Related papers: Some mathematical problems in numerical relativity
The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…
In spite of their evident logical character, particle statistics symmetries are not among the inherently quantum features exploited in quantum computation. A difficulty may be that, being a constant of motion of a unitary evolution, a…
The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…
The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process…
Quantum computing is gaining increased attention as a potential way to speed up simulations of physical systems, and it is also of interest to apply it to simulations of classical plasmas. However, quantum information science is…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
Simulation especially real-time simulation have been widely used for the design and testing of real-time systems. The advancement of simulation tools has largely attributed to the evolution of computing technologies. With the reduced cost…
The indefinite sign of the Hamiltonian constraint means that solutions to Einstein's equations must achieve a delicate balance--often among numerically large terms that nearly cancel. If numerical errors cause a violation of the Hamiltonian…
Over the past two decades, the rapid surge in data-intensive computational techniques for statistical modeling may have had the effect of diminishing the use of applied mathematics in causal scientific inquiry. In this paper, co-authored by…
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful…
We focus on three distinct lines of recent developments: edge modes and boundary charges in gravitational physics, relational dynamics in classical and quantum gravity, and quantum reference frames. We argue that these research directions…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
In contrast to set-point tracking which aims to reduce the tracking error between the tracker and the reference, tracking-in-range problems only focus on whether the tracker is within a given range around the reference, making it more…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Modern applications of strong gravitational lensing require the ability to use precise and varied observational data to constrain complex lens models. I discuss two sets of computational methods for lensing calculations. The first is a new…
Numerical MHD codes have become extraordinarily powerful tools with which to study accretion turbulence. They have been used primarily to extract values for the classical $\alpha$ parameter, and to follow complex evolutionary development.…
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…
Due to the absence of symmetries under time and spatial translations in a general curved spacetime, the energy and momentum of matter is not conserved as it is in flat space. This means, for example, that the flux of matter energy through a…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…