33,513 research outputs found
Uncertainty Analyses in the Finite-Difference Time-Domain Method
Providing estimates of the uncertainty in results obtained by Computational Electromagnetic (CEM) simulations is essential when determining the acceptability of the results. The Monte Carlo method (MCM) has been previously used to quantify the uncertainty in CEM simulations. Other computationally efficient methods have been investigated more recently, such as the polynomial chaos method (PCM) and the method of moments (MoM). This paper introduces a novel implementation of the PCM and the MoM into the finite-difference time -domain method. The PCM and the MoM are found to be computationally more efficient than the MCM, but can provide poorer estimates of the uncertainty in resonant electromagnetic compatibility data
Signatures of Infinity: Nonergodicity and Resource Scaling in Prediction, Complexity, and Learning
We introduce a simple analysis of the structural complexity of
infinite-memory processes built from random samples of stationary, ergodic
finite-memory component processes. Such processes are familiar from the well
known multi-arm Bandit problem. We contrast our analysis with
computation-theoretic and statistical inference approaches to understanding
their complexity. The result is an alternative view of the relationship between
predictability, complexity, and learning that highlights the distinct ways in
which informational and correlational divergences arise in complex ergodic and
nonergodic processes. We draw out consequences for the resource divergences
that delineate the structural hierarchy of ergodic processes and for processes
that are themselves hierarchical.Comment: 8 pages, 1 figure; http://csc.ucdavis.edu/~cmg/compmech/pubs/soi.pd
Deterministic Dynamics and Chaos: Epistemology and Interdisciplinary Methodology
We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary
relation between mathematics and psychology, focused on the mathematical theory
of deterministic dynamical systems, and in particular, on the theory of chaos.
On one hand, there is the direct classic relation: the application of
mathematics to psychology. On the other hand, we propose the converse relation
which consists in the formulation of new abstract mathematical problems
appearing from processes and structures under research of psychology. The
bidirectional multidisciplinary relation from-to pure mathematics, largely
holds with the "hard" sciences, typically physics and astronomy. But it is
rather new, from the social and human sciences, towards pure mathematics
- …