相关论文: Pseudo-spectral apparent horizon finders: an effic…
We present a novel approximation algorithm for $k$-median that achieves an approximation guarantee of $1+\sqrt{3}+\epsilon$, improving upon the decade-old ratio of $3+\epsilon$. Our approach is based on two components, each of which, we…
We study novel robust zero-order algorithms with acceleration for the solution of real-time optimization problems. In particular, we propose a family of extremum seeking dynamics that can be universally modeled as singularly perturbed…
Learning-based planners leveraging Graph Neural Networks can learn search guidance applicable to large search spaces, yet their potential to address symmetries remains largely unexplored. In this paper, we introduce a graph representation…
Recently a new algorithm for sampling posteriors of unnormalised probability densities, called ABC Shadow, was proposed in [8]. This talk introduces a global optimisation procedure based on the ABC Shadow simulation dynamics. First the…
In this paper, by regarding the two-subspace Kaczmarz method [20] as an alternated inertial randomized Kaczmarz algorithm we present a new convergence rate estimate which is shown to be better than that in [20] under a mild condition.…
We prove existence of a countable family of spherically symmetric self-similar wave maps from 3+1 Minkowski spacetime into the 3-sphere. These maps can be viewed as excitations of the ground state wave map found previously by Shatah. The…
Bayesian models offer great flexibility for clustering applications---Bayesian nonparametrics can be used for modeling infinite mixtures, and hierarchical Bayesian models can be utilized for sharing clusters across multiple data sets. For…
In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. The proposed filter is named as adaptive sparse-grid Gauss-Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the dimensions…
In this work, we theoretically investigate strong gravitational lensing effects and evaluate various lensing observables of a static, spherically symmetric solution in the context of effective quantum gravity (EQG). Among the three types of…
We obtain an asymptotic solution for $\ep \to 0$ of the Cauchy problem for linear first-order symmetric hyperbolic systems with oscillatory initial values written in the eikonal form of geometric optics with frequency $1/\ep$, but with…
Regular and spherically symmetric black holes that solve the singularity problems of the Schwarzschild solution are phenomenologically viable at large distance but usually suffer from the Cauchy horizon instability. To overcome this…
We investigate the inverse Cauchy and data completion problems for elliptic partial differential equations in a bounded domain $D \subset \mathbb{R}^d$, $d \ge 2$, with a special emphasis on the steady-state heat conduction in anisotropic…
Fr\'echet regression has received considerable attention to model metric-space valued responses that are complex and non-Euclidean data, such as probability distributions and vectors on the unit sphere. However, existing Fr\'echet…
The requirement that a trapped spacetime domain forms in finite time for distant observers is logically possible and sometimes unavoidable, but its consequences are not yet fully understood. In spherical symmetry, the characterization of…
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle,…
Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. While subspace-based methods offer cost-effective super-resolution parameter estimation, they demand precise array calibration, posing…
Recent spectral clustering methods are a propular and powerful technique for data clustering. These methods need to solve the eigenproblem whose computational complexity is $O(n^3)$, where $n$ is the number of data samples. In this paper, a…
This paper presents a fast algorithm to solve a spectral estimation problem for two-dimensional random fields. The latter is formulated as a convex optimization problem with the Itakura-Saito pseudodistance as the objective function subject…
We consider analytic, vacuum spacetimes that admit compact, non-degenerate Cauchy horizons. Many years ago we proved that, if the null geodesic generators of such a horizon were all \textit{closed} curves, then the enveloping spacetime…
As the Cosmic Microwave Background (CMB) radiation is observed to higher and higher angular resolution the size of the resulting datasets becomes a serious constraint on their analysis. In particular current algorithms to determine the…