Search results for "topological"

Topological systems and Artin glueing

2012

Abstract Using methods of categorical fuzzy topology, the paper shows a relation between topological systems of S. Vickers and Artin glueing of M. Artin. Inspired by the problem of interrelations between algebra and topology, we show the necessary and sufficient conditions for the category, obtained by Artin glueing along an adjoint functor, to be (co)algebraic and (co)monadic, incorporating the respective result of G. Wraith. As a result, we confirm the algebraic nature of the category of topological systems, showing that it is monadic.

Analyzing the Correlation of Classical and Community-aware Centrality Measures in Complex Networks

2021

International audience; Identifying influential nodes in social networks is a fundamental issue. Indeed, it has many applications, such as inhibiting epidemic spreading, accelerating information diffusion, preventing terrorist attacks, and much more. Classically, centrality measures quantify the node's importance based on various topological properties of the network, such as Degree and Betweenness. Nonetheless, these measures are agnostic of the community structure, although it is a ubiquitous characteristic encountered in many real-world networks. To overcome this drawback, there is a growing trend to design so-called community-aware centrality measures. Although several works investigate…

From Topology to Quasi-Topology. The Complexity of the Notional Domain

2016

This article examines a fundamental metalinguistic construction of the theory of enunciative operations: the notional domain. In particular, we try to explain some elementary topological concepts on which this construction is based and we try to show the key role they play in the description of some basic linguistic operations.

Flots de Smale en dimension 3: présentations finies de voisinages invariants d'ensembles selles

2002

Abstract Given a vector field X on a compact 3-manifold, and a hyperbolic saddle-like set K of that vector field, we consider all the filtering neighbourhood of K: by such, we mean any submanifold which boundary is tranverse to X, the maximal invariant of which is equal to K and which intersection with every orbit of X is connected. Up to topological equivalence, there is only a finite number of such neighbourhoods. We give a finite combinatorial presentation of the global dynamics on any such neighbourhood. A key step is the construction of a unique model of the germ of X along K; this model is, roughly speaking, the simplest three-dimensional manifold and the simplest Smale flow exhibitin…

Bader’s topological analysis of the electron density in the pressure-induced phase transitions/amorphization in α-quartz from the catastrophe theory …

2013

In this work, the Bader's topological analysis of the electron density, coupled with Thom's catastrophe theory, was used to characterize the pressure-induced transformations in α-quartz. In particular, ab initio calculations of the α-quartz structures in the range 0-105 Gpa have been performed at the HF/DFT exchange-correlation terms level, using Hamiltonians based on a WC1LYP hybrid scheme. The electron densities calculated throughout the ab initio wave functions have been analysed by means of the Bader's theory, seeking for some catastrophic mechanism in the sense of Thom's theory. The analysis mainly showed that there is a typical fold catastrophe feature involving an O-O interaction at …

A Bader’s topological approach for the investigation of the high pressure stability field of the Mg-perovskite phase

2014

Characterization of the pressure induced Ringwoodite toMg-perovskite and Mg-wüstite phase transition by Catastrophe Theory

2010

The pressure-induced ringwoodite to Mg-perovskite and periclase post-spinel phase transition: a Bader’s topological analysis of the ab initio electro…

2011

In order to characterize the pressure-induced decomposition of ringwoodite (c-Mg2SiO4), the topological analysis of the electron density q(r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians based on the Becke- LYP scheme containing hybrid Hartree– Fock/density functional exchange–correlation terms. The equation of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite -> Mg-perovskite + periclase) occurring at the transition zone–lower…

A large-energy-gap oxide topological insulator based on the superconductor BaBiO3

2013

Mixed-valent perovskite oxides based on BaBiO3 (BBO) are, like cuperates, well-known high-Tc superconductors. Recent ab inito calculations have assigned the high-Tc superconductivity to a correlation-enhanced electron--phonon coupling mechanism, stimulating the prediction and synthesis of new superconductor candidates among mixed-valent thallium perovskites. Existing superconductivity has meant that research has mainly focused on hole-doped compounds, leaving electron-doped compounds relatively unexplored. Here we demonstrate through ab inito calculations that BBO emerges as a topological insulator (TI) in the electron-doped region, where the spin-orbit coupling (SOC) effect is significant.…

Unraveling materials Berry curvature and Chern numbers from real-time evolution of Bloch states

2019

Materials can be classified by the topological character of their electronic structure and, in this perspective, global attributes immune to local deformations have been discussed in terms of Berry curvature and Chern numbers. Except for instructional simple models, linear response theories have been ubiquitously employed in calculations of topological properties of real materials. Here we propose a completely different and versatile approach to get the topological characteristics of materials by calculating physical observables from the real-time evolving Bloch states: the cell-averaged current density reveals the anomalous velocities whose integration leads to the conductivity quantum. Re…