Related papers: Exact CHY Integrand Construction Using Combinatori…
The structure of symplectic integrators up to fourth-order can be completely and analytical understood when the factorization (split) coefficents are related linearly but with a uniform nonlinear proportional factor. The analytic form of…
Questions that seek to determine whether a hyperplane arrangement property, be it geometric, arithmetic or topological, is of a combinatorial nature (that is determined by the intersection lattice) are abundant in the literature. To tackle…
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.…
Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal…
Chen's iterated integrals are treated within synthetic differential geometry. The main result is that iterated integrals produce a subcomplex of the de Rham complex on the free path space as well as based path spaces.
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
We consider the conformal properties of geometries described by higher-rank line elements. A crucial role is played by the conformal Killing equation (CKE). We introduce the concept of null-flat spaces in which the line element can be…
Motivated by a use case in theoretical hadron physics, we revisit an application of a pole-sum fit to dressing functions of a confined quark propagator. More precisely, we investigate approaches to determine the number and positions of the…
Polaritonic lattice configurations in dimensions $D=2$ are used as simulators of topological phases, based on symmetry class A Hamiltonians. Numerical and topological studies are performed in order to characterise the bulk topology of…
We present a novel framework for deriving on-shell recursion relations, with a specific focus on biadjoint and pure Yang-Mills theories. Starting from the double-cover CHY factorization formulae, we identify a suitable set of independent…
The inverse design of nonlocal metasurfaces requires the precise optimization of lattice geometry to engineer spatial dispersion and high-Q resonances. However, gradient-based optimization is frequently bottle-necked by the evaluation of…
We consider general integrable curve nets in Euclidean space as a particular integrable geometry invariant with respect to rigid motions and net-preserving reparameterisations. For the purpose of their description, we first give an overview…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by…
Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…
We obtain many objects of discrete differential geometry as reductions of skew parallelogram nets, a system of lattice equations that may be formulated for any unit associative algebra. The Lax representation is linear in the spectral…
We study a question that lies at the intersection of classical research subjects in Topological Graph Theory and Graph Drawing: Computing a drawing of a graph with a prescribed number of crossings on a given set $S$ of points, while…
Defect-adaptive surface-code methods have substantially advanced the construction of valid logical patches on imperfect hardware, but fault-tolerant computation also requires executable logical oper ations on the resulting irregular…
Reconstructing spectral functions from propagator data is difficult as solving the analytic continuation problem or applying an inverse integral transformation are ill-conditioned problems. Recent work has proposed using neural networks to…
Inspired by recent work by Tarasov and Venugopalan, we calculate the one-loop quark box diagrams relevant to polarized and unpolarized Deep Inelastic Scattering (DIS) by introducing off-forward momentum $l^\mu$ as an infrared regulator. In…