Related papers: Discrete Basis Parameterization for the Gauge Theo…
We study discretizations of Hamiltonian systems on the probability density manifold equipped with the $L^2$-Wasserstein metric. Based on discrete optimal transport theory, several Hamiltonian systems on graph (lattice) with different…
This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data…
S and U-duality dictate that graviton scattering amplitudes in IIB superstring theory be automorphic functions on the appropriate fundamental domain which describe the inequivalent vacua of (compactified) theories. A constrained functional…
In this paper two new families of arbitrary high order accurate spectral DG finite element methods are derived on staggered Cartesian grids for the solution of the inc.NS equations in two and three space dimensions. Pressure and velocity…
We report the construction of a three-dimensional template bank for the search for gravitational waves from inspiralling binaries consisting of spinning compact objects. The parameter space consists of two dimensions describing the mass…
We study the reflection amplitudes of affine Toda field theories with boundary, following the ideas developed by Fring and Koberle and focusing our attention on the $E_{n}$ series elements, because of their interesting structure of higher…
The gradient discretisation method (GDM) -- a generic framework encompassing many numerical methods -- is studied for a general stochastic Stefan problem with multiplicative noise. The convergence of the numerical solutions is proved by…
To illustrate the unitarity of the massive gauge field theory described in the foregoing papers, we calculate the scattering amplitudes up to the fourth order of perturbation by the optical theorem and the Landau-Cutkosky rule. In the…
Discarding the prejudice about fine tuning, we propose a novel and efficient approach to identify relevant regions of fundamental parameter space in supersymmetric models with some amount of fine tuning. The essential idea is the mapping of…
The five parameter gaussian damped sinusoid equation is a reasonable model for betatron motion with chromatic decoherence of the proton bunch centroid signal in the ring at the Spallation Neutron Source. A geometric method for efficiently…
Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…
Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fundamental properties, such as relations between convergence characteristics of their various…
The unitary S-matrix for the space-time non-commutative QED is constructed using the $\star$-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, perturbation theory is formulated and Feynman…
We develop an algebraic multigrid method for solving the non-Hermitian Wilson discretization of the 2-dimensional Dirac equation. The proposed approach uses a bootstrap setup algorithm based on a multigrid eigensolver. It computes test…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
We design a discrete Bernstein--Gelfand--Gelfand (BGG) diagram on polygonal meshes based on the DDR framework; the diagram is made of a discrete Stokes polygonal complex and a tensorised Discrete De Rham complex, and the BGG construction…
This paper develops a framework for differentially private $e$-values under Gaussian differential privacy ($\mu$-GDP). We characterize the canonical noise mechanism, establishing that optimal multiplicative perturbation follows a Gaussian…
The detection of stochastic gravitational wave background (SGWB) is among the leading scientific goals of the space-borne gravitational wave observatory, which would have significant impact on astrophysics and fundamental physics. In this…
The D0-brane/Banks-Fischler-Shenker-Susskind matrix theory is a strongly coupled quantum system with an interesting gravity dual. We develop a scheme to derive bootstrap bounds on simple correlators in the matrix theory at infinite $N$ at…
Large, multi-dimensional spatio-temporal datasets are omnipresent in modern science and engineering. An effective framework for handling such data are Gaussian process deep generative models (GP-DGMs), which employ GP priors over the latent…