Related papers: Spectral Characteristic Evolution: A New Algorithm…

Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…

In representation learning, Convolutional Sparse Coding (CSC) enables unsupervised learning of features by jointly optimising both an \(\ell_2\)-norm fidelity term and a sparsity enforcing penalty. This work investigates using a…

Numerical relativity simulations provide the most precise templates for the gravitational waves produced by binary black hole mergers. However, many of these simulations use an incomplete waveform extraction technique -- extrapolation --…

We analyse the Cauchy problem on a characteristic cone, including its vertex, for the Einstein equations in arbitrary dimensions. We use a wave map gauge, solve the obtained constraints and show gauge conservation.

We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation…

Anomaly detection aims to distinguish observations that are rare and different from the majority. While most existing algorithms assume that instances are i.i.d., in many practical scenarios, links describing instance-to-instance…

We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime…

We present a new study of remnant black hole properties from 13 binary black hole systems, numerically evolved using the Spectral Einstein Code. The mass, spin, and recoil velocity of each remnant were determined quasi-locally from apparent…

A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…

Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…

A new general Lie-algebraic approach is proposed to solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras $su_{pd}(2)$ as their dynamic symmetry algebras. The method makes use of an…

Spectral-type subspace clustering algorithms have shown excellent performance in many subspace clustering applications. The existing spectral-type subspace clustering algorithms either focus on designing constraints for the reconstruction…

Evolutionary computation methods have been successfully applied to neural networks since two decades ago, while those methods cannot scale well to the modern deep neural networks due to the complicated architectures and large quantities of…

We derive the spectral properties of adjacency matrix of complex networks and of their Laplacian by the replica method combined with a dynamical population algorithm. By assuming the order parameter to be a product of Gaussian…

Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…

Clustering explores meaningful patterns in the non-labeled data sets. Cluster Ensemble Selection (CES) is a new approach, which can combine individual clustering results for increasing the performance of the final results. Although CES can…

We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…

State-of-the-art methods for Convolutional Sparse Coding usually employ Fourier-domain solvers in order to speed up the convolution operators. However, this approach is not without shortcomings. For example, Fourier-domain representations…

The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…

Recently, many evolutionary computation methods have been developed to solve the feature selection problem. However, the studies focused mainly on small-scale issues, resulting in stagnation issues in local optima and numerical instability…