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Enumerative Geometry is concerned with the number of solutions to a structured system of polynomial equations, when the structure comes from geometry. Enumerative real algebraic geometry studies real ...
Toric Ideals, Real Toric Varieties, and the Algebraic Moment Map
Geometric modeling projective after surface after surface linear projection
2014/12/29
This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties. In ...
Algebraic Properties of a Family of Generalized Laguerre Polynomials
Generalized laguerre polynomials algebraic properties negative integral value parameter
2014/12/24
We study the algebraic properties of Generalized Laguerre Polynomials for negative integral values of the parameter. For integers r,n≥0 , we conjecture that L(−1−n−r)n(x)=∑nj=0(nW...
The algebraic method provides useful techniques to identify models in designs and to understand aliasing of polynomial models. The present note surveys the topic of Gr¨obner bases in experimental desi...
Outliers and patterns of outliers in contingency tables with Algebraic Statistics
Algebraic Statistics goodness-of-fi t tests log-linear mod-els toric models
2011/3/18
In this paper we provide a definition of pattern of outliers in contingency tables within a model-based framework. In particular, we make use of log-linear models and exact goodness-of-fit tests to sp...
Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast with Algebraic Optimal Step Size
Atrial fibrillation (AF) blind source separation (BSS) independent component analysis (ICA) iterative optimization kurtosis
2010/3/10
Independent component analysis (ICA) aims at decomposing an observed random vector into
statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algo...
Linear stochastic differential-algebraic equations with constant coefficients
Stochastic differential-algebraic equations Random distributions
2009/4/23
We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a gene...
Linear stochastic differential-algebraic equations with constant coefficients
differential-algebraic equations constant coefficients white noise
2009/4/3
We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a gene...
Open Problems in Algebraic Statistics
Algebraic statistics contingency tables hidden variables Schur modules maximum likelihood conditional independence
2010/4/30
Algebraic statistics is concerned with the study of probabilistic models
and techniques for statistical inference using methods from algebra and geometry. This
article presents a list of open mathem...
Algebraic geometry of Gaussian Bayesian networks
Algebraic geometry Gaussian Bayesian networks
2010/4/28
Conditional independence models in the Gaussian case are algebraic varieties in the
cone of positive definite covariance matrices. We study these varieties in the case of Bayesian
networks, with a v...
Algebraic statistical models
Algebraic statistics computational algebraic geometry exponential family maximum likelihood estimation
2010/4/27
Many statistical models are algebraic in that they are defined in terms of polynomial
constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of
such models are typ...
Algebraic Bayesian analysis of contingency tables with possibly zero-probability cells
Algebraic statistics Bayes factor Compatible priors Exponential family Log-linear model Model-instance
2010/4/27
In this paper we consider a Bayesian analysis of contingency tables allowing
for the possibility that cells may have probability zero. In this sense we
depart from standard log-linear modeling that ...