Related papers: Hiding canonicalisation in tensor computer algebra
We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both…
An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue function on an affine space of symmetric…
Many computer algebra systems have more than 1000 built-in functions, making expertise difficult. Using mock dialog boxes, this article describes a proposed interactive general-purpose wizard for organizing optional transformations and…
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of…
Canonical Polyadic Decomposition (CPD) of a third-order tensor is a minimal decomposition into a sum of rank-$1$ tensors. We find new mild deterministic conditions for the uniqueness of individual rank-$1$ tensors in CPD and present an…
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
Mixed Boolean-Arithmetic (MBA) obfuscation is a common technique used to transform simple expressions into semantically equivalent but more complex combinations of boolean and arithmetic operators. Its widespread usage in DRM systems,…
Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…
Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened…
We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay)=B(x,y) on a vector space over F in the following cases: (i) F is an algebraically closed field of characteristic…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras. The approach relies on the use of logical formulas as…
Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are…
In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, the problem of identifying…
The Normalization transformation plays a key role in the compilation of Diderot programs. The transformations are complicated and it would be easy for a bug to go undetected. To increase our confidence in normalization part of the compiler…
There are two permutation groups that they share the same character table of order 1344. We take up natural representations on 8 and 14 letters respectively. The purpose of this paper is to examine the semi-simple structure of centralizing…
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…
Tokenisation is the first step in almost all NLP tasks, and state-of-the-art transformer-based language models all use subword tokenisation algorithms to process input text. Existing algorithms have problems, often producing tokenisations…
Modern advances in general-purpose computer algebra systems offer solutions to a variety of problems, which in the past required substantial time investments by trained mathematicians. An excellent example of such development are the…
A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of…