Open Access. Powered by Scholars. Published by Universities.®
- Keyword
Articles 1 - 4 of 4
Full-Text Articles in Probability
Reconstructability Analysis With Fourier Transforms, Martin Zwick
Reconstructability Analysis With Fourier Transforms, Martin Zwick
Systems Science Faculty Publications and Presentations
Fourier methods used in two‐ and three‐dimensional image reconstruction can be used also in reconstructability analysis (RA). These methods maximize a variance‐type measure instead of information‐theoretic uncertainty, but the two measures are roughly collinear and the Fourier approach yields results close to that of standard RA. The Fourier method, however, does not require iterative calculations for models with loops. Moreover, the error in Fourier RA models can be assessed without actually generating the full probability distributions of the models; calculations scale with the size of the data rather than the state space. State‐based modeling using the Fourier approach is also …
Multi-Level Decomposition Of Probalistic Relations, Stanislaw Grygiel, Martin Zwick, Marek Perkowski
Multi-Level Decomposition Of Probalistic Relations, Stanislaw Grygiel, Martin Zwick, Marek Perkowski
Systems Science Faculty Publications and Presentations
Two methods of decomposition of probabilistic relations are presented in this paper. They consist of splitting relations (blocks) into pairs of smaller blocks related to each other by new variables generated in such a way so as to minimize a cost function which depends on the size and structure of the result. The decomposition is repeated iteratively until a stopping criterion is met. Topology and contents of the resulting structure develop dynamically in the decomposition process and reflect relationships hidden in the data.
Control Uniqueness In Reconstructability Analysis, Martin Zwick
Control Uniqueness In Reconstructability Analysis, Martin Zwick
Systems Science Faculty Publications and Presentations
When the reconstructability analysis of a directed system yields a structure in which a generated variable appears in more than one subsystem, information from all of the subsystems can be used in modeling the relationship between generating and generated variables. The conceptualization and procedure proposed here is discussed in relation to Klir's concept of control uniqueness.
Set-Theoretic Reconstructability Of Elementary Cellular Automata, Martin Zwick, Hui Shu
Set-Theoretic Reconstructability Of Elementary Cellular Automata, Martin Zwick, Hui Shu
Systems Science Faculty Publications and Presentations
Set-theoretic reconstructability analysis is used to characterize the structures of the mappings of elementary cellular automata. The minimum complexity structure for each ECA mapping, indexed by parameter σ, is more effective than the λ parameter of Langton as a predictor of chaotic dynamics.