A0434
Title: The role of history in measurement
Authors: Ioannis Paraskevopoulos - Universidad Pontificia Comillas (Spain) [presenting]
Abstract: The dependence and independence alternatives for a general evolution process in Banach and reflexive Banach spaces are investigated. We want to extend the limits of computation beyond Hilbert spaces. In particular, we examine whether the evolution process depends on its known history. We argue that multidimensional integration exists in reflexive Banach space if the solution obeys the functional central limit theorem and its error has limited variation, above from dilation and below from erosion boundaries. There exists a two-way mapping from reflexive Banach to Banach and back. The evolution process would depend on its history in 3/4 of all existing scenarios and this would necessarily imply that the integrable curves are quasi-periodic depending only on $x_0$, past initial conditions. One possible scenario will be that no model exists and reversibility will be unattainable as it would map to infinite possible initial points of the past. We offer two frameworks to evaluate these scenarios one is with a stochastic chain that builds on memory and another with a Deep learning Artificial Intelligent system armed with a non-linear operator in Banach $\mathcal{B}$. Either can capture all possibilities of dependence and independence in both Banach and the reflexive Banach spaces.
