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A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
polynomial-time algorithm determining quadratic Lyapunov functions nonlinear systems
2015/7/13
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
An Excursion from Enumerative Geometry to Solving Systems of Polynomial Equations with Macaulay 2
To solve the polynomial equations mathematics geometry cross theory
2014/12/29
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics ha...
Lattice polytopes, Hecke operators, and the Ehrhart polynomial
Grid polyhedron the singular lattice polyhedron
2014/12/25
Let P be a simple lattice polytope. We define an action of the Hecke operators on E(P), the Ehrhart polynomial of P, and describe their effect on the coefficients of E(P). We also describe how the Bri...
Efficient Density Estimation via Piecewise Polynomial Approximation
Efficient Density Estimation Piecewise Polynomial Approximation
2013/6/14
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary dis...
An Approximate Approach to E-optimal Designs for Weighted Polynomial Regression by Using Tchebycheff Systems and Orthogonal Polynomials
An Approximate Approach E-optimal Designs Weighted Polynomial Regression Using Tchebycheff Systems Orthogonal Polynomials
2013/4/28
In statistics, experimental designs are methods for making efficient experiments. E-optimal designs are the multisets of experimental conditions which minimize the maximum axis of the confidence ellip...
Flexible Mixture Modeling with the Polynomial Gaussian Cluster-Weighted Model
Mixture of distributions Mixture of regressions Polynomial regression Model-based clustering Model-based classification Cluster-weighted models.
2012/9/18
In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows fo...
Approximate Interval Method for Epistemic Uncertainty Propagation using Polynomial Chaos and Evidence Theory
Approximate Interval Method Epistemic Uncertainty Propagation
2011/7/19
The paper builds upon a recent approach to find the approximate bounds of a real function using Polynomial Chaos expansions.
Uniform bias study and Bahadur representation for local polynomial estimators of the conditional quantile function
Bahadur representation Conditional quantile function Local polynomial estimation Econometrics of Auctions
2011/6/20
This paper investigates the bias and the weak Bahadur representation of a local
polynomial estimator of the conditional quantile function and its derivatives.
The bias and Bahadur remainder term are...
Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes
Hermite polynomials of a Gaussian process long–memory parameter non–Gaussian Rosenblatt
2011/6/16
We consider stationary processes with long memory which are non–Gaussian and represented
as Hermite polynomials of a Gaussian process. We focus on the corresponding
wavelet coefficients and study th...
Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection
Adaptation to anisotropy inhomogeneity via dyadic piecewise polynomial selection
2011/3/23
This article is devoted to nonlinear approximation and estimation via piecewise polynomials built on partitions into dyadic rectangles. The approximation rate is studied over possibly inhomogeneous an...
Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection
anisotropy inhomogeneity piecewise polynomial
2011/3/22
This article is devoted to nonlinear approximation and estimation via piecewise polynomials built on partitions into dyadic rectangles. The approximation rate is studied over possibly inhomogeneous an...
Sequentially Updated Residuals and Detection of Stationary Errors in Polynomial Regression Models
Autoregressive unit root Change-point Control chart Nonparametric smoothing Sequential analysis Weighted partial sum process
2010/3/9
The question whether a time series behaves as a random walk or as a stationary
process is an important and delicate problem, particularly arising in financial statistics,
econometrics, and engineeri...
On polynomial chaos and integrability。
A simple construction of polynomial estimators for
densities and distributions on the unit interval is presented. For-
Lipschitz densities the error for the mean square deviation is characterized.
...
Characterizations of polynomial-Gaussian processes that are Markovian
Characterizations polynomial-Gaussian processes Markovian
2009/9/21
We consider questions of characterizing a stochastic
process X = (X,,t 2 0) by the properties of the first two conditional
moments. Our first result is a new version of the classical P. Levy
charac...