological operators, respectively. This relation motivates joint studies between topology and this theory. We endeavor by rough set theory to enlarge the knowledge we obtain from the information systems, for this reason, we apply the abstract concept of ideal structures to build new generalized approximation spaces with less vagueness. In the present work, we employ a novel type of nearly open sets in topology so-called ``${\mathcal{L}}$-${\theta\beta}_{\lambda}$-open" with an ideal structure to introduce novel approximation spaces satisfying the desired properties concerning shrinking the boundary region of uncertainty and expanding the domain of confirmed information. We set up the fundamentals of the proposed rough paradigms and demonstrate their superiority over the preceding paradigms induced by some nearly open sets. Two algorithms are furnished to illustrate the way of specifying the family of ${\mathcal{L}}$-${\theta\beta}_{\lambda}$-open sets and exploring whether a subset is ${\mathcal{L}}$-${\theta\beta}_{\lambda}$-definable or ${\mathcal{L}}$-${\theta\beta}_{\lambda}$-rough. Then, we put forward the concepts of rough membership relations and functions and uncover their core characterizations. Finally, we examine the proposed models to model a real situation in the Chemistry field and clarify how our models improve the outcomes of generalized approximation spaces over the previous models.

Diffeomorphisms of Foliated Manifolds I

The set $Diff(M)$ of all diffeomorphisms of manifold $M$ onto itself is the group related to composition and inverse mapping. The group of diffeomorphisms of smooth manifolds is of great importance in differential geometry and analysis. It is known that the group $Diff(M)$ is topological group in compact open topology.In this paper we investigate the group $Diff_{F}(M)$ of diffeomorphisms foliated manifold $(M,F)$ with foliated compact open topology. In this paper we prove that if all leaves of the the foliation $F$ are closed subsets of $M$ then the foliated compact open topology of the group $Diff_{F}(M)$ coincides with compact open topology. In addition it is studied the question on the dimension of the group of isometries of foliated manifold is studied when foliation generated by riemannian submersion.

Node Importance Evaluation of Urban Rail Transit Based on Signaling System Failure: A Case Study of the Nanjing Metro

Assessing the importance of nodes in urban rail transit systems helps enhance their ability to respond to emergencies and improve reliability in view of the fact that most of the existing methods for evaluating the importance of rail transit nodes ignore the disturbance effect of signaling system failures and are unable to objectively identify critical stations in specific disturbance scenarios. Therefore, this paper proposed a method for evaluating the importance of urban rail transit nodes in signaling system failure scenarios. The method was based on the research background of the signaling system failure that occurs most frequently and analyzed the network failure mechanism after the occurrence of a disturbance. The node importance evaluation indices were selected from the network topology and network operation performance in two aspects. The variation coefficient–VIKOR method was employed to comprehensively assess the significance of urban rail transit stations during signaling system failures. The Nanjing Metro network was also used as an example to evaluate the importance of network stations. The results showed that under the attack method of signaling system failure, most ECC and interlocking stations experienced significantly higher network performance losses compared to the original attack method, and a few interchange stations showed smaller performance losses. The critical stations identified based on the proposed method are mainly distributed in the passenger flow backbone of the Nanjing Metro and were constructed in the early stage; of these, 85% are ECC stations or interlocking stations, which are easily neglected in daily management, in contrast to interchange stations with heavy passenger flow. The results of this study can provide an important reference for the stable operation and sustainable construction of urban rail transit.

A multi-instrument study of UV bursts and associated surges in AR 12957

The relationship between UV bursts and solar surges is complex, with these events sometimes being observed together and sometimes being observed independently. Why this sporadic association exists is unknown; however, it likely relates to the physical conditions at the site of the energy release that drives these events. Here, we aim to better understand the relationship between UV bursts and solar surges through a multi-instrument analysis of several associated events that occurred around the trailing sunspot in AR $12957$. We used data from Solar Orbiter, the Solar Dynamics Observatory (SDO), and the Interface Region Imaging Spectrograph (IRIS) to achieve our aims. These data were sampled on 3 March 2022 between $09$:$30$:$30$ UT and $11$:$00$:$00$ UT, during which time a coordinated observing campaign associated with the Slow Solar Wind Connection Solar Orbiter Observing Plan (SOOP) took place. Numerous small-scale negative polarity magnetic magnetic features (MMFs) were observed to move quickly (potentially up to $3.3$ km s$^ $) away from a sunspot until they collided with a more stable positive polarity plage region around $7$ Mm away. Several UV bursts were identified in IRIS slit-jaw imager (SJI) $1400$ data co-spatial to where these opposite polarity fields interacted, with spatial scales ($2$ Mm$<$) and lifetimes ($20<$ minutes) larger than typical values for such events. Two surges were also observed to occur at these locations, with one being short ($5$ Mm) and hot (bright in the IRIS SJI images), whilst the other was a cooler (dark in coronal imaging channels), longer surge that appeared to fill an active region loop. Magnetic reconnection between the negative polarity MMFs around the sunspot and the positive polarity plage region appears to be the driver of these events. Both the speed of the MMFs and the locally open magnetic topology of the plage region could possibly have been important for forming the surges.

Non-degenerate metrics, hypersurface deformation algebra, non-anomalous representations and density weights in quantum gravity

Classical General Relativity is a dynamical theory of spacetime metrics of Lorentzian signature. In particular the classical metric field is nowhere degenerate in spacetime. In its initial value formulation with respect to a Cauchy surface the induced metric is of Euclidian signature and nowhere degenerate on it. It is only under this assumption of non-degeneracy of the induced metric that one can derive the hypersurface deformation algebra between the initial value constraints which is absolutely transparent from the fact that the inverse of the induced metric is needed to close the algebra. This statement is independent of the density weight that one may want to equip the spatial metric with. Accordingly, the very definition of a non-anomalous representation of the hypersurface deformation algebra in quantum gravity has to address the issue of non-degeneracy of the induced metric that is needed in the classical theory. In the Hilbert space representation employed in Loop Quantum Gravity (LQG) most emphasis has been laid to define an inverse metric operator on the dense domain of spin network states although they represent induced quantum geometries which are degenerate almost everywhere. It is no surprise that demonstration of closure of the constraint algebra on this domain meets difficulties because it is a sector of the quantum theory which is classically forbidden and which lies outside the domain of definition of the classical hypersurface deformation algebra. Various suggestions for addressing the issue such as non-standard operator topologies, dual spaces (habitats) and density weights have been proposed to address this issue with respect to the quantum dynamics of LQG. In this article we summarise these developments and argue that insisting on a dense domain of non-degenerate states within the LQG representation may provide a natural resolution of the issue thereby possibly avoiding the above mentioned non-standard constructions.

Attention-Guided and Topology-Enhanced Shift Graph Convolutional Network for Skeleton-Based Action Recognition

Graph Convolutional Networks (GCNs) have emerged as a game-changer in skeleton-based action recognition. However, most previous works are resource-heavy, with large FLoating-number OPerations (FLOPs) limiting the model’s potential. A recent work involving shift operators to GCN (Shift-GCN) has successfully introduced a lightweight GCN, but there is still a performance gap compared to previous results. Inspired by Shift-GCN, we propose an innovative and novel model named attention-guided and topology-enhanced shift graph convolutional network (AT-Shift-GCN), which continues the lightweight benchmark and provides a more powerful performance. We employ a topological transfer operation to aggregate the information flow of different channels and extract spatial information. In addition, to extract temporal information across scales, we apply attention to interacting with shift convolution kernels of different lengths. Furthermore, we integrate an ultralight spatiotemporal attention module to fuse spatiotemporal details and provide robust neighborhood representation. In summary, AT-Shift-GCN is a breakthrough in skeleton-based action recognition that provides a lightweight model with enhanced performance on three datasets.

Fast mobility analysis for generative design applications through a real vector space representation of mobilities

During the early stages of design, mechanisms are commonly modeled as perfect joints assembled with infinitely rigid bodies. This representation enables the prediction of the system’s mobilities through a mobility analysis. However, traditional mobility analysis tools can be computationally expensive or lack critical information, such as the type or direction of mobilities. It hinders the generation of topology and configuration through generative design schemes.In this paper, we propose an alternative approach to mobility analysis based on a real vector space representation of mobilities. Our method provides relevant information for early design steps while being computationally effective through a novel formulation of series and parallel assembly topological operations. A benchmark on four selected use cases highlights an acceleration of 3 to 4 orders of magnitude compared to traditional approaches. Additionally, design rules on the joints’ positions can be automatically generated with our approach. It enables the automation of the complete design process, including topology and configuration. As such, we provide guidelines to develop a generative design scheme dedicated to the synthesis of guiding mechanisms.

Symbolic extended dynamic mode decomposition.

In this paper, we present a new method of performing extended dynamic mode decomposition (EDMD) on systems, which admit a symbolic representation. EDMD generates estimates of the Koopman operator, K, for a dynamical system by defining a dictionary of observables on the space and producing an estimate, Km, which is restricted to be invariant on the span of this dictionary. A central question for the EDMD is what should the dictionary be? We consider a class of chaotic dynamical systems with a known or estimable generating partition. For these systems, we construct an effective dictionary from indicators of the "cylinder sets," which arise in defining the "symbolic system" from the generating partition. We prove strong operator topology convergence for both the projection onto the span of our dictionary and for Km. We also prove practical finite-step estimation bounds for the projection and Km as well. Finally, we demonstrate some numerical results on eigenspectrum estimation and forecasting applied to the dyadic map and the logistic map.

On the holographic dual of a topological symmetry operator

We study the holographic dual of a topological symmetry operator in the context of the AdS/CFT correspondence. Symmetry operators arise from topological field theories localized on a subspace of the boundary conformal field theory spacetime. We use bottom up considerations to construct the topological sector associated with their bulk counterparts. In particular, by exploiting the structure of entanglement wedge reconstruction we argue that the bulk counterpart has a nontopological world volume action, i.e., it describes a dynamical object. As a consequence, we find that there are no global p-form symmetries for p≥0 in asymptotically anti–de Sitter spacetimes, which includes the case of noninvertible symmetries. Provided one has a suitable notion of subregion-subregion duality, our argument for the absence of bulk global symmetries applies to more general spacetimes. These considerations also motivate us to consider for general QFTs (holographic or not) the notion of lower-form symmetries, namely, (−m)-form symmetries for m≥2. Published by the American Physical Society 2024

BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data

We compute the expectation values of BPS Wilson loops in the mass-deformed ABJM theory using the Fermi gas technique. We obtain explicit results in terms of Airy functions, effectively resumming the full 1/N expansion up to exponentially small terms. These expressions enable us to derive multi-point correlation functions for topological operators belonging to the stress tensor multiplet, in the presence of a 1/2-BPS Wilson line. From the one-point correlator, we recover the ABJM Bremsstrahlung function, confirming nicely previous results obtained through latitude Wilson loops. Likewise, higher point correlators can be used to extract iteratively new defect CFT data for higher dimensional topological operators. We present a detailed example of the dimension-two operator appearing in the OPE of two stress tensor multiplets.

Topological nonlocal operations on toroidal flux qubits

Topological nonlocal operations on toroidal flux qubits

Some Issues On Topological Operators Via Ideals

Some Issues On Topological Operators Via Ideals

Particle-soliton degeneracies from spontaneously broken non-invertible symmetry

We study non-invertible topological symmetry operators in massive quantum field theories in (1+1) dimensions. In phases where this symmetry is spontaneously broken we show that the particle spectrum often has degeneracies dictated by the non-invertible symmetry and we deduce a procedure to determine the allowed multiplets. These degeneracies are robust predictions and do not require integrability or other special features of renormalization group flows. We exhibit these conclusions in examples where the spectrum is known, recovering soliton and particle degeneracies. For instance, the Tricritical Ising model deformed by the subleading ℤ2 odd operator flows to a gapped phase with two degenerate vacua. This flow enjoys a Fibonacci fusion category symmetry which implies a threefold degeneracy of its particle states, relating the mass of solitons interpolating between vacua and particles supported in a single vacuum.

On the symmetry TFT of Yang-Mills-Chern-Simons theory

Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that its one-form symmetry defects have nontrivial braiding, namely they are charged under the same symmetry they generate, which is then anomalous. This poses a few puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk. First, the braiding between lines at the boundary seems to be ill-defined when such lines are pulled into the bulk. Second, the Symmetry TFT appears to be too trivial to allow for topological boundary conditions encoding all the different global variants. We show that both of these puzzles can be solved by including endable (tubular) surfaces in the class of bulk topological operators one has to consider. In this way, we are able to reproduce all global variants of the theory, with their symmetries and their anomalies. We check the validity of our proposal also against a top-down holographic realization of the same class of theories.

Crypto-preorders, topological relations, information and logic

ABSTRACT As is well known, any preorder R on a set U induces an Alexandrov topology on U . In some interesting cases related to data mining an Alexandrov topology can be transformed into different types of logico-algebraic models. In some cases, (pre)topological operators provided by Pointless Topology may define a topological space on U even if R is not a preorder. If this is the case, then we call R a crypto-preorder. The paper studies the conditions under which a relation R is a crypto-preorder and how to transform a crypto-preorder into a proper preorder.

Topology Design and Operation of Distribution Network Based on Multi-Objective Framework and Heuristic Strategies

Topology Design and Operation of Distribution Network Based on Multi-Objective Framework and Heuristic Strategies

Mitigation Strategy of Neutral-Point DC for Transformer Caused by Metro Stray Currents

Metro stray currents flowing into neutral-point-grounded transformers can cause serious direct current (DC) bias. Affected by both metro train and urban power grid operations, transformer neutral-point DC caused by metro stray current is complex, dynamic, and time-varying, which changes the DC bias risk level of transformers. Thus, just installing blocking devices (BDs) at transformer neutral points with high instantaneous DC may make it difficult to comprehensively mitigate DC bias and lead to increased BD installation. To solve this, through optimizing BD installation placements, a mitigation method for transformer DC bias is proposed. In the proposed method, the DC bias risk level and BD installation number are included in the constraint and objective functions. To evaluate the risk level of transformer DC bias, four indicators are proposed considering the distribution characteristics of neutral DC. To optimize the BD installation placements, the effects of both the metro train dynamic operation and the operation topology of the urban power grid on neutral DCs are considered. The Monte Carlo method is used to sample the train operation conditions and a relation matrix among transformers is established. Applying the method to a certain power system, the result of BD installation placements shows that the transformers supplying the metro system must have BDs installed at their neutral points.

Encoding signal propagation on topology-programmed DNA origami.

Biological systems often rely on topological transformation to reconfigure connectivity between nodes to guide the flux of molecular information. Here we develop a topology-programmed DNA origami system that encodes signal propagation at the nanoscale, analogous to topologically efficient information processing in cellular systems. We present a systematic molecular implementation of topological operations involving 'glue-cut' processes that can prompt global conformational change of DNA origami structures, with demonstrated major topological properties including genus, number of boundary components and orientability. By spatially arranging reactive DNA hairpins, we demonstrate signal propagation across transmission paths of varying lengths and orientations, and curvatures on the curved surfaces of three-dimensional origamis. These DNA origamis can also form dynamic scaffolds for regulating the spatial and temporal signal propagations whereby topological transformations spontaneously alter the location of nodes and boundary of signal propagation network. We anticipate that our strategy for topological operations will provide a general route to manufacture dynamic DNA origami nanostructures capable of performing global structural transformations under programmable control.