SIGMOIDAL-TYPE SERIES EXPANSION

Series expansion of Wiener integrals via block pulse functions

In this paper, a suitable numerical method based on block pulse functions is introduced to approximate the Wiener integrals which the exact solution of them is not exist or it may be so hard to find their exact solutions. Furthermore, the error analysis of this method is given. Some numerical examples are provided which show that the approximation method has a good degree of accuracy. The main ...

Series Expansion Optimization

In this chapter we present an innovative approach to combine common results of Markov decision theory and series expansions for optimization. We call our algorithm the series expansion optimization algorithm. Our algorithm efficiently determines the optimal policy of continuous-time Markov decision processes exactly or alternatively up to an arbitrarily small precision. We prove its convergence...

Sicegar: R package for sigmoidal and double-sigmoidal curve fitting

Sigmoidal and double-sigmoidal dynamics are commonly observed in many areas of biology. Here we present sicegar, an R package for the automated fitting and classification of sigmoidal and double-sigmoidal data. The package categorizes data into one of three categories, "no signal," "sigmoidal," or "double-sigmoidal," by rigorously fitting a series of mathematical models to the data. The data is...

New Expansion and Infinite Series

Different from the Taylor polynomials, a new formula for function expansion is proposed where the terms are not polynomials. A new infinite series based on the new formula is also proposed, and the new infinite series can keep some important properties of the original functions. Some forms of remainder are also presented for analysis of convergence. In order to show some internal relationships ...

Volterra and Fliess Series Expansion