Related papers: Exact CHY Integrand Construction Using Combinatori…
We derive the full system of canonical differential equations for all planar two-loop massless six-particle master integrals, and determine analytically the boundary conditions. This fully specifies the solutions, which may be written as…
One frequently needs to interpolate or approximate gradients on simplicial meshes. Unfortunately, there are very few explicit mathematical results governing the interpolation or approximation of vector-valued functions on Delaunay meshes in…
In this letter we study how the exact non-perturbative integrability methods in 4D N=4 Super-Yang-Mills can work efficiently together with the numerical conformal bootstrap techniques to go beyond the spectral observables and access…
Preconditioning techniques are crucial for enhancing the efficiency of solving large-scale linear equation systems that arise from partial differential equation (PDE) discretization. These techniques, such as Incomplete Cholesky…
This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calder\'on calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density…
Causal structure learning has been a challenging task in the past decades and several mainstream approaches such as constraint- and score-based methods have been studied with theoretical guarantees. Recently, a new approach has transformed…
In this thesis, we study the integrands of a special four-point correlation function formed of protected half-BPS operators and scattering amplitudes in planar supersymmetric $\mathcal{N}=4$ Yang-Mills. We use the `soft-collinear bootstrap'…
When simulating partial differential equations, hybrid solvers combine coarse numerical solvers with learned correctors. They promise accelerated simulations while adhering to physical constraints. However, as shown in our theoretical…
Mechanistic interpretability aims to reverse-engineer transformer computations by identifying causal circuits through activation patching. However, scaling these interventions across diverse prompts and task families produces…
Purpose: The goal of this work is to extend the capabilities of RAKI, a k-space interpolating neural network, to reconstruct high-quality images from in-plane accelerated simultaneous multislice imaging acquisitions. This method is referred…
The graph Laplacian is a fundamental object in the analysis of and optimization on graphs. This operator can be extended to a simplicial complex $K$ and therefore offers a way to perform ``signal processing" on $p$-(co)chains of $K$.…
We generalize the unifying relations for tree amplitudes to the $1$-loop Feynman integrands. By employing the $1$-loop CHY formula, we construct differential operators which transmute the $1$-loop gravitational Feynman integrand to Feynman…
We construct a finite convergent semi-quadratic presentation for the Chinese monoid by adding column generators and using combinatorial properties of insertion algorithms on Chinese staircases. We extend this presentation into a coherent…
Using the point fusion procedure we obtain the new integrable systems from the Elliptic Schlesinger system (ESS). These new systems have the pole orders higher than one in the matrix of the Lax operator. Quadratic Poisson algebras on the…
Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are…
This paper presents a class of structure-preserving numerical methods for quantum optimal control problems, based on commutator-free Cayley integrators. Starting from the Krotov framework, we reformulate the forward and backward propagation…
We design a Quasi-Polynomial time deterministic approximation algorithm for computing the integral of a multi-dimensional separable function, supported by some underlying hyper-graph structure, appropriately defined. Equivalently, our…
In attempting to understand how combinatorial modifications alter algebraic properties of monomial ideals, several authors have investigated the process of adding "whiskers" to graphs. In this paper, we study a similar construction to build…
Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…
We present two lists of multi-component systems of integrable difference equations defined on the edges of a $\mathbb{Z}^2$ graph. The integrability of these systems is manifested by their Lax formulation which is a consequence of the…