14,704 research outputs found
Bayesian fractional polynomials
This paper sets out to implement the Bayesian paradigm for fractional polynomial models under the assumption of normally distributed error terms. Fractional polynomials widen the class of ordinary polynomials and offer an additive and transportable modelling approach. The methodology is based on a Bayesian linear model with a quasi-default hyper-g prior and combines variable selection with parametric modelling of additive effects. AMarkov chain Monte Carlo algorithm for the exploration of the model space is presented. This theoretically well-founded stochastic search constitutes a substantial improvement to ad hoc stepwise procedures for the fitting of fractional polynomial models. The method is applied to a data set on the relationship between ozone levels and meteorological parameters, previously analysed in the literatur
Tropical geometries and dynamics of biochemical networks. Application to hybrid cell cycle models
We use the Litvinov-Maslov correspondence principle to reduce and hybridize
networks of biochemical reactions. We apply this method to a cell cycle
oscillator model. The reduced and hybridized model can be used as a hybrid
model for the cell cycle. We also propose a practical recipe for detecting
quasi-equilibrium QE reactions and quasi-steady state QSS species in
biochemical models with rational rate functions and use this recipe for model
reduction. Interestingly, the QE/QSS invariant manifold of the smooth model and
the reduced dynamics along this manifold can be put into correspondence to the
tropical variety of the hybridization and to sliding modes along this variety,
respectivelyComment: conference SASB 2011, to be published in Electronic Notes in
Theoretical Computer Scienc
Quasi-optimal multiplication of linear differential operators
We show that linear differential operators with polynomial coefficients over
a field of characteristic zero can be multiplied in quasi-optimal time. This
answers an open question raised by van der Hoeven.Comment: To appear in the Proceedings of the 53rd Annual IEEE Symposium on
Foundations of Computer Science (FOCS'12
Formal Desingularization of Surfaces - The Jung Method Revisited -
In this paper we propose the concept of formal desingularizations as a
substitute for the resolution of algebraic varieties. Though a usual resolution
of algebraic varieties provides more information on the structure of
singularities there is evidence that the weaker concept is enough for many
computational purposes. We give a detailed study of the Jung method and show
how it facilitates an efficient computation of formal desingularizations for
projective surfaces over a field of characteristic zero, not necessarily
algebraically closed. The paper includes a generalization of Duval's Theorem on
rational Puiseux parametrizations to the multivariate case and a detailed
description of a system for multivariate algebraic power series computations.Comment: 33 pages, 2 figure
Quasi-ordinary singularities and Newton trees
In this paper we study some properties of the class of nu-quasi-ordinary
hypersurface singularities. They are defined by a very mild condition on its
(projected) Newton polygon. We associate with them a Newton tree and
characterize quasi-ordinary hypersurface singularities among nu-quasi-ordinary
hypersurface singularities in terms of their Newton tree. A formula to compute
the discriminant of a quasi-ordinary Weierstrass polynomial in terms of the
decorations of its Newton tree is given. This allows to compute the
discriminant avoiding the use of determinants and even for non Weierstrass
prepared polynomials. This is important for applications like algorithmic
resolutions. We compare the Newton tree of a quasi-ordinary singularity and
those of its curve transversal sections. We show that the Newton trees of the
transversal sections do not give the tree of the quasi-ordinary singularity in
general. It does if we know that the Newton tree of the quasi-ordinary
singularity has only one arrow.Comment: 32 page
Thomas Decomposition of Algebraic and Differential Systems
In this paper we consider disjoint decomposition of algebraic and non-linear
partial differential systems of equations and inequations into so-called simple
subsystems. We exploit Thomas decomposition ideas and develop them into a new
algorithm. For algebraic systems simplicity means triangularity, squarefreeness
and non-vanishing initials. For differential systems the algorithm provides not
only algebraic simplicity but also involutivity. The algorithm has been
implemented in Maple
Hopf Algebras of m-permutations, (m+1)-ary trees, and m-parking functions
The m-Tamari lattice of F. Bergeron is an analogue of the clasical Tamari
order defined on objects counted by Fuss-Catalan numbers, such as m-Dyck paths
or (m+1)-ary trees. On another hand, the Tamari order is related to the product
in the Loday-Ronco Hopf algebra of planar binary trees. We introduce new
combinatorial Hopf algebras based on (m+1)-ary trees, whose structure is
described by the m-Tamari lattices.
In the same way as planar binary trees can be interpreted as sylvester
classes of permutations, we obtain (m+1)-ary trees as sylvester classes of what
we call m-permutations. These objects are no longer in bijection with
decreasing (m+1)-ary trees, and a finer congruence, called metasylvester,
allows us to build Hopf algebras based on these decreasing trees. At the
opposite, a coarser congruence, called hyposylvester, leads to Hopf algebras of
graded dimensions (m+1)^{n-1}, generalizing noncommutative symmetric functions
and quasi-symmetric functions in a natural way. Finally, the algebras of packed
words and parking functions also admit such m-analogues, and we present their
subalgebras and quotients induced by the various congruences.Comment: 51 page
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