Related papers: On FGLM Algorithms with Tropical Gr\"obner bases
We consider three modifications of our involutive algorithm for computing Janet bases. These modifications are related to degree compatible monomial orders and specify selection strategies for non-multiplicative prolongations. By using the…
Over the past decade, the Gr\"obner basis theory and automatic solver generation have lead to a large number of solutions to geometric vision problems. In practically all cases, the derived solvers apply a fixed elimination template to…
The aim of this paper is to introduce a certain number of tools and results suitable for the study of valuations of higher rank on function fields of algebraic varieties. This will be based on a study of higher rank quasi-monomial…
We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages…
We consider the tropical variety $\mathcal{T}(I)$ of a prime ideal $I$ generated by the polynomials $f_1, ..., f_r$ and revisit the regular projection technique introduced by Bieri and Groves from a computational point of view. In…
The evolving capabilities of large language models are accompanied by growing sizes and deployment costs, necessitating effective inference optimisation techniques. We propose a novel pruning method utilising centrality measures from graph…
The pretrain-transfer paradigm, which underpins the success of large language models (LLMs), has demonstrated the immense power of creating foundation models that learn generalizable representations from vast datasets. However, extending…
One iteration of standard $k$-means (i.e., Lloyd's algorithm) or standard EM for Gaussian mixture models (GMMs) scales linearly with the number of clusters $C$, data points $N$, and data dimensionality $D$. In this study, we explore whether…
We continue, in this second article, the study of the the algebraic tools which play a role in tropical algebra. We especially examine here the polynomial algebras over idempotent semi-fields. this work is motivated by the development of…
Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While perturbation theory is a…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The…
Some algorithms for the numerically exact treatment of fermion determinants are summarised. This is not supposed to be a review, rather a concise handbook. The audience is expected to have a basic understanding of how to put fermions on a…
Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to…
In this paper we introduce a working generalization of the theory of Gr\"obner bases for algebras of partial difference polynomials with constant coefficients. One obtains symbolic (formal) computation for systems of linear or non-linear…
This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial…
The Berlekamp--Massey--Sakata algorithm and the Scalar-FGLM algorithm both compute the ideal of relations of a multidimensional linear recurrent sequence.Whenever quering a single sequence element is prohibitive, the bottleneck of these…
Among the methods for solving ODE-IVPs, the class of General Linear Methods (GLMs) is able to encompass most of them, ranging from Linear Multistep Formulae (LMF) to RK formulae. Moreover, it is possible to obtain methods able to overcome…
We fix the supports A=(A_1,...,A_k) of a list of tropical polynomials and define the tropical resultant TR(A) to be the set of choices of coefficients such that the tropical polynomials have a common solution. We prove that TR(A) is the…
Variational quantum eigensolver ans\"atze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis…