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Tractable Fitting with Convex Polynomials via Sum-of-Squares
Tractable Fitting Convex Polynomials Sum-of-Squares
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2015/7/10
We consider the problem of fitting given data (u_1,y_1),...,(u_m,y_m), where u_i in {bf R}^n and y_i in {bf R}, with a convex polynomial f$. A technique to solve this problem using sum of squares pol...
Skew Schubert Polynomials
Oblique schubert polynomial bloom the symmetry group oblique schubert polynomials non-negative integer coefficient
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2014/12/29
We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction o...
On the Galois Group of generalized Laguerre polynomials
Newton polygon Galois group of big generalized laguerre polynomials
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2014/12/25
Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be “large.” For a fixed α∈ℚ-ℤ <0 , Filaseta and Lam have shown that the nth deg...
Specializations of one-parameter families of polynomials
K number field algebraic geometry polynomials generalized laguerre polynomials
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2014/12/25
Let K be a number field, and suppose λ(x,t)∈K[x,t] is irreducible over K(t). Using algebraic geometry and group theory, we describe conditions under which the K-exceptional set of λ, i.e. the set of α...
Asymptotic behavior of the magnetization near critical and tricritical points via Ginzburg-Landau polynomials
Asymptotic behavior of magnetization gold landau lattice model of the spin
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2014/12/25
The purpose of this paper is to prove connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg–Landa...
Algebraic Properties of a Family of Generalized Laguerre Polynomials
Generalized laguerre polynomials algebraic properties negative integral value parameter
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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...
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
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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...
Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional
Best polynomial approximation ℓ 1 norm composite hypothe-ses Hermite polynomial minimax lower bound nonsmooth functional optimal rate of convergence
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2011/6/17
A general lower bound is developed for the minimax risk when
estimating an arbitrary functional. The bound is based on testing
two composite hypotheses and is shown to be effective in estimating
th...
Analysis of 24-Hour Ambulatory Blood Pressure Monitoring Data using Orthonormal Polynomials in the Linear Mixed Model
Cubic Spline DASH Study Graphical Display
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2010/10/19
The use of 24-hour ambulatory blood pressure monitoring (ABPM) in clinical practice and observational epidemiological studies has grown considerably in the past 25 years. ABPM is a very effective tech...
An identity of Jack polynomials
generalised hypergeometric functions real complex
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2010/10/14
In this work it is propose an alterative proof of one of basic properties of the zonal polynomials. This identity is generalised for the Jack polynomials.
Nonparametric estimation of the mixing density using polynomials
Nonparametric estimation mixing density polynomials
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2010/3/10
We consider the problem of estimating the mixing density f from n i.i.d. observations distributed according to amixture density with unknown mixing distribution. In contrast with finite mixtures model...
The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory
The infinite divisibility orthogonal polynomials a constant recursion formula
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2009/9/21
We calculate Voicdescu's R-transform of the compactly
supported probability measure on R induced from the orthogonal
polynomials with a constant recursion formula, and investigate its
infinite divi...
Generating functions of orthogonal polynomials and Szego-Jacobi parameters
Interacting Fock space probability measure orthogonal polynomial Szegii-Jacobi parameters
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2009/9/21
In this paper, we present a more direct way to compute
the SzeggJacobi parameters from a generating function than that in
[S] and [6]. Our study is motivated by the notions of one-mode interacting
...
The expected number of zeros of a random system of p-adic polynomials
co-area formula Kac-Rice formula localfield Gaussian q-binomial formula
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2009/4/23
We study the simultaneous zeros of a random family of d polynomials in d variables over the p-adic numbers.For a family of natural models, we obtain an explicit constant for the expected number of zer...
The expected number of zeros of a random system of p-adic polynomials
random system p-adic polynomials natural models
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2009/4/3
We study the simultaneous zeros of a random family of d polynomials in d variables over the p-adic numbers.For a family of natural models, we obtain an explicit constant for the expected number of zer...