88,901 research outputs found
Exploring multimodal data fusion through joint decompositions with flexible couplings
A Bayesian framework is proposed to define flexible coupling models for joint
tensor decompositions of multiple data sets. Under this framework, a natural
formulation of the data fusion problem is to cast it in terms of a joint
maximum a posteriori (MAP) estimator. Data driven scenarios of joint posterior
distributions are provided, including general Gaussian priors and non Gaussian
coupling priors. We present and discuss implementation issues of algorithms
used to obtain the joint MAP estimator. We also show how this framework can be
adapted to tackle the problem of joint decompositions of large datasets. In the
case of a conditional Gaussian coupling with a linear transformation, we give
theoretical bounds on the data fusion performance using the Bayesian Cramer-Rao
bound. Simulations are reported for hybrid coupling models ranging from simple
additive Gaussian models, to Gamma-type models with positive variables and to
the coupling of data sets which are inherently of different size due to
different resolution of the measurement devices.Comment: 15 pages, 7 figures, revised versio
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
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