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About the canonical discussion of polynomial systems with parameters
, 2006
"... Given a parametric polynomial ideal I, the algorithm DISPGB, introduced by the author in 2002, builds up a binary tree describing a dichotomic discussion of the different reduced Gröbner bases depending on the values of the parameters. An improvement using a discriminant ideal to rewrite the tree wa ..."
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Cited by 3 (2 self)
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in the parameter space that characterizes the different kinds of solutions. This provides the minimal canonical discussion of the ideal I and can also be used to obtain the minimal canonical comprehensive Gröbner basis. With the new algorithm, we completely realize the objective proposed by Weispfenning in 1992.
Hierarchical singular value decomposition of tensors
 SIAM Journal on Matrix Analysis and Applications
"... Abstract. We define the hierarchical singular value decomposition (SVD) for tensors of order d ≥ 2. This hierarchical SVD has properties like the matrix SVD (and collapses to the SVD in d = 2), and we prove these. In particular, one can find low rank (almost) best approximations in a hierarchical fo ..."
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Cited by 178 (11 self)
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format (HTucker) which requires only O((d − 1)k3 + dnk) parameters, where d is the order of the tensor, n the size of the modes and k the (hierarchical) rank. The HTucker format is a specialization of the Tucker format and it contains as a special case all (canonical) rank k tensors. Based on this new
STATE AND PARAMETER ESTIMATION FOR CANONIC MODELS OF NEURAL OSCILLATORS
, 2010
"... We consider the problem of how to recover the state and parameter values of typical model neurons, such as HindmarshRose, FitzHughNagumo, MorrisLecar, from invitro measurements of membrane potentials. In control theory, in terms of observer design, model neurons qualify as locally observable. H ..."
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Cited by 1 (0 self)
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. However, unlike most models traditionally addressed in control theory, no parameterindependent diffeomorphism exists, such that the original model equations can be transformed into adaptive canonic observer form. For a large class of model neurons, however, state and parameter reconstruction is possible
A critical role for the right frontoinsular cortex in switching between centralexecutive and defaultmode networks.
 Proc Natl Acad Sci USA
, 2008
"... Cognitively demanding tasks that evoke activation in the brain's centralexecutive network (CEN) have been consistently shown to evoke decreased activation (deactivation) in the defaultmode network (DMN). The neural mechanisms underlying this switch between activation and deactivation of larg ..."
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Cited by 178 (1 self)
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related fMRI responses across the entire brain using the method developed by Henson and colleagues (26). Briefly, this method provides a way to estimate the peak latency of the BOLD response at each voxel using the ratio of the derivative to canonical parameter estimates (see SI Materials and Methods
Canonical probabilistic models for knowledge engineering
, 2000
"... The hardest task in knowledge engineering for probabilistic graphical models, such as Bayesian networks and influence diagrams, is obtaining their numerical parameters. Models based on acyclic directed graphs and composed of discrete variables, currently most common in practice, require for every va ..."
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Cited by 39 (14 self)
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variable a number of parameters that is exponential in the number of its parents in the graph, which makes elicitation from experts or learning from databases a daunting task. In this paper, we review the so called canonical models, whose main advantage is that they require much fewer parameters. We
Deep Canonical Correlation Analysis
"... We introduce Deep Canonical Correlation Analysis (DCCA), a method to learn complex nonlinear transformations of two views of data such that the resulting representations are highly linearly correlated. Parameters of both transformations are jointly learned to maximize the (regularized) total correla ..."
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Cited by 20 (4 self)
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We introduce Deep Canonical Correlation Analysis (DCCA), a method to learn complex nonlinear transformations of two views of data such that the resulting representations are highly linearly correlated. Parameters of both transformations are jointly learned to maximize the (regularized) total
On the notion of canonical dimension for algebraic groups
, 2005
"... We define and study a numerical invariant of an algebraic group action which we call the canonical dimension. We then apply the resulting theory to the problem of computing the minimal number of parameters required to define a generic hypersurface of degree d in P n−1. ..."
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Cited by 30 (4 self)
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We define and study a numerical invariant of an algebraic group action which we call the canonical dimension. We then apply the resulting theory to the problem of computing the minimal number of parameters required to define a generic hypersurface of degree d in P n−1.
Canonical and grand canonical theory of spinodal instabilities
, 1991
"... Abstract In the context of the mean field approximation t o the LandauGinzburgWilson functional integral describing the equilibrium properties of a system with a conserved order parameter, we analyze the conditions for critical instabilities in the canonical ensemble. By introducing a constraint i ..."
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Abstract In the context of the mean field approximation t o the LandauGinzburgWilson functional integral describing the equilibrium properties of a system with a conserved order parameter, we analyze the conditions for critical instabilities in the canonical ensemble. By introducing a constraint
On the regularization of canonical correlation analysis
 in Proceedings of the International Conference on Independent Component Analysis and Blind Source Separation (ICA2003), S
, 2003
"... By elucidating a parallel between canonical correlation analysis (CCA) and least squares regression (LSR), we show how regularization of CCA can be performed and interpreted in the same spirit as the regularization applied in ridge regression (RR). Furthermore, the results presented may have an im ..."
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Cited by 8 (1 self)
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By elucidating a parallel between canonical correlation analysis (CCA) and least squares regression (LSR), we show how regularization of CCA can be performed and interpreted in the same spirit as the regularization applied in ridge regression (RR). Furthermore, the results presented may have
Results 11  20
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1,867