Related papers: A Guide to the Bott Index and Localizer Index

We discuss a generalisation of the Herbert formula for double points, when the normal bundle of an immersion admits an additional structure, and an application.

In this paper, we formulate the real-space Chern number in a supercell framework. In this framework, the overlap matrix between two corners of the Brillouin zone (BZ) is derived from diagonalizing the real-space Hamiltonian with periodic…

We propose a new inference framework called localized conformal prediction. It generalizes the framework of conformal prediction by offering a single-test-sample adaptive construction that emphasizes a local region around this test sample,…

Stochastic (Anderson) localization is the spatial localization of the wave-function of quantum particles in random media. We show, that a corresponding phenomenon can stabilize spatial solitons in optical resonators: spatial solitons in…

In recent years, correlated insulating states, unconventional superconductivity, and topologically non-trivial phases have all been observed in several moir\'e heterostructures. However, understanding of the physical mechanisms behind these…

The concept of the local Chern marker has gained a lot of attention especially in the field of ultracold quantum gases in optical lattices and artificial gauge fields. We investigate in further detail the microscopic real-space…

Many tools and techniques measure local structure in materials in contexts ranging from biology to geology. We provide a survey of those tools and metrics that are especially useful for analyzing particulate soft matter. The metrics we…

We extend the Berry-phase concept of polarization to insulators having a non-zero value of the Chern invariant. The generalization to such Chern insulators requires special care because of the partial occupation of chiral edge states. We…

We investigate the Bose glass phase and the insulator-to-superfluid transition in the two-dimensional disordered boson Hubbard model in the Villain representation via Monte Carlo simulations. In the Bose glass phase the probability…

Change detection, i.e., anomaly detection from local maps built by a mobile robot at multiple different times, is a challenging problem to solve in practice. Most previous work either cannot be applied to scenarios where the size of the map…

Recent development on fractional Chern insulators and proximate phases call for a real space representation of isolated Chern bands. Here we propose a new method for a general construction of optimally localized Wannier functions from such…

We present a higher index theorem for a certain class of etale one-dimensional complex-analytic groupoids. The novelty is the use of the local anomaly formula established in a previous paper, which represents the bivariant Chern character…

Recently we developed supervisor localization, a top-down approach to distributed control of discrete-event systems. Its essence is the allocation of monolithic (global) control action among the local control strategies of individual…

This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and…

We give a characterisation of functors whose induced functor on the level of localisations is an equivalence and where the isomorphism inverse is induced by some kind of replacements such as projective resolutions or cofibrant replacements.

The behavior of two-dimensional coupled map lattices is studied with respect to the global stabilization of unstable local fixed points without external control. It is numerically shown under which circumstances such inherent global…

This paper describes a predictive control method to search for unstable periodic orbits of the generalized tent map. The invariant set containing periodic orbits is a repelling set with a complicated Cantor-like structure. Therefore, a…

This paper defines new intersection homology groups. The basic idea is this. Ordinary homology is locally trivial. Intersection homology is not. It may have significant local cycles. A local-global cycle is defined to be a family of such…

Detailed understanding of the role of single dopant atoms in host materials has been crucial for the continuing miniaturization in the semiconductor industry as local charging and trapping of electrons can completely change the behaviour of…

The training of deep neural network classifiers results in decision boundaries which geometry is still not well understood. This is in direct relation with classification problems such as so called adversarial examples. We introduce…