Search results for "topological"

K-theory of function rings

1990

AbstractThe ring R of continuous functions on a compact topological space Xwith values in R or C is considered. It is shown that the algebraic K-theory of such rings with coefficients in ZkZ, k any positive integer, agrees with the topological K-theory of the underlying space X with the same coefficient rings. The proof is based on the result that the map from Rδ (R with discrete topology) to R (R with compact-open topology) induces a natural isomorphism between the homologies with coefficients in ZkZ of the classifying spaces of the respective infinite general linear groups. Some remarks on the situation with X not compact are added.

Normed vector spaces consisting of classes of convex sets

1965

Topology-based goodness-of-fit tests for sliced spatial data

2023

In materials science and many other application domains, 3D information can often only be extrapolated by taking 2D slices. In topological data analysis, persistence vineyards have emerged as a powerful tool to take into account topological features stretching over several slices. In the present paper, we illustrate how persistence vineyards can be used to design rigorous statistical hypothesis tests for 3D microstructure models based on data from 2D slices. More precisely, by establishing the asymptotic normality of suitable longitudinal and cross-sectional summary statistics, we devise goodness-of-fit tests that become asymptotically exact in large sampling windows. We illustrate the test…

Optimal rates of convergence for persistence diagrams in Topological Data Analysis

2013

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.

A Communication-Aware Topological Mapping Technique for NoCs

2008

Networks---on---Chip (NoCs) have been proposed as a promising solution to the complex on-chip communication problems derived from the increasing number of processor cores. The design of NoCs involves several key issues, being the topological mapping (the mapping of the Intellectual Properties (IPs) to network nodes) one of them. Several proposals have been focused on topological mapping last years, but they require the experimental validation of each mapping considered. In this paper, we propose a communication-aware topological mapping technique for NoCs. This technique is based on the experimental correlation of the network model with the actual network performance, thus avoiding the need…

Topology Inference and Signal Representation Using Dictionary Learning

2019

This paper presents a Joint Graph Learning and Signal Representation algorithm, called JGLSR, for simultaneous topology learning and graph signal representation via a learned over-complete dictionary. The proposed algorithm alternates between three main steps: sparse coding, dictionary learning, and graph topology inference. We introduce the “transformed graph” which can be considered as a projected graph in the transform domain spanned by the dictionary atoms. Simulation results via synthetic and real data show that the proposed approach has a higher performance when compared to the well-known algorithms for joint undirected graph topology inference and signal representation, when there is…

Floquet engineering of magnetism in topological insulator thin films

2023

Dynamic manipulation of magnetism in topological materials is demonstrated here via a Floquet engineering approach using circularly polarized light. Increasing the strength of the laser field, besides the expected topological phase transition, the magnetically doped topological insulator thin film also undergoes a magnetic phase transition from ferromagnetism to paramagnetism, whose critical behavior strongly depends on the quantum quenching. In sharp contrast to the equilibrium case, the non-equilibrium Curie temperatures vary for different time scale and experimental setup, not all relying on change of topology. Our discoveries deepen the understanding of the relationship between topology…

Structural, chemical and dynamical trends in graphene grain boundaries

2010

Grain boundaries are topological defects that often have a disordered character. Disorder implies that understanding general trends is more important than accurate investigations of individual grain boundaries. Here we present trends in the grain boundaries of graphene. We use density-functional tight-binding method to calculate trends in energy, atomic structure (polygon composition), chemical reactivity (dangling bond density), corrugation heights (inflection angles), and dynamical properties (vibrations), as a function of lattice orientation mismatch. The observed trends and their mutual interrelations are plausibly explained by structure, and supported by past experiments.

Prediction of Weak Topological Insulators in Layered Semiconductors

2012

We report the discovery of weak topological insulators by ab initio calculations in a honeycomb lattice. We propose a structure with an odd number of layers in the primitive unit-cell as a prerequisite for forming weak topological insulators. Here, the single-layered KHgSb is the most suitable candidate for its large bulk energy gap of 0.24 eV. Its side surface hosts metallic surface states, forming two anisotropic Dirac cones. Though the stacking of even-layered structures leads to trivial insulators, the structures can host a quantum spin Hall layer with a large bulk gap, if an additional single layer exists as a stacking fault in the crystal. The reported honeycomb compounds can serve as…

Heusler Compounds—A Material Class With Exceptional Properties

2011

The class of Heusler compounds, including the XYZ and the X2YZ compounds, has not only an endless number of members, but also a vast variety of properties can be found in this class of materials, ranging from semiconductors, half-metallic ferromagnets, superconductors, and topological insulators to shape memory alloys. With this review article, we would like to provide an overview of Heusler compounds, focusing on their structure, properties, and potential applications.