Performance Of Topology Research Articles

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

This work elucidates a methodological approach employed in the process of planning the expansion of distribution network (DN) lines, wherein the amalgamation of system reconfiguration capabilities with operational equilibrium and reliability is paramount. The expansion proposals for the DN and the radial operation schemes post-expansion are encompassed. We formulate a bi-objective DN planning optimization model that concurrently addresses resource optimization configuration and operational optimization. Subsequently, the NSGA-II algorithm is employed to solve the optimization model, providing a coordinated presentation of multiple alternative solutions. However, this problem diverges from conventional bi-objective optimization problems due to its nature as a bi-objective optimization problem with embedded sub-optimization problem, consequently imposing a substantial computational burden. To address this issue, heuristic algorithms are designed to optimize system operational configuration, which is regarded as a sub-optimization problem. The proposed metric, model, and algorithms are validated on two case studies using the IEEE 33-bus and 70-bus test systems. Notably, the proposed method achieves solution efficiency by over 200 times compared to existing methods.

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.

Learning Topological Operations on Meshes with Application to Block Decomposition of Polygons

We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement learning with no prior heuristics. The actions performed on the mesh are standard local and global element operations. The goal is to minimize the deviation of the node degrees from their ideal values, which in the case of interior vertices leads to a minimization of irregular nodes.

EMM EMUS Observations of FUV Aurora on Mars: Dependence on Magnetic Topology, Local Time, and Season

AbstractWe present a comprehensive study of the nightside aurora phenomenon on Mars, utilizing observations from EMUS onboard Emirates Mars Mission. The oxygen emission at 130.4 nm is by far the brightest FUV auroral emission line observed at Mars. Our statistical analysis reveals geographic, solar zenith angle, local time, and seasonal dependencies of auroral occurrence. Higher occurrence of aurora is observed in regions of open magnetic topology, where crustal magnetic fields are either very weak or both strong and vertical. Aurora occurs more frequently closer to the terminator and is more likely on the dusk side than on the dawn side of the night hemisphere. A pronounced auroral feature appears close to midnight local times in the southern hemisphere, consistent with the spot of energetic electron fluxes previously identified in the Mars Global Surveyor data. This auroral spot is more frequent after midnight than before. Additionally, some regions on Mars are “aurora voids” where essentially no aurora occurs. Aurora exhibits a seasonal dependence, with a major enhancement near perihelion. Non–crustal field aurora additionally shows a secondary enhancement near Ls 30°. This seasonal variability is a combination of the variability in ionospheric photoelectrons and thermospheric atomic oxygen abundance. Auroral occurrence also shows an increase with the rise of Solar Cycle 25. The brightest auroral pixels are observed during space weather events such as Coronal Mass Ejections and Stream Interaction Regions. These observations not only shed light on where and when Martian aurora occurs, but also add to our understanding of Mars' magnetic environment and its interaction with the heliosphere.

On the topological indices and graph operation

As we know that some chemically interesting graphs can be obtained by different graph operations on some general or particular graphs, it is important to study such graph operations in order to understand how it is related to the corresponding topological indices of the original graphs. In [A. Miličević, A. Nikolić and S. Trinajstić, On reformulated Zagreb indices, Mol. Divers. 8 (2004) 393–399], authors defined two new variants of Corona product and investigated some topological indices. In this paper, we extended the work and found the formulas of the F-index, hyper-Zagreb index, and Sigma index for double join of graphs based on the total graph and double corona of graphs based on the total graph. Moreover, some applications of the derived results are also discussed.

Topo: Towards a fine-grained topological data processing framework on Tianhe-3 supercomputer

Big data frameworks are widely deployed in supercomputers for analyzing large-scale datasets. Topological data processing is an emerging approach that focuses on analyzing the topological structures in high-dimensional scientific data. However, incorporating topological data processing into current big data frameworks presents three main challenges: (1) The frequent data exchange poses challenges to the traditional coarse-grained parallelism. (2) The spatial topology makes parallel programming harder using oversimplified MapReduce APIs. (3) The massive intermediate data and NUMA architecture hinder resource utilization and scalability on novel supercomputers and many-core processors.In this paper, we present Topo, a generic distributed framework that enhances topological data processing on many-core supercomputers. Topo relies on three concepts. (1) It employs fine-grained parallelism, with awareness of topological structures in datasets, to support interactions among collaborative workers before each shuffle phase. (2) It provides intuitive APIs for topological data operations. (3) It implements efficient collective I/O and NUMA-aware dynamic task scheduling to improve multi-threading and load balancing. We evaluate Topo's performance on the Tianhe-3 supercomputer, which utilizes state-of-the-art ARM many-core processors. Experimental results of execution time show that compared to popular frameworks, Topo achieves an average speedup of 5.3× and 6.3×, with a maximum speedup of 8.4× and 20×, on HPC workloads and big data benchmarks, respectively. Topo further reduces total execution time on processing skewed datasets by 41%.

Extending families of disjoint hypercyclic operators

In the present note, we solve two open questions posed by Salas in [33] about disjoint hypercyclic operators. First, we show that given any family T1,…,TN of disjoint hypercyclic operators, one can always select an operator T such that the extended family T1,…,TN,T of operators remains disjoint hypercyclic. In fact, we prove that the set of operators T which can extend the family of disjoint hypercyclic operators is dense in the strong operator topology in the algebra of bounded operators. Second, we show the existence of two disjoint weakly mixing operators that fail to possess a dense d-hypercyclic manifold. Thus, these operators satisfy the Disjoint Blow-up/Collapse property but fail to satisfy the Strong Disjoint Blow-up/Collapse property, a notion which was introduced by Salas as a sufficient condition for having a dense linear manifold of disjoint hypercyclic vectors.

Implications of Defect Density and Polymer Interactions for CO2 Capture on Amine-Functionalized MIL-101(Cr).

Rising anthropogenic carbon emissions have dire environmental consequences, necessitating remediative approaches, which includes use of solid sorbents. Here, aminopolymers (poly(ethylene imine) (PEI) and poly(propylene imine) (PPI)) are supported within solid mesoporous MIL-101(Cr) to examine effects of support defect density on aminopolymer-MOF interactions for CO2 uptake and stability during uptake-regeneration cycles. Using simulated flue gas (10 % CO2 in He), MIL-101(Cr)-ρhigh (higher defect density) shows 33 % higher uptake capacity per gram adsorbent than MIL-101(Cr)-ρlow (lower defect density) at 308 K, consistent with increased availability of undercoordinated Cr adsorption sites at missing linker defects. Increasing aminopolymer weight loadings (10-50 wt.%) within MIL-101(Cr)-ρlow and MIL-101(Cr)-ρhigh increases amine efficiencies and CO2 uptake capacities relative to bare MOFs, though both incur CO2 diffusion limitations through confined, viscous polymer phases at higher (40-50 wt.%) loadings. Benchmarked against SBA-15, lower polymer packing densities (PPI>PEI), weaker and less abundant van der Waals interactions between aminopolymers and pore walls, and open framework topology increase amine efficiencies. Interactions between amines and Cr defect sites incur amine efficiency losses but grant higher thermal and oxidative stability during uptake-regeneration cycling. Finally, >25 % higher CO2 uptake capacities are achieved for aminopolymer/MIL-101(Cr)-ρhigh under humid conditions, demonstrating promise for realistic applications.

Multifidelity topology design of a maritime survey operation with UUVs

Multifidelity topology design of a maritime survey operation with UUVs

Advancing Front Surface Mapping

AbstractWe present Advancing Front Mapping (AFM), a novel algorithm for the computation of injective maps to simple planar domains. AFM is inspired by the advancing front meshing paradigm, which is here revisited to operate on two embeddings at once, becoming a tool for compatible mesh generation. AFM extends the capabilities of existing robust approaches, supporting a broader set of embeddings (star‐shaped polygons) with a direct approach, without resorting to intermediate constructions. Our method only relies on two topological operators (split and flip) and on the computation of segment intersections, thus permitting to compute a valid embedding without solving any numerical problem. AFM is therefore easy to implement, debug and deploy. This article is mainly focused on the presentation of the compatible advancing front idea and on the demonstration that the algorithm provably converges to an injective map. We also complement our theoretical analysis with an extensive practical validation, executing more than one billion advancing front moves on 36K mapping tasks.

On the continuity in q of the family of the limit q-Durrmeyer operators

Abstract This study deals with the one-parameter family { D q } q ∈ [ 0 , 1 ] {\left\{{D}_{q}\right\}}_{q\in \left[0,1]} of Bernstein-type operators introduced by Gupta and called the limit q q -Durrmeyer operators. The continuity of this family with respect to the parameter q q is examined in two most important topologies of the operator theory, namely, the strong and uniform operator topologies. It is proved that { D q } q ∈ [ 0 , 1 ] {\left\{{D}_{q}\right\}}_{q\in \left[0,1]} is continuous in the strong operator topology for all q ∈ [ 0 , 1 ] q\in \left[0,1] . When it comes to the uniform operator topology, the continuity is preserved solely at q = 0 q=0 and fails at all q ∈ ( 0 , 1 ] . q\in \left(0,1]. In addition, a few estimates for the distance between two limit q q -Durrmeyer operators have been derived in the operator norm on C [ 0 , 1 ] C\left[0,1] .

Characterization of neighborhood operators based on neighborhood relationships

Abstract Neighborhood relationships play a pivotal role in rough set theory, addressing the limitations of equivalence relations. This article focuses on defining upper and lower approximation operators using neighborhood relationships and exploring their properties in terms of serialization, inverse serialization, reflexivity, symmetry, transitivity, and Euclidean relations. Furthermore, a necessary and sufficient condition for the upper approximation operator to function as a topological closure operator is derived. Overall, this research sheds light on the significance of neighborhood relationships and their implications within rough set theory.

Catalytic synthesis of aspirin by a single crystal of cadmium phosphomolybdate with (412·612·84)(46)2 topological structure

To green-catalyze the synthesis of aspirin, we designed and synthesized a novel and unreported cadmium phosphomolybdate crystal compound (C2N2H10)4{Cd3[P4Mo6O26(OH)5]2}·6H2O as a catalyst for the synthesis reaction of aspirin using hydrothermal synthesis, and structurally characterized. Single-crystal X-ray diffraction analysis showed that the compound has a 4,8-connected inorganic open topology (412·612·84)(46)2. The optimal process conditions for the reaction of salicylic acid and acetic anhydride were determined by screening the catalyst dosage, temperature, and reaction time. The reaction temperature was set at 80 °C, the catalyst dosage was 0.09 g, and the reaction time was 25 min. The industry's most often utilized catalyst for aspirin manufacturing is concentrated sulfuric acid, which has strong oxidizing and corrosive qualities, resulting in difficult issues such as low synthetic product yield, large equipment needs, and substantial environmental damage. The experimental results of the (C2N2H10)4{Cd3[P4Mo6O26(OH)5]2}·6H2O catalytic synthesis of aspirin reveal that as a solid acid catalyst, its catalytic activity is similar to the commonly used catalyst concentrated H2SO4. Synthetic catalysts, on the other hand, have the advantages of high efficiency, selectivity, conversion rate, ease of recovery, and the ability to be recycled several times without polluting equipment, all of which are consistent with modern ``green'' catalysts. The results of this work suggest that the supramolecular compounds of polymetallic oxonate that we designed and produced hydrothermally can serve as catalysts in drug synthesis reactions to mitigate environmental pollution, hence providing new opportunities for the development of environmentally friendly medications.

Remark on Intuitionistic Fuzzy Temporal Modal Topological Structures

In a series of papers, we have discussed the concept of a modal topological structure modified, extended and illustrated by examples from intuitionistic fuzzy sets. Here, the concept of a temporal modal topological structure is introduced and illustrated with four different intuitionistic fuzzy temporal modal topological structures. These structures are based on intuitionistic fuzzy topological, temporal and modal operators. They are extensions of the temporal topological structures as well as of the modal topological structures.