Error coefficients are ubiquitous in systems. In particular, errors reasoning verification must be considered regarding safety-critical We present a method that can applied to systems described by the polynomial error assertion (PEA). The implication relationship between PEAs converted an inclusion zero sets of PEAs; then transformed into first-order logic. Combined with quantifier elimination ...

This paper proposes a new deterministic sampling strategy for constructing polynomial chaos approximations for expensive physics simulation models. The proposed approach, effectively subsampled quadratures involves sparsely subsampling an existing tensor grid using QR column pivoting. For polynomial interpolation using hyperbolic or total order sets, we then solve the following square least squ...

Let a “complex probability” be a normalizable complex distribution P (x) defined on R. A real and positive probability distribution p(z), defined on the complex plane C, is said to be a positive representation of P (x) if 〈Q(x)〉P = 〈Q(z)〉p, where Q(x) is any polynomial in R D and Q(z) its analytical extension on C. In this paper it is shown that every complex probability admits a real represent...

A neural network based technique is presented, which is able to successfully extract polynomial classification rules from labeled electroencephalogram (EEG) signals. To represent the classification rules in an analytical form, we use the polynomial neural networks trained by a modified Group Method of Data Handling (GMDH). The classification rules were extracted from clinical EEG data that were...

Polynomial maps offer analytical properties used to obtain better performances in the scope of chaos synchronization under noisy channels. This paper presents a new method to simplify equations of the Exact Polynomial Kalman Filter (ExPKF) given in [1]. This faster algorithm is compared to other estimators showing that performances of all considered observers vanish rapidly with the channel noi...

This paper introduces a Moving Finite Elements Method (MFEM) based on cubic Hermite polynomial local approximations to handle Population Balance Equations (PBE) modeling breakage phenomena. The adequacy and performance of the MFEM framework are tested in two case studies involving breakage: a benchmark problem with known analytical solution and the hydrolysis of starch. Both examples emphasize ...

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires ...