In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of set high-dimensional data representing quantities interest computational or analytical model. For purpose, employ Grassmannian diffusion maps, two-step nonlinear dimension reduction technique wh...

Abstract Basic oxygen steel making is a complex chemical and physical industrial process that reduces mix of pig iron recycled scrap into low-carbon steel. Good understanding the ability to predict how it will evolve requires long operator experience, but this can be augmented with target prediction systems. Such systems may use machine learning learn model based on history, have an advantage i...

We study a fundamental problem in micro economics called optimal auction design: A seller wishes to sell an item to a group of self-interested agents. Each agent i has a privately known value for winning the object. Given a joint distribution of these values, the goal is to construct an optimal auction, i.e. a truth revealing protocol that maximizes the seller’s expected revenue. We introduce a...

An input and output model is used for the development of a model based predictive control framework for linear model structures. Diierent MPC algorithms which are based on linear state space models or linear polynomial models t into this framework. A new identiication horizon is introduced in order to represent the past.

The Tutte polynomial TG(X,Y ) of a graph G is a classical invariant, important in combinatorics and statistical mechanics. An essential feature of the Tutte polynomial is the duality for planar graphs G , TG(X,Y ) = TG∗(Y,X) where G∗ denotes the dual graph. We examine this property from the perspective of manifold topology, formulating polynomial invariants for higher-dimensional simplicial com...

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.

background: identification of disease risk factors can help in the prevention of diseases. in assessing the predictive value of continuous variables, a routine procedure is to categorize the factors. this yield to inability to detect non‑linear relationship, if exist. multivariate fractional polynomial (mfp) modeling is a flexible method to reveal non‑linear associations. we aim to demonstrate ...