Related papers: Topology reconstruction for asymmetric systems by …
Accurate determination of the complex effective permittivity is fundamental to optical material engineering, but it remains a critical metrology challenge for heterogeneous systems. In polymer blends and optical composites, scattering and…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…
Recent years have witnessed the remarkable success of applying Graph machine learning (GML) to node/graph classification and link prediction. However, edge classification task that enjoys numerous real-world applications such as social…
Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures…
A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…
We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…
There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can…
We showcase a topological mapping framework for a challenging indoor warehouse setting. At the most abstract level, the warehouse is represented as a Topological Graph where the nodes of the graph represent a particular warehouse…
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…
Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…
Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement…
This paper concerns a fast, one-step iterative technique of imaging extended perfectly conducting cracks with Dirichlet boundary condition. In order to reconstruct the shape of cracks from scattered field data measured at the boundary, we…
We propose a new method to overcome the nodal plane problem for the tomographic reconstruction of molecular orbitals with twofold mirror antisymmetry in the length form based on high-order harmonic generation. It is shown that, by carrying…
Bifurcation phenomena are common in multi-dimensional multi-parameter dynamical systems. Normal form theory suggests that the bifurcations themselves are driven by relatively few parameters; however, these are often nonlinear combinations…
We investigate topological properties of density matrices motivated by the question to what extent phenomena like topological insulators and superconductors can be generalized to mixed states in the framework of open quantum systems. The…
Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge obstruction at the cost of a symmetry anomaly and zero-energy boundary modes. One can also make use of the symmetry to enumerate the…
The latent space model is one of the well-known methods for statistical inference of network data. While the model has been much studied for a single network, it has not attracted much attention to analyze collectively when multiple…
We study edge-isoperimetric inequalities in chamber graphs of affine hyperplane arrangements. Our approach is topological: to a set of chambers we associate its thickening in Euclidean space and estimate its edge boundary through the…