Related papers: CTTK: A new method to solve the initial data const…
Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d=2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range…
Numerical relativity codes now being developed will evolve initial data representing colliding black holes at a relatively late stage in the collision. The choice of initial data used for code development has been made on the basis of…
We construct solutions of the constraint equation with non constant mean curvature on an asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain exponent appearing in the equations,…
In the light front quantisation scheme initial conditions are usually provided on a single lightlike hyperplane. This, however, is insufficient to yield a unique solution of the field equations. We investigate under which additional…
Conformal symmetry provides a systematic approximation to QCD in both its perturbative and nonperturbative domains. One can use the AdS/CFT correspondence between Anti-de Sitter space and conformal gauge theories to obtain an analytically…
One of the current major challenges surrounding the use of quantum annealers for solving practical optimization problems is their inability to encode even moderately sized problems---the main reason for this being the rigid layout of their…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
General relativity (GR) admits two alternative formulations with the same dynamics attributing the gravitational phenomena to torsion or nonmetricity of the manifold's connection. They lead, respectively, to the teleparallel equivalent of…
In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint…
The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the…
A first principles quantum formalism to describe the non-adiabatic dynamics of electrons and nuclei based on a second quantization representation (SQR) of the electronic motion combined with the usual representation of the nuclear…
We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the…
Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are…
In real-world scenarios, complex data such as multispectral images and multi-frame videos inherently exhibit robust low-rank property. This property is vital for multi-dimensional inverse problems, such as tensor completion, spectral…
Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and certifying quantum processors and simulators. Existing techniques either rely on projective measurements of the system before and after coherent…
The ADM approach to canonical general relativity combined with Dirac's method of quantizing constrained systems leads to the Wheeler-DeWitt equation. A number of mathematical as well as physical difficulties that arise in connection with…
Following from a question of Wheeler, why does the Hamiltonian constraint ${\cal H}$ of GR have the particular form it does? A first answer, by Hojman, Kucha\v{r} and Teitelboim, is that using embeddability into spacetime as a principle…
We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control,…
Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD…