Related papers: On the Block-Decomposability of 1-Parameter Matrix…
Decomposing oceanic and atmospheric flow fields into their slowly evolving balanced components and fast evolving wave components is essential for understanding processes like spontaneous wave emission. To study these processes, the…
A flow decomposition method based on canonical correlation analysis is proposed in this paper to optimally dissect complex flows into mutually orthogonal modes that are ranked by their cross-correlation with an observable. It is…
Covariance matrices are central to data assimilation and inverse methods derived from statistical estimation theory. Previous work has considered the application of an all-at-once diffusion-based representation of a covariance matrix…
Stanley decompositions are used in invariant theory and the theory of normal forms for dynamical systems to provide a unique way of writing each invariant as a polynomial in the Hilbert basis elements. Since the required Stanley…
Partly inspired by Sato's theory of the Kadomtsev-Petviashvili (KP) hierarchy, we start with a quite general hierarchy of linear ordinary differential equations in a space of matrices and derive from it a matrix Riccati hierarchy. The…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…
We propose that the broad architecture of the renormalization group flow in quantum field theories is, at least in part, fixed by unitarity. The precise statement is summarized in the Unitarity Flow Conjecture, which states that the…
Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors.…
Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…
Direct methods to obtain global stability modes are restricted by the daunting sizes and complexity of Jacobians encountered in general three-dimensional flows. Jacobian-free iterative approaches such as Arnoldi methods have greatly…
In this paper we study the initial boundary value problem for the system $\Delta v= u_{x_1},\ u_t-\mbox{div}\left(\left((a|\mathbf{q}|+m)I+(b-a)\frac{\mathbf{q}\otimes\mathbf{q}}{|\mathbf{q}|}\right)\nabla u\right)=-\nabla…
In this paper we close the gap between end-to-end diversity coding and intra-session network coding for unicast connections resilient against single link failures. In particular, we show that coding operations are sufficient to perform at…
We investigate matrix models in three dimensions where the global $\text{SU}(N)$ symmetry acts via the adjoint map. Analyzing their ground state which is homogeneous in space and can carry either a unique or multiple fixed charges, we show…
Network flow formulations are among the most successful tools to solve optimization problems. Such formulations correspond to determining an optimal flow in a network. One particular class of network flow formulations is the arc flow, where…
Deflation techniques are typically used to shift isolated clusters of small eigenvalues in order to obtain a tighter distribution and a smaller condition number. Such changes induce a positive effect in the convergence behavior of Krylov…
We present a scalable approach for simplifying the stability analysis of cluster synchronization patterns on directed networks. When a network has directional couplings, decomposition of the coupling matrix into independent blocks (which in…
Dense prediction tasks have enjoyed a growing complexity of encoder architectures, decoders, however, have remained largely the same. They rely on individual blocks decoding intermediate feature maps sequentially. We introduce banks, shared…
The paper presents a dynamic solution method for dynamic minimum parametric networks flow. The solution method solves the problem for a special parametric dynamic network with linear lower bound functions of a single parameter. Instead…
Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…
Various numerical linear algebra problems can be formulated as evaluating bivariate function of matrices. The most notable examples are the Fr\'echet derivative along a direction, the evaluation of (univariate) functions of…