Search · four archives
Search · four archives
19 papers · ranked by Valyu relevance
Eric Evert, Michiel Vandecappelle, Lieven De Lathauwer
—The canonical polyadic decomposition (CPD) is a fundamental tensor decomposition which expresses a tensor as a sum of rank one tensors. In stark contrast to the matrix case, with light assumptions, the CPD of a low rank tensor is (essentially) unique. The essential uniqueness of CPD makes this decomposition a powerful…
Ignat Domanov, Lieven De Lathauwer
We find conditions that guarantee that a decomposition of a generic third-order tensor in a minimal number of rank-1 tensors (canonical polyadic decomposition (CPD)) is unique up to permutation of rank-1 tensors. Then we consider the case when the tensor and all its rank-1 terms have symmetric frontal slices (INDSCAL).…
Jérémy E. Cohen, Nicolas Gillis
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionarybased tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors…
Sudip Sasmal, Markus Schröder, Oriol Vendrell
We propose an approach to represent the second-quantized electronic Hamiltonian in a compact sumof-products (SOP) form. The approach is based on the canonical polyadic decomposition (CPD) of the original Hamiltonian projected onto the sub-Fock spaces formed by groups of spin orbitals. The algorithm for obtaining the…
Mao Ge, Yong Lv, Cancan Yi, Yi Zhang + 1 more
Gears are key components in rotation machinery and its fault vibration signals usually show strong nonlinear and non-stationary characteristics. It is not easy for classical time-frequency domain analysis methods to recognize different gear working conditions. Therefore, this paper presents a joint fault diagnosis…
Ethan C. Hung, Enio Hodzic, Zhixin Cyrillus Tan, Aaron S. Meyer
Tensor factorization is a dimensionality reduction method applied to multidimensional arrays. These methods are useful for identifying patterns within a variety of biomedical datasets due to their ability to preserve the organizational structure of experiments and therefore aid in generating meaningful insights.…
Daniele Dorigoni, Mehregan Doroudiani, Joshua Drewitt, Martijn Hidding + 4 more
Zeta generators are derivations associated with odd Riemann zeta values that act freely on the Lie algebra of the fundamental group of Riemann surfaces with marked points. The genus-zero incarnation of zeta generators are Ihara derivations of certain Lie polynomials in two generators that can be obtained from the…
Steven Duplij
A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in the Wedderburn decomposition), a general form of polyadic structures is given by block-shift matrices. We combine these forms to get a…
Jorge Caravantes, M. Ángeles Gómez-Molleda, Laureano González-Vega
The aim of this paper is to give a canonical representation for the elements in the ring of the continuous piecewise polynomial functions. While general piecewise polynomial functions are interesting in general, most applications of them to CAGD require the functions to be continuous. In fact, splines are, by…
Barbu Berceanu
| 1. | Introduction and statement of results | 1 | | --- | --- | --- | | 2. | Canonical forms of polynomials | 3 | | 3. | Decomposition of polynomials | 5 | | 4. | Indecomposable polynomials | 8 | | 5. | Ritt presentation | 12 | | 6. | A complete presentation | 14 | | 7. | Appendix | 16 | | References | | 20 |
Dijana Kreso, Robert F. Tichy
We study Diophantine equations of type $fx=gy$, where both f and g have at least two distinct critical points (roots of the derivative) and equal critical values at at most two distinct critical points. Various classical families of polynomials $f_n_n$ are such that $f_n$ satisfies these assumptions for all n. Our…
Stefan Müller, Georg Regensburger
We provide fundamental results on positive solutions to parametrized systems of generalized polynomial inequalities (with real exponents and positive parameters), including generalized polynomial equations. In doing so, we also offer a new perspective on fewnomials and (generalized) mass-action systems. We find that…
Doyon Kim
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\operatorname {GL}(r,{\mathbb {R}})$$\end{document} GL ( r , R ) part I: Combinatorics Authors: Doyon Kim We give a…
Robert John O’Shea
Graph canonisation and isomorphism testing representation are fundamental computational problems, whose complexity has remained unsolved to date. This study examines graph eigenprojections, demonstrating that linear-ordering transformations induce canonical properties therein to yield polynomial-time canonisation and…
Roland Wittler
To index or compare sequences efficiently, often k-mers, i.e., substrings of fixed length k, are used. For efficient indexing or storage, k-mers are often encoded as integers, e.g., applying some bijective mapping between all possible σ^k^ k-mers and the interval [0, σ^k^ −1], where σ is the alphabet size. In many…
Robersy Sanchez, Jesús Barreto
Experimental studies reveal that genome architecture splits into natural domains suggesting a well-structured genomic architecture, where, for each species, genome populations are integrated by individual mutational variants. Herein, we show that the architecture of population genomes from the same or closed related…
Ahmet Altun, Isaac Francois Leach, Frank Neese, Giovanni Bistoni
We introduce the fragment-pairwise Local Energy Decomposition (fp-LED) scheme for precise quantification of individual interactions contributing to the binding energy of arbitrary chemical entities, such as protein-ligand binding energies, lattice energies of molecular crystals, or association energies of large…
Pencho Yordanov, Jörg Stelling
Kirchhoff polynomials are central for deriving symbolic steady-state expressions of models whose dynamics are governed by linear diffusion on graphs. In biology, such models have been unified under a common linear framework subsuming studies across areas such as enzyme kinetics, G-protein coupled receptors, ion…
Authors not listed
We present a vector-based method to balance chemical reactions. The algorithm builds candidates in a deterministic way, removes duplicates, and always prints coefficients in the lowest whole-number form. For redox cases, electrons and protons/hydroxide are treated explicitly, so both mass and charge are balanced. We…