Zobrazeno 1 - 10
of 450
pro vyhledávání: '"Mourrain, P."'
We study the problem of representing multivariate polynomials with rational coefficients, which are nonnegative and strictly positive on finite semialgebraic sets, using rational sums of squares. We focus on the case of finite semialgebraic sets S de
Externí odkaz:
http://arxiv.org/abs/2410.04845
Geometrically continuous splines are piecewise polynomial functions defined on a collection of patches which are stitched together through transition maps. They are called $G^{r}$-splines if, after composition with the transition maps, they are conti
Externí odkaz:
http://arxiv.org/abs/2305.09096
Autor:
Wei Qin, Fang Liang, Sheng-Jia Lin, Cassidy Petree, Kevin Huang, Yu Zhang, Lin Li, Pratishtha Varshney, Philippe Mourrain, Yanmei Liu, Gaurav K. Varshney
Publikováno v:
Nature Communications, Vol 15, Iss 1, Pp 1-14 (2024)
Abstract Advancements in CRISPR technology, particularly the development of base editors, revolutionize genetic variant research. When combined with model organisms like zebrafish, base editors significantly accelerate and refine in vivo analysis of
Externí odkaz:
https://doaj.org/article/b54b641e8c0c4138aa73c3df5d38c836
The representation of positive polynomials on a semi-algebraic set in terms of sums of squares is a central question in real algebraic geometry, which the Positivstellensatz answers. In this paper, we study the effective Putinar's Positivestellensatz
Externí odkaz:
http://arxiv.org/abs/2212.09551
Given rational univariate polynomials f and g such that gcd(f, g) and f / gcd(f, g) are relatively prime, we show that g is non-negative on all the real roots of f if and only if g is a sum of squares of rational polynomials modulo f. We complete our
Externí odkaz:
http://arxiv.org/abs/2112.00490
Autor:
Baldi, Lorenzo, Mourrain, Bernard
We analyse the representation of positive polynomials in terms of Sums of Squares. We provide a quantitative version of Putinar's Positivstellensatz over a compact basic semialgebraic set S, with a new polynomial bound on the degree of the positivity
Externí odkaz:
http://arxiv.org/abs/2111.11258
This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable system of equa
Externí odkaz:
http://arxiv.org/abs/2110.11133
Autor:
Rochelle L. Coulson, Valentina Frattini, Caitlin E. Moyer, Jennifer Hodges, Peter Walter, Philippe Mourrain, Yi Zuo, Gordon X. Wang
Publikováno v:
iScience, Vol 27, Iss 4, Pp 109259- (2024)
Summary: Fragile X syndrome (FXS) is caused by the loss of fragile X messenger ribonucleoprotein (FMRP), a translational regulator that binds the transcripts of proteins involved in synaptic function and plasticity. Dysregulated protein synthesis is
Externí odkaz:
https://doaj.org/article/eda84da98ffe4e3aac6c377083d3d94c
Publikováno v:
Journal of Symbolic Computation, Elsevier, 2022, 113, pp.193-210
In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gaussian mixture models from datasets. We investigate symmetric tensor deco
Externí odkaz:
http://arxiv.org/abs/2106.00555
Autor:
Baldi, Lorenzo, Mourrain, Bernard
We present a new algorithm for computing the real radical of an ideal and, more generally, the-radical of, which is based on convex moment optimization. A truncated positive generic linear functional vanishing on the generators of is computed solving
Externí odkaz:
http://arxiv.org/abs/2102.09367