Related papers: irbasis: Open-source database and software for int…
Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space of the forcing terms to the space of the solutions with the…
Accurate computation of the Green's function is crucial for connecting experimental observations to the underlying quantum states. A major challenge in evaluating the Green's function in the time domain lies in the efficient simulation of…
The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid-structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a…
Implicit neural representations (INR) have been recently adopted in various applications ranging from computer vision tasks to physics simulations by solving partial differential equations. Among existing INR-based works, multi-layer…
A new perspective of the Green's function in a boundary value problem as the only eigenstate in an auxiliary formulation is introduced. In this treatment, the Green's function can be perceived as a defect state in the presence of a…
The Gibbs partition function is an important quantity in describing statistical properties of a system in thermodynamic equilibrium. There are several proposals to calculate the partition functions on near-team quantum computers. However,…
Iris is an extensible application that provides astronomers with a user-friendly interface capable of ingesting broad-band data from many different sources in order to build, explore, and model spectral energy distributions (SEDs). Iris…
Many applications of Green's functions (GFs) require their evaluation over intervals or at multiple points, motivating quantum algorithms that return an efficiently computable functional representation rather than mere point estimates. We…
Neural program embeddings have demonstrated considerable promise in a range of program analysis tasks, including clone identification, program repair, code completion, and program synthesis. However, most existing methods generate neural…
We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green's representation formula in…
Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain simple representations for the Green's function of the Dirac-Oscillator and Dirac-Coulomb problems. This is accomplished…
GTIRB is an intermediate representation for binary analysis and rewriting tools including disassemblers, lifters, analyzers, rewriters, and pretty-printers. GTIRB is designed to enable communication between tools in a format that provides…
We present examples where the use of belief functions provided sound and elegant solutions to real life problems. These are essentially characterized by ?missing' information. The examples deal with 1) discriminant analysis using a learning…
The `equation-free toolbox' empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable you to immediately use microscopic simulators to perform macro-scale system level tasks and analysis, because…
The ill-posed analytic continuation problem for Green's functions or self-energies can be done using the Pad\'e rational polynomial approximation. However, to extract accurate results from this approximation, high precision input data of…
A general technique to analyze the classical interaction between ideal topological insulators, and electromagnetic sources and fields, has been previously elaborated. Nevertheless it is not immediately applicable in the laboratory as it…
Hybrid spectral-spatial representations are introduced to rapidly calculate periodic scalar and dyadic Green's functions of the Helmholtz equation for 2D and 3D configurations with a 1D (linear) periodicity. The presented schemes work…
A matrix basis formulation is introduced to represent the 3 x 3 dyadic Green's functions in the frequency domain for the Maxwell's equations and the elastic wave equation in layered media. The formulation can be used to decompose the…
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo-conformal representation. In special cases, this representation reduces to ordinary- or logarithmic-conformal field…