Related papers: Higher-order signal processing with the Dirac oper…
The notion of translation (shift) is straightforward in classical signal processing, however, it is challenging on an irregular graph structure. In this work, we present an approach to characterize the translation operator in various signal…
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary…
Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…
We discuss the construction and properties of an approximate solution of the Ginsparg-Wilson equation, the so-called chirally improved lattice Dirac operator. In particular we study the behavior of its eigenmodes in smooth instanton…
We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectrum against possibly non-self-adjoint potential perturbations…
Graph Neural Networks achieve state-of-the-art performance on a plethora of graph classification tasks, especially due to pooling operators, which aggregate learned node embeddings hierarchically into a final graph representation. However,…
The Dirac electron in the organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure is analyzed using a tight-binding model with nearest-neighbor transfer energies and four molecules per unit cell. By noting that the Dirac point between…
Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. Graph signal processing works have heretofore assumed knowledge of the…
We consider a two-dimensional massless Dirac operator coupled to a magnetic field $B$ and an electric potential $V$ growing at infinity. We find a characterization of the spectrum of the resulting operator $H$ in terms of the relation…
Focusing on coupling between edges, we generalize the relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian -- the generalization of the graph…
We develop elliptic regularity theory for Dirac operators in a very general framework: we consider Dirac operators linear over $C^*$-algebras, on noncompact manifolds, and in families which are not necessarily locally trivial fibre bundles.
In this note we extend the Dirac method to partial differential equations involving higher order roots of differential operators.
We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and formulate a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle.…
We study the contribution from dipole operators to one-loop Fierz identities and provide the resulting QCD and QED shifts to the tree-level relations for all four-fermion operators. The results simplify one-loop basis changes as well as…
Finding important edges in a graph is a crucial problem for various research fields, such as network epidemics, signal processing, machine learning, and sensor networks. In this paper, we tackle the problem based on sampling theory on…
We explore a new simple N=2 SQM model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model…
The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of Neuberger's lattice Dirac operator, is shown to have analogous properties…
We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…
Let $\Omega\subset\mathbb{R}^3$ be an open set, we study the spectral properties of the free Dirac operator $\mathcal{H}$ coupled with the singular potential $V_\kappa=(\epsilon I_4 +\mu\beta+\eta(\alpha\cdot N))\delta_{\partial\Omega}$.…
The overlap Dirac operator at nonzero quark chemical potential involves the computation of the sign function of a non-Hermitian matrix. In this talk we present an iterative method, first proposed by us in Ref. [1], which allows for an…