Large VC-dimension classiers can learn dicult tasks, but are usually impractical because they generalize well only if they are trained with huge quantities of data. In this paper we show that even very high-order polynomial classiers can be trained with a small amount of training data and yet generalize better than classiers with a smaller VC-dimension. This is achieved with a maximum margin al...

Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a new method for evaluating integrals that include orthogonal polynomials. The method is illustrated by obtaining the following integral result that involves the Bessel function and associated Laguerre polynomial: integral(infinity)(0) x(v)e(-x/2) J(v)(mu x)L-n(2v)(x)dx = 2(v)Ga...

Let K be an arbitrary field of characteristic p > 0, let A be one of the following algebras: Pn := K[x1, . . . , xn] is a polynomial algebra, D(Pn) is the ring of differential operators on Pn, D(Pn) ⊗ Pm, the n’th Weyl algebra An, the n’th Weyl algebra An ⊗ Pm with polynomial coefficients Pm, the power series algebra K[[x1, . . . , xn]], Tk1,...,kn is the subalgebra of D(Pn) generated by Pn and...

Large VC-dimension classifiers can learn difficult tasks, but are usually impractical because they generalize well only if they are trained with huge quantities of data. In this paper we show that even high-order polynomial classifiers in high dimensional spaces can be trained with a small amount of training data and yet generalize better than classifiers with a smaller VC-dimension. This is ac...

The contribution is focused on a control design and simulation of multi input output (MIMO) linear continuous-time systems. Suitable and efficient tools for description and controller derivation are algebraic notions as rings, polynomial matrices, and Diophantine equations. The generalized MIMO PI controller design is studied for stable and unstable systems. A unified approach through matrix Di...

In this paper we present a randomized algorithm for computing the collection of maximal layers for a point set in E (k = f(n)). The input to our algorithm is a point set P = {p1, ..., pn} with pi ∈ E . The proposed algorithm achieves a runtime of O ( kn 2− 1 log k +logk (1+ 2 k+1 ) log n ) when P is a random order and a runtime of O(knk (k−1))/2 log n) for an arbitrary P . Both bounds hold in e...

for every $1leq s< n$, the $s^{th}$ derivative of a polynomial $p(z)$ of degree $n$ is a polynomial $p^{(s)}(z)$ whose degree is $(n-s)$. this paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. besides, our result gives interesting refinements of some well-known results.

in this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. we transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters value, ambiguity and fuzziness.