Let $$X_N$$ be an N-dimensional subspace of $$L_2$$ functions on a probability space $$(\Omega , \mu )$$ spanned by uniformly bounded Riesz basis $$\Phi _N$$ . Given integer $$1\le v\le N$$ and exponent p\le 2$$ we obtain universal discretization for the integral norms $$L_p(\Omega ,\mu from collection all subspaces v elements with number m required points satisfying $$m\ll v(\log N)^2(\log v)^...

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

Abstract The proof of convergence adaptive discretization-based algorithms for semi-infinite programs (SIPs) usually relies on compact host sets the upper- and lower-level variables. This assumption is violated in some applications, we show that indeed problems can arise when are applied to SIPs with unbounded To mitigate these problems, first examine underlying assumptions algorithms. We do th...

Discretization of continuous variables so they may be used in conjunction with machine learning or statistical techniques that require nominal data is an important problem to be solved in developing generally applicable methods for data mining. This paper introduces a new technique for discretization of such variables based on zeta, a measure of strength of association between nominal variables...

Many data mining and machine learning algorithms require databases in which objects are described by discrete attributes. However, it is very common that the attributes are in the ratio or interval scales. In order to apply these algorithms, the original attributes must be transformed into the nominal or ordinal scale via discretization. An appropriate transformation is crucial because of the l...

Continuously-Adaptive Discretization for Message-Passing (CAD-MP) is a new message-passing algorithm for approximate inference. Most message-passing algorithms approximate continuous probability distributions using either: a family of continuous distributions such as the exponential family; a particle-set of discrete samples; or a fixed, uniform discretization. In contrast, CAD-MP uses a discre...