Related papers: Factoring Perfect Reconstruction Filter Banks into…
An intrinsically causal approach to lifting factorization, called the Causal Complementation Algorithm, is developed for arbitrary two-channel perfect reconstruction FIR filter banks. This addresses an engineering shortcoming of the…
Group lifting structures are introduced to provide an algebraic framework for studying lifting factorizations of two-channel perfect reconstruction finite-impulse-response (FIR) filter banks. The lifting factorizations generated by a group…
We generalize the classical lifting and recombination scheme for rational and absolute factorization of bivariate polynomials to the case of a critical fiber. We explore different strategies for recombinations of the analytic factors,…
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and $\varepsilon$-factorised differential equations. The algorithm consists of two steps. In the first step, we use a new geometric…
This note presents the basic mathematical structure of a new integer factorization method based on systems of linear Diophantine equations.
This paper extends the existing theory of perfect reconstruction two-channel filter banks from bipartite graphs to non-bipartite graphs. By generalizing the concept of downsampling/upsampling we establish the frame of two-channel filter…
We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. We study two distinct cases of causal inference:…
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
Although Deep Convolutional Neural Networks (CNNs) have liberated their power in various computer vision tasks, the most important components of CNN, convolutional layers and fully connected layers, are still limited to linear…
This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler…
In this paper we investigate factorizations of polynomials over the ring of dual quaternions into linear factors. While earlier results assume that the norm polynomial is real ("motion polynomials"), we only require the absence of real…
High-order methods gain more and more attention in computational fluid dynamics. However, the potential advantage of these methods depends critically on the availability of efficient elliptic solvers. With spectral-element methods, static…
The theory of group lifting structures is applied to linear phase lifting factorizations for the two nontrivial classes of two-channel linear phase perfect reconstruction filter banks, the whole- and half-sample symmetric classes. Group…
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…
An algebraic framework for the investigation of linear dynamic output feedback is introduced. Pivotal in the present theory is the problem of causal factorization, i.e. the problem of factoring two systems over each other through a causal…
Multidimensional factorization method is formulated in arbitrary curvilinear coordinates. Particular cases of polar and spherical coordinates are considered and matrix potentials with separating variables are constructed. A new class of…
In this paper, we enhance a recent algorithm for approximate spectral factorization of matrix functions, extending its capabilities to precisely factorize rational matrices when an exact lower-upper triangular factorization is available.…
Lifting uses a representative of indistinguishable individuals to exploit symmetries in probabilistic relational models, denoted as parametric factor graphs, to speed up inference while maintaining exact answers. In this paper, we show how…
The Boolean matrix factorization problem consists in approximating a matrix by the Boolean product of two smaller Boolean matrices. To obtain optimal solutions when the matrices to be factorized are small, we propose SAT and MaxSAT…
In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…